Research Article Reactive Power Control of Single-Stage Three...
Transcript of Research Article Reactive Power Control of Single-Stage Three...
Research ArticleReactive Power Control of Single-Stage Three-PhasePhotovoltaic System during Grid Faults Using Recurrent FuzzyCerebellar Model Articulation Neural Network
Faa-Jeng Lin Kuang-Chin Lu and Hsuan-Yu Lee
Department of Electrical Engineering National Central University Chungli 320 Taiwan
Correspondence should be addressed to Faa-Jeng Lin linfjeencuedutw
Received 15 June 2014 Accepted 27 July 2014 Published 24 August 2014
Academic Editor Franca Morazzoni
Copyright copy 2014 Faa-Jeng Lin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
This study presents a new active and reactive power control scheme for a single-stage three-phase grid-connected photovoltaic (PV)system during grid faultsThe presented PV system utilizes a single-stage three-phase current-controlled voltage-source inverter toachieve the maximum power point tracking (MPPT) control of the PV panel with the function of low voltage ride through (LVRT)Moreover a formula based on positive sequence voltage for evaluating the percentage of voltage sag is derived to determine the ratioof the injected reactive current to satisfy the LVRT regulations To reduce the risk of overcurrent during LVRT operation a currentlimit is predefined for the injection of reactive current Furthermore the control of active and reactive power is designed using a two-dimensional recurrent fuzzy cerebellar model articulation neural network (2D-RFCMANN) In addition the online learning lawsof 2D-RFCMANN are derived according to gradient descent method with varied learning-rate coefficients for network parametersto assure the convergence of the tracking error Finally some experimental tests are realized to validate the effectiveness of theproposed control scheme
1 Introduction
The cerebellar model articulation neural network (CMANN)is a lookup-table based neural network which can be thoughtof as a learning mechanism that simulates mammalian cere-bellum Basically the input space of the CMANN is dividedinto discrete states which are called elements Moreoverseveral elements construct a block and an overlapped areaformed by quantized blocks is called hypercube Differenthypercubes can be obtained by shifting each block a smallinterval Furthermore the CMANN assigns each hypercubeto a memory cell for storing learning information To obtainthe output of the CMANN for given input data onlythe hypercubes covering the input data will be activatedand effectively contribute to the corresponding output Thebasic concept of the CMANN is to store learned data intohypercubes and the data can easily be recalled with lessoccupied storage space Consequently the behavior of storingthe learned information in the CMANN is similar to the
action of the cerebellar in mammalian Advantages of theCMANN include fast learning good localization capabilityand simplicity of computation [1] However in the generalCMANN there are only two kinds of states in the mappedarea of the state space that is 1 and 0 This directly affectsthe generalization capability of CMANN and may result indiscontinuous output [2 3] In order to acquire the derivativeinformation of input and output variables a CMANN with adifferentiable Gaussian receptive field basis function has beenproposed in [4] Due to the lack of time-delayed feedbackin its inherent feedforward neural network structure theapplication domain of CMANN is limited to static mappingproblems In addition a recurrent fuzzy CMANN (RFC-MANN)withGaussian receptive field basis functionwas pro-posed in [5] to overcome the aforementioned disadvantage ofCMANN In this study a two-dimensional RFCMANN (2D-RFCMANN) with Gaussian basis function control schemeis proposed for the active and reactive power control of thesingle-stage three-phase grid-connected photovoltaic (PV)
Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 760743 13 pageshttpdxdoiorg1011552014760743
2 International Journal of Photoenergy
system The first dimension of the 2D-RFCMANN is for thetracking error input and the second dimension of the 2D-RFCMANN is for the derivative of the tracking error input
The penetration of renewable energy sources hasincreased significantly because of raising awareness of theenvironmental issues and the deregulation of the electricpower distribution industry Among these renewable energysources PV system is one of the main candidates to playan important role in the future of power distributionHowever the connection of a large number of distributedenergy sources (DESs) to the electrical power grid can causeinstability when electrical disturbances appear in the gridOne of the most challenging disturbances is the voltagesags [6 7] The sources of the voltage sags are various suchas short circuits between phases or phases and groundlightning and overloads To minimize the negative effectsof a large number of DESs on the reliability of the powergrids different countries have defined various low voltageride through (LVRT) regulations for DESs EON has definedthe voltage profile of the low voltage ride through (LVRT)at the grid connection for type-2 generating plants [8] Gridregulations require that the DESs have to inject reactivecurrent to support grid stability during grid faults [8] inwhich 1 pu of reactive current is required as the depth of thesag reaches 50 In this study the EON LVRT regulationis adopted to determine the ratio of the required reactivecurrent during grid faults
The asymmetrical grid voltage sags will worsen the per-formance of the grid-connected inverter (GCI) especially thedegradation of the power quality caused by the power rippleand the increase of current harmonic distortion In orderto overcome these disadvantages some control methodsbased on symmetric components have been proposed todeal with unbalanced grid faults [9ndash13] A control schemewhich can adjust the characteristics of power quality byusing two adjustable control parameters was developed in[9] In [10] a selective active power quality control based onvarious current reference generating methods was proposedReference [11] has proposed a control method to minimizethe peak value of the injection current during the voltagesag In [12] a positive and negative sequences currentinjection method was proposed to provide the active powerand reactive current without exceeding the current limitof inverter The flexible reactive current injection schemeintroduced in [13] provides voltage support during voltage sagby injecting reactive current via both positive and negativesequences However the aforementioned control methodsprincipally focus on the power control of grid-connectedinverter whereas the fulfillment of the LVRT requirementand the control of the power flow between the dc-link bus andac grid during grid faults are not well explored In this studythe 2D-RFCMANN control scheme is proposed to controlnot only the output voltage of the PV panel via the maximumpower point tracking (MPPT) in normal condition butalso the reactive power based on LVRT requirement withconsidering the power balance between dc-link bus and acgrid during grid faults
In this study the analysis of the instantaneousactivereactive output power of the three-phase GCI during
grid faults is carried out by using symmetric componentmethod The MPPT control of PV system is also consideredto ensure the power balance during grid faults Subsequentlythe dual second-order generalized integrator phase-lockedloop (DSOGI-PLL) method [10 14 15] is adopted forsynchronizing the GCI to the grid Moreover a new formulawhich is based on the positive sequence voltage is derivedto evaluate the percentage of voltage sag and to determinethe injected currents during the grid faults Furthermorethe network structure and online training algorithms ofnetwork parameters of the proposed 2D-RFCMANN for theactive and reactive power control are discussed in detailFurthermore two types of grid faults are tested and discussedto evaluate the performance of the proposed control schemeThe paper is organized as follows In Section 2 the grid-connected PV system is introduced In Section 3 theinstantaneous activereactive power formulation DSOGI-PLL synchronization mechanism and the control strategyof the grid-connected PV system during grid faults arediscussed The 2D-RFCMANN is presented in Section 4 InSection 5 the features of the proposed control scheme areexamined by some experimental results Finally Section 6draws the conclusions
2 System Description
Figure 1 shows the block diagrams of the proposed single-stage three-phase grid-connected PV system The behaviorof the PV panel is emulated by a Chroma 62100H-600S PVpanel simulator operating at 203Vdc output voltage withmaximum output power 1 kW The power grid was emu-lated by three programmable 2 kVA single-phase KIKUSUIPCR2000LE AC power supplies feeding a Y-connected100Ωphase resistive load and connected to the GCI witha 3 kVA Y-998779 transformer The 2 kVA three-phase GCI withoutput 110Vrms line to line voltage is connected to the PVpanel simulator through a dc-link capacitor and connectedto the Y-998779 transformer with three 10mHphase couplinginductorsThe switching frequency119891sw GCI of the three-phaseGCI is set at 10 kHz Table 1 shows the parameters of theexperimental setup Moreover the control system is installedon a desktop personal computer (PC) which includes an ADconverter card (PCI-1716) a PC-based control system anda DA converter card (MRC-6810) In the PC-based controlsystem the SIMULINK control package is adopted for theimplementation of the proposed algorithms of theMPPT andLVRTcontrolThe analog input signals include output voltage119881pv and current 119868pv of the PV panel simulator the outputline voltages V
119886119887 V119887119888 and V
119888119886 and line currents 119894
119886 119894119887 and
119894119888of the GCI The control output of the PC-based control
system is the three-phase reference currents of GCI 119894lowast
119886 119894lowast
119887
and 119894lowast
119888 Furthermore the emulated faults occur at the point
of common coupling (PCC)In Figure 1 the output currents of the GCI are controlled
by the maximum power point (MPP) voltage 119881lowast
pv in the nor-mal conditionThe adoptedMPPTmethod is the incrementalconductance (IC) method with a fixed incremental step sizeset for the voltage [16] Moreover if a grid fault occurs at the
International Journal of Photoenergy 3
DC
AC
Three-phase GCI
Current controlled
PWM
L
110220
LoadPCC
Emulatedfault
PC
AD converter
MPPT and LVRT control
PC-based control system
PV panel Grid
DA converter
Vpv+
minus
Ipv
Cpv
Vpv
ia ib ic
ia ib ic
ilowasta ilowastb i
lowastc
Y Δ
100ΩY-connected
= 3120601ab bc ca
ab bc caVpv Ipv
radic31 2
Figure 1 Block diagrams of experimental single-stage three-phase grid-connected PV system
Table 1 Parameters of experimental setup
Dc-link capacitor 119862pv 3360mFGrid connection inductor 119871 10mHInverter output voltage V
119886119887 V119887119888 V119888119886
110Vrms line to line 60HzInverter maximum current 119868max 5Arms (71 A peak current)Emulated PV panel 119881oc 236V 119868sc 60 A 1 kWSwitching frequency 119891sw GCI 10 kHz
