Research Article Performance of an Ocean Energy Conversion...
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Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 260514, 14 pages http://dx.doi.org/10.1155/2013/260514 Research Article Performance of an Ocean Energy Conversion System with DFIG Sensorless Control I. Garrido, 1 Aitor J. Garrido, 1 M. Alberdi, 1 M. Amundarain, 1 and O. Barambones 2 1 Department of Automatic Control and Systems Engineering, EUITI de Bilbao, University of the Basque Country (UPV/EHU), Rafael Moreno 3, 48013 Bilbao, Spain 2 Department of Automatic Control and Systems Engineering, EUI de Vitoria-Gasteiz, University of the Basque Country (UPV/EHU), Nieves Cano 12, 01006 Vitoria-Gasteiz, Spain Correspondence should be addressed to I. Garrido; [email protected] Received 24 February 2013; Accepted 21 May 2013 Academic Editor: Massimo Scalia Copyright © 2013 I. Garrido et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e 2009/28/EC Directive requires Member States of the European Union to adopt a National Action Plan for Renewable Energy. In this context, the Basque Energy Board, EVE, is committed to research activities such as the Mutriku Oscillating Water Column plant, OWC. is is an experimental facility whose concept consists of a turbine located in a pneumatic energy collection chamber and a doubly fed induction generator that converts energy extracted by the turbine into a form that can be returned to the network. e turbo-generator control requires a precise knowledge of system parameters and of the rotor angular velocity in particular. us, to remove the rotor speed sensor implies a simplification of the hardware that is always convenient in rough working conditions. In this particular case, a Luenberger based observer is considered and the effectiveness of the proposed control is shown by numerical simulations. Comparing these results with those obtained using a traditional speed sensor, it is shown that the proposed solution provides better performance since it increases power extraction in the sense that it allows a more reliable and robust performance of the plant, which is even more relevant in a hostile environment as the ocean. 1. Introduction ere is a current need not only for greater energy accessi- bility but also to prevent that the energy consumption envi- ronmental impact grows to the point that causes irreversible damage to the planet. In this sense, the European Parliament has backed up a climate change package which aims to achieve by 2020 a 20% reduction of greenhouse gas emissions, a 20% increment in energy efficiency, and a 20% of renewable share within European Union (EU) countries. At the same time, recent developments have highlighted that relying so heavily on fossil and fission-based energy poses a security, economic, and human threat. e British Petroleum oil spill in the Gulf of Mexico caused extensive damage on the econ- omy and welfare of the region, the “Arab Spring” has triggered oil-price volatility, and Japan’s Fukushima nuclear catastro- phe has brought about doubts over the role of fission-based energy. In recent studies [1, 2], Drs. Jacobson and Delucchi stated that “barriers to a 100% conversion to wind water and solar power worldwide are primarily social and political, not technological or even economic.” Based on their studies, all the world energy needs might be satisfied from wind, water, and solar power, considering 720,000 0.75 MW wave devices. In any case, the advantages are many since it is a clean, free, readily available, and safe source of energy that, even when it currently requires further research, it is called to play a main roll in a near future. e Spanish Council of Ministers on 11th November 2011 approved the Renewable Energies Plan for 2011–2020. is plan includes the design of new energy scenarios and incor- porating the objectives given in the Directive 2009/28/EC of the European Parliament on the promotion of the use of energy from renewable sources, which sets binding minimum targets for the whole of the European Union and for each of the Member States. In particular, this plan highlights the marine energy potential that Spain possesses with special
Transcript of Research Article Performance of an Ocean Energy Conversion...
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 260514 14 pageshttpdxdoiorg1011552013260514
Research ArticlePerformance of an Ocean Energy Conversion Systemwith DFIG Sensorless Control
I Garrido1 Aitor J Garrido1 M Alberdi1 M Amundarain1 and O Barambones2
1 Department of Automatic Control and Systems Engineering EUITI de Bilbao University of the Basque Country (UPVEHU)Rafael Moreno 3 48013 Bilbao Spain
2Department of Automatic Control and Systems Engineering EUI de Vitoria-Gasteiz University of the Basque Country (UPVEHU)Nieves Cano 12 01006 Vitoria-Gasteiz Spain
Correspondence should be addressed to I Garrido izaskungarridoehues
Received 24 February 2013 Accepted 21 May 2013
Academic Editor Massimo Scalia
Copyright copy 2013 I Garrido et alThis is an open access article distributed under theCreativeCommonsAttributionLicensewhichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The 200928EC Directive requires Member States of the European Union to adopt a National Action Plan for Renewable EnergyIn this context the Basque Energy Board EVE is committed to research activities such as the Mutriku Oscillating Water Columnplant OWCThis is an experimental facility whose concept consists of a turbine located in a pneumatic energy collection chamberand a doubly fed induction generator that converts energy extracted by the turbine into a form that can be returned to the networkThe turbo-generator control requires a precise knowledge of system parameters and of the rotor angular velocity in particularThusto remove the rotor speed sensor implies a simplification of the hardware that is always convenient in rough working conditions Inthis particular case a Luenberger based observer is considered and the effectiveness of the proposed control is shown by numericalsimulations Comparing these results with those obtained using a traditional speed sensor it is shown that the proposed solutionprovides better performance since it increases power extraction in the sense that it allows a more reliable and robust performanceof the plant which is even more relevant in a hostile environment as the ocean
1 Introduction
There is a current need not only for greater energy accessi-bility but also to prevent that the energy consumption envi-ronmental impact grows to the point that causes irreversibledamage to the planet In this sense the European Parliamenthas backed up a climate change package which aims toachieve by 2020 a 20 reduction of greenhouse gas emissionsa 20 increment in energy efficiency and a 20 of renewableshare within European Union (EU) countries At the sametime recent developments have highlighted that relying soheavily on fossil and fission-based energy poses a securityeconomic and human threat The British Petroleum oil spillin the Gulf of Mexico caused extensive damage on the econ-omy andwelfare of the region the ldquoArab Springrdquo has triggeredoil-price volatility and Japanrsquos Fukushima nuclear catastro-phe has brought about doubts over the role of fission-basedenergy In recent studies [1 2] Drs Jacobson and Delucchi
stated that ldquobarriers to a 100 conversion to wind water andsolar power worldwide are primarily social and political nottechnological or even economicrdquo Based on their studies allthe world energy needs might be satisfied from wind waterand solar power considering 720000 075MWwave devicesIn any case the advantages are many since it is a clean freereadily available and safe source of energy that even when itcurrently requires further research it is called to play a mainroll in a near future
The Spanish Council of Ministers on 11th November 2011approved the Renewable Energies Plan for 2011ndash2020 Thisplan includes the design of new energy scenarios and incor-porating the objectives given in the Directive 200928ECof the European Parliament on the promotion of the use ofenergy from renewable sources which sets bindingminimumtargets for the whole of the European Union and for eachof the Member States In particular this plan highlights themarine energy potential that Spain possesses with special
2 Mathematical Problems in Engineering
Figure 1 OWC for the Nereida project by the EVE
emphasis in wave energy with the potential to satisfy 15of EU energy demand cutting 136MTMWh off the CO
2
emissions by 2050 The proposals are directed mainly to theRampD not only of new designs and components aiming toimprove equipment fatigue and reduce the cost but also ofdemonstration programs for prototypes testing as well asto develop infrastructure to validate experimental devicesMajor efforts are being made in the Basque Country throughthe Nereida Project promoted by Basque Energy Board(EVE) which has developed an Oscillating Water Column(OWC) integrated in a breakwater located in Mutriku andinvolves a C57M investment The plant consists of 16turbines 185 kW each with an estimated overall power of296 kW (see Figure 1) It was inaugurated in July 2011 [3 4]and produced 200000 kWh during the first year while itwas estimated 600000 kWh production per year Althoughthe difference is mainly due to a storm that damaged thecontrol room and kept the facility closed during the bestwavemonths an improvement in the power generation couldhighly benefit the system
In this power plant the water surface inside a chambermoves up and down under the wave action causing to inhaleand exhale air through the opening at the top The bidirec-tional air flow is applied to a special kind of turbine calledWells turbine which provides unidirectional rotation despiteof the air flow direction [5 6] Thus the Wells turbine trans-forms the wave potential into mechanical energy that will betransmitted to a double feed induction generator which feedsAC power to the grid For that two pulse-width-modulatedthree phase converters are connected back to back betweenthe rotor terminal and the utility grid with a DC link Thestator circuit is directly connected to the grid while the rotorwinding is connected via slip-rings to the rotor side converter[7]
TheOWC system located inMutriku uses a vector controlscheme coupled with cascaded Proportional-Integral-Deriv-ative (PID) controller for current and power loops [8] Thisscheme allows power tracking while the Rotor and GridSide Converters RSCGSC are controlled independentlyBesides it has fault-ride-through (FRT) capabilities and theOWC system also implements a complementary modifiedantiwind-up PID based valve control for incoming air flowinto the turbine [9ndash11] The choice of valve control has been
mainly determined by the fact that it is the control used inMutriku New Grid Codes oblige distributed power-genera-tion systems to remain connected to the power network dur-ing the fault to avoidmassive chain disconnections so that theimplementation of an adequate FRT capability is indispens-able in this kind of systems to ensure its stability and uninter-rupted operation [12ndash17]
All mechanical parts should be designed to withstand theocean hostile environment and it has to be considered that theturbo-generator control requires a precise knowledge of thesystem parameters and of the rotor speed in particular In thiscontext the most suitable option is to remove the mechanicalspeed sensor at the rotor shaft so as to simplify the hardwarewith the consequent reduction in installation and mainte-nance costs increment of disturbance rejection and plantreliability improvement However in order to eliminate thespeed sensor from the drive some of the state variables suchas rotor angular velocity and flux have to be estimated frommeasured states Besides accuracy robustness and sensitiv-ity against parameter deviation can be improved by choosingclosed loop observers [18 19] Therefore dynamic perfor-mance and steady-state speed accuracy for the lower speedrange have been achieved in this particular case consideringa closed loop speed observer based in a Luenberger system toestimate the rotor speed from the measured stator voltagesand currents [20 21]
After all these considerations and taking into account thecost effectiveness and improved performance that a speedobserver can afford this paper presents a new sensorless vec-tor control scheme in order to improve the power extractionin theMutriku OWC whose results can easily be extended toother wave power plantsThe rest of the paper is organized asfollows In Section 2 the OWC is presented and both itsmodules the capture chamber and the turbine that generatesenergy are explained Next in Section 3 the proposed sensor-less control scheme is stated In Section 4 simulation resultsfor a representative case-study comparing different controlledcases have been obtained And finally some concluding re-marks are presented in the last section
2 Mutriku OWC Description
21 MutrikuWaveModel and OWCCapture Chamber Usingdata from the Bilbao-Vizcaya exterior buoy of the State Net-work Ports the annual average wave height is around 2mwith period of about 10 s Statistical study of wave directionsreveals the predominance of northeast swell type wave [2223] In order to study regular waves (see also [24]) it is nec-essary to take into account the spectrum of the wave climatedata that measures the correlation between wave frequencyand wave energy as it may be observed in Figure 2
This representative spectrum of the wave climate is buoydriven since it uses a linear wave propagationmodel to trans-form measures obtained by an offshore wave rider buoy indeep water to the OWC location in the coast
Mathematical Problems in Engineering 3
006 008 01 012 014 016 018 020
1
2
3
4
5
6
7
8
Wave frequency (Hz)
Wav
e spe
ctra
l den
sity
(m2s)
Figure 2 Representative spectrum of the wave climate
Taking these data into consideration a regular wave maybe modelled assuming that its height and frequency corre-spond to the peak given in Figure 2 so that it can be writtenas follows
119875wf =1205881199081198921198602120582
16119879119908
[1 +4120587ℎ120582
sinh (4120587ℎ120582)]
120582 =1198921198792
119908
2120587tanh(2120587ℎ
120582)
(1)
A thorough overview of wave theory and models may befound in [25]
The breakwater housing the OWC plant is located at adepth of 5m belowMESTLW (Maximum Equinoctial SpringTide Low Water) with respect to Level 0 at Mutriku portThe opening that transmits the wave oscillations to each aircolumn is 320m high and 400mwideThe lowest point is atminus340m so that the opening is always below sea level [26]
The power available from the air flow in the OWC cham-ber which parameters are presented in Figure 3 may be ex-pressed in terms of the air pressure drop and the kineticenergy as follows
119875in = (119889119901 +120588V2119909
2) V119909119886 (2)
For a complete description see [25]
22 Turbo-Generator Module In the Mutriku OWC the tur-bines are fixed-pitch which means that they present a robustperformance due to the lack of air flow rectifying devicessince they always rotate in the same direction regardless ofthe air flow and are vertically mounted with a butterfly typevalve at the bottom to isolate the chamber if necessary Tominimize the height of the plant room the length of theturbo-generation assembly has been designed to be relativelysmall 283m high by 125m maximum width and approxi-mately 1200 kg (see Figures 1 and 4)
Turbine
Front wall
120582
A
h
x Back wall
SWL
a
b120579
Figure 3 OWC capture chamber
The equations used for modelling the pressure dropacross rotor and the torque produced by turbine are (see [27])
119889119901 = 119862119886119870(
1
119886) [V2119909+ (119903120596
119903)2
] (3)
119879119905= 119862119905119870119903 [V2119909+ (119903120596
119903)2
] (4)
where119870 is the turbine constant defined as
119870 =120588119887119899119897
2(5)
so that it may be deduced that the torque
119879119905=119889119901119862119905119903119886
119862119886
(6)
The flow coefficient 120601 is usually defined as the nondimen-sional quantity corresponding to the tangent of the angle ofattack at the blade tip The flow coefficient is
120601 =V119909
119903120596119903
(7)
Finally the flow rate and turbine performance can be calcu-lated as
119902 = V119909119886
120578119905=119879119905120596119903
119889119901119902
(8)
Thus it may be observed from (3) and (7) that for a givenrotational speed it is possible to establish a linear relationshipbetween the pressure drop and the flow rate This facilitatesan adequate coupling between the turbine and the OWCwhich also depends on the pressure drop input Besides thedeveloped torque that is to say the turbine power depends
4 Mathematical Problems in Engineering
(a) (b)
Figure 4 Turbines for the Mutriku OWC project by the EVE
0 02 04 06 08 1 12 14 16 18 2
0
01
02
03
04
05
06
minus01
Ct
(torq
ue co
effici
ent)
120601 (flow coefficient)
120601 = 03
Figure 5 Torque coefficient versus flow coefficient from the datash-eet turbine specifications
on the pressure drop the power coefficient and the torquecoefficient (6) It is the relationship of this torque coefficientagainst the flow coefficient that determines one of the char-acteristic curves of theWells turbine under study It is partic-ularly interesting the behaviour of the torque coefficient 119862
119905
shown in Figure 5 since it shows that it is negative during thestart-up phase whichmeans that due to the properties of theturbine the AC machine acts as a motor until it overcomesthe drag forces acting on the blades Figure 5 also shows thatwhen the flux coefficient reaches a critical value the torquecoefficient will drop drastically which is commonly known asthe stalling behaviour of theWells turbineOn the other handwhen the turbine velocity increases the flow rate decreases(see (7)) Therefore accelerating the turbine adequately willavoid that the turbine enters into stalling behaviour drasti-cally dropping its efficiency
It may be seen in Figure 6 how the performance ofthe Wells turbine deteriorates when the flow coefficient ap-proaches the corresponding 119862
119905critical value of Figure 5 03