PCC the fault voltages at theGCI terminals appear differentlyfrom the fault voltages at the PCC [6 7] Furthermore in thenormal condition of the grid the GCI regulates the activepower injecting into the grid and maintains the 119881pv voltageso as to track the MPP for maximizing the energy extractionOn the other hand in the fault conditions of the grid thereactive power control can mitigate the effects of voltagesag by injecting additional reactive current to the grid toride through the perturbation and support the grid voltageIn addition the injecting current has to meet the LVRTregulations without going beyond the GCI current limit 119868maxsimultaneously
3 Reactive Power Control Strategyduring Grid Faults
31 Instantaneous Power Formulation under Grid Fault Con-ditions For a three-phase GCI the instantaneous active andreactive power outputs at the grid connection point aredescribed as follows [17]
119875 = k sdot i = V119886119894119886+ V119887119894119887+ V119888119894119888 (1)
119876 = k times i = kperp
sdot i
=1
radic3[(V119886minus V119887) 119894119888+ (V119887minus V119888) 119894119886+ (V119888minus V119886) 119894119887]
(2)
where kperp
= (1radic3) [0 1 minus1
minus1 0 1
1 minus1 0
] k k = [V119886
V119887V119888]119879and i =
[119894119886
119894119887
119894119888]119879 represent the three phase voltages and currents of
the GCI respectively 119875 and 119876 represent the instantaneousactive and reactive power outputs of the GCI respectivelyIn (1) and (2) k
perpand k are orthogonal only when the
three voltages of k are balancedThe asymmetric three-phasevoltage and current vector are represented as
k = k+ + kminus
i = i+ + iminus(3)
where k+ = [V+119886
V+119887
V+119888]119879 and kminus = [Vminus
119886Vminus119887
Vminus119888]119879 represent
the positive and negative sequences of v respectively i+ =
[119894+
119886119894+
119887119894+
119888]119879 and iminus = [119894
minus
119886119894minus
119887119894minus
119888]119879 represent the positive
and negative sequences of i respectively Note that the zerosequence of v and i does not exist due to the three-phasethree-wire AC system configuration of the GCI As a result119875 and 119876 in (1) and (2) can be rewritten as
119875 = k sdot i = (k+ + kminus) sdot (i+ + iminus)
= k+ sdot i+ + kminus sdot iminus + k+ sdot iminus + kminus sdot i+(4)
119876 = kperp
sdot i = (k+perp
+ kminusperp) sdot (i+ + iminus)
= k+perp
sdot i+ + kminusperp
sdot iminus + k+perp
sdot iminus + kminusperp
sdot i+(5)
where the corresponding orthogonal vectors in (5) can bederived by using the matrix transformation in (2) Thus the
4 International Journal of Photoenergy
abc ++
+
dq
VCOPI
Low pass filter
SOGIBP filter
SOGIBP filter
v+d
v+q
120579e
120579e
SRF-PLL
1
sminus
120572120573
120572120573998400120572
q998400120572
q998400120573
998400120573
+120572
+120573
120572
120573
e
ea
b
c
05
05
Figure 2 Schematic diagram of DSOGI-PLL
instantaneous active and reactive output power of the GCIcan be obtained by using (4) and (5) under both normal andabnormal conditions of the grid
32 Grid Synchronization of GCI The active and reactivepower control of the GCI is based on a synchronous ref-erence frame (SRF) with proportional-integral (PI) or 2D-RFCMANN controllers Moreover it is important to detectthe phase angle of the voltage at PCC in order to synchronizewith the grid during grid faults At present the most popularPLL structure is the synchronous reference frame PLL (SRF-PLL) [14]The input three-phase voltages of the SRF-PLL canbe given by
[
[
V119886
V119887
V119888
]
]
=1003816100381610038161003816119881+1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890minus
2
3120587)
sin(120579119890+
2
3120587)
]]]]]]
]
+1003816100381610038161003816119881minus1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890+
2
3120587)
sin(120579119890minus
2
3120587)
]]]]]]
]
(6)
where |119881+
| and |119881minus
| are the amplitude of the positive andnegative sequence of the three-phase voltage 120579
119890= 120596119890119905 and
120596119890is the utility angular frequency In the SRF-PLL first
the Clarke transformation is applied to transfer the three-phase voltages from the 119886119887119888 natural reference frame to the 120572120573
stationary reference frame [14 15] V120572and V120573are the voltages
of 120572 120573 axis which can be expressed as
[V120572
V120573
] = radic2
3
[[[
[
3
20
radic3
2radic3
]]]
]
[V119886
V119887
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890)
minus cos (120579119890)] + radic
3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890)
cos (120579119890)]
(7)
Then (7) can be expressed in the synchronous referenceframe by using Park transformation in the following [15]
[V119889
V119902
] = [
[
cos (120579119890) sin (120579
119890)
minus sin (120579119890) cos (120579
119890)
]
]
[V120572
V120573
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890minus 120579119890)
minus cos (120579119890minus 120579119890)]
+ radic3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890minus 120579119890)
cos (120579119890minus 120579119890)] (8)
where V119889 V119902are the voltages of the 119889119902 axis 120579
119890= 119890119905 and
119890is the angular frequency of the 119889119902 synchronous reference
frame Suppose that 120579119890is close to 120579
119890 then sin(120579
119890minus 120579119890) is
approximately equal to 120579119890minus 120579119890 and V
119889is approximately equal
to (radic62)[|119881+
|(120579119890minus120579119890)+|119881minus
| sin(2120579119890)]The negative sequence
component voltage of V119889can be filtered by using a properly
designed low pass filterThe difference between 120579119890and 120579119890will
approach zero due to the closed-loop control of 120579119890that makes
V119889approach zero Therefore with 120579
119890asymp 120579119890in steady state the
phase angle detected by the SRF-PLL will be in phase withthe input voltage vector However the dynamic behavior ofthe SRF-PLL will become poor under asymmetric grid faults[15] In order to overcome this disadvantage of SRF-PLL adual second-order generalized integrator PLL (DSOGI-PLL)based on the extraction of the positive sequence has beenproposed in [10 14 15] Define k+
120572120573= [V+120572
V+120573]119879
as the positivesequence voltage vector on the 120572120573 reference frame and it canbe calculated as [10]
k+120572120573
=1
2[1 minus119902
119902 1][
[
V1015840120572
V1015840120573
]
]
(9)
where 119902 = 119890minus1198951205872 is a phase-shift operator in the time domain
V1015840120572and V1015840120573are the filtered voltages of V
120572and V120573 respectively
The schematic diagram of DSOGI-PLL is shown in Figure 2where the dual second-order generalized integrator (SOGI)in Figure 2 is used to generate V1015840
120572 V1015840120573 and in-quadrature
voltages 119902V1015840120572and 119902V1015840
120573of V1015840120572and V1015840
120573 Furthermore V+
119889and V+
119902
which are depicted in Figure 2 are the positive sequencevoltages on the 119889119902 synchronous reference frame In additiona voltage-controlled oscillator (VCO) is employed to convertthe input voltage into
119890 Finally 120579
119890is successfully obtained
by DSOGI-PLL by using the positive sequence voltagesAccording to [15] the instantaneous active and reactive
power outputs of the GCI can be calculated by using the
International Journal of Photoenergy 5
voltage and current in the 119889119902 synchronous reference frameas follows
119876 =3
2(V119902119894119889minus V119889119894119902) 119875 =
3
2(V119889119894119889+ V119902119894119902) (10)
where 119894119889and 119894119902are the currents of the 119889 119902 axis As mentioned
above an adequate tracking of the grid angular position ofthe SRF-PLL will make V
119889approach zeroThus the active and
reactive power outputs of the GCI can be represented as
119876 =3
2V119902119894119889 119875 =
3
2V119902119894119902 (11)
Accordingly 119875 and 119876 can be regulated by controlling 119894119902and
119894119889
33 Reactive and Active Power Control during Grid FaultsThe positive sequence voltages of the three-phase line volt-ages V+
119886119887 V+119887119888 and V+
119888119886can be expressed as follows
[[[[
[
V+119886119887
V+119887119888
V+119888119886
]]]]
]
=1
3
[
[
1 119886 1198862
1198862
1 119886
119886 1198862
1
]
]
[
[
V119886119887
V119887119888
V119888119886
]
]
= radic21003816100381610038161003816119881+
119897
1003816100381610038161003816
[[[[[[
[
sin 120579119890
sin(120579119890minus
2120587
3)
sin(120579119890+
2120587
3)
]]]]]]
]
(12)
where |119881+
119897| is the rms value of the magnitude of the positive
sequence voltage of the three-phase line voltages and theoperator 119886 is equal to 119890
11989521205873 Since V+119886119887 V+119887119888 and V+
119888119886are
symmetric and balanced |119881+119897| can be expressed as
1003816100381610038161003816119881+
119897
1003816100381610038161003816 = radic1
3(V+119886119887
2
+ V+119887119888
2
+ V+119888119886
2
) (13)
Note that V+119886119887 V+119887119888 and V+
119888119886are equal to the magnitude of the
three-phase line voltages when the line voltages are balancedAccording to (12) if the line voltages are unbalanced V+
119886119887
V+119887119888 and V+
119888119886will be changed with the degree of unbalance
Therefore |119881+
119897| is adopted to evaluate the depth of voltage sag
119881sag during grid faults in this study The required percentageof compensation reactive current 119868
lowast
119903during grid faults for
LVRT can be expressed as a function of 119881sag [8]
119868lowast
119903=
0 where 119881sag lt 01
200119881sag where 01 lt 119881sag le 05
100 where 119881sag gt 05
(14)
and 119881sag is defined as follows
119881sag equiv 1 minus
1003816100381610038161003816119881+
119897
1003816100381610038161003816
119881basepu (15)
where119881base is the base value of voltage which equals 110 Vrmsin this study The grid regulation by EON demands reactivecurrent injection during fault condition to support the gridstability when 119881sag is greater than 01 pu Moreover theapparent output power of GCI will be changed due to thevoltage sag at PCC under grid faultsTherefore it is necessaryto calculate the maximum allowable apparent power in orderto decide the maximum injection reactive and active powerThe maximum apparent power 119878 can be expressed as
119878 = (1003816100381610038161003816V119886
1003816100381610038161003816rms +1003816100381610038161003816V119887
1003816100381610038161003816rms +1003816100381610038161003816V119888
1003816100381610038161003816rms) 119868max (16)
where 119868max is the rms value of the GCI current limit and|V119886|rms |V119887|rms and |V
119888|rms are the rms values of V
119886 V119887 and V
119888
respectively Thus the required injection reactive power 119876lowast
and the allowable maximum output active power 119875lowast of GCI
as follows can be derived from (14) and (16)
119876lowast
= 119878119868lowast
119903 119875
lowast
= 119878radic1 minus 119868lowast2119903
(17)
A PV system should inject a certain reactive power inorder to support the voltage sag at the PCC according to theLVRT requirements during grid faults If 119875lowast is greater than 119875then the active power reference 119875ref is set to equal the valueof 119875 before the grid faults Therefore all the power generatedby the PV panel can be totally delivered into the grid duringgrid faults and the MPPT control can be operated to keeptracking the MPP On the other hand if 119875
lowast is smaller than119875 then 119875ref is set to 119875
lowast Thus the output active power will becontrolled to follow 119875ref and the GCI gives up tracking theMPPConsequently the power balance between119875pv and119875 canbe held during grid faults
4 D-RFCMANN Control Scheme
41 Description of 2D-RFCMANN The structure of 2D-RFCMANN with 2 inputs and 1 output is depicted inFigure 3(a) which consists of five spaces input space fuzzi-fication space receptive-field space weight space and outspace Moreover one of the fuzzy if-then rules of the pro-posed 2D-RFCMANN is realized as follows
119877119894
11989511198952
If 1199091is 11989111198941198951
and 1199092is 11989121198941198952
then
11991011989411989511198952
= 11990811989411989511198952
for 119894 = 1 2 119899119894
1198951 1198952= 1 2 119899
119895
(18)
where 119899119894
= 3 is the number of the layers for each inputdimension 119899
119895= 4 is the number of blocks for each layer
11989111198941198951
is the fuzzy set for the first input 119894th layer and 1198951th
block 11989121198941198952
is the fuzzy set for the second input 119894th layerand 1198952th block 119908
11989411989511198952
is the corresponding output weight inthe consequent part Furthermore the signal propagation andthe basic function in each space of the 2D-RFCMANN areintroduced as follows
Space 1 (input space) In this space the input variables 1199091
and 1199092are both divided into 119899
119890regions (which are called
ldquoelementsrdquo)Thenumber of 119899119890represents the input resolution
6 International Journal of Photoenergy
Input space
Fuzzification space
Receptive-fieldSpace
Recurrent unit
x1
x2
f1ij1
f2ij2
fpijp
rpijp
sum
xp
zminus1
y2pijp
Output space
y5o
h111
h121
w111
w121
hij1j2
hn119894n119895n119895
wij1j2
wn119894n119895n119895
Weight space
(a) Structure of 2D-RFCMANN
S1
S1
S2
S2
S3
S3
S4
S4
S5
S5
S6
S6
S7
S7
S8
S8
S9
S9
S10
S10
f111
f111
f211f221
f231
f121
f131
f212
f112
f212
f222
f232
f122
f132
f113
f123
f213
f223
f233
f133
f114
f214f224
f234
f124
f134
H1
H2
H3
Layer 1 Layer 1
Layer 2
Layer 2
Layer 3
Layer 3
x2
x1
(3 5)
(b) 2D-RFCMANN with 119901 = 2 119899119894= 3 and 119899
119895= 4 and its configuration of receptive-field space
activated by state (3 5)
Figure 3 Two-dimensional RFCMANN
For example a 2D-RFMANN with 119899119890
= 10 is shown as inFigure 3(b)
Space 2 (fuzzification space) According to the concept ofCMANN several elements can be accumulated as a block
In this space each block performs a Gaussian receptive-field basis function The fuzzification of the correspondingmembership function in the 2D-RFCMANN is realizedby the Gaussian basis function which can be expressedas
International Journal of Photoenergy 7
DC
AC
Current controlled
PWMPC-based control system
L SSR
Instantaneous active and
reactive power calculation
dqabc
LimiterLimiter
3-phase grid
Grid fault signal
Y
110220
PI22D-RFCMANN2
Three-phaseGCI
MPPT
SW1
PI12D-RFCMANN1
+
P
Q
Q
PV panel
DSOGI-PLL
calculation
Active and reactive power
references calculation
P
+
SW20
+
ia ib ic
ia
ib
ic
ilowasta
ilowastq
ilowastb ilowastc
ilowastd
ab bc ca
ab
bc ca
radic31 2
Vpv
Vsag
Vsag
Cpv
Vpv
VpvI pv
100Ω
Imax
Δminus
minus
minus
minus
minus
minus
minus
e
Pre fPre f
Qlowast
++
+
+
+ Vlowastpv
Y-Δ
Figure 4 Schematic diagram of PC-based control system
119891119901119894119895119901(119873) = exp(minus
(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205902
119901119894119895119901
)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
1199102
119901119894119895119901
(119873) = 119909119901(119873) + 119903
119901119894119895119901
119891119901119894119895119901(119873 minus 1)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
(19)
where 119891119901119894119895119901
(119873) is the output of the 119895119901th block of the 119894th layer
of the 119901th input variable 119898119901119894119895119901
and 120590119901119894119895119901
are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901
represents the recurrent weight of the 119895119901th block of the
119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891
119901119894119895119901
(119873 minus 1) represents the valueof 119891119901119894119895119901
(119873) through time delay Note that the memory term119891119901119894119895119901
(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer
Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903
119901119894119895119901
119898119901119894119895119901
and 120590119901119894119895119901
Themultidimensional receptive-field function is defined as
ℎ11989411989511198952(119873) = 119891
11198941198951(119873) 11989121198941198952(119873)
= exp(minus
(1199102
11198941198951
(119873) minus 11989811198941198951
)2
1205902
11198941198951
)
times exp(minus
(1199102
21198941198952
(119873) minus 11989821198941198952
)2
1205902
21198941198952
)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(20)
where ℎ11989411989511198952
(119873) is associated with the ith layer and the 1198951th
block for input 1199091and the 119895
2th block for input 119909
2according
to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891
111119891211
119891112
119891211
and so forth are called receptive fields (or hypercube)
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
2 International Journal of Photoenergy
system The first dimension of the 2D-RFCMANN is for thetracking error input and the second dimension of the 2D-RFCMANN is for the derivative of the tracking error input
The penetration of renewable energy sources hasincreased significantly because of raising awareness of theenvironmental issues and the deregulation of the electricpower distribution industry Among these renewable energysources PV system is one of the main candidates to playan important role in the future of power distributionHowever the connection of a large number of distributedenergy sources (DESs) to the electrical power grid can causeinstability when electrical disturbances appear in the gridOne of the most challenging disturbances is the voltagesags [6 7] The sources of the voltage sags are various suchas short circuits between phases or phases and groundlightning and overloads To minimize the negative effectsof a large number of DESs on the reliability of the powergrids different countries have defined various low voltageride through (LVRT) regulations for DESs EON has definedthe voltage profile of the low voltage ride through (LVRT)at the grid connection for type-2 generating plants [8] Gridregulations require that the DESs have to inject reactivecurrent to support grid stability during grid faults [8] inwhich 1 pu of reactive current is required as the depth of thesag reaches 50 In this study the EON LVRT regulationis adopted to determine the ratio of the required reactivecurrent during grid faults
The asymmetrical grid voltage sags will worsen the per-formance of the grid-connected inverter (GCI) especially thedegradation of the power quality caused by the power rippleand the increase of current harmonic distortion In orderto overcome these disadvantages some control methodsbased on symmetric components have been proposed todeal with unbalanced grid faults [9ndash13] A control schemewhich can adjust the characteristics of power quality byusing two adjustable control parameters was developed in[9] In [10] a selective active power quality control based onvarious current reference generating methods was proposedReference [11] has proposed a control method to minimizethe peak value of the injection current during the voltagesag In [12] a positive and negative sequences currentinjection method was proposed to provide the active powerand reactive current without exceeding the current limitof inverter The flexible reactive current injection schemeintroduced in [13] provides voltage support during voltage sagby injecting reactive current via both positive and negativesequences However the aforementioned control methodsprincipally focus on the power control of grid-connectedinverter whereas the fulfillment of the LVRT requirementand the control of the power flow between the dc-link bus andac grid during grid faults are not well explored In this studythe 2D-RFCMANN control scheme is proposed to controlnot only the output voltage of the PV panel via the maximumpower point tracking (MPPT) in normal condition butalso the reactive power based on LVRT requirement withconsidering the power balance between dc-link bus and acgrid during grid faults
In this study the analysis of the instantaneousactivereactive output power of the three-phase GCI during
grid faults is carried out by using symmetric componentmethod The MPPT control of PV system is also consideredto ensure the power balance during grid faults Subsequentlythe dual second-order generalized integrator phase-lockedloop (DSOGI-PLL) method [10 14 15] is adopted forsynchronizing the GCI to the grid Moreover a new formulawhich is based on the positive sequence voltage is derivedto evaluate the percentage of voltage sag and to determinethe injected currents during the grid faults Furthermorethe network structure and online training algorithms ofnetwork parameters of the proposed 2D-RFCMANN for theactive and reactive power control are discussed in detailFurthermore two types of grid faults are tested and discussedto evaluate the performance of the proposed control schemeThe paper is organized as follows In Section 2 the grid-connected PV system is introduced In Section 3 theinstantaneous activereactive power formulation DSOGI-PLL synchronization mechanism and the control strategyof the grid-connected PV system during grid faults arediscussed The 2D-RFCMANN is presented in Section 4 InSection 5 the features of the proposed control scheme areexamined by some experimental results Finally Section 6draws the conclusions
2 System Description
Figure 1 shows the block diagrams of the proposed single-stage three-phase grid-connected PV system The behaviorof the PV panel is emulated by a Chroma 62100H-600S PVpanel simulator operating at 203Vdc output voltage withmaximum output power 1 kW The power grid was emu-lated by three programmable 2 kVA single-phase KIKUSUIPCR2000LE AC power supplies feeding a Y-connected100Ωphase resistive load and connected to the GCI witha 3 kVA Y-998779 transformer The 2 kVA three-phase GCI withoutput 110Vrms line to line voltage is connected to the PVpanel simulator through a dc-link capacitor and connectedto the Y-998779 transformer with three 10mHphase couplinginductorsThe switching frequency119891sw GCI of the three-phaseGCI is set at 10 kHz Table 1 shows the parameters of theexperimental setup Moreover the control system is installedon a desktop personal computer (PC) which includes an ADconverter card (PCI-1716) a PC-based control system anda DA converter card (MRC-6810) In the PC-based controlsystem the SIMULINK control package is adopted for theimplementation of the proposed algorithms of theMPPT andLVRTcontrolThe analog input signals include output voltage119881pv and current 119868pv of the PV panel simulator the outputline voltages V
119886119887 V119887119888 and V
119888119886 and line currents 119894
119886 119894119887 and
119894119888of the GCI The control output of the PC-based control
system is the three-phase reference currents of GCI 119894lowast
119886 119894lowast