This behaviour is denoted stalling behaviour and it is thereason why control is particularly relevant in Wells turbines
In this way this undesired stalling behaviour can beavoided or delayed if the turbine accelerates fast enough inresponse to the incoming air flow in order to maintain ade-quate flow coefficient values (7) (see [8]) so as tomaintain theoptimal flow coefficient for an efficient conversion of pneu-matic power
0 1 2 3 4 5 6 7 8 9 10Time (s)
Stalling behavior
minus16minus14minus12minus10minus8minus6minus4minus2
024times104
Pow
er g
ener
ated
(W)
PgenPgenmean
Average value (12045kW)
Figure 6 Simulated power generated for 7000 Pa maximum pres-sure drop input under no control (stalling)
The Mutriku OWC consists of 16 chambers where eachchamber has a top opening that is connected to a verticallymounted turbo-generator module Each module is formedby two five-blade Wells turbines connected to an air cooledDFIG generator In this kind of induction machines widelyemployed in diverse generation applications the stator circuitis directly connected to the grid while the rotor windings areconnected via slip-rings to a three-phase AC-DC-AC sourceconverter that controls both the rotor and the grid currentsso that the rotor frequency is independent of the grid fre-quency
The turbine set has fresh water injectors which regularlyclean the blades of any accumulations of encrusted salt andon the other hand the turbo-generator control requires a pre-cise knowledge of system parameters and of the rotor speedin particularThus to remove the speed sensor rotor is to sim-plify the hardware with the consequent reduction in instal-lation and maintenance costs A detailed description of theOWC numerical model may be found in [28]
3 A Sensorless Control Scheme
In this section a sensorless control scheme with an observerfor the induction rotor speed based on a disturbance model
Mathematical Problems in Engineering 5
ControlWells turbine Air flow valve
Grid
Flow valveCrowbar
Gearbox OWC
Chamberpressure
transducer
Grid
GSC Vdc RSC Rotor
RSCGSC
Grid
Stator
Network
dp
Crowbar
WavesABC
C
a b c
g
ABC
A
B
C
A
B
C
A
B
C
g
A
B
C
+
minus
+
minus
Break waterDFIG
Figure 7 OWC control scheme
is presented AC drives without speed sensors on the rotorshaft compose a common strategy for cost reduction androbustness especially in hostile environments (see [29ndash35])The proposed observer aims to accurately estimate the rotorangular velocity by employing the stator current and statorvoltage as input variables in a closed loop observer structurethat was first introduced in [18]
A point tracking technique will be implemented for thecontrol to track a curve that yields the maximum possiblepower from the sea for any given environmental conditionsThis Tracking Characteristic Curve (TCC) is predefined foreach turbine by adjusting the shaft speed of the OWC turbo-generator so that the flow coefficient 120601 remains boundedyielding a maximum stalling-free torque coefficient 119862
119905
Therefore for a given pressure drop input 119889119901 there is a uniquegenerator slip and a power reference required to satisfy theconditions of maximum wave energy extraction In our par-ticular case this TCC is achieved based on a previous study ofthe Wells turbine at hand using the characteristic curve pro-vided by the manufacturer (see Figure 5) and the requiredslip values are shown in Table 1
The control scheme is shown in Figure 7 and its designrequires taking into account the dynamics of the turbo-generator module In particular in the DFIG-based OWCgeneration system themaximumpower objective is achievedby regulating the current of the rotor in the RSC In order toachieve independent control of the stator active power119875 andreactive power 119876 the direct and quadrature components ofthe rotor currents 119894
119902119903 119894119889119903are used to provide the required volt-
age signal V119902119903 V119889119903
by means of PI controllers Besides sincethe OWC air flow control actuator is a throttle-valve subjectto saturation it was necessary to consider an integral wind-up
Table 1 Pressure drop input versus slip reference and correspondingflux coefficient variation
dPAVERAGE (Pa) slipAVER () Flow Coef 1205930ndash5500 minus056 0ndash029875500ndash5790 minus234 0ndash029995790ndash5975 minus413 0ndash029955975ndash6175 minus600 0ndash029996175ndash6375 minus790 0ndash029956375ndash6600 minus986 0ndash029956600ndash6850 minus1194 0ndash029996850ndash7100 minus1406 0ndash029987100ndash7375 minus1628 0ndash029987375ndash7670 minus1860 0ndash02999
effect in order to avoid this undesired phenomenon Thesteps for tuning a PID controller via the closed-loop Ziegler-Nichols method consist of considering all controller gainszero and then increasing the proportional gain 119870
119901up to a
value 119870119901
= 119870119888119903
where sustained oscillations occur withperiod 119875
119888119903 Using this procedure some initial values for the
controller parameters were obtained and afterwards refinedin an experimental trial-and-error basis In this way theobtained throttle valve controller gains are119870
119901= 06119879
119894= 05
and 119879119889= 0125 for initial 119870
119888119903= 004 and 119875
119888119903= 0008 values
Then the output control drives the valve into the demandedposition against a counterbalance weight Once in positionit is hold steady by an electromagnetic brake In the eventof a control failure or in the case that the grid connection islost or an emergency closure is demanded the brake supply isinterrupted and the valve closes by means of the influence of
6 Mathematical Problems in Engineering
Grid
120579r
120579f
PLLabc dq
RSC
CDFIG
120596r
Control
Voltage
Voltage Ps Qs
Q
PI PIIlowastdr
Ilowastqr
Iqr
PWM
Vqr1+
Vdr1+
Vqr2
Vqr
Vdr
Vdr2measurement
dp
PIPI
Qs
Ps
+
minus
minus
+
+
+
minus
Idrminus
minus
Psref
sref
Inabc Vnabc
Igabc
IsabcIrabc
Figure 8 Control loop for the RSC
the weight In this way the modulation of the valve aims toadjust the pressure drop across the turbine rotor
Thus the proposed sensorless speed controller activelycontrols the rotor slip by means of the rotor side converterof the DFIG that acts as control actuator so as to avoid thestalling behaviour and to increase the output power Thefunctioning of the control scheme is detailed as follows TheDFIG is attached to theWells turbine by means of a gear boxThe DFIG stator windings are connected directly to the gridwhile the rotor windings are connected to the back to back(ACDCAC) converter
The converter is composed of aGSC connected to the gridand a rotor RSC connected to the wound rotor windingsTheRSC controls the active (119875
119904) and reactive (119876
119904) power of the
DFIG independently while the GSC controls the DC voltageand grid side reactive power
As indicated before the RSC operates as control actuatorand its objective is to regulate the DFIG rotor speed by vary-ing the rotor slip in accordance with the control law signalprovided by the rotational speed controller in such a way thatit establishes themaximum power generation allowed at eachtime instant for the current wave without entering in stallingIn order to achieve this it is needed an independent regula-tion of the stator active power (by means of speed control)and reactive power
The control loop of the RSC is depicted in Figure 8 andthe corresponding loop for the GSC would be similar
This converter controls the active power (119875119904) and reactive
power (119876119904) of the DFIG In order to achieve independent
control of them the instantaneous three-phase rotor currents119894119903abc are sampled and transformed into 119889-119902 components 119894
119902119903
and 119894119889119903
in the stator-flux oriented reference frame In thiscontext119875
119904and119876
119904can be represented as functions of the indi-
vidual current components Then the reference active power
is compared with the power losses and compensated by thestator flux estimator to form the reference 119902-current 119894lowast
119902119903 which
is then passed through a standard PI controller Its output V1199021199031
is in turn compensated by V1199021199032
to generate the 119902 voltage signalV119902119903 The RSC reactive power control is also used to maintain
a constant stator voltage within the desired range when theDFIG is connected to weak power networks without reactivepower compensationWhen connected to strong power gridsthis controlmay be set to zeroThe reference reactive power iscompared with its actual measurement to generate the errorsignal which is passed through a PI controller to provide thereference signal 119894lowast
119889119903Then it is compared with its actual signal
119894119889119903
to generate an error which is then used to provide therequired 119902-voltage signal V
1198891199031by means of a PI controller In
turn this voltage is compensated by V1198891199032
to generate the 119889voltage signal V
119889119903and used by the PWM module to generate
the IGBT gate control signals necessary to drive the RSCconverter jointly with the 119902-component signal V
119902119903already
obtainedWhen a grid fault is detected the primarily objective
of the implemented control is the uninterrupted operationfeature of the wave energy plant For this purpose the rotor isshort-circuited by a crowbar and theRSC is blocked to protectit from the rotor high currents causing the loss of controlof active power and reactive power of the DFIG In order tocontrol the acceleration of the turbo-generator group theflow is typically reduced accordingly with themodified powerreference regulating the throttle air valve When the rotorcurrent and DC-link voltage are low enough the crowbaris turned off and the RSC is restarted Meanwhile the GSCkeeps the DC-link capacitor voltage constant and the gridside reactive power controllability of the GSC is useful duringthe process of voltage reestablishment After voltage recoverya second crowbar circuit activation may happen if the rotor
Mathematical Problems in Engineering 7
currents or the DC-link voltage exceed their maximumallowed values When the voltage and frequency of the net-work return to steady-state values the references are mod-ified again restoring the normal functioning of the systemFor a detailed description of the different parts of the controlscheme (see [36]) further information about DFIG controldevices by means of RSC and GSC may be found in [37ndash39]
For this purpose a simple Luenberger based observer forthe rotor flux and angular velocity will be proposed Fieldoriented decoupling is applied giving all expressions in thestator-flux reference frame where the 119889-axis is aligned withthe stator flux linkage vectorΨ
119904 so thatΨ
119889119904= Ψ119904andΨ
119902119904= 0
This leads to the following relationships (see [38])
119889119902119904
119889119905= 1198861119902119904+ 1198862119902119903+ 1198863120596119903119889119903+ 1198864V119902119904+ 119896119894(119894119902119904minus 119902119904)
119889119889119904
119889119905= 1198861119889119904+ 1198862119889119903minus 1198863120596119903119902119903+ 1198864V119889119904+ 119896119894(119894119889119904minus 119889119904)
119889119902119903
119889120591= 1198865119902119904+ 1198866119902119903minus 120577119889minus 1198962(119903119903119889minus 120577119889)
119889119889119903
119889120591= 1198865119889119904+ 1198866119889119903+ 120577119902+ 1198962(119903119902119903minus 120577119902)
(9)
where V119889119904 V119902119904 119889119904 119902119904 119889119904 119902119904are the estimated components
of the stator voltage current and flux vector of the rotor in thereference frame and
1198861= minus
1198771199041198712
119903+ 1198771199031198712
119898
119908119871119903
1198862=119877119903119871119898
119908119871119903
1198863=119871119898
119908
1198864=119871119903
119908 119886
5=119877119903119871119898
119871119903
1198864= minus
119877119903
119871119903
119908 = 119871119904119871119903minus 1198712
119898
(10)
The structure of this observer is based on treating as distur-bances 120577
119902 120577119889the corresponding vectors 120596
119903119902119903 120596119903119889119903so as to
remove the coupling between cocoordinates as follows
119889120577119902
119889120591= 1198961(119894119889119904minus 119889119904)
119889120577119889
119889120591= minus1198961(119894119902119904minus 119902119904)
(11)
The disturbance vector has the same angular velocity as allother vector components Both disturbance and flux vectorshave the same phase and proportional amplitudes so that thevelocity may be estimated as
119903= 119878(radic
1205772
119902+ 1205772
119889
2
119889119903+ 2
119902119903
) + 1198964(119881 minus 119881
119891) (12)
Error variables
idriqr
120577q
120577d
Estimation
r
dr
qr
idrqr
120577qd
qrdr
120577qd idr
iqr
Vf
VVf
V
dsqs
iqs
idsControl variables
Figure 9 Control loop for the state observer
where 119878 denotes the sign of the angular velocityThe observergains 119896
1 1198964have small values and are selected experimentally
while 1198962depends on the rotor speed
1198962= 119886 + 119887 sdot
10038161003816100381610038161003816119903119891
10038161003816100381610038161003816(13)
being 119886 and 119887 constants and |119903119891| the absolute value of the
estimated filtered rotor speed 119881119891denotes the filtered signal
of the control 119881 which is defined as
119881 = 119903119902120577119889minus 119903119889120577119902
119889119881119891
119889120591=
1
1198791
(119881 minus 119881119891) (14)
The control loop for this state observer is depicted in Figure 9A comprehensive description of Luenberger observers maybe found in [40 41]
As it has been explained before the stator is connected tothe grid so that the influence of the stator resistance is smalland the stator magnetizing current 119894
119898119904is considered to be
constant [42] For this purpose it is assumed that themachineworks away from themagnetic saturation limitsThus119879
119890may
be defined as
119879119890= minus119870119879119894119902119903 (15)
Therefore the generator slip may be controlled by regulatingthe rotor current 119894
119902119903 while the stator reactive power 119876
119904
119876119904=3
2
minus 1205961199041198712
119898119894119898119904(119894119898119904minus 119894119889119903)
119871119904
(16)
may be controlled by regulating the rotor current 119894119889119903 Con-
sequently from 119879119890= minus119870
119879119894119902119903
with 119870119879= 119871119898119894119898119904
119871119904being
a torque constant and taking into account that 119875 = 119879120596the sensorless controller that has been designed solves thepower tracking problem for DFIG-based OWC power plantsin a hostile environment since it allows to achieve maximumpower extraction by matching the desired generator slipreference to avoid the stalling behaviour
4 Simulation Results
As it has been indicated the Nereida OWC demo project[3] includes 16 Wells turbines in a newly constructed rubble
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Decision SciencesAdvances in
Discrete MathematicsJournal of
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
2 Mathematical Problems in Engineering
Figure 1 OWC for the Nereida project by the EVE
emphasis in wave energy with the potential to satisfy 15of EU energy demand cutting 136MTMWh off the CO
2
emissions by 2050 The proposals are directed mainly to theRampD not only of new designs and components aiming toimprove equipment fatigue and reduce the cost but also ofdemonstration programs for prototypes testing as well asto develop infrastructure to validate experimental devicesMajor efforts are being made in the Basque Country throughthe Nereida Project promoted by Basque Energy Board(EVE) which has developed an Oscillating Water Column(OWC) integrated in a breakwater located in Mutriku andinvolves a C57M investment The plant consists of 16turbines 185 kW each with an estimated overall power of296 kW (see Figure 1) It was inaugurated in July 2011 [3 4]and produced 200000 kWh during the first year while itwas estimated 600000 kWh production per year Althoughthe difference is mainly due to a storm that damaged thecontrol room and kept the facility closed during the bestwavemonths an improvement in the power generation couldhighly benefit the system
In this power plant the water surface inside a chambermoves up and down under the wave action causing to inhaleand exhale air through the opening at the top The bidirec-tional air flow is applied to a special kind of turbine calledWells turbine which provides unidirectional rotation despiteof the air flow direction [5 6] Thus the Wells turbine trans-forms the wave potential into mechanical energy that will betransmitted to a double feed induction generator which feedsAC power to the grid For that two pulse-width-modulatedthree phase converters are connected back to back betweenthe rotor terminal and the utility grid with a DC link Thestator circuit is directly connected to the grid while the rotorwinding is connected via slip-rings to the rotor side converter[7]
TheOWC system located inMutriku uses a vector controlscheme coupled with cascaded Proportional-Integral-Deriv-ative (PID) controller for current and power loops [8] Thisscheme allows power tracking while the Rotor and GridSide Converters RSCGSC are controlled independentlyBesides it has fault-ride-through (FRT) capabilities and theOWC system also implements a complementary modifiedantiwind-up PID based valve control for incoming air flowinto the turbine [9ndash11] The choice of valve control has been
mainly determined by the fact that it is the control used inMutriku New Grid Codes oblige distributed power-genera-tion systems to remain connected to the power network dur-ing the fault to avoidmassive chain disconnections so that theimplementation of an adequate FRT capability is indispens-able in this kind of systems to ensure its stability and uninter-rupted operation [12ndash17]
All mechanical parts should be designed to withstand theocean hostile environment and it has to be considered that theturbo-generator control requires a precise knowledge of thesystem parameters and of the rotor speed in particular In thiscontext the most suitable option is to remove the mechanicalspeed sensor at the rotor shaft so as to simplify the hardwarewith the consequent reduction in installation and mainte-nance costs increment of disturbance rejection and plantreliability improvement However in order to eliminate thespeed sensor from the drive some of the state variables suchas rotor angular velocity and flux have to be estimated frommeasured states Besides accuracy robustness and sensitiv-ity against parameter deviation can be improved by choosingclosed loop observers [18 19] Therefore dynamic perfor-mance and steady-state speed accuracy for the lower speedrange have been achieved in this particular case consideringa closed loop speed observer based in a Luenberger system toestimate the rotor speed from the measured stator voltagesand currents [20 21]
After all these considerations and taking into account thecost effectiveness and improved performance that a speedobserver can afford this paper presents a new sensorless vec-tor control scheme in order to improve the power extractionin theMutriku OWC whose results can easily be extended toother wave power plantsThe rest of the paper is organized asfollows In Section 2 the OWC is presented and both itsmodules the capture chamber and the turbine that generatesenergy are explained Next in Section 3 the proposed sensor-less control scheme is stated In Section 4 simulation resultsfor a representative case-study comparing different controlledcases have been obtained And finally some concluding re-marks are presented in the last section
2 Mutriku OWC Description
21 MutrikuWaveModel and OWCCapture Chamber Usingdata from the Bilbao-Vizcaya exterior buoy of the State Net-work Ports the annual average wave height is around 2mwith period of about 10 s Statistical study of wave directionsreveals the predominance of northeast swell type wave [2223] In order to study regular waves (see also [24]) it is nec-essary to take into account the spectrum of the wave climatedata that measures the correlation between wave frequencyand wave energy as it may be observed in Figure 2
This representative spectrum of the wave climate is buoydriven since it uses a linear wave propagationmodel to trans-form measures obtained by an offshore wave rider buoy indeep water to the OWC location in the coast
Mathematical Problems in Engineering 3
006 008 01 012 014 016 018 020
1
2
3
4
5
6
7
8
Wave frequency (Hz)
Wav
e spe
ctra
l den
sity
(m2s)
Figure 2 Representative spectrum of the wave climate
Taking these data into consideration a regular wave maybe modelled assuming that its height and frequency corre-spond to the peak given in Figure 2 so that it can be writtenas follows
119875wf =1205881199081198921198602120582
16119879119908
[1 +4120587ℎ120582
sinh (4120587ℎ120582)]
120582 =1198921198792
119908
2120587tanh(2120587ℎ
120582)
(1)
A thorough overview of wave theory and models may befound in [25]
The breakwater housing the OWC plant is located at adepth of 5m belowMESTLW (Maximum Equinoctial SpringTide Low Water) with respect to Level 0 at Mutriku portThe opening that transmits the wave oscillations to each aircolumn is 320m high and 400mwideThe lowest point is atminus340m so that the opening is always below sea level [26]
The power available from the air flow in the OWC cham-ber which parameters are presented in Figure 3 may be ex-pressed in terms of the air pressure drop and the kineticenergy as follows
119875in = (119889119901 +120588V2119909
2) V119909119886 (2)
For a complete description see [25]
22 Turbo-Generator Module In the Mutriku OWC the tur-bines are fixed-pitch which means that they present a robustperformance due to the lack of air flow rectifying devicessince they always rotate in the same direction regardless ofthe air flow and are vertically mounted with a butterfly typevalve at the bottom to isolate the chamber if necessary Tominimize the height of the plant room the length of theturbo-generation assembly has been designed to be relativelysmall 283m high by 125m maximum width and approxi-mately 1200 kg (see Figures 1 and 4)
Turbine
Front wall
120582
A
h
x Back wall
SWL
a
b120579
Figure 3 OWC capture chamber
The equations used for modelling the pressure dropacross rotor and the torque produced by turbine are (see [27])
119889119901 = 119862119886119870(
1
119886) [V2119909+ (119903120596
119903)2
] (3)
119879119905= 119862119905119870119903 [V2119909+ (119903120596
119903)2
] (4)
where119870 is the turbine constant defined as
119870 =120588119887119899119897
2(5)
so that it may be deduced that the torque
119879119905=119889119901119862119905119903119886
119862119886
(6)
The flow coefficient 120601 is usually defined as the nondimen-sional quantity corresponding to the tangent of the angle ofattack at the blade tip The flow coefficient is
120601 =V119909
119903120596119903
(7)
Finally the flow rate and turbine performance can be calcu-lated as
119902 = V119909119886
120578119905=119879119905120596119903
119889119901119902
(8)
Thus it may be observed from (3) and (7) that for a givenrotational speed it is possible to establish a linear relationshipbetween the pressure drop and the flow rate This facilitatesan adequate coupling between the turbine and the OWCwhich also depends on the pressure drop input Besides thedeveloped torque that is to say the turbine power depends
4 Mathematical Problems in Engineering
(a) (b)
Figure 4 Turbines for the Mutriku OWC project by the EVE
0 02 04 06 08 1 12 14 16 18 2
0
01
02
03
04
05
06
minus01
Ct
(torq
ue co
effici
ent)
120601 (flow coefficient)
120601 = 03
Figure 5 Torque coefficient versus flow coefficient from the datash-eet turbine specifications
on the pressure drop the power coefficient and the torquecoefficient (6) It is the relationship of this torque coefficientagainst the flow coefficient that determines one of the char-acteristic curves of theWells turbine under study It is partic-ularly interesting the behaviour of the torque coefficient 119862
119905
shown in Figure 5 since it shows that it is negative during thestart-up phase whichmeans that due to the properties of theturbine the AC machine acts as a motor until it overcomesthe drag forces acting on the blades Figure 5 also shows thatwhen the flux coefficient reaches a critical value the torquecoefficient will drop drastically which is commonly known asthe stalling behaviour of theWells turbineOn the other handwhen the turbine velocity increases the flow rate decreases(see (7)) Therefore accelerating the turbine adequately willavoid that the turbine enters into stalling behaviour drasti-cally dropping its efficiency
It may be seen in Figure 6 how the performance ofthe Wells turbine deteriorates when the flow coefficient ap-proaches the corresponding 119862
119905critical value of Figure 5 03
This behaviour is denoted stalling behaviour and it is thereason why control is particularly relevant in Wells turbines
In this way this undesired stalling behaviour can beavoided or delayed if the turbine accelerates fast enough inresponse to the incoming air flow in order to maintain ade-quate flow coefficient values (7) (see [8]) so as tomaintain theoptimal flow coefficient for an efficient conversion of pneu-matic power
0 1 2 3 4 5 6 7 8 9 10Time (s)
Stalling behavior
minus16minus14minus12minus10minus8minus6minus4minus2
024times104
Pow
er g
ener
ated
(W)
PgenPgenmean
Average value (12045kW)
Figure 6 Simulated power generated for 7000 Pa maximum pres-sure drop input under no control (stalling)
The Mutriku OWC consists of 16 chambers where eachchamber has a top opening that is connected to a verticallymounted turbo-generator module Each module is formedby two five-blade Wells turbines connected to an air cooledDFIG generator In this kind of induction machines widelyemployed in diverse generation applications the stator circuitis directly connected to the grid while the rotor windings areconnected via slip-rings to a three-phase AC-DC-AC sourceconverter that controls both the rotor and the grid currentsso that the rotor frequency is independent of the grid fre-quency
The turbine set has fresh water injectors which regularlyclean the blades of any accumulations of encrusted salt andon the other hand the turbo-generator control requires a pre-cise knowledge of system parameters and of the rotor speedin particularThus to remove the speed sensor rotor is to sim-plify the hardware with the consequent reduction in instal-lation and maintenance costs A detailed description of theOWC numerical model may be found in [28]
3 A Sensorless Control Scheme
In this section a sensorless control scheme with an observerfor the induction rotor speed based on a disturbance model
Mathematical Problems in Engineering 5
ControlWells turbine Air flow valve
Grid
Flow valveCrowbar
Gearbox OWC
Chamberpressure
transducer
Grid
GSC Vdc RSC Rotor
RSCGSC
Grid
Stator
Network
dp
Crowbar
WavesABC
C
a b c
g
ABC
A
B
C
A
B
C
A
B
C
g
A
B
C
+
minus
+
minus
Break waterDFIG
Figure 7 OWC control scheme
is presented AC drives without speed sensors on the rotorshaft compose a common strategy for cost reduction androbustness especially in hostile environments (see [29ndash35])The proposed observer aims to accurately estimate the rotorangular velocity by employing the stator current and statorvoltage as input variables in a closed loop observer structurethat was first introduced in [18]
A point tracking technique will be implemented for thecontrol to track a curve that yields the maximum possiblepower from the sea for any given environmental conditionsThis Tracking Characteristic Curve (TCC) is predefined foreach turbine by adjusting the shaft speed of the OWC turbo-generator so that the flow coefficient 120601 remains boundedyielding a maximum stalling-free torque coefficient 119862
119905
Therefore for a given pressure drop input 119889119901 there is a uniquegenerator slip and a power reference required to satisfy theconditions of maximum wave energy extraction In our par-ticular case this TCC is achieved based on a previous study ofthe Wells turbine at hand using the characteristic curve pro-vided by the manufacturer (see Figure 5) and the requiredslip values are shown in Table 1
The control scheme is shown in Figure 7 and its designrequires taking into account the dynamics of the turbo-generator module In particular in the DFIG-based OWCgeneration system themaximumpower objective is achievedby regulating the current of the rotor in the RSC In order toachieve independent control of the stator active power119875 andreactive power 119876 the direct and quadrature components ofthe rotor currents 119894
119902119903 119894119889119903are used to provide the required volt-
age signal V119902119903 V119889119903
by means of PI controllers Besides sincethe OWC air flow control actuator is a throttle-valve subjectto saturation it was necessary to consider an integral wind-up
Table 1 Pressure drop input versus slip reference and correspondingflux coefficient variation
dPAVERAGE (Pa) slipAVER () Flow Coef 1205930ndash5500 minus056 0ndash029875500ndash5790 minus234 0ndash029995790ndash5975 minus413 0ndash029955975ndash6175 minus600 0ndash029996175ndash6375 minus790 0ndash029956375ndash6600 minus986 0ndash029956600ndash6850 minus1194 0ndash029996850ndash7100 minus1406 0ndash029987100ndash7375 minus1628 0ndash029987375ndash7670 minus1860 0ndash02999
effect in order to avoid this undesired phenomenon Thesteps for tuning a PID controller via the closed-loop Ziegler-Nichols method consist of considering all controller gainszero and then increasing the proportional gain 119870
119901up to a
value 119870119901
= 119870119888119903
where sustained oscillations occur withperiod 119875
119888119903 Using this procedure some initial values for the
controller parameters were obtained and afterwards refinedin an experimental trial-and-error basis In this way theobtained throttle valve controller gains are119870
119901= 06119879
119894= 05
and 119879119889= 0125 for initial 119870
119888119903= 004 and 119875
119888119903= 0008 values
Then the output control drives the valve into the demandedposition against a counterbalance weight Once in positionit is hold steady by an electromagnetic brake In the eventof a control failure or in the case that the grid connection islost or an emergency closure is demanded the brake supply isinterrupted and the valve closes by means of the influence of
6 Mathematical Problems in Engineering
Grid
120579r
120579f
PLLabc dq
RSC
CDFIG
120596r
Control
Voltage
Voltage Ps Qs
Q
PI PIIlowastdr
Ilowastqr
Iqr
PWM
Vqr1+
Vdr1+
Vqr2
Vqr
Vdr
Vdr2measurement
dp
PIPI
Qs
Ps
+
minus
minus
+
+
+
minus
Idrminus
minus
Psref
sref
Inabc Vnabc
Igabc
IsabcIrabc
Figure 8 Control loop for the RSC
the weight In this way the modulation of the valve aims toadjust the pressure drop across the turbine rotor
Thus the proposed sensorless speed controller activelycontrols the rotor slip by means of the rotor side converterof the DFIG that acts as control actuator so as to avoid thestalling behaviour and to increase the output power Thefunctioning of the control scheme is detailed as follows TheDFIG is attached to theWells turbine by means of a gear boxThe DFIG stator windings are connected directly to the gridwhile the rotor windings are connected to the back to back(ACDCAC) converter
The converter is composed of aGSC connected to the gridand a rotor RSC connected to the wound rotor windingsTheRSC controls the active (119875
119904) and reactive (119876
119904) power of the
DFIG independently while the GSC controls the DC voltageand grid side reactive power
As indicated before the RSC operates as control actuatorand its objective is to regulate the DFIG rotor speed by vary-ing the rotor slip in accordance with the control law signalprovided by the rotational speed controller in such a way thatit establishes themaximum power generation allowed at eachtime instant for the current wave without entering in stallingIn order to achieve this it is needed an independent regula-tion of the stator active power (by means of speed control)and reactive power
The control loop of the RSC is depicted in Figure 8 andthe corresponding loop for the GSC would be similar
This converter controls the active power (119875119904) and reactive
power (119876119904) of the DFIG In order to achieve independent
control of them the instantaneous three-phase rotor currents119894119903abc are sampled and transformed into 119889-119902 components 119894
119902119903
and 119894119889119903
in the stator-flux oriented reference frame In thiscontext119875
119904and119876
119904can be represented as functions of the indi-
vidual current components Then the reference active power
is compared with the power losses and compensated by thestator flux estimator to form the reference 119902-current 119894lowast
119902119903 which
is then passed through a standard PI controller Its output V1199021199031
is in turn compensated by V1199021199032
to generate the 119902 voltage signalV119902119903 The RSC reactive power control is also used to maintain
a constant stator voltage within the desired range when theDFIG is connected to weak power networks without reactivepower compensationWhen connected to strong power gridsthis controlmay be set to zeroThe reference reactive power iscompared with its actual measurement to generate the errorsignal which is passed through a PI controller to provide thereference signal 119894lowast
119889119903Then it is compared with its actual signal
119894119889119903
to generate an error which is then used to provide therequired 119902-voltage signal V
1198891199031by means of a PI controller In
turn this voltage is compensated by V1198891199032
to generate the 119889voltage signal V
119889119903and used by the PWM module to generate
the IGBT gate control signals necessary to drive the RSCconverter jointly with the 119902-component signal V
119902119903already
obtainedWhen a grid fault is detected the primarily objective
of the implemented control is the uninterrupted operationfeature of the wave energy plant For this purpose the rotor isshort-circuited by a crowbar and theRSC is blocked to protectit from the rotor high currents causing the loss of controlof active power and reactive power of the DFIG In order tocontrol the acceleration of the turbo-generator group theflow is typically reduced accordingly with themodified powerreference regulating the throttle air valve When the rotorcurrent and DC-link voltage are low enough the crowbaris turned off and the RSC is restarted Meanwhile the GSCkeeps the DC-link capacitor voltage constant and the gridside reactive power controllability of the GSC is useful duringthe process of voltage reestablishment After voltage recoverya second crowbar circuit activation may happen if the rotor
Mathematical Problems in Engineering 7
currents or the DC-link voltage exceed their maximumallowed values When the voltage and frequency of the net-work return to steady-state values the references are mod-ified again restoring the normal functioning of the systemFor a detailed description of the different parts of the controlscheme (see [36]) further information about DFIG controldevices by means of RSC and GSC may be found in [37ndash39]
For this purpose a simple Luenberger based observer forthe rotor flux and angular velocity will be proposed Fieldoriented decoupling is applied giving all expressions in thestator-flux reference frame where the 119889-axis is aligned withthe stator flux linkage vectorΨ
119904 so thatΨ
119889119904= Ψ119904andΨ
119902119904= 0
This leads to the following relationships (see [38])
119889119902119904
119889119905= 1198861119902119904+ 1198862119902119903+ 1198863120596119903119889119903+ 1198864V119902119904+ 119896119894(119894119902119904minus 119902119904)
119889119889119904
119889119905= 1198861119889119904+ 1198862119889119903minus 1198863120596119903119902119903+ 1198864V119889119904+ 119896119894(119894119889119904minus 119889119904)
119889119902119903
119889120591= 1198865119902119904+ 1198866119902119903minus 120577119889minus 1198962(119903119903119889minus 120577119889)
119889119889119903
119889120591= 1198865119889119904+ 1198866119889119903+ 120577119902+ 1198962(119903119902119903minus 120577119902)
(9)
where V119889119904 V119902119904 119889119904 119902119904 119889119904 119902119904are the estimated components