119887
and 119894lowast
119888 Furthermore the emulated faults occur at the point
of common coupling (PCC)In Figure 1 the output currents of the GCI are controlled
by the maximum power point (MPP) voltage 119881lowast
pv in the nor-mal conditionThe adoptedMPPTmethod is the incrementalconductance (IC) method with a fixed incremental step sizeset for the voltage [16] Moreover if a grid fault occurs at the
International Journal of Photoenergy 3
DC
AC
Three-phase GCI
Current controlled
PWM
L
110220
LoadPCC
Emulatedfault
PC
AD converter
MPPT and LVRT control
PC-based control system
PV panel Grid
DA converter
Vpv+
minus
Ipv
Cpv
Vpv
ia ib ic
ia ib ic
ilowasta ilowastb i
lowastc
Y Δ
100ΩY-connected
= 3120601ab bc ca
ab bc caVpv Ipv
radic31 2
Figure 1 Block diagrams of experimental single-stage three-phase grid-connected PV system
Table 1 Parameters of experimental setup
Dc-link capacitor 119862pv 3360mFGrid connection inductor 119871 10mHInverter output voltage V
119886119887 V119887119888 V119888119886
110Vrms line to line 60HzInverter maximum current 119868max 5Arms (71 A peak current)Emulated PV panel 119881oc 236V 119868sc 60 A 1 kWSwitching frequency 119891sw GCI 10 kHz
PCC the fault voltages at theGCI terminals appear differentlyfrom the fault voltages at the PCC [6 7] Furthermore in thenormal condition of the grid the GCI regulates the activepower injecting into the grid and maintains the 119881pv voltageso as to track the MPP for maximizing the energy extractionOn the other hand in the fault conditions of the grid thereactive power control can mitigate the effects of voltagesag by injecting additional reactive current to the grid toride through the perturbation and support the grid voltageIn addition the injecting current has to meet the LVRTregulations without going beyond the GCI current limit 119868maxsimultaneously
3 Reactive Power Control Strategyduring Grid Faults
31 Instantaneous Power Formulation under Grid Fault Con-ditions For a three-phase GCI the instantaneous active andreactive power outputs at the grid connection point aredescribed as follows [17]
119875 = k sdot i = V119886119894119886+ V119887119894119887+ V119888119894119888 (1)
119876 = k times i = kperp
sdot i
=1
radic3[(V119886minus V119887) 119894119888+ (V119887minus V119888) 119894119886+ (V119888minus V119886) 119894119887]
(2)
where kperp
= (1radic3) [0 1 minus1
minus1 0 1
1 minus1 0
] k k = [V119886
V119887V119888]119879and i =
[119894119886
119894119887
119894119888]119879 represent the three phase voltages and currents of
the GCI respectively 119875 and 119876 represent the instantaneousactive and reactive power outputs of the GCI respectivelyIn (1) and (2) k
perpand k are orthogonal only when the
three voltages of k are balancedThe asymmetric three-phasevoltage and current vector are represented as
k = k+ + kminus
i = i+ + iminus(3)
where k+ = [V+119886
V+119887
V+119888]119879 and kminus = [Vminus
119886Vminus119887
Vminus119888]119879 represent
the positive and negative sequences of v respectively i+ =
[119894+
119886119894+
119887119894+
119888]119879 and iminus = [119894
minus
119886119894minus
119887119894minus
119888]119879 represent the positive
and negative sequences of i respectively Note that the zerosequence of v and i does not exist due to the three-phasethree-wire AC system configuration of the GCI As a result119875 and 119876 in (1) and (2) can be rewritten as
119875 = k sdot i = (k+ + kminus) sdot (i+ + iminus)
= k+ sdot i+ + kminus sdot iminus + k+ sdot iminus + kminus sdot i+(4)
119876 = kperp
sdot i = (k+perp
+ kminusperp) sdot (i+ + iminus)
= k+perp
sdot i+ + kminusperp
sdot iminus + k+perp
sdot iminus + kminusperp
sdot i+(5)
where the corresponding orthogonal vectors in (5) can bederived by using the matrix transformation in (2) Thus the
4 International Journal of Photoenergy
abc ++
+
dq
VCOPI
Low pass filter
SOGIBP filter
SOGIBP filter
v+d
v+q
120579e
120579e
SRF-PLL
1
sminus
120572120573
120572120573998400120572
q998400120572
q998400120573
998400120573
+120572
+120573
120572
120573
e
ea
b
c
05
05
Figure 2 Schematic diagram of DSOGI-PLL
instantaneous active and reactive output power of the GCIcan be obtained by using (4) and (5) under both normal andabnormal conditions of the grid
32 Grid Synchronization of GCI The active and reactivepower control of the GCI is based on a synchronous ref-erence frame (SRF) with proportional-integral (PI) or 2D-RFCMANN controllers Moreover it is important to detectthe phase angle of the voltage at PCC in order to synchronizewith the grid during grid faults At present the most popularPLL structure is the synchronous reference frame PLL (SRF-PLL) [14]The input three-phase voltages of the SRF-PLL canbe given by
[
[
V119886
V119887
V119888
]
]
=1003816100381610038161003816119881+1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890minus
2
3120587)
sin(120579119890+
2
3120587)
]]]]]]
]
+1003816100381610038161003816119881minus1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890+
2
3120587)
sin(120579119890minus
2
3120587)
]]]]]]
]
(6)
where |119881+
| and |119881minus
| are the amplitude of the positive andnegative sequence of the three-phase voltage 120579
119890= 120596119890119905 and
120596119890is the utility angular frequency In the SRF-PLL first
the Clarke transformation is applied to transfer the three-phase voltages from the 119886119887119888 natural reference frame to the 120572120573
stationary reference frame [14 15] V120572and V120573are the voltages
of 120572 120573 axis which can be expressed as
[V120572
V120573
] = radic2
3
[[[
[
3
20
radic3
2radic3
]]]
]
[V119886
V119887
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890)
minus cos (120579119890)] + radic
3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890)
cos (120579119890)]
(7)
Then (7) can be expressed in the synchronous referenceframe by using Park transformation in the following [15]
[V119889
V119902
] = [
[
cos (120579119890) sin (120579
119890)
minus sin (120579119890) cos (120579
119890)
]
]
[V120572
V120573
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890minus 120579119890)
minus cos (120579119890minus 120579119890)]
+ radic3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890minus 120579119890)
cos (120579119890minus 120579119890)] (8)
where V119889 V119902are the voltages of the 119889119902 axis 120579
119890= 119890119905 and
119890is the angular frequency of the 119889119902 synchronous reference
frame Suppose that 120579119890is close to 120579
119890 then sin(120579
119890minus 120579119890) is
approximately equal to 120579119890minus 120579119890 and V
119889is approximately equal
to (radic62)[|119881+
|(120579119890minus120579119890)+|119881minus
| sin(2120579119890)]The negative sequence
component voltage of V119889can be filtered by using a properly
designed low pass filterThe difference between 120579119890and 120579119890will
approach zero due to the closed-loop control of 120579119890that makes
V119889approach zero Therefore with 120579
119890asymp 120579119890in steady state the
phase angle detected by the SRF-PLL will be in phase withthe input voltage vector However the dynamic behavior ofthe SRF-PLL will become poor under asymmetric grid faults[15] In order to overcome this disadvantage of SRF-PLL adual second-order generalized integrator PLL (DSOGI-PLL)based on the extraction of the positive sequence has beenproposed in [10 14 15] Define k+
120572120573= [V+120572
V+120573]119879
as the positivesequence voltage vector on the 120572120573 reference frame and it canbe calculated as [10]
k+120572120573
=1
2[1 minus119902
119902 1][
[
V1015840120572
V1015840120573
]
]
(9)
where 119902 = 119890minus1198951205872 is a phase-shift operator in the time domain
V1015840120572and V1015840120573are the filtered voltages of V
120572and V120573 respectively
The schematic diagram of DSOGI-PLL is shown in Figure 2where the dual second-order generalized integrator (SOGI)in Figure 2 is used to generate V1015840
120572 V1015840120573 and in-quadrature
voltages 119902V1015840120572and 119902V1015840
120573of V1015840120572and V1015840
120573 Furthermore V+
119889and V+
119902
which are depicted in Figure 2 are the positive sequencevoltages on the 119889119902 synchronous reference frame In additiona voltage-controlled oscillator (VCO) is employed to convertthe input voltage into
119890 Finally 120579
119890is successfully obtained
by DSOGI-PLL by using the positive sequence voltagesAccording to [15] the instantaneous active and reactive
power outputs of the GCI can be calculated by using the
International Journal of Photoenergy 5
voltage and current in the 119889119902 synchronous reference frameas follows
119876 =3
2(V119902119894119889minus V119889119894119902) 119875 =
3
2(V119889119894119889+ V119902119894119902) (10)
where 119894119889and 119894119902are the currents of the 119889 119902 axis As mentioned
above an adequate tracking of the grid angular position ofthe SRF-PLL will make V
119889approach zeroThus the active and
reactive power outputs of the GCI can be represented as
119876 =3
2V119902119894119889 119875 =
3
2V119902119894119902 (11)
Accordingly 119875 and 119876 can be regulated by controlling 119894119902and
119894119889
33 Reactive and Active Power Control during Grid FaultsThe positive sequence voltages of the three-phase line volt-ages V+
119886119887 V+119887119888 and V+
119888119886can be expressed as follows
[[[[
[
V+119886119887
V+119887119888
V+119888119886
]]]]
]
=1
3
[
[
1 119886 1198862
1198862
1 119886
119886 1198862
1
]
]
[
[
V119886119887
V119887119888
V119888119886
]
]
= radic21003816100381610038161003816119881+
119897
1003816100381610038161003816
[[[[[[
[
sin 120579119890
sin(120579119890minus
2120587
3)
sin(120579119890+
2120587
3)
]]]]]]
]
(12)
where |119881+
119897| is the rms value of the magnitude of the positive
sequence voltage of the three-phase line voltages and theoperator 119886 is equal to 119890
11989521205873 Since V+119886119887 V+119887119888 and V+
119888119886are
symmetric and balanced |119881+119897| can be expressed as
1003816100381610038161003816119881+
119897
1003816100381610038161003816 = radic1
3(V+119886119887
2
+ V+119887119888
2
+ V+119888119886
2
) (13)
Note that V+119886119887 V+119887119888 and V+
119888119886are equal to the magnitude of the
three-phase line voltages when the line voltages are balancedAccording to (12) if the line voltages are unbalanced V+
119886119887
V+119887119888 and V+
119888119886will be changed with the degree of unbalance
Therefore |119881+
119897| is adopted to evaluate the depth of voltage sag
119881sag during grid faults in this study The required percentageof compensation reactive current 119868
lowast
119903during grid faults for
LVRT can be expressed as a function of 119881sag [8]
119868lowast
119903=
0 where 119881sag lt 01
200119881sag where 01 lt 119881sag le 05
100 where 119881sag gt 05
(14)
and 119881sag is defined as follows
119881sag equiv 1 minus
1003816100381610038161003816119881+
119897
1003816100381610038161003816
119881basepu (15)
where119881base is the base value of voltage which equals 110 Vrmsin this study The grid regulation by EON demands reactivecurrent injection during fault condition to support the gridstability when 119881sag is greater than 01 pu Moreover theapparent output power of GCI will be changed due to thevoltage sag at PCC under grid faultsTherefore it is necessaryto calculate the maximum allowable apparent power in orderto decide the maximum injection reactive and active powerThe maximum apparent power 119878 can be expressed as