of the stator voltage current and flux vector of the rotor in thereference frame and
1198861= minus
1198771199041198712
119903+ 1198771199031198712
119898
119908119871119903
1198862=119877119903119871119898
119908119871119903
1198863=119871119898
119908
1198864=119871119903
119908 119886
5=119877119903119871119898
119871119903
1198864= minus
119877119903
119871119903
119908 = 119871119904119871119903minus 1198712
119898
(10)
The structure of this observer is based on treating as distur-bances 120577
119902 120577119889the corresponding vectors 120596
119903119902119903 120596119903119889119903so as to
remove the coupling between cocoordinates as follows
119889120577119902
119889120591= 1198961(119894119889119904minus 119889119904)
119889120577119889
119889120591= minus1198961(119894119902119904minus 119902119904)
(11)
The disturbance vector has the same angular velocity as allother vector components Both disturbance and flux vectorshave the same phase and proportional amplitudes so that thevelocity may be estimated as
119903= 119878(radic
1205772
119902+ 1205772
119889
2
119889119903+ 2
119902119903
) + 1198964(119881 minus 119881
119891) (12)
Error variables
idriqr
120577q
120577d
Estimation
r
dr
qr
idrqr
120577qd
qrdr
120577qd idr
iqr
Vf
VVf
V
dsqs
iqs
idsControl variables
Figure 9 Control loop for the state observer
where 119878 denotes the sign of the angular velocityThe observergains 119896
1 1198964have small values and are selected experimentally
while 1198962depends on the rotor speed
1198962= 119886 + 119887 sdot
10038161003816100381610038161003816119903119891
10038161003816100381610038161003816(13)
being 119886 and 119887 constants and |119903119891| the absolute value of the
estimated filtered rotor speed 119881119891denotes the filtered signal
of the control 119881 which is defined as
119881 = 119903119902120577119889minus 119903119889120577119902
119889119881119891
119889120591=
1
1198791
(119881 minus 119881119891) (14)
The control loop for this state observer is depicted in Figure 9A comprehensive description of Luenberger observers maybe found in [40 41]
As it has been explained before the stator is connected tothe grid so that the influence of the stator resistance is smalland the stator magnetizing current 119894
119898119904is considered to be
constant [42] For this purpose it is assumed that themachineworks away from themagnetic saturation limitsThus119879
119890may
be defined as
119879119890= minus119870119879119894119902119903 (15)
Therefore the generator slip may be controlled by regulatingthe rotor current 119894
119902119903 while the stator reactive power 119876
119904
119876119904=3
2
minus 1205961199041198712
119898119894119898119904(119894119898119904minus 119894119889119903)
119871119904
(16)
may be controlled by regulating the rotor current 119894119889119903 Con-
sequently from 119879119890= minus119870
119879119894119902119903
with 119870119879= 119871119898119894119898119904
119871119904being
a torque constant and taking into account that 119875 = 119879120596the sensorless controller that has been designed solves thepower tracking problem for DFIG-based OWC power plantsin a hostile environment since it allows to achieve maximumpower extraction by matching the desired generator slipreference to avoid the stalling behaviour
4 Simulation Results
As it has been indicated the Nereida OWC demo project[3] includes 16 Wells turbines in a newly constructed rubble
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
006 008 01 012 014 016 018 020
1
2
3
4
5
6
7
8
Wave frequency (Hz)
Wav
e spe
ctra
l den
sity
(m2s)
Figure 2 Representative spectrum of the wave climate
Taking these data into consideration a regular wave maybe modelled assuming that its height and frequency corre-spond to the peak given in Figure 2 so that it can be writtenas follows
119875wf =1205881199081198921198602120582
16119879119908
[1 +4120587ℎ120582
sinh (4120587ℎ120582)]
120582 =1198921198792
119908
2120587tanh(2120587ℎ
120582)
(1)
A thorough overview of wave theory and models may befound in [25]
The breakwater housing the OWC plant is located at adepth of 5m belowMESTLW (Maximum Equinoctial SpringTide Low Water) with respect to Level 0 at Mutriku portThe opening that transmits the wave oscillations to each aircolumn is 320m high and 400mwideThe lowest point is atminus340m so that the opening is always below sea level [26]
The power available from the air flow in the OWC cham-ber which parameters are presented in Figure 3 may be ex-pressed in terms of the air pressure drop and the kineticenergy as follows
119875in = (119889119901 +120588V2119909
2) V119909119886 (2)
For a complete description see [25]
22 Turbo-Generator Module In the Mutriku OWC the tur-bines are fixed-pitch which means that they present a robustperformance due to the lack of air flow rectifying devicessince they always rotate in the same direction regardless ofthe air flow and are vertically mounted with a butterfly typevalve at the bottom to isolate the chamber if necessary Tominimize the height of the plant room the length of theturbo-generation assembly has been designed to be relativelysmall 283m high by 125m maximum width and approxi-mately 1200 kg (see Figures 1 and 4)
Turbine
Front wall
120582
A
h
x Back wall
SWL
a
b120579
Figure 3 OWC capture chamber
The equations used for modelling the pressure dropacross rotor and the torque produced by turbine are (see [27])
119889119901 = 119862119886119870(
1
119886) [V2119909+ (119903120596
119903)2
] (3)
119879119905= 119862119905119870119903 [V2119909+ (119903120596
119903)2
] (4)
where119870 is the turbine constant defined as
119870 =120588119887119899119897
2(5)
so that it may be deduced that the torque
119879119905=119889119901119862119905119903119886
119862119886
(6)
The flow coefficient 120601 is usually defined as the nondimen-sional quantity corresponding to the tangent of the angle ofattack at the blade tip The flow coefficient is
120601 =V119909
119903120596119903
(7)
Finally the flow rate and turbine performance can be calcu-lated as
119902 = V119909119886
120578119905=119879119905120596119903
119889119901119902
(8)
Thus it may be observed from (3) and (7) that for a givenrotational speed it is possible to establish a linear relationshipbetween the pressure drop and the flow rate This facilitatesan adequate coupling between the turbine and the OWCwhich also depends on the pressure drop input Besides thedeveloped torque that is to say the turbine power depends
4 Mathematical Problems in Engineering
(a) (b)
Figure 4 Turbines for the Mutriku OWC project by the EVE
0 02 04 06 08 1 12 14 16 18 2
0
01
02
03
04
05
06
minus01
Ct
(torq
ue co
effici
ent)
120601 (flow coefficient)
120601 = 03
Figure 5 Torque coefficient versus flow coefficient from the datash-eet turbine specifications
on the pressure drop the power coefficient and the torquecoefficient (6) It is the relationship of this torque coefficientagainst the flow coefficient that determines one of the char-acteristic curves of theWells turbine under study It is partic-ularly interesting the behaviour of the torque coefficient 119862
119905
shown in Figure 5 since it shows that it is negative during thestart-up phase whichmeans that due to the properties of theturbine the AC machine acts as a motor until it overcomesthe drag forces acting on the blades Figure 5 also shows thatwhen the flux coefficient reaches a critical value the torquecoefficient will drop drastically which is commonly known asthe stalling behaviour of theWells turbineOn the other handwhen the turbine velocity increases the flow rate decreases(see (7)) Therefore accelerating the turbine adequately willavoid that the turbine enters into stalling behaviour drasti-cally dropping its efficiency
It may be seen in Figure 6 how the performance ofthe Wells turbine deteriorates when the flow coefficient ap-proaches the corresponding 119862
119905critical value of Figure 5 03
This behaviour is denoted stalling behaviour and it is thereason why control is particularly relevant in Wells turbines
In this way this undesired stalling behaviour can beavoided or delayed if the turbine accelerates fast enough inresponse to the incoming air flow in order to maintain ade-quate flow coefficient values (7) (see [8]) so as tomaintain theoptimal flow coefficient for an efficient conversion of pneu-matic power
0 1 2 3 4 5 6 7 8 9 10Time (s)
Stalling behavior
minus16minus14minus12minus10minus8minus6minus4minus2
024times104
Pow
er g
ener
ated
(W)
PgenPgenmean
Average value (12045kW)
Figure 6 Simulated power generated for 7000 Pa maximum pres-sure drop input under no control (stalling)
The Mutriku OWC consists of 16 chambers where eachchamber has a top opening that is connected to a verticallymounted turbo-generator module Each module is formedby two five-blade Wells turbines connected to an air cooledDFIG generator In this kind of induction machines widelyemployed in diverse generation applications the stator circuitis directly connected to the grid while the rotor windings areconnected via slip-rings to a three-phase AC-DC-AC sourceconverter that controls both the rotor and the grid currentsso that the rotor frequency is independent of the grid fre-quency
The turbine set has fresh water injectors which regularlyclean the blades of any accumulations of encrusted salt andon the other hand the turbo-generator control requires a pre-cise knowledge of system parameters and of the rotor speedin particularThus to remove the speed sensor rotor is to sim-plify the hardware with the consequent reduction in instal-lation and maintenance costs A detailed description of theOWC numerical model may be found in [28]
3 A Sensorless Control Scheme
In this section a sensorless control scheme with an observerfor the induction rotor speed based on a disturbance model
Mathematical Problems in Engineering 5
ControlWells turbine Air flow valve
Grid
Flow valveCrowbar
Gearbox OWC
Chamberpressure
transducer
Grid
GSC Vdc RSC Rotor
RSCGSC
Grid
Stator
Network
dp
Crowbar
WavesABC
C
a b c
g
ABC
A
B
C
A
B
C
A
B
C
g
A
B
C
+
minus
+
minus
Break waterDFIG
Figure 7 OWC control scheme
is presented AC drives without speed sensors on the rotorshaft compose a common strategy for cost reduction androbustness especially in hostile environments (see [29ndash35])The proposed observer aims to accurately estimate the rotorangular velocity by employing the stator current and statorvoltage as input variables in a closed loop observer structurethat was first introduced in [18]
A point tracking technique will be implemented for thecontrol to track a curve that yields the maximum possiblepower from the sea for any given environmental conditionsThis Tracking Characteristic Curve (TCC) is predefined foreach turbine by adjusting the shaft speed of the OWC turbo-generator so that the flow coefficient 120601 remains boundedyielding a maximum stalling-free torque coefficient 119862
119905
Therefore for a given pressure drop input 119889119901 there is a uniquegenerator slip and a power reference required to satisfy theconditions of maximum wave energy extraction In our par-ticular case this TCC is achieved based on a previous study ofthe Wells turbine at hand using the characteristic curve pro-vided by the manufacturer (see Figure 5) and the requiredslip values are shown in Table 1
The control scheme is shown in Figure 7 and its designrequires taking into account the dynamics of the turbo-generator module In particular in the DFIG-based OWCgeneration system themaximumpower objective is achievedby regulating the current of the rotor in the RSC In order toachieve independent control of the stator active power119875 andreactive power 119876 the direct and quadrature components ofthe rotor currents 119894
119902119903 119894119889119903are used to provide the required volt-
age signal V119902119903 V119889119903
by means of PI controllers Besides sincethe OWC air flow control actuator is a throttle-valve subjectto saturation it was necessary to consider an integral wind-up
Table 1 Pressure drop input versus slip reference and correspondingflux coefficient variation
dPAVERAGE (Pa) slipAVER () Flow Coef 1205930ndash5500 minus056 0ndash029875500ndash5790 minus234 0ndash029995790ndash5975 minus413 0ndash029955975ndash6175 minus600 0ndash029996175ndash6375 minus790 0ndash029956375ndash6600 minus986 0ndash029956600ndash6850 minus1194 0ndash029996850ndash7100 minus1406 0ndash029987100ndash7375 minus1628 0ndash029987375ndash7670 minus1860 0ndash02999
effect in order to avoid this undesired phenomenon Thesteps for tuning a PID controller via the closed-loop Ziegler-Nichols method consist of considering all controller gainszero and then increasing the proportional gain 119870
119901up to a
value 119870119901
= 119870119888119903
where sustained oscillations occur withperiod 119875
119888119903 Using this procedure some initial values for the
controller parameters were obtained and afterwards refinedin an experimental trial-and-error basis In this way theobtained throttle valve controller gains are119870
119901= 06119879
119894= 05
and 119879119889= 0125 for initial 119870
119888119903= 004 and 119875
119888119903= 0008 values
Then the output control drives the valve into the demandedposition against a counterbalance weight Once in positionit is hold steady by an electromagnetic brake In the eventof a control failure or in the case that the grid connection islost or an emergency closure is demanded the brake supply isinterrupted and the valve closes by means of the influence of
6 Mathematical Problems in Engineering
Grid
120579r
120579f
PLLabc dq
RSC
CDFIG
120596r
Control
Voltage
Voltage Ps Qs
Q
PI PIIlowastdr
Ilowastqr
Iqr
PWM
Vqr1+
Vdr1+
Vqr2
Vqr
Vdr
Vdr2measurement
dp
PIPI
Qs
Ps
+
minus
minus
+
+
+
minus
Idrminus
minus
Psref
sref
Inabc Vnabc
Igabc
IsabcIrabc
Figure 8 Control loop for the RSC
the weight In this way the modulation of the valve aims toadjust the pressure drop across the turbine rotor
Thus the proposed sensorless speed controller activelycontrols the rotor slip by means of the rotor side converterof the DFIG that acts as control actuator so as to avoid thestalling behaviour and to increase the output power Thefunctioning of the control scheme is detailed as follows TheDFIG is attached to theWells turbine by means of a gear boxThe DFIG stator windings are connected directly to the gridwhile the rotor windings are connected to the back to back(ACDCAC) converter
The converter is composed of aGSC connected to the gridand a rotor RSC connected to the wound rotor windingsTheRSC controls the active (119875
119904) and reactive (119876
119904) power of the
DFIG independently while the GSC controls the DC voltageand grid side reactive power
As indicated before the RSC operates as control actuatorand its objective is to regulate the DFIG rotor speed by vary-ing the rotor slip in accordance with the control law signalprovided by the rotational speed controller in such a way thatit establishes themaximum power generation allowed at eachtime instant for the current wave without entering in stallingIn order to achieve this it is needed an independent regula-tion of the stator active power (by means of speed control)and reactive power
The control loop of the RSC is depicted in Figure 8 andthe corresponding loop for the GSC would be similar
This converter controls the active power (119875119904) and reactive
power (119876119904) of the DFIG In order to achieve independent
control of them the instantaneous three-phase rotor currents119894119903abc are sampled and transformed into 119889-119902 components 119894
119902119903
and 119894119889119903
in the stator-flux oriented reference frame In thiscontext119875
119904and119876
119904can be represented as functions of the indi-
vidual current components Then the reference active power
is compared with the power losses and compensated by thestator flux estimator to form the reference 119902-current 119894lowast
119902119903 which
is then passed through a standard PI controller Its output V1199021199031
is in turn compensated by V1199021199032
to generate the 119902 voltage signalV119902119903 The RSC reactive power control is also used to maintain
a constant stator voltage within the desired range when theDFIG is connected to weak power networks without reactivepower compensationWhen connected to strong power gridsthis controlmay be set to zeroThe reference reactive power iscompared with its actual measurement to generate the errorsignal which is passed through a PI controller to provide thereference signal 119894lowast
119889119903Then it is compared with its actual signal
119894119889119903
to generate an error which is then used to provide therequired 119902-voltage signal V
1198891199031by means of a PI controller In
turn this voltage is compensated by V1198891199032
to generate the 119889voltage signal V
119889119903and used by the PWM module to generate
the IGBT gate control signals necessary to drive the RSCconverter jointly with the 119902-component signal V
119902119903already
obtainedWhen a grid fault is detected the primarily objective
of the implemented control is the uninterrupted operationfeature of the wave energy plant For this purpose the rotor isshort-circuited by a crowbar and theRSC is blocked to protectit from the rotor high currents causing the loss of controlof active power and reactive power of the DFIG In order tocontrol the acceleration of the turbo-generator group theflow is typically reduced accordingly with themodified powerreference regulating the throttle air valve When the rotorcurrent and DC-link voltage are low enough the crowbaris turned off and the RSC is restarted Meanwhile the GSCkeeps the DC-link capacitor voltage constant and the gridside reactive power controllability of the GSC is useful duringthe process of voltage reestablishment After voltage recoverya second crowbar circuit activation may happen if the rotor
Mathematical Problems in Engineering 7
currents or the DC-link voltage exceed their maximumallowed values When the voltage and frequency of the net-work return to steady-state values the references are mod-ified again restoring the normal functioning of the systemFor a detailed description of the different parts of the controlscheme (see [36]) further information about DFIG controldevices by means of RSC and GSC may be found in [37ndash39]