119878 = (1003816100381610038161003816V119886
1003816100381610038161003816rms +1003816100381610038161003816V119887
1003816100381610038161003816rms +1003816100381610038161003816V119888
1003816100381610038161003816rms) 119868max (16)
where 119868max is the rms value of the GCI current limit and|V119886|rms |V119887|rms and |V
119888|rms are the rms values of V
119886 V119887 and V
119888
respectively Thus the required injection reactive power 119876lowast
and the allowable maximum output active power 119875lowast of GCI
as follows can be derived from (14) and (16)
119876lowast
= 119878119868lowast
119903 119875
lowast
= 119878radic1 minus 119868lowast2119903
(17)
A PV system should inject a certain reactive power inorder to support the voltage sag at the PCC according to theLVRT requirements during grid faults If 119875lowast is greater than 119875then the active power reference 119875ref is set to equal the valueof 119875 before the grid faults Therefore all the power generatedby the PV panel can be totally delivered into the grid duringgrid faults and the MPPT control can be operated to keeptracking the MPP On the other hand if 119875
lowast is smaller than119875 then 119875ref is set to 119875
lowast Thus the output active power will becontrolled to follow 119875ref and the GCI gives up tracking theMPPConsequently the power balance between119875pv and119875 canbe held during grid faults
4 D-RFCMANN Control Scheme
41 Description of 2D-RFCMANN The structure of 2D-RFCMANN with 2 inputs and 1 output is depicted inFigure 3(a) which consists of five spaces input space fuzzi-fication space receptive-field space weight space and outspace Moreover one of the fuzzy if-then rules of the pro-posed 2D-RFCMANN is realized as follows
119877119894
11989511198952
If 1199091is 11989111198941198951
and 1199092is 11989121198941198952
then
11991011989411989511198952
= 11990811989411989511198952
for 119894 = 1 2 119899119894
1198951 1198952= 1 2 119899
119895
(18)
where 119899119894
= 3 is the number of the layers for each inputdimension 119899
119895= 4 is the number of blocks for each layer
11989111198941198951
is the fuzzy set for the first input 119894th layer and 1198951th
block 11989121198941198952
is the fuzzy set for the second input 119894th layerand 1198952th block 119908
11989411989511198952
is the corresponding output weight inthe consequent part Furthermore the signal propagation andthe basic function in each space of the 2D-RFCMANN areintroduced as follows
Space 1 (input space) In this space the input variables 1199091
and 1199092are both divided into 119899
119890regions (which are called
ldquoelementsrdquo)Thenumber of 119899119890represents the input resolution
6 International Journal of Photoenergy
Input space
Fuzzification space
Receptive-fieldSpace
Recurrent unit
x1
x2
f1ij1
f2ij2
fpijp
rpijp
sum
xp
zminus1
y2pijp
Output space
y5o
h111
h121
w111
w121
hij1j2
hn119894n119895n119895
wij1j2
wn119894n119895n119895
Weight space
(a) Structure of 2D-RFCMANN
S1
S1
S2
S2
S3
S3
S4
S4
S5
S5
S6
S6
S7
S7
S8
S8
S9
S9
S10
S10
f111
f111
f211f221
f231
f121
f131
f212
f112
f212
f222
f232
f122
f132
f113
f123
f213
f223
f233
f133
f114
f214f224
f234
f124
f134
H1
H2
H3
Layer 1 Layer 1
Layer 2
Layer 2
Layer 3
Layer 3
x2
x1
(3 5)
(b) 2D-RFCMANN with 119901 = 2 119899119894= 3 and 119899
119895= 4 and its configuration of receptive-field space
activated by state (3 5)
Figure 3 Two-dimensional RFCMANN
For example a 2D-RFMANN with 119899119890
= 10 is shown as inFigure 3(b)
Space 2 (fuzzification space) According to the concept ofCMANN several elements can be accumulated as a block
In this space each block performs a Gaussian receptive-field basis function The fuzzification of the correspondingmembership function in the 2D-RFCMANN is realizedby the Gaussian basis function which can be expressedas
International Journal of Photoenergy 7
DC
AC
Current controlled
PWMPC-based control system
L SSR
Instantaneous active and
reactive power calculation
dqabc
LimiterLimiter
3-phase grid
Grid fault signal
Y
110220
PI22D-RFCMANN2
Three-phaseGCI
MPPT
SW1
PI12D-RFCMANN1
+
P
Q
Q
PV panel
DSOGI-PLL
calculation
Active and reactive power
references calculation
P
+
SW20
+
ia ib ic
ia
ib
ic
ilowasta
ilowastq
ilowastb ilowastc
ilowastd
ab bc ca
ab
bc ca
radic31 2
Vpv
Vsag
Vsag
Cpv
Vpv
VpvI pv
100Ω
Imax
Δminus
minus
minus
minus
minus
minus
minus
e
Pre fPre f
Qlowast
++
+
+
+ Vlowastpv
Y-Δ
Figure 4 Schematic diagram of PC-based control system
119891119901119894119895119901(119873) = exp(minus
(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205902
119901119894119895119901
)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
1199102
119901119894119895119901
(119873) = 119909119901(119873) + 119903
119901119894119895119901
119891119901119894119895119901(119873 minus 1)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
(19)
where 119891119901119894119895119901
(119873) is the output of the 119895119901th block of the 119894th layer
of the 119901th input variable 119898119901119894119895119901
and 120590119901119894119895119901
are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901
represents the recurrent weight of the 119895119901th block of the
119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891
119901119894119895119901
(119873 minus 1) represents the valueof 119891119901119894119895119901
(119873) through time delay Note that the memory term119891119901119894119895119901
(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer
Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903
119901119894119895119901
119898119901119894119895119901
and 120590119901119894119895119901
Themultidimensional receptive-field function is defined as
ℎ11989411989511198952(119873) = 119891
11198941198951(119873) 11989121198941198952(119873)
= exp(minus
(1199102
11198941198951
(119873) minus 11989811198941198951
)2
1205902
11198941198951
)
times exp(minus
(1199102
21198941198952
(119873) minus 11989821198941198952
)2
1205902
21198941198952
)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(20)
where ℎ11989411989511198952
(119873) is associated with the ith layer and the 1198951th
block for input 1199091and the 119895
2th block for input 119909
2according
to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891
111119891211
119891112
119891211
and so forth are called receptive fields (or hypercube)
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 3
DC
AC
Three-phase GCI
Current controlled
PWM
L
110220
LoadPCC
Emulatedfault
PC
AD converter
MPPT and LVRT control
PC-based control system
PV panel Grid
DA converter
Vpv+
minus
Ipv
Cpv
Vpv
ia ib ic
ia ib ic
ilowasta ilowastb i
lowastc
Y Δ
100ΩY-connected
= 3120601ab bc ca
ab bc caVpv Ipv
radic31 2
Figure 1 Block diagrams of experimental single-stage three-phase grid-connected PV system
Table 1 Parameters of experimental setup
Dc-link capacitor 119862pv 3360mFGrid connection inductor 119871 10mHInverter output voltage V
119886119887 V119887119888 V119888119886
110Vrms line to line 60HzInverter maximum current 119868max 5Arms (71 A peak current)Emulated PV panel 119881oc 236V 119868sc 60 A 1 kWSwitching frequency 119891sw GCI 10 kHz
PCC the fault voltages at theGCI terminals appear differentlyfrom the fault voltages at the PCC [6 7] Furthermore in thenormal condition of the grid the GCI regulates the activepower injecting into the grid and maintains the 119881pv voltageso as to track the MPP for maximizing the energy extractionOn the other hand in the fault conditions of the grid thereactive power control can mitigate the effects of voltagesag by injecting additional reactive current to the grid toride through the perturbation and support the grid voltageIn addition the injecting current has to meet the LVRTregulations without going beyond the GCI current limit 119868maxsimultaneously
3 Reactive Power Control Strategyduring Grid Faults
31 Instantaneous Power Formulation under Grid Fault Con-ditions For a three-phase GCI the instantaneous active andreactive power outputs at the grid connection point aredescribed as follows [17]
119875 = k sdot i = V119886119894119886+ V119887119894119887+ V119888119894119888 (1)
119876 = k times i = kperp
sdot i
=1
radic3[(V119886minus V119887) 119894119888+ (V119887minus V119888) 119894119886+ (V119888minus V119886) 119894119887]
(2)
where kperp
= (1radic3) [0 1 minus1
minus1 0 1
1 minus1 0
] k k = [V119886
V119887V119888]119879and i =
[119894119886
119894119887
119894119888]119879 represent the three phase voltages and currents of
the GCI respectively 119875 and 119876 represent the instantaneousactive and reactive power outputs of the GCI respectivelyIn (1) and (2) k
perpand k are orthogonal only when the
three voltages of k are balancedThe asymmetric three-phasevoltage and current vector are represented as
k = k+ + kminus
i = i+ + iminus(3)
where k+ = [V+119886
V+119887
V+119888]119879 and kminus = [Vminus
119886Vminus119887
Vminus119888]119879 represent
the positive and negative sequences of v respectively i+ =
[119894+
119886119894+
119887119894+
119888]119879 and iminus = [119894
minus
119886119894minus
119887119894minus
119888]119879 represent the positive
and negative sequences of i respectively Note that the zerosequence of v and i does not exist due to the three-phasethree-wire AC system configuration of the GCI As a result119875 and 119876 in (1) and (2) can be rewritten as
119875 = k sdot i = (k+ + kminus) sdot (i+ + iminus)
= k+ sdot i+ + kminus sdot iminus + k+ sdot iminus + kminus sdot i+(4)
119876 = kperp
sdot i = (k+perp
+ kminusperp) sdot (i+ + iminus)
= k+perp
sdot i+ + kminusperp
sdot iminus + k+perp
sdot iminus + kminusperp
sdot i+(5)
where the corresponding orthogonal vectors in (5) can bederived by using the matrix transformation in (2) Thus the
4 International Journal of Photoenergy
abc ++
+
dq
VCOPI
Low pass filter
SOGIBP filter
SOGIBP filter
v+d
v+q
120579e
120579e
SRF-PLL
1
sminus
120572120573
120572120573998400120572
q998400120572
q998400120573
998400120573
+120572
+120573
120572
120573
e
ea
b
c
05
05
Figure 2 Schematic diagram of DSOGI-PLL
instantaneous active and reactive output power of the GCIcan be obtained by using (4) and (5) under both normal andabnormal conditions of the grid
32 Grid Synchronization of GCI The active and reactivepower control of the GCI is based on a synchronous ref-erence frame (SRF) with proportional-integral (PI) or 2D-RFCMANN controllers Moreover it is important to detectthe phase angle of the voltage at PCC in order to synchronizewith the grid during grid faults At present the most popularPLL structure is the synchronous reference frame PLL (SRF-PLL) [14]The input three-phase voltages of the SRF-PLL canbe given by
[
[
V119886
V119887
V119888
]
]
=1003816100381610038161003816119881+1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890minus
2
3120587)
sin(120579119890+
2
3120587)
]]]]]]
]
+1003816100381610038161003816119881minus1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890+
2
3120587)
sin(120579119890minus
2
3120587)
]]]]]]
]
(6)
where |119881+
| and |119881minus
| are the amplitude of the positive andnegative sequence of the three-phase voltage 120579
119890= 120596119890119905 and
120596119890is the utility angular frequency In the SRF-PLL first
the Clarke transformation is applied to transfer the three-phase voltages from the 119886119887119888 natural reference frame to the 120572120573
stationary reference frame [14 15] V120572and V120573are the voltages
of 120572 120573 axis which can be expressed as
[V120572
V120573
] = radic2
3
[[[
[
3
20
radic3
2radic3
]]]
]
[V119886
V119887
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890)
minus cos (120579119890)] + radic
3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890)
cos (120579119890)]
(7)
Then (7) can be expressed in the synchronous referenceframe by using Park transformation in the following [15]
[V119889
V119902
] = [
[
cos (120579119890) sin (120579
119890)
minus sin (120579119890) cos (120579
119890)
]
]
[V120572
V120573
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890minus 120579119890)
minus cos (120579119890minus 120579119890)]
+ radic3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890minus 120579119890)
cos (120579119890minus 120579119890)] (8)
where V119889 V119902are the voltages of the 119889119902 axis 120579
119890= 119890119905 and
119890is the angular frequency of the 119889119902 synchronous reference
frame Suppose that 120579119890is close to 120579
119890 then sin(120579
119890minus 120579119890) is
approximately equal to 120579119890minus 120579119890 and V
119889is approximately equal
to (radic62)[|119881+
|(120579119890minus120579119890)+|119881minus
| sin(2120579119890)]The negative sequence
component voltage of V119889can be filtered by using a properly
designed low pass filterThe difference between 120579119890and 120579119890will
approach zero due to the closed-loop control of 120579119890that makes
V119889approach zero Therefore with 120579
119890asymp 120579119890in steady state the
phase angle detected by the SRF-PLL will be in phase withthe input voltage vector However the dynamic behavior ofthe SRF-PLL will become poor under asymmetric grid faults[15] In order to overcome this disadvantage of SRF-PLL adual second-order generalized integrator PLL (DSOGI-PLL)based on the extraction of the positive sequence has beenproposed in [10 14 15] Define k+
120572120573= [V+120572
V+120573]119879
as the positivesequence voltage vector on the 120572120573 reference frame and it canbe calculated as [10]
k+120572120573
=1
2[1 minus119902
119902 1][
[
V1015840120572
V1015840120573
]
]
(9)
where 119902 = 119890minus1198951205872 is a phase-shift operator in the time domain
V1015840120572and V1015840120573are the filtered voltages of V
120572and V120573 respectively
The schematic diagram of DSOGI-PLL is shown in Figure 2where the dual second-order generalized integrator (SOGI)in Figure 2 is used to generate V1015840
120572 V1015840120573 and in-quadrature
voltages 119902V1015840120572and 119902V1015840
120573of V1015840120572and V1015840
120573 Furthermore V+
119889and V+
119902
which are depicted in Figure 2 are the positive sequencevoltages on the 119889119902 synchronous reference frame In additiona voltage-controlled oscillator (VCO) is employed to convertthe input voltage into
119890 Finally 120579
119890is successfully obtained
by DSOGI-PLL by using the positive sequence voltagesAccording to [15] the instantaneous active and reactive
power outputs of the GCI can be calculated by using the
International Journal of Photoenergy 5
voltage and current in the 119889119902 synchronous reference frameas follows
119876 =3
2(V119902119894119889minus V119889119894119902) 119875 =
3
2(V119889119894119889+ V119902119894119902) (10)
where 119894119889and 119894119902are the currents of the 119889 119902 axis As mentioned
above an adequate tracking of the grid angular position ofthe SRF-PLL will make V
119889approach zeroThus the active and
reactive power outputs of the GCI can be represented as
119876 =3
2V119902119894119889 119875 =
3
2V119902119894119902 (11)
Accordingly 119875 and 119876 can be regulated by controlling 119894119902and
119894119889
33 Reactive and Active Power Control during Grid FaultsThe positive sequence voltages of the three-phase line volt-ages V+
119886119887 V+119887119888 and V+
119888119886can be expressed as follows
[[[[
[
V+119886119887
V+119887119888
V+119888119886
]]]]
]
=1
3
[
[
1 119886 1198862
1198862
1 119886
119886 1198862
1
]
]
[
[
V119886119887
V119887119888
V119888119886
]
]
= radic21003816100381610038161003816119881+
119897
1003816100381610038161003816
[[[[[[
[
sin 120579119890
sin(120579119890minus
2120587
3)
sin(120579119890+
2120587
3)
]]]]]]
]
(12)
where |119881+
119897| is the rms value of the magnitude of the positive
sequence voltage of the three-phase line voltages and theoperator 119886 is equal to 119890
11989521205873 Since V+119886119887 V+119887119888 and V+
119888119886are
symmetric and balanced |119881+119897| can be expressed as
1003816100381610038161003816119881+
119897
1003816100381610038161003816 = radic1
3(V+119886119887
2
+ V+119887119888
2
+ V+119888119886
2
) (13)
Note that V+119886119887 V+119887119888 and V+
119888119886are equal to the magnitude of the
three-phase line voltages when the line voltages are balancedAccording to (12) if the line voltages are unbalanced V+
119886119887
V+119887119888 and V+
119888119886will be changed with the degree of unbalance
Therefore |119881+
119897| is adopted to evaluate the depth of voltage sag
119881sag during grid faults in this study The required percentageof compensation reactive current 119868
lowast
119903during grid faults for
LVRT can be expressed as a function of 119881sag [8]
119868lowast
119903=
0 where 119881sag lt 01
200119881sag where 01 lt 119881sag le 05
100 where 119881sag gt 05
(14)
and 119881sag is defined as follows
119881sag equiv 1 minus
1003816100381610038161003816119881+
119897
1003816100381610038161003816
119881basepu (15)
where119881base is the base value of voltage which equals 110 Vrmsin this study The grid regulation by EON demands reactivecurrent injection during fault condition to support the gridstability when 119881sag is greater than 01 pu Moreover theapparent output power of GCI will be changed due to thevoltage sag at PCC under grid faultsTherefore it is necessaryto calculate the maximum allowable apparent power in orderto decide the maximum injection reactive and active powerThe maximum apparent power 119878 can be expressed as
119878 = (1003816100381610038161003816V119886
1003816100381610038161003816rms +1003816100381610038161003816V119887
1003816100381610038161003816rms +1003816100381610038161003816V119888
1003816100381610038161003816rms) 119868max (16)
where 119868max is the rms value of the GCI current limit and|V119886|rms |V119887|rms and |V
119888|rms are the rms values of V
119886 V119887 and V
119888
respectively Thus the required injection reactive power 119876lowast
and the allowable maximum output active power 119875lowast of GCI
as follows can be derived from (14) and (16)
119876lowast
= 119878119868lowast
119903 119875
lowast
= 119878radic1 minus 119868lowast2119903
(17)
A PV system should inject a certain reactive power inorder to support the voltage sag at the PCC according to theLVRT requirements during grid faults If 119875lowast is greater than 119875then the active power reference 119875ref is set to equal the valueof 119875 before the grid faults Therefore all the power generatedby the PV panel can be totally delivered into the grid duringgrid faults and the MPPT control can be operated to keeptracking the MPP On the other hand if 119875
lowast is smaller than119875 then 119875ref is set to 119875
lowast Thus the output active power will becontrolled to follow 119875ref and the GCI gives up tracking theMPPConsequently the power balance between119875pv and119875 canbe held during grid faults
4 D-RFCMANN Control Scheme
41 Description of 2D-RFCMANN The structure of 2D-RFCMANN with 2 inputs and 1 output is depicted inFigure 3(a) which consists of five spaces input space fuzzi-fication space receptive-field space weight space and outspace Moreover one of the fuzzy if-then rules of the pro-posed 2D-RFCMANN is realized as follows
119877119894
11989511198952
If 1199091is 11989111198941198951
and 1199092is 11989121198941198952
then
11991011989411989511198952
= 11990811989411989511198952
for 119894 = 1 2 119899119894
1198951 1198952= 1 2 119899
119895
(18)
where 119899119894
= 3 is the number of the layers for each inputdimension 119899
119895= 4 is the number of blocks for each layer
11989111198941198951
is the fuzzy set for the first input 119894th layer and 1198951th
block 11989121198941198952
is the fuzzy set for the second input 119894th layerand 1198952th block 119908
11989411989511198952
is the corresponding output weight inthe consequent part Furthermore the signal propagation andthe basic function in each space of the 2D-RFCMANN areintroduced as follows
Space 1 (input space) In this space the input variables 1199091
and 1199092are both divided into 119899
119890regions (which are called
ldquoelementsrdquo)Thenumber of 119899119890represents the input resolution
6 International Journal of Photoenergy
Input space
Fuzzification space
Receptive-fieldSpace
Recurrent unit
x1
x2
f1ij1
f2ij2
fpijp
rpijp
sum
xp
zminus1
y2pijp
Output space
y5o
h111
h121
w111
w121
hij1j2
hn119894n119895n119895
wij1j2
wn119894n119895n119895
Weight space
(a) Structure of 2D-RFCMANN
S1
S1
S2
S2
S3
S3
S4
S4
S5
S5
S6
S6
S7
S7
S8
S8
S9
S9
S10
S10
f111
f111
f211f221
f231
f121
f131
f212
f112
f212
f222
f232
f122
f132
f113
f123
f213
f223
f233
f133
f114
f214f224
f234
f124
f134
H1
H2
H3
Layer 1 Layer 1
Layer 2
Layer 2
Layer 3
Layer 3
x2
x1
(3 5)
(b) 2D-RFCMANN with 119901 = 2 119899119894= 3 and 119899
119895= 4 and its configuration of receptive-field space
activated by state (3 5)
Figure 3 Two-dimensional RFCMANN
For example a 2D-RFMANN with 119899119890
= 10 is shown as inFigure 3(b)
Space 2 (fuzzification space) According to the concept ofCMANN several elements can be accumulated as a block
In this space each block performs a Gaussian receptive-field basis function The fuzzification of the correspondingmembership function in the 2D-RFCMANN is realizedby the Gaussian basis function which can be expressedas
International Journal of Photoenergy 7
DC
AC
Current controlled
PWMPC-based control system
L SSR
Instantaneous active and
reactive power calculation
dqabc
LimiterLimiter
3-phase grid
Grid fault signal
Y
110220
PI22D-RFCMANN2
Three-phaseGCI
MPPT
SW1
PI12D-RFCMANN1
+
P
Q
Q
PV panel
DSOGI-PLL
calculation
Active and reactive power
references calculation
P
+
SW20
+
ia ib ic
ia
ib
ic
ilowasta
ilowastq
ilowastb ilowastc
ilowastd
ab bc ca
ab
bc ca
radic31 2
Vpv
Vsag
Vsag
Cpv
Vpv
VpvI pv
100Ω
Imax
Δminus
minus
minus
minus
minus
minus
minus
e
Pre fPre f
Qlowast
++
+
+
+ Vlowastpv
Y-Δ
Figure 4 Schematic diagram of PC-based control system
119891119901119894119895119901(119873) = exp(minus
(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205902
119901119894119895119901
)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
1199102
119901119894119895119901
(119873) = 119909119901(119873) + 119903
119901119894119895119901
119891119901119894119895119901(119873 minus 1)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
(19)
where 119891119901119894119895119901
(119873) is the output of the 119895119901th block of the 119894th layer