For this purpose a simple Luenberger based observer forthe rotor flux and angular velocity will be proposed Fieldoriented decoupling is applied giving all expressions in thestator-flux reference frame where the 119889-axis is aligned withthe stator flux linkage vectorΨ
119904 so thatΨ
119889119904= Ψ119904andΨ
119902119904= 0
This leads to the following relationships (see [38])
119889119902119904
119889119905= 1198861119902119904+ 1198862119902119903+ 1198863120596119903119889119903+ 1198864V119902119904+ 119896119894(119894119902119904minus 119902119904)
119889119889119904
119889119905= 1198861119889119904+ 1198862119889119903minus 1198863120596119903119902119903+ 1198864V119889119904+ 119896119894(119894119889119904minus 119889119904)
119889119902119903
119889120591= 1198865119902119904+ 1198866119902119903minus 120577119889minus 1198962(119903119903119889minus 120577119889)
119889119889119903
119889120591= 1198865119889119904+ 1198866119889119903+ 120577119902+ 1198962(119903119902119903minus 120577119902)
(9)
where V119889119904 V119902119904 119889119904 119902119904 119889119904 119902119904are the estimated components
of the stator voltage current and flux vector of the rotor in thereference frame and
1198861= minus
1198771199041198712
119903+ 1198771199031198712
119898
119908119871119903
1198862=119877119903119871119898
119908119871119903
1198863=119871119898
119908
1198864=119871119903
119908 119886
5=119877119903119871119898
119871119903
1198864= minus
119877119903
119871119903
119908 = 119871119904119871119903minus 1198712
119898
(10)
The structure of this observer is based on treating as distur-bances 120577
119902 120577119889the corresponding vectors 120596
119903119902119903 120596119903119889119903so as to
remove the coupling between cocoordinates as follows
119889120577119902
119889120591= 1198961(119894119889119904minus 119889119904)
119889120577119889
119889120591= minus1198961(119894119902119904minus 119902119904)
(11)
The disturbance vector has the same angular velocity as allother vector components Both disturbance and flux vectorshave the same phase and proportional amplitudes so that thevelocity may be estimated as
119903= 119878(radic
1205772
119902+ 1205772
119889
2
119889119903+ 2
119902119903
) + 1198964(119881 minus 119881
119891) (12)
Error variables
idriqr
120577q
120577d
Estimation
r
dr
qr
idrqr
120577qd
qrdr
120577qd idr
iqr
Vf
VVf
V
dsqs
iqs
idsControl variables
Figure 9 Control loop for the state observer
where 119878 denotes the sign of the angular velocityThe observergains 119896
1 1198964have small values and are selected experimentally
while 1198962depends on the rotor speed
1198962= 119886 + 119887 sdot
10038161003816100381610038161003816119903119891
10038161003816100381610038161003816(13)
being 119886 and 119887 constants and |119903119891| the absolute value of the
estimated filtered rotor speed 119881119891denotes the filtered signal
of the control 119881 which is defined as
119881 = 119903119902120577119889minus 119903119889120577119902
119889119881119891
119889120591=
1
1198791
(119881 minus 119881119891) (14)
The control loop for this state observer is depicted in Figure 9A comprehensive description of Luenberger observers maybe found in [40 41]
As it has been explained before the stator is connected tothe grid so that the influence of the stator resistance is smalland the stator magnetizing current 119894
119898119904is considered to be
constant [42] For this purpose it is assumed that themachineworks away from themagnetic saturation limitsThus119879
119890may
be defined as
119879119890= minus119870119879119894119902119903 (15)
Therefore the generator slip may be controlled by regulatingthe rotor current 119894
119902119903 while the stator reactive power 119876
119904
119876119904=3
2
minus 1205961199041198712
119898119894119898119904(119894119898119904minus 119894119889119903)
119871119904
(16)
may be controlled by regulating the rotor current 119894119889119903 Con-
sequently from 119879119890= minus119870
119879119894119902119903
with 119870119879= 119871119898119894119898119904
119871119904being
a torque constant and taking into account that 119875 = 119879120596the sensorless controller that has been designed solves thepower tracking problem for DFIG-based OWC power plantsin a hostile environment since it allows to achieve maximumpower extraction by matching the desired generator slipreference to avoid the stalling behaviour
4 Simulation Results
As it has been indicated the Nereida OWC demo project[3] includes 16 Wells turbines in a newly constructed rubble
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
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Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
(a) (b)
Figure 4 Turbines for the Mutriku OWC project by the EVE
0 02 04 06 08 1 12 14 16 18 2
0
01
02
03
04
05
06
minus01
Ct
(torq
ue co
effici
ent)
120601 (flow coefficient)
120601 = 03
Figure 5 Torque coefficient versus flow coefficient from the datash-eet turbine specifications
on the pressure drop the power coefficient and the torquecoefficient (6) It is the relationship of this torque coefficientagainst the flow coefficient that determines one of the char-acteristic curves of theWells turbine under study It is partic-ularly interesting the behaviour of the torque coefficient 119862
119905
shown in Figure 5 since it shows that it is negative during thestart-up phase whichmeans that due to the properties of theturbine the AC machine acts as a motor until it overcomesthe drag forces acting on the blades Figure 5 also shows thatwhen the flux coefficient reaches a critical value the torquecoefficient will drop drastically which is commonly known asthe stalling behaviour of theWells turbineOn the other handwhen the turbine velocity increases the flow rate decreases(see (7)) Therefore accelerating the turbine adequately willavoid that the turbine enters into stalling behaviour drasti-cally dropping its efficiency
It may be seen in Figure 6 how the performance ofthe Wells turbine deteriorates when the flow coefficient ap-proaches the corresponding 119862
119905critical value of Figure 5 03
This behaviour is denoted stalling behaviour and it is thereason why control is particularly relevant in Wells turbines
In this way this undesired stalling behaviour can beavoided or delayed if the turbine accelerates fast enough inresponse to the incoming air flow in order to maintain ade-quate flow coefficient values (7) (see [8]) so as tomaintain theoptimal flow coefficient for an efficient conversion of pneu-matic power
0 1 2 3 4 5 6 7 8 9 10Time (s)
Stalling behavior
minus16minus14minus12minus10minus8minus6minus4minus2
024times104
Pow
er g
ener
ated
(W)
PgenPgenmean
Average value (12045kW)
Figure 6 Simulated power generated for 7000 Pa maximum pres-sure drop input under no control (stalling)
The Mutriku OWC consists of 16 chambers where eachchamber has a top opening that is connected to a verticallymounted turbo-generator module Each module is formedby two five-blade Wells turbines connected to an air cooledDFIG generator In this kind of induction machines widelyemployed in diverse generation applications the stator circuitis directly connected to the grid while the rotor windings areconnected via slip-rings to a three-phase AC-DC-AC sourceconverter that controls both the rotor and the grid currentsso that the rotor frequency is independent of the grid fre-quency
The turbine set has fresh water injectors which regularlyclean the blades of any accumulations of encrusted salt andon the other hand the turbo-generator control requires a pre-cise knowledge of system parameters and of the rotor speedin particularThus to remove the speed sensor rotor is to sim-plify the hardware with the consequent reduction in instal-lation and maintenance costs A detailed description of theOWC numerical model may be found in [28]
3 A Sensorless Control Scheme
In this section a sensorless control scheme with an observerfor the induction rotor speed based on a disturbance model
Mathematical Problems in Engineering 5
ControlWells turbine Air flow valve
Grid
Flow valveCrowbar
Gearbox OWC
Chamberpressure
transducer
Grid
GSC Vdc RSC Rotor
RSCGSC
Grid
Stator
Network
dp
Crowbar
WavesABC
C
a b c
g
ABC
A
B
C
A
B
C
A
B
C
g
A
B
C
+
minus
+
minus
Break waterDFIG
Figure 7 OWC control scheme
is presented AC drives without speed sensors on the rotorshaft compose a common strategy for cost reduction androbustness especially in hostile environments (see [29ndash35])The proposed observer aims to accurately estimate the rotorangular velocity by employing the stator current and statorvoltage as input variables in a closed loop observer structurethat was first introduced in [18]
A point tracking technique will be implemented for thecontrol to track a curve that yields the maximum possiblepower from the sea for any given environmental conditionsThis Tracking Characteristic Curve (TCC) is predefined foreach turbine by adjusting the shaft speed of the OWC turbo-generator so that the flow coefficient 120601 remains boundedyielding a maximum stalling-free torque coefficient 119862
119905
Therefore for a given pressure drop input 119889119901 there is a uniquegenerator slip and a power reference required to satisfy theconditions of maximum wave energy extraction In our par-ticular case this TCC is achieved based on a previous study ofthe Wells turbine at hand using the characteristic curve pro-vided by the manufacturer (see Figure 5) and the requiredslip values are shown in Table 1
The control scheme is shown in Figure 7 and its designrequires taking into account the dynamics of the turbo-generator module In particular in the DFIG-based OWCgeneration system themaximumpower objective is achievedby regulating the current of the rotor in the RSC In order toachieve independent control of the stator active power119875 andreactive power 119876 the direct and quadrature components ofthe rotor currents 119894
119902119903 119894119889119903are used to provide the required volt-
age signal V119902119903 V119889119903
by means of PI controllers Besides sincethe OWC air flow control actuator is a throttle-valve subjectto saturation it was necessary to consider an integral wind-up
Table 1 Pressure drop input versus slip reference and correspondingflux coefficient variation
dPAVERAGE (Pa) slipAVER () Flow Coef 1205930ndash5500 minus056 0ndash029875500ndash5790 minus234 0ndash029995790ndash5975 minus413 0ndash029955975ndash6175 minus600 0ndash029996175ndash6375 minus790 0ndash029956375ndash6600 minus986 0ndash029956600ndash6850 minus1194 0ndash029996850ndash7100 minus1406 0ndash029987100ndash7375 minus1628 0ndash029987375ndash7670 minus1860 0ndash02999
effect in order to avoid this undesired phenomenon Thesteps for tuning a PID controller via the closed-loop Ziegler-Nichols method consist of considering all controller gainszero and then increasing the proportional gain 119870
119901up to a
value 119870119901
= 119870119888119903
where sustained oscillations occur withperiod 119875
119888119903 Using this procedure some initial values for the
controller parameters were obtained and afterwards refinedin an experimental trial-and-error basis In this way theobtained throttle valve controller gains are119870
119901= 06119879
119894= 05
and 119879119889= 0125 for initial 119870
119888119903= 004 and 119875
119888119903= 0008 values
Then the output control drives the valve into the demandedposition against a counterbalance weight Once in positionit is hold steady by an electromagnetic brake In the eventof a control failure or in the case that the grid connection islost or an emergency closure is demanded the brake supply isinterrupted and the valve closes by means of the influence of
6 Mathematical Problems in Engineering
Grid
120579r
120579f
PLLabc dq
RSC
CDFIG
120596r
Control
Voltage
Voltage Ps Qs
Q
PI PIIlowastdr
Ilowastqr
Iqr
PWM
Vqr1+
Vdr1+
Vqr2
Vqr
Vdr
Vdr2measurement
dp
PIPI
Qs
Ps
+
minus
minus
+
+
+
minus
Idrminus
minus
Psref
sref
Inabc Vnabc
Igabc
IsabcIrabc
Figure 8 Control loop for the RSC
the weight In this way the modulation of the valve aims toadjust the pressure drop across the turbine rotor
Thus the proposed sensorless speed controller activelycontrols the rotor slip by means of the rotor side converterof the DFIG that acts as control actuator so as to avoid thestalling behaviour and to increase the output power Thefunctioning of the control scheme is detailed as follows TheDFIG is attached to theWells turbine by means of a gear boxThe DFIG stator windings are connected directly to the gridwhile the rotor windings are connected to the back to back(ACDCAC) converter
The converter is composed of aGSC connected to the gridand a rotor RSC connected to the wound rotor windingsTheRSC controls the active (119875
119904) and reactive (119876
119904) power of the
DFIG independently while the GSC controls the DC voltageand grid side reactive power
As indicated before the RSC operates as control actuatorand its objective is to regulate the DFIG rotor speed by vary-ing the rotor slip in accordance with the control law signalprovided by the rotational speed controller in such a way thatit establishes themaximum power generation allowed at eachtime instant for the current wave without entering in stallingIn order to achieve this it is needed an independent regula-tion of the stator active power (by means of speed control)and reactive power
The control loop of the RSC is depicted in Figure 8 andthe corresponding loop for the GSC would be similar
This converter controls the active power (119875119904) and reactive
power (119876119904) of the DFIG In order to achieve independent
control of them the instantaneous three-phase rotor currents119894119903abc are sampled and transformed into 119889-119902 components 119894
119902119903
and 119894119889119903
in the stator-flux oriented reference frame In thiscontext119875
119904and119876
119904can be represented as functions of the indi-
vidual current components Then the reference active power
is compared with the power losses and compensated by thestator flux estimator to form the reference 119902-current 119894lowast
119902119903 which
is then passed through a standard PI controller Its output V1199021199031
is in turn compensated by V1199021199032
to generate the 119902 voltage signalV119902119903 The RSC reactive power control is also used to maintain
a constant stator voltage within the desired range when theDFIG is connected to weak power networks without reactivepower compensationWhen connected to strong power gridsthis controlmay be set to zeroThe reference reactive power iscompared with its actual measurement to generate the errorsignal which is passed through a PI controller to provide thereference signal 119894lowast
119889119903Then it is compared with its actual signal
119894119889119903
to generate an error which is then used to provide therequired 119902-voltage signal V
1198891199031by means of a PI controller In
turn this voltage is compensated by V1198891199032
to generate the 119889voltage signal V
119889119903and used by the PWM module to generate
the IGBT gate control signals necessary to drive the RSCconverter jointly with the 119902-component signal V
119902119903already
obtainedWhen a grid fault is detected the primarily objective
of the implemented control is the uninterrupted operationfeature of the wave energy plant For this purpose the rotor isshort-circuited by a crowbar and theRSC is blocked to protectit from the rotor high currents causing the loss of controlof active power and reactive power of the DFIG In order tocontrol the acceleration of the turbo-generator group theflow is typically reduced accordingly with themodified powerreference regulating the throttle air valve When the rotorcurrent and DC-link voltage are low enough the crowbaris turned off and the RSC is restarted Meanwhile the GSCkeeps the DC-link capacitor voltage constant and the gridside reactive power controllability of the GSC is useful duringthe process of voltage reestablishment After voltage recoverya second crowbar circuit activation may happen if the rotor
Mathematical Problems in Engineering 7
currents or the DC-link voltage exceed their maximumallowed values When the voltage and frequency of the net-work return to steady-state values the references are mod-ified again restoring the normal functioning of the systemFor a detailed description of the different parts of the controlscheme (see [36]) further information about DFIG controldevices by means of RSC and GSC may be found in [37ndash39]
For this purpose a simple Luenberger based observer forthe rotor flux and angular velocity will be proposed Fieldoriented decoupling is applied giving all expressions in thestator-flux reference frame where the 119889-axis is aligned withthe stator flux linkage vectorΨ
119904 so thatΨ
119889119904= Ψ119904andΨ
119902119904= 0
This leads to the following relationships (see [38])
119889119902119904
119889119905= 1198861119902119904+ 1198862119902119903+ 1198863120596119903119889119903+ 1198864V119902119904+ 119896119894(119894119902119904minus 119902119904)
119889119889119904
119889119905= 1198861119889119904+ 1198862119889119903minus 1198863120596119903119902119903+ 1198864V119889119904+ 119896119894(119894119889119904minus 119889119904)
119889119902119903
119889120591= 1198865119902119904+ 1198866119902119903minus 120577119889minus 1198962(119903119903119889minus 120577119889)
119889119889119903
119889120591= 1198865119889119904+ 1198866119889119903+ 120577119902+ 1198962(119903119902119903minus 120577119902)
(9)
where V119889119904 V119902119904 119889119904 119902119904 119889119904 119902119904are the estimated components
of the stator voltage current and flux vector of the rotor in thereference frame and
1198861= minus
1198771199041198712
119903+ 1198771199031198712
119898
119908119871119903
1198862=119877119903119871119898
119908119871119903
1198863=119871119898
119908
1198864=119871119903
119908 119886
5=119877119903119871119898
119871119903
1198864= minus
119877119903
119871119903
119908 = 119871119904119871119903minus 1198712
119898
(10)
The structure of this observer is based on treating as distur-bances 120577
119902 120577119889the corresponding vectors 120596
119903119902119903 120596119903119889119903so as to
remove the coupling between cocoordinates as follows
119889120577119902
119889120591= 1198961(119894119889119904minus 119889119904)
119889120577119889
119889120591= minus1198961(119894119902119904minus 119902119904)
(11)
The disturbance vector has the same angular velocity as allother vector components Both disturbance and flux vectorshave the same phase and proportional amplitudes so that thevelocity may be estimated as
119903= 119878(radic
1205772
119902+ 1205772
119889
2
119889119903+ 2
119902119903
) + 1198964(119881 minus 119881
119891) (12)
Error variables
idriqr
120577q
120577d
Estimation
r
dr
qr
idrqr
120577qd
qrdr
120577qd idr
iqr
Vf
VVf
V
dsqs
iqs
idsControl variables
Figure 9 Control loop for the state observer
where 119878 denotes the sign of the angular velocityThe observergains 119896
1 1198964have small values and are selected experimentally
while 1198962depends on the rotor speed
1198962= 119886 + 119887 sdot
10038161003816100381610038161003816119903119891
10038161003816100381610038161003816(13)
being 119886 and 119887 constants and |119903119891| the absolute value of the
estimated filtered rotor speed 119881119891denotes the filtered signal
of the control 119881 which is defined as
119881 = 119903119902120577119889minus 119903119889120577119902
119889119881119891
119889120591=
1
1198791
(119881 minus 119881119891) (14)
The control loop for this state observer is depicted in Figure 9A comprehensive description of Luenberger observers maybe found in [40 41]
As it has been explained before the stator is connected tothe grid so that the influence of the stator resistance is smalland the stator magnetizing current 119894
119898119904is considered to be
constant [42] For this purpose it is assumed that themachineworks away from themagnetic saturation limitsThus119879
119890may
be defined as
119879119890= minus119870119879119894119902119903 (15)
Therefore the generator slip may be controlled by regulatingthe rotor current 119894
119902119903 while the stator reactive power 119876
119904
119876119904=3
2
minus 1205961199041198712
119898119894119898119904(119894119898119904minus 119894119889119903)
119871119904
(16)
may be controlled by regulating the rotor current 119894119889119903 Con-
sequently from 119879119890= minus119870
119879119894119902119903
with 119870119879= 119871119898119894119898119904
119871119904being
a torque constant and taking into account that 119875 = 119879120596the sensorless controller that has been designed solves thepower tracking problem for DFIG-based OWC power plantsin a hostile environment since it allows to achieve maximumpower extraction by matching the desired generator slipreference to avoid the stalling behaviour
4 Simulation Results
As it has been indicated the Nereida OWC demo project[3] includes 16 Wells turbines in a newly constructed rubble
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
ControlWells turbine Air flow valve
Grid
Flow valveCrowbar
Gearbox OWC
Chamberpressure
transducer
Grid
GSC Vdc RSC Rotor
RSCGSC
Grid
Stator
Network
dp
Crowbar
WavesABC
C
a b c
g
ABC
A
B
C
A
B
C
A
B
C
g
A
B
C
+
minus
+
minus
Break waterDFIG
Figure 7 OWC control scheme
is presented AC drives without speed sensors on the rotorshaft compose a common strategy for cost reduction androbustness especially in hostile environments (see [29ndash35])The proposed observer aims to accurately estimate the rotorangular velocity by employing the stator current and statorvoltage as input variables in a closed loop observer structurethat was first introduced in [18]
A point tracking technique will be implemented for thecontrol to track a curve that yields the maximum possiblepower from the sea for any given environmental conditionsThis Tracking Characteristic Curve (TCC) is predefined foreach turbine by adjusting the shaft speed of the OWC turbo-generator so that the flow coefficient 120601 remains boundedyielding a maximum stalling-free torque coefficient 119862
119905
Therefore for a given pressure drop input 119889119901 there is a uniquegenerator slip and a power reference required to satisfy theconditions of maximum wave energy extraction In our par-ticular case this TCC is achieved based on a previous study ofthe Wells turbine at hand using the characteristic curve pro-vided by the manufacturer (see Figure 5) and the requiredslip values are shown in Table 1
The control scheme is shown in Figure 7 and its designrequires taking into account the dynamics of the turbo-generator module In particular in the DFIG-based OWCgeneration system themaximumpower objective is achievedby regulating the current of the rotor in the RSC In order toachieve independent control of the stator active power119875 andreactive power 119876 the direct and quadrature components ofthe rotor currents 119894
119902119903 119894119889119903are used to provide the required volt-
age signal V119902119903 V119889119903
by means of PI controllers Besides sincethe OWC air flow control actuator is a throttle-valve subjectto saturation it was necessary to consider an integral wind-up
Table 1 Pressure drop input versus slip reference and correspondingflux coefficient variation
dPAVERAGE (Pa) slipAVER () Flow Coef 1205930ndash5500 minus056 0ndash029875500ndash5790 minus234 0ndash029995790ndash5975 minus413 0ndash029955975ndash6175 minus600 0ndash029996175ndash6375 minus790 0ndash029956375ndash6600 minus986 0ndash029956600ndash6850 minus1194 0ndash029996850ndash7100 minus1406 0ndash029987100ndash7375 minus1628 0ndash029987375ndash7670 minus1860 0ndash02999
effect in order to avoid this undesired phenomenon Thesteps for tuning a PID controller via the closed-loop Ziegler-Nichols method consist of considering all controller gainszero and then increasing the proportional gain 119870
119901up to a
value 119870119901
= 119870119888119903
where sustained oscillations occur withperiod 119875
119888119903 Using this procedure some initial values for the
controller parameters were obtained and afterwards refinedin an experimental trial-and-error basis In this way theobtained throttle valve controller gains are119870
119901= 06119879
119894= 05
and 119879119889= 0125 for initial 119870
119888119903= 004 and 119875
119888119903= 0008 values
Then the output control drives the valve into the demandedposition against a counterbalance weight Once in positionit is hold steady by an electromagnetic brake In the eventof a control failure or in the case that the grid connection islost or an emergency closure is demanded the brake supply isinterrupted and the valve closes by means of the influence of
6 Mathematical Problems in Engineering
Grid
120579r
120579f
PLLabc dq
RSC
CDFIG
120596r
Control
Voltage
Voltage Ps Qs
Q
PI PIIlowastdr
Ilowastqr
Iqr
PWM
Vqr1+
Vdr1+
Vqr2
Vqr
Vdr
Vdr2measurement
dp
PIPI
Qs
Ps
+
minus
minus
+
+
+
minus
Idrminus
minus
Psref
sref
Inabc Vnabc
Igabc
IsabcIrabc
Figure 8 Control loop for the RSC
the weight In this way the modulation of the valve aims toadjust the pressure drop across the turbine rotor
Thus the proposed sensorless speed controller activelycontrols the rotor slip by means of the rotor side converterof the DFIG that acts as control actuator so as to avoid thestalling behaviour and to increase the output power Thefunctioning of the control scheme is detailed as follows TheDFIG is attached to theWells turbine by means of a gear boxThe DFIG stator windings are connected directly to the gridwhile the rotor windings are connected to the back to back(ACDCAC) converter
The converter is composed of aGSC connected to the gridand a rotor RSC connected to the wound rotor windingsTheRSC controls the active (119875
119904) and reactive (119876
119904) power of the
DFIG independently while the GSC controls the DC voltageand grid side reactive power
As indicated before the RSC operates as control actuatorand its objective is to regulate the DFIG rotor speed by vary-ing the rotor slip in accordance with the control law signalprovided by the rotational speed controller in such a way thatit establishes themaximum power generation allowed at eachtime instant for the current wave without entering in stallingIn order to achieve this it is needed an independent regula-tion of the stator active power (by means of speed control)and reactive power
The control loop of the RSC is depicted in Figure 8 andthe corresponding loop for the GSC would be similar
This converter controls the active power (119875119904) and reactive
power (119876119904) of the DFIG In order to achieve independent
control of them the instantaneous three-phase rotor currents119894119903abc are sampled and transformed into 119889-119902 components 119894
119902119903
and 119894119889119903
in the stator-flux oriented reference frame In thiscontext119875
119904and119876
119904can be represented as functions of the indi-
vidual current components Then the reference active power
is compared with the power losses and compensated by thestator flux estimator to form the reference 119902-current 119894lowast
119902119903 which
is then passed through a standard PI controller Its output V1199021199031
is in turn compensated by V1199021199032
to generate the 119902 voltage signalV119902119903 The RSC reactive power control is also used to maintain
a constant stator voltage within the desired range when theDFIG is connected to weak power networks without reactivepower compensationWhen connected to strong power gridsthis controlmay be set to zeroThe reference reactive power iscompared with its actual measurement to generate the errorsignal which is passed through a PI controller to provide thereference signal 119894lowast
119889119903Then it is compared with its actual signal
119894119889119903
to generate an error which is then used to provide therequired 119902-voltage signal V
1198891199031by means of a PI controller In
turn this voltage is compensated by V1198891199032
to generate the 119889voltage signal V
119889119903and used by the PWM module to generate
the IGBT gate control signals necessary to drive the RSCconverter jointly with the 119902-component signal V
119902119903already
obtainedWhen a grid fault is detected the primarily objective
of the implemented control is the uninterrupted operationfeature of the wave energy plant For this purpose the rotor isshort-circuited by a crowbar and theRSC is blocked to protectit from the rotor high currents causing the loss of controlof active power and reactive power of the DFIG In order tocontrol the acceleration of the turbo-generator group theflow is typically reduced accordingly with themodified powerreference regulating the throttle air valve When the rotorcurrent and DC-link voltage are low enough the crowbaris turned off and the RSC is restarted Meanwhile the GSCkeeps the DC-link capacitor voltage constant and the gridside reactive power controllability of the GSC is useful duringthe process of voltage reestablishment After voltage recoverya second crowbar circuit activation may happen if the rotor
Mathematical Problems in Engineering 7
currents or the DC-link voltage exceed their maximumallowed values When the voltage and frequency of the net-work return to steady-state values the references are mod-ified again restoring the normal functioning of the systemFor a detailed description of the different parts of the controlscheme (see [36]) further information about DFIG controldevices by means of RSC and GSC may be found in [37ndash39]
For this purpose a simple Luenberger based observer forthe rotor flux and angular velocity will be proposed Fieldoriented decoupling is applied giving all expressions in thestator-flux reference frame where the 119889-axis is aligned withthe stator flux linkage vectorΨ
119904 so thatΨ
119889119904= Ψ119904andΨ
119902119904= 0
This leads to the following relationships (see [38])
119889119902119904
119889119905= 1198861119902119904+ 1198862119902119903+ 1198863120596119903119889119903+ 1198864V119902119904+ 119896119894(119894119902119904minus 119902119904)
119889119889119904
119889119905= 1198861119889119904+ 1198862119889119903minus 1198863120596119903119902119903+ 1198864V119889119904+ 119896119894(119894119889119904minus 119889119904)
119889119902119903
119889120591= 1198865119902119904+ 1198866119902119903minus 120577119889minus 1198962(119903119903119889minus 120577119889)
119889119889119903
119889120591= 1198865119889119904+ 1198866119889119903+ 120577119902+ 1198962(119903119902119903minus 120577119902)
(9)
where V119889119904 V119902119904 119889119904 119902119904 119889119904 119902119904are the estimated components
of the stator voltage current and flux vector of the rotor in thereference frame and
1198861= minus
1198771199041198712
119903+ 1198771199031198712
119898
119908119871119903
1198862=119877119903119871119898
119908119871119903
1198863=119871119898
119908
1198864=119871119903
119908 119886
5=119877119903119871119898
119871119903
1198864= minus
119877119903
119871119903
119908 = 119871119904119871119903minus 1198712
119898
(10)
The structure of this observer is based on treating as distur-bances 120577
119902 120577119889the corresponding vectors 120596
119903119902119903 120596119903119889119903so as to
remove the coupling between cocoordinates as follows
119889120577119902
119889120591= 1198961(119894119889119904minus 119889119904)
119889120577119889
119889120591= minus1198961(119894119902119904minus 119902119904)
(11)
The disturbance vector has the same angular velocity as allother vector components Both disturbance and flux vectorshave the same phase and proportional amplitudes so that thevelocity may be estimated as
119903= 119878(radic
1205772
119902+ 1205772
119889
2
119889119903+ 2
119902119903
) + 1198964(119881 minus 119881
119891) (12)
Error variables
idriqr
120577q
120577d
Estimation
r
dr
qr
idrqr
120577qd
qrdr
120577qd idr
iqr
Vf
VVf
V
dsqs
iqs
idsControl variables
Figure 9 Control loop for the state observer
where 119878 denotes the sign of the angular velocityThe observergains 119896
1 1198964have small values and are selected experimentally
while 1198962depends on the rotor speed
1198962= 119886 + 119887 sdot
10038161003816100381610038161003816119903119891
10038161003816100381610038161003816(13)
being 119886 and 119887 constants and |119903119891| the absolute value of the
estimated filtered rotor speed 119881119891denotes the filtered signal
of the control 119881 which is defined as
119881 = 119903119902120577119889minus 119903119889120577119902
119889119881119891
119889120591=
1
1198791
(119881 minus 119881119891) (14)
The control loop for this state observer is depicted in Figure 9A comprehensive description of Luenberger observers maybe found in [40 41]
As it has been explained before the stator is connected tothe grid so that the influence of the stator resistance is smalland the stator magnetizing current 119894
119898119904is considered to be
constant [42] For this purpose it is assumed that themachineworks away from themagnetic saturation limitsThus119879
119890may
be defined as
119879119890= minus119870119879119894119902119903 (15)
Therefore the generator slip may be controlled by regulatingthe rotor current 119894
119902119903 while the stator reactive power 119876
119904
119876119904=3
2
minus 1205961199041198712
119898119894119898119904(119894119898119904minus 119894119889119903)
119871119904
(16)
may be controlled by regulating the rotor current 119894119889119903 Con-
sequently from 119879119890= minus119870
119879119894119902119903
with 119870119879= 119871119898119894119898119904
119871119904being
a torque constant and taking into account that 119875 = 119879120596the sensorless controller that has been designed solves thepower tracking problem for DFIG-based OWC power plantsin a hostile environment since it allows to achieve maximumpower extraction by matching the desired generator slipreference to avoid the stalling behaviour
4 Simulation Results
As it has been indicated the Nereida OWC demo project[3] includes 16 Wells turbines in a newly constructed rubble
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
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Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
Grid
120579r
120579f
PLLabc dq
RSC
CDFIG
120596r
Control
Voltage
Voltage Ps Qs
Q
PI PIIlowastdr
Ilowastqr
Iqr
PWM
Vqr1+
Vdr1+
Vqr2
Vqr
Vdr
Vdr2measurement
dp
PIPI
Qs
Ps
+
minus
minus
+
+
+
minus
Idrminus
minus
Psref
sref
Inabc Vnabc
Igabc
IsabcIrabc
Figure 8 Control loop for the RSC
the weight In this way the modulation of the valve aims toadjust the pressure drop across the turbine rotor
Thus the proposed sensorless speed controller activelycontrols the rotor slip by means of the rotor side converterof the DFIG that acts as control actuator so as to avoid thestalling behaviour and to increase the output power Thefunctioning of the control scheme is detailed as follows TheDFIG is attached to theWells turbine by means of a gear boxThe DFIG stator windings are connected directly to the gridwhile the rotor windings are connected to the back to back(ACDCAC) converter
The converter is composed of aGSC connected to the gridand a rotor RSC connected to the wound rotor windingsTheRSC controls the active (119875
119904) and reactive (119876
119904) power of the
DFIG independently while the GSC controls the DC voltageand grid side reactive power
As indicated before the RSC operates as control actuatorand its objective is to regulate the DFIG rotor speed by vary-ing the rotor slip in accordance with the control law signalprovided by the rotational speed controller in such a way thatit establishes themaximum power generation allowed at eachtime instant for the current wave without entering in stallingIn order to achieve this it is needed an independent regula-tion of the stator active power (by means of speed control)and reactive power
The control loop of the RSC is depicted in Figure 8 andthe corresponding loop for the GSC would be similar
This converter controls the active power (119875119904) and reactive
power (119876119904) of the DFIG In order to achieve independent