of the 119901th input variable 119898119901119894119895119901
and 120590119901119894119895119901
are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901
represents the recurrent weight of the 119895119901th block of the
119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891
119901119894119895119901
(119873 minus 1) represents the valueof 119891119901119894119895119901
(119873) through time delay Note that the memory term119891119901119894119895119901
(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer
Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903
119901119894119895119901
119898119901119894119895119901
and 120590119901119894119895119901
Themultidimensional receptive-field function is defined as
ℎ11989411989511198952(119873) = 119891
11198941198951(119873) 11989121198941198952(119873)
= exp(minus
(1199102
11198941198951
(119873) minus 11989811198941198951
)2
1205902
11198941198951
)
times exp(minus
(1199102
21198941198952
(119873) minus 11989821198941198952
)2
1205902
21198941198952
)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(20)
where ℎ11989411989511198952
(119873) is associated with the ith layer and the 1198951th
block for input 1199091and the 119895
2th block for input 119909
2according
to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891
111119891211
119891112
119891211
and so forth are called receptive fields (or hypercube)
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
4 International Journal of Photoenergy
abc ++
+
dq
VCOPI
Low pass filter
SOGIBP filter
SOGIBP filter
v+d
v+q
120579e
120579e
SRF-PLL
1
sminus
120572120573
120572120573998400120572
q998400120572
q998400120573
998400120573
+120572
+120573
120572
120573
e
ea
b
c
05
05
Figure 2 Schematic diagram of DSOGI-PLL
instantaneous active and reactive output power of the GCIcan be obtained by using (4) and (5) under both normal andabnormal conditions of the grid
32 Grid Synchronization of GCI The active and reactivepower control of the GCI is based on a synchronous ref-erence frame (SRF) with proportional-integral (PI) or 2D-RFCMANN controllers Moreover it is important to detectthe phase angle of the voltage at PCC in order to synchronizewith the grid during grid faults At present the most popularPLL structure is the synchronous reference frame PLL (SRF-PLL) [14]The input three-phase voltages of the SRF-PLL canbe given by
[
[
V119886
V119887
V119888
]
]
=1003816100381610038161003816119881+1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890minus
2
3120587)
sin(120579119890+
2
3120587)
]]]]]]
]
+1003816100381610038161003816119881minus1003816100381610038161003816
[[[[[[
[
sin (120579119890)
sin(120579119890+
2
3120587)
sin(120579119890minus
2
3120587)
]]]]]]
]
(6)
where |119881+
| and |119881minus
| are the amplitude of the positive andnegative sequence of the three-phase voltage 120579
119890= 120596119890119905 and
120596119890is the utility angular frequency In the SRF-PLL first
the Clarke transformation is applied to transfer the three-phase voltages from the 119886119887119888 natural reference frame to the 120572120573
stationary reference frame [14 15] V120572and V120573are the voltages
of 120572 120573 axis which can be expressed as
[V120572
V120573
] = radic2
3
[[[
[
3
20
radic3
2radic3
]]]
]
[V119886
V119887
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890)
minus cos (120579119890)] + radic
3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890)
cos (120579119890)]
(7)
Then (7) can be expressed in the synchronous referenceframe by using Park transformation in the following [15]
[V119889
V119902
] = [
[
cos (120579119890) sin (120579
119890)
minus sin (120579119890) cos (120579
119890)
]
]
[V120572
V120573
]
= radic3
2
1003816100381610038161003816119881+1003816100381610038161003816 [
sin (120579119890minus 120579119890)
minus cos (120579119890minus 120579119890)]
+ radic3
2
1003816100381610038161003816119881minus1003816100381610038161003816 [
sin (120579119890minus 120579119890)
cos (120579119890minus 120579119890)] (8)
where V119889 V119902are the voltages of the 119889119902 axis 120579
119890= 119890119905 and
119890is the angular frequency of the 119889119902 synchronous reference
frame Suppose that 120579119890is close to 120579
119890 then sin(120579
119890minus 120579119890) is
approximately equal to 120579119890minus 120579119890 and V
119889is approximately equal
to (radic62)[|119881+
|(120579119890minus120579119890)+|119881minus
| sin(2120579119890)]The negative sequence
component voltage of V119889can be filtered by using a properly
designed low pass filterThe difference between 120579119890and 120579119890will
approach zero due to the closed-loop control of 120579119890that makes
V119889approach zero Therefore with 120579
119890asymp 120579119890in steady state the
phase angle detected by the SRF-PLL will be in phase withthe input voltage vector However the dynamic behavior ofthe SRF-PLL will become poor under asymmetric grid faults[15] In order to overcome this disadvantage of SRF-PLL adual second-order generalized integrator PLL (DSOGI-PLL)based on the extraction of the positive sequence has beenproposed in [10 14 15] Define k+
120572120573= [V+120572
V+120573]119879
as the positivesequence voltage vector on the 120572120573 reference frame and it canbe calculated as [10]
k+120572120573
=1
2[1 minus119902
119902 1][
[
V1015840120572
V1015840120573
]
]
(9)
where 119902 = 119890minus1198951205872 is a phase-shift operator in the time domain
V1015840120572and V1015840120573are the filtered voltages of V
120572and V120573 respectively
The schematic diagram of DSOGI-PLL is shown in Figure 2where the dual second-order generalized integrator (SOGI)in Figure 2 is used to generate V1015840
120572 V1015840120573 and in-quadrature
voltages 119902V1015840120572and 119902V1015840
120573of V1015840120572and V1015840
120573 Furthermore V+
119889and V+
119902
which are depicted in Figure 2 are the positive sequencevoltages on the 119889119902 synchronous reference frame In additiona voltage-controlled oscillator (VCO) is employed to convertthe input voltage into
119890 Finally 120579
119890is successfully obtained
by DSOGI-PLL by using the positive sequence voltagesAccording to [15] the instantaneous active and reactive
power outputs of the GCI can be calculated by using the
International Journal of Photoenergy 5
voltage and current in the 119889119902 synchronous reference frameas follows
119876 =3
2(V119902119894119889minus V119889119894119902) 119875 =
3
2(V119889119894119889+ V119902119894119902) (10)
where 119894119889and 119894119902are the currents of the 119889 119902 axis As mentioned
above an adequate tracking of the grid angular position ofthe SRF-PLL will make V
119889approach zeroThus the active and
reactive power outputs of the GCI can be represented as
119876 =3
2V119902119894119889 119875 =
3
2V119902119894119902 (11)
Accordingly 119875 and 119876 can be regulated by controlling 119894119902and
119894119889
33 Reactive and Active Power Control during Grid FaultsThe positive sequence voltages of the three-phase line volt-ages V+
119886119887 V+119887119888 and V+
119888119886can be expressed as follows
[[[[
[
V+119886119887
V+119887119888
V+119888119886
]]]]
]
=1
3
[
[
1 119886 1198862
1198862
1 119886
119886 1198862
1
]
]
[
[
V119886119887
V119887119888
V119888119886
]
]
= radic21003816100381610038161003816119881+
119897
1003816100381610038161003816
[[[[[[
[
sin 120579119890
sin(120579119890minus
2120587
3)
sin(120579119890+
2120587
3)
]]]]]]
]
(12)
where |119881+
119897| is the rms value of the magnitude of the positive
sequence voltage of the three-phase line voltages and theoperator 119886 is equal to 119890
11989521205873 Since V+119886119887 V+119887119888 and V+
119888119886are
symmetric and balanced |119881+119897| can be expressed as
1003816100381610038161003816119881+
119897
1003816100381610038161003816 = radic1
3(V+119886119887
2
+ V+119887119888
2
+ V+119888119886
2
) (13)
Note that V+119886119887 V+119887119888 and V+
119888119886are equal to the magnitude of the
three-phase line voltages when the line voltages are balancedAccording to (12) if the line voltages are unbalanced V+
119886119887
V+119887119888 and V+
119888119886will be changed with the degree of unbalance
Therefore |119881+
119897| is adopted to evaluate the depth of voltage sag
119881sag during grid faults in this study The required percentageof compensation reactive current 119868
lowast
119903during grid faults for
LVRT can be expressed as a function of 119881sag [8]
119868lowast
119903=
0 where 119881sag lt 01
200119881sag where 01 lt 119881sag le 05
100 where 119881sag gt 05
(14)
and 119881sag is defined as follows
119881sag equiv 1 minus
1003816100381610038161003816119881+
119897
1003816100381610038161003816
119881basepu (15)
where119881base is the base value of voltage which equals 110 Vrmsin this study The grid regulation by EON demands reactivecurrent injection during fault condition to support the gridstability when 119881sag is greater than 01 pu Moreover theapparent output power of GCI will be changed due to thevoltage sag at PCC under grid faultsTherefore it is necessaryto calculate the maximum allowable apparent power in orderto decide the maximum injection reactive and active powerThe maximum apparent power 119878 can be expressed as
119878 = (1003816100381610038161003816V119886
1003816100381610038161003816rms +1003816100381610038161003816V119887
1003816100381610038161003816rms +1003816100381610038161003816V119888
1003816100381610038161003816rms) 119868max (16)
where 119868max is the rms value of the GCI current limit and|V119886|rms |V119887|rms and |V
119888|rms are the rms values of V
119886 V119887 and V
119888
respectively Thus the required injection reactive power 119876lowast
and the allowable maximum output active power 119875lowast of GCI
as follows can be derived from (14) and (16)
119876lowast
= 119878119868lowast
119903 119875
lowast
= 119878radic1 minus 119868lowast2119903
(17)
A PV system should inject a certain reactive power inorder to support the voltage sag at the PCC according to theLVRT requirements during grid faults If 119875lowast is greater than 119875then the active power reference 119875ref is set to equal the valueof 119875 before the grid faults Therefore all the power generatedby the PV panel can be totally delivered into the grid duringgrid faults and the MPPT control can be operated to keeptracking the MPP On the other hand if 119875
lowast is smaller than119875 then 119875ref is set to 119875
lowast Thus the output active power will becontrolled to follow 119875ref and the GCI gives up tracking theMPPConsequently the power balance between119875pv and119875 canbe held during grid faults
4 D-RFCMANN Control Scheme
41 Description of 2D-RFCMANN The structure of 2D-RFCMANN with 2 inputs and 1 output is depicted inFigure 3(a) which consists of five spaces input space fuzzi-fication space receptive-field space weight space and outspace Moreover one of the fuzzy if-then rules of the pro-posed 2D-RFCMANN is realized as follows
119877119894
11989511198952
If 1199091is 11989111198941198951
and 1199092is 11989121198941198952
then
11991011989411989511198952
= 11990811989411989511198952
for 119894 = 1 2 119899119894
1198951 1198952= 1 2 119899
119895
(18)
where 119899119894
= 3 is the number of the layers for each inputdimension 119899