control of them the instantaneous three-phase rotor currents119894119903abc are sampled and transformed into 119889-119902 components 119894
119902119903
and 119894119889119903
in the stator-flux oriented reference frame In thiscontext119875
119904and119876
119904can be represented as functions of the indi-
vidual current components Then the reference active power
is compared with the power losses and compensated by thestator flux estimator to form the reference 119902-current 119894lowast
119902119903 which
is then passed through a standard PI controller Its output V1199021199031
is in turn compensated by V1199021199032
to generate the 119902 voltage signalV119902119903 The RSC reactive power control is also used to maintain
a constant stator voltage within the desired range when theDFIG is connected to weak power networks without reactivepower compensationWhen connected to strong power gridsthis controlmay be set to zeroThe reference reactive power iscompared with its actual measurement to generate the errorsignal which is passed through a PI controller to provide thereference signal 119894lowast
119889119903Then it is compared with its actual signal
119894119889119903
to generate an error which is then used to provide therequired 119902-voltage signal V
1198891199031by means of a PI controller In
turn this voltage is compensated by V1198891199032
to generate the 119889voltage signal V
119889119903and used by the PWM module to generate
the IGBT gate control signals necessary to drive the RSCconverter jointly with the 119902-component signal V
119902119903already
obtainedWhen a grid fault is detected the primarily objective
of the implemented control is the uninterrupted operationfeature of the wave energy plant For this purpose the rotor isshort-circuited by a crowbar and theRSC is blocked to protectit from the rotor high currents causing the loss of controlof active power and reactive power of the DFIG In order tocontrol the acceleration of the turbo-generator group theflow is typically reduced accordingly with themodified powerreference regulating the throttle air valve When the rotorcurrent and DC-link voltage are low enough the crowbaris turned off and the RSC is restarted Meanwhile the GSCkeeps the DC-link capacitor voltage constant and the gridside reactive power controllability of the GSC is useful duringthe process of voltage reestablishment After voltage recoverya second crowbar circuit activation may happen if the rotor
Mathematical Problems in Engineering 7
currents or the DC-link voltage exceed their maximumallowed values When the voltage and frequency of the net-work return to steady-state values the references are mod-ified again restoring the normal functioning of the systemFor a detailed description of the different parts of the controlscheme (see [36]) further information about DFIG controldevices by means of RSC and GSC may be found in [37ndash39]
For this purpose a simple Luenberger based observer forthe rotor flux and angular velocity will be proposed Fieldoriented decoupling is applied giving all expressions in thestator-flux reference frame where the 119889-axis is aligned withthe stator flux linkage vectorΨ
119904 so thatΨ
119889119904= Ψ119904andΨ
119902119904= 0
This leads to the following relationships (see [38])
119889119902119904
119889119905= 1198861119902119904+ 1198862119902119903+ 1198863120596119903119889119903+ 1198864V119902119904+ 119896119894(119894119902119904minus 119902119904)
119889119889119904
119889119905= 1198861119889119904+ 1198862119889119903minus 1198863120596119903119902119903+ 1198864V119889119904+ 119896119894(119894119889119904minus 119889119904)
119889119902119903
119889120591= 1198865119902119904+ 1198866119902119903minus 120577119889minus 1198962(119903119903119889minus 120577119889)
119889119889119903
119889120591= 1198865119889119904+ 1198866119889119903+ 120577119902+ 1198962(119903119902119903minus 120577119902)
(9)
where V119889119904 V119902119904 119889119904 119902119904 119889119904 119902119904are the estimated components
of the stator voltage current and flux vector of the rotor in thereference frame and
1198861= minus
1198771199041198712
119903+ 1198771199031198712
119898
119908119871119903
1198862=119877119903119871119898
119908119871119903
1198863=119871119898
119908
1198864=119871119903
119908 119886
5=119877119903119871119898
119871119903
1198864= minus
119877119903
119871119903
119908 = 119871119904119871119903minus 1198712
119898
(10)
The structure of this observer is based on treating as distur-bances 120577
119902 120577119889the corresponding vectors 120596
119903119902119903 120596119903119889119903so as to
remove the coupling between cocoordinates as follows
119889120577119902
119889120591= 1198961(119894119889119904minus 119889119904)
119889120577119889
119889120591= minus1198961(119894119902119904minus 119902119904)
(11)
The disturbance vector has the same angular velocity as allother vector components Both disturbance and flux vectorshave the same phase and proportional amplitudes so that thevelocity may be estimated as
119903= 119878(radic
1205772
119902+ 1205772
119889
2
119889119903+ 2
119902119903
) + 1198964(119881 minus 119881
119891) (12)
Error variables
idriqr
120577q
120577d
Estimation
r
dr
qr
idrqr
120577qd
qrdr
120577qd idr
iqr
Vf
VVf
V
dsqs
iqs
idsControl variables
Figure 9 Control loop for the state observer
where 119878 denotes the sign of the angular velocityThe observergains 119896
1 1198964have small values and are selected experimentally
while 1198962depends on the rotor speed
1198962= 119886 + 119887 sdot
10038161003816100381610038161003816119903119891
10038161003816100381610038161003816(13)
being 119886 and 119887 constants and |119903119891| the absolute value of the
estimated filtered rotor speed 119881119891denotes the filtered signal
of the control 119881 which is defined as
119881 = 119903119902120577119889minus 119903119889120577119902
119889119881119891
119889120591=
1
1198791
(119881 minus 119881119891) (14)
The control loop for this state observer is depicted in Figure 9A comprehensive description of Luenberger observers maybe found in [40 41]
As it has been explained before the stator is connected tothe grid so that the influence of the stator resistance is smalland the stator magnetizing current 119894
119898119904is considered to be
constant [42] For this purpose it is assumed that themachineworks away from themagnetic saturation limitsThus119879
119890may
be defined as
119879119890= minus119870119879119894119902119903 (15)
Therefore the generator slip may be controlled by regulatingthe rotor current 119894
119902119903 while the stator reactive power 119876
119904
119876119904=3
2
minus 1205961199041198712
119898119894119898119904(119894119898119904minus 119894119889119903)
119871119904
(16)
may be controlled by regulating the rotor current 119894119889119903 Con-
sequently from 119879119890= minus119870
119879119894119902119903
with 119870119879= 119871119898119894119898119904
119871119904being
a torque constant and taking into account that 119875 = 119879120596the sensorless controller that has been designed solves thepower tracking problem for DFIG-based OWC power plantsin a hostile environment since it allows to achieve maximumpower extraction by matching the desired generator slipreference to avoid the stalling behaviour
4 Simulation Results
As it has been indicated the Nereida OWC demo project[3] includes 16 Wells turbines in a newly constructed rubble
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
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OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
currents or the DC-link voltage exceed their maximumallowed values When the voltage and frequency of the net-work return to steady-state values the references are mod-ified again restoring the normal functioning of the systemFor a detailed description of the different parts of the controlscheme (see [36]) further information about DFIG controldevices by means of RSC and GSC may be found in [37ndash39]
For this purpose a simple Luenberger based observer forthe rotor flux and angular velocity will be proposed Fieldoriented decoupling is applied giving all expressions in thestator-flux reference frame where the 119889-axis is aligned withthe stator flux linkage vectorΨ
119904 so thatΨ
119889119904= Ψ119904andΨ
119902119904= 0
This leads to the following relationships (see [38])
119889119902119904
119889119905= 1198861119902119904+ 1198862119902119903+ 1198863120596119903119889119903+ 1198864V119902119904+ 119896119894(119894119902119904minus 119902119904)
119889119889119904
119889119905= 1198861119889119904+ 1198862119889119903minus 1198863120596119903119902119903+ 1198864V119889119904+ 119896119894(119894119889119904minus 119889119904)
119889119902119903
119889120591= 1198865119902119904+ 1198866119902119903minus 120577119889minus 1198962(119903119903119889minus 120577119889)
119889119889119903
119889120591= 1198865119889119904+ 1198866119889119903+ 120577119902+ 1198962(119903119902119903minus 120577119902)
(9)
where V119889119904 V119902119904 119889119904 119902119904 119889119904 119902119904are the estimated components
of the stator voltage current and flux vector of the rotor in thereference frame and
1198861= minus
1198771199041198712
119903+ 1198771199031198712
119898
119908119871119903
1198862=119877119903119871119898
119908119871119903
1198863=119871119898
119908
1198864=119871119903
119908 119886
5=119877119903119871119898
119871119903
1198864= minus
119877119903
119871119903
119908 = 119871119904119871119903minus 1198712
119898
(10)
The structure of this observer is based on treating as distur-bances 120577
119902 120577119889the corresponding vectors 120596
119903119902119903 120596119903119889119903so as to
remove the coupling between cocoordinates as follows
119889120577119902
119889120591= 1198961(119894119889119904minus 119889119904)
119889120577119889
119889120591= minus1198961(119894119902119904minus 119902119904)
(11)
The disturbance vector has the same angular velocity as allother vector components Both disturbance and flux vectorshave the same phase and proportional amplitudes so that thevelocity may be estimated as
119903= 119878(radic
1205772
119902+ 1205772
119889
2
119889119903+ 2
119902119903
) + 1198964(119881 minus 119881
119891) (12)
Error variables
idriqr
120577q
120577d
Estimation
r
dr
qr
idrqr
120577qd
qrdr
120577qd idr
iqr
Vf
VVf
V
dsqs
iqs
idsControl variables
Figure 9 Control loop for the state observer
where 119878 denotes the sign of the angular velocityThe observergains 119896
1 1198964have small values and are selected experimentally
while 1198962depends on the rotor speed
1198962= 119886 + 119887 sdot
10038161003816100381610038161003816119903119891
10038161003816100381610038161003816(13)
being 119886 and 119887 constants and |119903119891| the absolute value of the
estimated filtered rotor speed 119881119891denotes the filtered signal
of the control 119881 which is defined as
119881 = 119903119902120577119889minus 119903119889120577119902
119889119881119891
119889120591=
1
1198791
(119881 minus 119881119891) (14)
The control loop for this state observer is depicted in Figure 9A comprehensive description of Luenberger observers maybe found in [40 41]
As it has been explained before the stator is connected tothe grid so that the influence of the stator resistance is smalland the stator magnetizing current 119894
119898119904is considered to be
constant [42] For this purpose it is assumed that themachineworks away from themagnetic saturation limitsThus119879
119890may
be defined as
119879119890= minus119870119879119894119902119903 (15)
Therefore the generator slip may be controlled by regulatingthe rotor current 119894
119902119903 while the stator reactive power 119876
119904
119876119904=3
2
minus 1205961199041198712
119898119894119898119904(119894119898119904minus 119894119889119903)
119871119904
(16)
may be controlled by regulating the rotor current 119894119889119903 Con-
sequently from 119879119890= minus119870
119879119894119902119903
with 119870119879= 119871119898119894119898119904
119871119904being
a torque constant and taking into account that 119875 = 119879120596the sensorless controller that has been designed solves thepower tracking problem for DFIG-based OWC power plantsin a hostile environment since it allows to achieve maximumpower extraction by matching the desired generator slipreference to avoid the stalling behaviour
4 Simulation Results
As it has been indicated the Nereida OWC demo project[3] includes 16 Wells turbines in a newly constructed rubble
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Decision SciencesAdvances in
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Mathematical Problems in Engineering
Table 2 System parameters
Turbine Generator Converter119899 = 5 (2 blade rows) Rated Power (kW) = 185 DC-Link voltage (V) = 800119870 = 05 Width (m) = 125 (t-g module) Pmax (pu) = 04119903119905= 0375 Height (m) = 283 (t-g module) Rated Current (A) = 12
119886119905= 23562 Pole pairs = 2 Max Transitory Current (A) = 228
HubTip Ratio = 043 119877119903= 00334
119877119904= 00181
Switching Freq (kHz) = 144
Solidity per row () = 40 119871119897119903= 016
119871119897119904= 013
Cut-off Freq Current Filters (kHz) = 132
Target speed range (rpm) = 1000ndash3900 119871119898= 7413 Cut-off Freq Grid Voltage Filter (kHz) = 132
Tip Mach no = 015ndash047 Inertia Constant119867 = 306
0 2 4 6 8 10 12 14 16 18 20
0
1
2
Time (s)
minus2
minus1
Roto
r flux
dax
is (o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus2
minus1
Roto
r flux
qax
is (o
bser
ver)
(b)
Figure 10 Rotor flux for 7000 Pa maximum pressure drop input (observer)
0
1
2
minus2
minus1
Roto
r flux
dax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(a)
0
1
2
minus2
minus1
Roto
r flux
qax
is (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 11 Rotor flux for 7000 Pa maximum pressure drop input (sensor)
mound breakwater in the Basque location of Mutriku in thenorthern coast of Spain The main objective of this sectionis to demonstrate the viability of the proposed rotor angularvelocity observer to help develop this OWC technology withWells turbine power take-off for future commercial plantsFor this reason the simulation data and wave model havebeen chosen taking into account the spectrum of the waveclimate ofMutriku and theOWCsystemparameters are listedin Table 2
For this purpose the maximum power tracking perfor-mance of system subject to the proposed speed estimatorwithstator current based feedback has been tested by means ofnumerical simulations The control strategy is composed ofa double feed induction generator DFIG that is controlledwith a vector field oriented strategy a crowbar and an airflow control The crowbar protects the RSC enforcing short-circuit when overcurrents in the rotor occur while the airvalve regulates the incoming air flow so as to avoid stalling
Finally the main control loop regulates both active and reac-tive power of the DFIG using the currents as control variablesto match the modified power reference (see Figure 7) See[36] for a detailed explanation of this control and [43] for asummary on fault tolerance control
41 Balance Faults This sensorless control has been appliedconsidering a scenario where waves produce a typical vari-ation for 7000 Pa maximum pressure drop input and abalanced grid fault has been implemented with an 85reduction of the grid voltage applied at 10 s and clearedat 15 s For comparison purposes the same study case hasbeen considered with and without sensor In particular inFigure 10 the rotor flux obtainedwith the proposed sensorlesscontroller is plotted so as to compare it with that obtainedusing a control where the velocity is computed via a tradi-tional sensor plotted in Figure 11 As it may be observed thereexists no significant difference between them
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 9
040506070809
111121314
Roto
r spe
ed o
bser
ver
0 2 4 6 8 10 12 14 16 18 20Time (s)
Figure 12 Rotor angular velocity for 7000 Pa maximum pressure drop input (observer)
0
1
2
Activ
e pow
er (o
bser
ver)
0
2
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1
minus6
minus4
minus2
times104
times104
(a)
Activ
e pow
er (s
enso
r)Re
activ
e pow
er (s
enso
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
0
2
minus1
minus6
minus4
minus2
times104
times104
(b)
Figure 13 Active and reactive power generated using sensorless control (a) versus traditional control (b)
Similarly due to the FRT capability of the control schemeit may be seen in Figure 12 that after the transitory 120596
119903does
not increase during the voltage dip which also affects the fluxvalue Besides it should be highlighted that in the MutrikuWOC technical solution the given reference is the pressuredrop whilst the reference for the rotor angular velocity 120596lowast
119903
is not readily accessible so that the proposed estimator withstator current based feedback suits perfectly the requirementsof the system
Analogously a comparative study for the power generatedhas been carried out in order to verify the performance of theproposed observer so as to obtain maximum power extrac-tion capability in the plant even when it is subject to voltagedips like the one described in the scenario at hand
Under these conditions it may be seen in Figure 13 theeffect of the fault over the active and reactive power at thestator terminals both with sensor and with the proposedobserver In both cases there is no active power consumptionduring the fault period and the reactive power overshootduring both the start and clearance of the fault is acceptable
Besides the generator oscillatory dynamics have been con-trolled while giving reactive power to the grid so that it con-tributes to the attenuation of the voltage dip In this contextboth figures show that the plant generates active and reactivepower during the fault period and particularly during thefault recovery since it is only during 100ms after the faultrecovery that the generator absorbs a little amount of power(less than 60 of the nominal power) These voltage dips areusually caused by remote grid faults in the power system andwould normally require disconnecting the generator from thegrid until the faults are cleared However normative relativeto this requirement tends to enforcemaintaining active powerdelivery and reactive power support to the grid so that gridcodes now require ride through voltage dips like the onepresented in this paper
In order to compare the simulation results obtained usingthe proposed observer with those obtained using a traditionalsensor with the controller a performance evolution function119869 is used This performance function is defined by (16) interms of the tracking error where 119890(120591) represents the error
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Figure 14 Active power performance Traditional control (mdash) versus sensorless control (- -)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
minus1
0
1
minus1
0
1
minus1
a(o
bser
ver)
b(o
bser
ver)
c(o
bser
ver)
(b)
Figure 15 Voltages for the balance fault (a) versus negative sequence unbalance fault (b)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
(a)
0
1
minus1 a(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 b(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
0
1
minus1 c(o
bser
ver)
9 92 94 96 98 10 102 104 106 108 11Time (s)
(b)
Figure 16 Detail of the voltages for the balance fault (a) versus unbalance fault (b)
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 11
Roto
r cur
rent
s (ob
serv
er)
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus2
minus15
minus1
minus05
0
05
1
15
2
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
Roto
r cur
rent
s (ob
serv
er)
minus2
minus15
minus1
minus05
0
05
1
15
2
(b)
Figure 17 Rotor currents for the balance fault (a) versus negative sequence unbalance fault (b)
95 96 97 98 99 10 101 102 103 104 105
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
Time (s)
(a)
Roto
r cur
rent
s (ob
serv
er)
minus08
minus06
minus04
minus02
0
02
04
06
08
95 96 97 98 99 10 101 102 103 104 105Time (s)
(b)
Figure 18 Detail of the rotor currents for the balance fault (a) versus unbalance fault (b)
between the desired reference value for the active power andthe value obtained from the system output as follows
119869 (119905) = int 1198902(120591) 119889120591 (17)
It can be observed in Figure 14 that the values of the perfor-mance evolution function for the case of the controller withobserver are slightly higher than those obtained with the sen-sor It must be taken into account that the control either withsensor or with observer yields similar results so that the rel-evance of the results relies on determining the rotor angularvelocity without the need of extra hardware from sensors justobserved bymeans of the stator voltages and currents For thisreason although in all cases the accumulated error measuredwith the cost function 119869 presents a similar increasing behav-ior as it should be expected from the 119871
2-norm accumulative
error defined in (17) it should be noticed that the system
power generated in both cases present a similar rate whilethe observer provides better performance since it increasespower extraction in the sense that the plant is more reliableand independent of external disturbances which is evenmore relevant in a hostile environment as the ocean
42 Unbalance Faults Simulation studies on the sensorlesscontrol for unbalance faults are carried out over a modifica-tion of the balance fault scenario studied in the last sectionwhere a representative example corresponding to the negativesequence is considered as seen in Figures 15 and 16 Previousanalyses were performed to confirm the relative significanceof the different frequency components present in the currentwaveforms corroborating that the negative sequence imposesthe most stringent control
The key problems in the response of a DFIG to an unbal-anced fault are illustrated in Figure 17 which shows the rotor
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
12 Mathematical Problems in Engineering
0 2 4 6 8 10 12 14 16 18 20770
780
790
800
810
820
830
840Vdc
(obs
erve
r)
Time (s)
(a)
0 2 4 6 8 10 12 14 16 18 20Time (s)
770
780
790
800
810
820
830
840
Vdc
(obs
erve
r)
(b)
Figure 19 DC-link voltage for the balance fault (a) versus negative sequence unbalance fault (b)
Activ
e pow
er (o
bser
ver)
Reac
tive p
ower
(obs
erve
r)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20Time (s)
0
1
2
minus1
times104
0
2
minus2
minus4
times104
(a)
Activ
e pow
er (o
bser
ver)
0
1
2
minus1
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
Reac
tive p
ower
(obs
erve
r)
0
2
minus2
minus4
times104
0 2 4 6 8 10 12 14 16 18 20Time (s)
(b)
Figure 20 Active and reactive power generated using sensorless control (a) versus traditional sensor (b) considering the negative sequenceunbalance fault study case
currents During the fault the negative sequence componentof the rotor currents is 25 times as large as the positivesequence component This forces the rotor voltage demandclose to the limits of the inverter making control of the DFIGmuch more difficult It can be seen from Figures 17 and 18that the most serious problem is the rotor overcurrent atfault initiation These overcurrents are alleviated by short-circuiting the rotor windings for a short period (known as acrowbar) removing the power electronics from the rotor cir-cuit to protect them from the high currents
Despite the value of the currents on the IGBTs it may beseen in Figures 19 and 20 that both the active and reactive
power supplies as well as the dc-link voltage are successfullycontrolled Thus even when this control scheme does notdiscern in the treatment of the different sequence currentcomponents during faults it ensures the continuity of supplyin compliance with actual requirements [44]
Although stator overcurrents may also occur they aregenerally of less concern because no vulnerable power elec-tronics are involved in the stator connection
The results obtained for the reference tests both withobserver and with sensor confirmed that the model behavedas expected since there are no obvious differences betweenthem The effect of the unbalance fault over the active
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 13
and reactive power at the stator terminals may be seen inFigure 20 for comparison purposes
5 Conclusions
This paper has proposed a new observer to estimate the rotorangular speed for the control of the Mutriku OWC wavepower generation demo plant within the Nereida projectfrom the Basque Energy Board (EVE) This closed loopobserver is based in a Luenberger system and estimates bothrotor angular velocity and fluxes using the measured statorvoltages and currents Due to the nature of this observer therotor angular velocity is computed from its flux and a vectorof cross-product state variables that is treated as disturbancesIn order to verify the performance of the proposed observerto obtain maximum power extraction capability in the planteven when it is subject to voltage dips a comparative studyfor the power generated with a traditional sensor and withthe proposed observer has been performed A point trackingtechnique has been implemented so that the control systemtracks a curve that yields the maximum possible power fromthe sea and no substantial differences between them havebeen found As a result it can be concluded that the proposedobserver scheme improves the plant reliability by increasingreliability and disturbance rejection while reducing cost andtherefore improving the power extraction when applied formaximum power generation purposes
Nomenclature
119875wf 119875in Incident wave power power available to turbine119892 V 119894 Gravitationalconstant voltage currentV119909 119889119901 Air flow speed pressure-drop across rotor
120588 120588119908 Air density seawater density
119886 119903 119899 Area of turbine duct mean radius of the turbinenumber of blades
119887 119897 Blade height blade chord length119902 120601 Flow rate flow coefficient120582 119879119908 Wavelength wave period
ℎ 119860 Water depth wave height120596119903 119879119905 Angular velocity torque
119862119886 119862119905 Power and torque coefficients
119871 119877 Ψ Inductance resistance flux119875119876 Active and reactive power
Subscripts
119889 119902 119904 119903 Direct and quadrature components statorand rotor side
119905 119892 119890 119898 Turbine generator electrical magnetizing
Acknowledgments
This work was supported in part by University of the BasqueCountry (UPVEHU) through Research Project GIU1102and the Research and TrainingUnit UFI1107 by theMinistryof Science and Innovation (MICINN) with Research ProjectENE2010-18345 and by the EU FP7 EFDA under the task
WP09-DIA-02-01 WP III-2-c The authors would also like tothank the collaboration of the Basque Energy Board (EVE)through Agreement UPVEHUEVE2362011 and the Span-ish National Fusion Laboratory (CIEMAT) UPVEHUCIE-MAT08190
References
[1] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[2] M Z Jacobson andMADelucchi ldquoProviding all global energywith wind water and solar power part I technologies energyresources quantities and areas of infrastructure andmaterialsrdquoEnergy Policy vol 39 no 3 pp 1154ndash1169 2011
[3] Basque Energy Board (EVE) httpwwweveesPromocion-de-inversionesProyectos-en-desarrolloMutrikuInstalacio-nesaspx
[4] Y Torre-EncisoMutrikuWave Power Plant FromConception toReality European Federation of Regional Energy and Environ-ment Agencies (FEDARENE) 2009 httpwwwfedareneorgdocumentsprojectsNereidaDocument01 Mutriku-OWCplantpdf
[5] A Thakker and R Abdulhadi ldquoEffect of blade profile on theperformance of wells turbine under unidirectional sinusoidaland real sea flow conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 51598 8 pages 2007
[6] T Setoguchi and M Takao ldquoCurrent status of self rectifying airturbines for wave energy conversionrdquo Energy Conversion andManagement vol 47 no 15-16 pp 2382ndash2396 2006
[7] W Qiao G K Venayagamoorthy and R G Harley ldquoReal-timeimplementation of a STATCOM on a wind farm equipped withdoubly fed induction generatorsrdquo IEEETransactions on IndustryApplications vol 45 no 1 pp 98ndash107 2009
[8] M Amundarain M Alberdi A J Garrido and I GarridoldquoModeling and simulation of wave energy generation plantsoutput power controlrdquo IEEETransactions on Industrial Electron-ics vol 58 no 1 pp 105ndash117 2011
[9] Y Zhou J Lian T Ma and W Wang ldquoDesign for motorcontroller in hybrid electric vehicle based on vector frequencyconversion technologyrdquoMathematical Problems in Engineeringvol 2010 Article ID 627836 21 pages 2010
[10] K J Astrom and T Hagglund Advanced PID Control ISA-TheInstrumentation Systems and Automation Society 2009
[11] R Vilanova V M Alfaro O Arrieta and C Pedret ldquoAnalysisof the claimed robustness for PIPID robust tuning rulesrdquo inProceedings of the 18thMediterraneanConference onControl andAutomation (MED rsquo10) pp 658ndash662 June 2010
[12] B C Rabelo Jr W Hofmann J L da Silva R G de Oliveiraand S R Silva ldquoReactive power control design in doubly fedinduction generators for wind turbinesrdquo IEEE Transactions onIndustrial Electronics vol 56 no 10 pp 4154ndash4162 2009
[13] ESB National Grid ldquoDiscussion Document for the Reviewof Requirements for Wind Turbine Generators Under SystemFault Conditionsrdquo 2003
[14] I Serban F Blaabjerg I Boldea and Z ChenA Study of DoublyFed Wind Power Generator Under Power System Faults EPEToulouse France 2003
[15] G Iwanski andWKoczara ldquoDFIG-based power generation sys-tem with UPS function for variable-speed applicationsrdquo IEEE
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
14 Mathematical Problems in Engineering
Transactions on Industrial Electronics vol 55 no 8 pp 3047ndash3054 2008
[16] G Abad M A Rodrıguez G Iwanski and J Poza ldquoDirectpower control of doubly-fed-induction-generator-based windturbines under unbalanced grid voltagerdquo IEEE Transactions onPower Electronics vol 25 no 2 pp 442ndash452 2010
[17] A J Garrido I Garrido M Amundarain and M AlberdildquoSliding-mode control of wave power generation plantsrdquo IEEETransactions on Industry Applications vol 48 no 6 pp 2372ndash2381 2012
[18] Z Krzeminski ldquoNew speed observer for control system ofinduction motorrdquo in Proceedings of the 3rd IEEE InternationalConference on Power Electronics and Drive Systems (PEDS rsquo99)pp 555ndash560 July 1999
[19] Z Krzeminski ldquoObserver of induction motor speed based onexact disturbance modelrdquo in Proceedings of the 13th Interna-tional Power Electronics and Motion Control Conference (EPE-PEMC rsquo08) pp 2294ndash2299 September 2008
[20] O Barambones P Alkorta A J Garrido I Garrido and F JMaseda ldquoAn adaptive sliding mode control scheme for induc-tionmotor drivesrdquo International Journal of Circuits Systems andSignal Processing vol 1 no 1 pp 73ndash78 2007
[21] O Barambones and A J Garrido ldquoAn adaptive variable struc-ture control law for sensorless induction motorsrdquo EuropeanJournal of Control vol 13 no 4 pp 282ndash392 2007
[22] J C Garcıa C Diego P F de Arroyabe C Garmendia and DRasilla El Clima Entre el Mar y la Montana The University ofCantabria Santander Spain 2004
[23] I Galparsoro et al ldquoatlas de energıa dek oleaje en la costaVasca La planificacion espacial marian como herramienta en laseleccion de zonas adecuadas para la instalacion de captadoresrdquoin Revista De Investigacion Marina pp 1ndash9 2008
[24] W K Tease J Lees and A Hall ldquoAdvances in oscillating watercolumn air turbine developmentrdquo inProceedings of the 7th Euro-pean Wave and Tidal Energy Conference Porto Portugal 2007
[25] M Alberdi M Amundarain A J Garrido I Garrido OCasquero and M De La Sen ldquoComplementary control ofoscillating water column-based wave energy conversion plantsto improve the instantaneous power outputrdquo IEEE Transactionson Energy Conversion vol 26 no 4 pp 1021ndash1032 2011
[26] Y Torre-Enciso I Ortubia L I Lopez de Aguileta and JMarques ldquoMutriku wave power plant from the thinking out tothe realityrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference pp 319ndash329 2009
[27] A El Marjani F Castro Ruiz M A Rodriguez and M TParra Santos ldquoNumerical modelling in wave energy conversionsystemsrdquo Energy vol 33 no 8 pp 1246ndash1253 2008
[28] M Amundarain M Alberdi A J Garrido I Garrido and JMaseda ldquoWave energy plants control strategies for avoiding thestalling behaviour in the Wells turbinerdquo Renewable Energy vol35 no 12 pp 2639ndash2648 2010
[29] P Guglielmi R Bojoi G Pellegrino A Cavagnino M Pastor-elli and A Boglietti ldquoHigh speed sensorless control for induc-tion machines in vacuum pump applicationrdquo in Proceedings ofthe 37th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo11) pp 1872ndash1878 November 2011
[30] R Cardenas R Pena G Asher J Clare and J Cartes ldquoMRASobserver for doubly fed inductionmachinesrdquo IEEETransactionson Energy Conversion vol 19 no 2 pp 467ndash468 2004
[31] R Cardenas R Pena J Clare G Asher and J Proboste ldquoMRASobservers for sensorless control of doubly-fed induction gener-atorsrdquo IEEE Transactions on Power Electronics vol 23 no 3 pp1075ndash1084 2008
[32] S Mueller M Deicke and RW De Doncker ldquoAdjustable speedgenerators for wind turbines based on doubly-fed inductionmachines and 4-quadrant IGBT converters linked to the rotorrdquoin Proceedings of the 35th IAS Annual Meeting and World Con-ference on Industrial Applications of Electrical Energy vol 4 pp2249ndash2254 October 2000
[33] L Morel H Godfroid A Mirzaian and J M KauffmannldquoDouble-fed induction machine converter optimisation andfield oriented control without position sensorrdquo IEE Proceedingsof Electric Power Applications vol 145 no 4 pp 360ndash368 l998
[34] H R Karimi and M Chadli ldquoRobust observer design forTakagi-Sugeno fuzzy systems with mixed neutral and discretedelays and unknown inputsrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 635709 13 pages 2012
[35] S Chen Y F Li J Zhang andWWang Active Sensor Planningfor Multiview Vision Tasks Springer 2008
[36] M Alberdi M Amundarain A J Garrido I Garrido and FJ Maseda ldquoFault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped withdoubly fed induction generator and airflow controlrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1501ndash1517 2011
[37] R Pena J C Clare and G M Asher ldquoA doubly fed inductiongenerator using back-to-back PWM converters supplying anisolated load from a variable speed wind turbinerdquo IEE Proceed-ings on Electric Power Applications vol 143 no 3 pp 231ndash2411996
[38] B K Bose Modern Power Electronics and AC Drives Prentice-Hall Englewood Cliffs NJ USA 2001
[39] I Sarasola J Poza M A Rodriguez and G Abad ldquoDirecttorque control design and experimental evaluation for thebrushless doubly fedmachinerdquo Energy Conversion andManage-ment vol 52 no 2 pp 1226ndash1234 2011
[40] A Lagrioui and H Mahmoudi ldquoSpeed and current control forthe PMSM using a Luenberger observerrdquo in Proceedings of theInternational Conference onMultimedia Computing and Systems(ICMCS rsquo11) April 2011
[41] M Trabelsi M Jouili M Boussak Y Koubaa and M GossaldquoRobustness and limitations of sensorless technique based onLuenberger state-Observer for induction motor drives underinverter faultsrdquo in Proceedings f the IEEE International Sympo-sium on Industrial Electronics (ISIE rsquo11) pp 716ndash721 June 2011
[42] Y Sayed M Abdelfatah M Abdel-Salam and S Abou-ShadildquoDesign of robust controller for vector controlled inductionmotor based on Q-parameterization theoryrdquo Electric PowerComponents and Systems vol 30 no 9 pp 981ndash999 2002
[43] M Benosman ldquoA survey of some recent results on nonlinearfault tolerant controlrdquo Mathematical Problems in Engineeringvol 2010 Article ID 586169 25 pages 2010
[44] BOE 2542006 PO 123 Response Requirements ofWind PowerGeneration to Network Voltage Dips
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
![downloads.hindawi.comdownloads.hindawi.com/journals/mpe/2014/746538.pdf · MathematicalProblems in Engineering Wazwaz [ , ] investigated the nonlinear Klein-Gordon equationsandfoundmanytypesofexacttravelingwavesolu-tions](https://static.fdocuments.in/doc/165x107/5f0af7937e708231d42e37af/mathematicalproblems-in-engineering-wazwaz-investigated-the-nonlinear-klein-gordon.jpg)