119895= 4 is the number of blocks for each layer
11989111198941198951
is the fuzzy set for the first input 119894th layer and 1198951th
block 11989121198941198952
is the fuzzy set for the second input 119894th layerand 1198952th block 119908
11989411989511198952
is the corresponding output weight inthe consequent part Furthermore the signal propagation andthe basic function in each space of the 2D-RFCMANN areintroduced as follows
Space 1 (input space) In this space the input variables 1199091
and 1199092are both divided into 119899
119890regions (which are called
ldquoelementsrdquo)Thenumber of 119899119890represents the input resolution
6 International Journal of Photoenergy
Input space
Fuzzification space
Receptive-fieldSpace
Recurrent unit
x1
x2
f1ij1
f2ij2
fpijp
rpijp
sum
xp
zminus1
y2pijp
Output space
y5o
h111
h121
w111
w121
hij1j2
hn119894n119895n119895
wij1j2
wn119894n119895n119895
Weight space
(a) Structure of 2D-RFCMANN
S1
S1
S2
S2
S3
S3
S4
S4
S5
S5
S6
S6
S7
S7
S8
S8
S9
S9
S10
S10
f111
f111
f211f221
f231
f121
f131
f212
f112
f212
f222
f232
f122
f132
f113
f123
f213
f223
f233
f133
f114
f214f224
f234
f124
f134
H1
H2
H3
Layer 1 Layer 1
Layer 2
Layer 2
Layer 3
Layer 3
x2
x1
(3 5)
(b) 2D-RFCMANN with 119901 = 2 119899119894= 3 and 119899
119895= 4 and its configuration of receptive-field space
activated by state (3 5)
Figure 3 Two-dimensional RFCMANN
For example a 2D-RFMANN with 119899119890
= 10 is shown as inFigure 3(b)
Space 2 (fuzzification space) According to the concept ofCMANN several elements can be accumulated as a block
In this space each block performs a Gaussian receptive-field basis function The fuzzification of the correspondingmembership function in the 2D-RFCMANN is realizedby the Gaussian basis function which can be expressedas
International Journal of Photoenergy 7
DC
AC
Current controlled
PWMPC-based control system
L SSR
Instantaneous active and
reactive power calculation
dqabc
LimiterLimiter
3-phase grid
Grid fault signal
Y
110220
PI22D-RFCMANN2
Three-phaseGCI
MPPT
SW1
PI12D-RFCMANN1
+
P
Q
Q
PV panel
DSOGI-PLL
calculation
Active and reactive power
references calculation
P
+
SW20
+
ia ib ic
ia
ib
ic
ilowasta
ilowastq
ilowastb ilowastc
ilowastd
ab bc ca
ab
bc ca
radic31 2
Vpv
Vsag
Vsag
Cpv
Vpv
VpvI pv
100Ω
Imax
Δminus
minus
minus
minus
minus
minus
minus
e
Pre fPre f
Qlowast
++
+
+
+ Vlowastpv
Y-Δ
Figure 4 Schematic diagram of PC-based control system
119891119901119894119895119901(119873) = exp(minus
(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205902
119901119894119895119901
)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
1199102
119901119894119895119901
(119873) = 119909119901(119873) + 119903
119901119894119895119901
119891119901119894119895119901(119873 minus 1)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
(19)
where 119891119901119894119895119901
(119873) is the output of the 119895119901th block of the 119894th layer
of the 119901th input variable 119898119901119894119895119901
and 120590119901119894119895119901
are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901
represents the recurrent weight of the 119895119901th block of the
119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891
119901119894119895119901
(119873 minus 1) represents the valueof 119891119901119894119895119901
(119873) through time delay Note that the memory term119891119901119894119895119901
(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer
Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903
119901119894119895119901
119898119901119894119895119901
and 120590119901119894119895119901
Themultidimensional receptive-field function is defined as
ℎ11989411989511198952(119873) = 119891
11198941198951(119873) 11989121198941198952(119873)
= exp(minus
(1199102
11198941198951
(119873) minus 11989811198941198951
)2
1205902
11198941198951
)
times exp(minus
(1199102
21198941198952
(119873) minus 11989821198941198952
)2
1205902
21198941198952
)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(20)
where ℎ11989411989511198952
(119873) is associated with the ith layer and the 1198951th
block for input 1199091and the 119895
2th block for input 119909
2according
to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891
111119891211
119891112
119891211
and so forth are called receptive fields (or hypercube)
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 5
voltage and current in the 119889119902 synchronous reference frameas follows
119876 =3
2(V119902119894119889minus V119889119894119902) 119875 =
3
2(V119889119894119889+ V119902119894119902) (10)
where 119894119889and 119894119902are the currents of the 119889 119902 axis As mentioned
above an adequate tracking of the grid angular position ofthe SRF-PLL will make V
119889approach zeroThus the active and
reactive power outputs of the GCI can be represented as
119876 =3
2V119902119894119889 119875 =
3
2V119902119894119902 (11)
Accordingly 119875 and 119876 can be regulated by controlling 119894119902and
119894119889
33 Reactive and Active Power Control during Grid FaultsThe positive sequence voltages of the three-phase line volt-ages V+
119886119887 V+119887119888 and V+
119888119886can be expressed as follows
[[[[
[
V+119886119887
V+119887119888
V+119888119886
]]]]
]
=1
3
[
[
1 119886 1198862
1198862
1 119886
119886 1198862
1
]
]
[
[
V119886119887
V119887119888
V119888119886
]
]
= radic21003816100381610038161003816119881+
119897
1003816100381610038161003816
[[[[[[
[
sin 120579119890
sin(120579119890minus
2120587
3)
sin(120579119890+
2120587
3)
]]]]]]
]
(12)
where |119881+
119897| is the rms value of the magnitude of the positive
sequence voltage of the three-phase line voltages and theoperator 119886 is equal to 119890
11989521205873 Since V+119886119887 V+119887119888 and V+
119888119886are
symmetric and balanced |119881+119897| can be expressed as
1003816100381610038161003816119881+
119897
1003816100381610038161003816 = radic1
3(V+119886119887
2
+ V+119887119888
2
+ V+119888119886
2
) (13)
Note that V+119886119887 V+119887119888 and V+
119888119886are equal to the magnitude of the
three-phase line voltages when the line voltages are balancedAccording to (12) if the line voltages are unbalanced V+
119886119887
V+119887119888 and V+
119888119886will be changed with the degree of unbalance
Therefore |119881+
119897| is adopted to evaluate the depth of voltage sag
119881sag during grid faults in this study The required percentageof compensation reactive current 119868
lowast
119903during grid faults for
LVRT can be expressed as a function of 119881sag [8]
119868lowast
119903=
0 where 119881sag lt 01
200119881sag where 01 lt 119881sag le 05
100 where 119881sag gt 05
(14)
and 119881sag is defined as follows
119881sag equiv 1 minus
1003816100381610038161003816119881+
119897
1003816100381610038161003816
119881basepu (15)
where119881base is the base value of voltage which equals 110 Vrmsin this study The grid regulation by EON demands reactivecurrent injection during fault condition to support the gridstability when 119881sag is greater than 01 pu Moreover theapparent output power of GCI will be changed due to thevoltage sag at PCC under grid faultsTherefore it is necessaryto calculate the maximum allowable apparent power in orderto decide the maximum injection reactive and active powerThe maximum apparent power 119878 can be expressed as
119878 = (1003816100381610038161003816V119886
1003816100381610038161003816rms +1003816100381610038161003816V119887
1003816100381610038161003816rms +1003816100381610038161003816V119888
1003816100381610038161003816rms) 119868max (16)
where 119868max is the rms value of the GCI current limit and|V119886|rms |V119887|rms and |V
119888|rms are the rms values of V
119886 V119887 and V
119888
respectively Thus the required injection reactive power 119876lowast
and the allowable maximum output active power 119875lowast of GCI
as follows can be derived from (14) and (16)
119876lowast
= 119878119868lowast
119903 119875
lowast
= 119878radic1 minus 119868lowast2119903
(17)
A PV system should inject a certain reactive power inorder to support the voltage sag at the PCC according to theLVRT requirements during grid faults If 119875lowast is greater than 119875then the active power reference 119875ref is set to equal the valueof 119875 before the grid faults Therefore all the power generatedby the PV panel can be totally delivered into the grid duringgrid faults and the MPPT control can be operated to keeptracking the MPP On the other hand if 119875
lowast is smaller than119875 then 119875ref is set to 119875
lowast Thus the output active power will becontrolled to follow 119875ref and the GCI gives up tracking theMPPConsequently the power balance between119875pv and119875 canbe held during grid faults
4 D-RFCMANN Control Scheme
41 Description of 2D-RFCMANN The structure of 2D-RFCMANN with 2 inputs and 1 output is depicted inFigure 3(a) which consists of five spaces input space fuzzi-fication space receptive-field space weight space and outspace Moreover one of the fuzzy if-then rules of the pro-posed 2D-RFCMANN is realized as follows
119877119894
11989511198952
If 1199091is 11989111198941198951
and 1199092is 11989121198941198952
then
11991011989411989511198952
= 11990811989411989511198952
for 119894 = 1 2 119899119894
1198951 1198952= 1 2 119899
119895
(18)
where 119899119894
= 3 is the number of the layers for each inputdimension 119899
119895= 4 is the number of blocks for each layer
11989111198941198951
is the fuzzy set for the first input 119894th layer and 1198951th
block 11989121198941198952
is the fuzzy set for the second input 119894th layerand 1198952th block 119908
11989411989511198952
is the corresponding output weight inthe consequent part Furthermore the signal propagation andthe basic function in each space of the 2D-RFCMANN areintroduced as follows
Space 1 (input space) In this space the input variables 1199091
and 1199092are both divided into 119899
119890regions (which are called
ldquoelementsrdquo)Thenumber of 119899119890represents the input resolution
6 International Journal of Photoenergy
Input space
Fuzzification space
Receptive-fieldSpace
Recurrent unit
x1
x2
f1ij1
f2ij2
fpijp
rpijp
sum
xp
zminus1
y2pijp
Output space
y5o
h111
h121
w111
w121
hij1j2
hn119894n119895n119895
wij1j2
wn119894n119895n119895
Weight space
(a) Structure of 2D-RFCMANN
S1
S1
S2
S2
S3
S3
S4
S4
S5
S5
S6
S6
S7
S7
S8
S8
S9
S9
S10
S10
f111
f111
f211f221
f231
f121
f131
f212
f112
f212
f222
f232
f122
f132
f113
f123
f213
f223
f233
f133
f114
f214f224
f234
f124
f134
H1
H2
H3
Layer 1 Layer 1
Layer 2
Layer 2
Layer 3
Layer 3
x2
x1
(3 5)
(b) 2D-RFCMANN with 119901 = 2 119899119894= 3 and 119899
119895= 4 and its configuration of receptive-field space
activated by state (3 5)
Figure 3 Two-dimensional RFCMANN
For example a 2D-RFMANN with 119899119890
= 10 is shown as inFigure 3(b)
Space 2 (fuzzification space) According to the concept ofCMANN several elements can be accumulated as a block
In this space each block performs a Gaussian receptive-field basis function The fuzzification of the correspondingmembership function in the 2D-RFCMANN is realizedby the Gaussian basis function which can be expressedas
International Journal of Photoenergy 7
DC
AC
Current controlled
PWMPC-based control system
L SSR
Instantaneous active and
reactive power calculation
dqabc
LimiterLimiter
3-phase grid
Grid fault signal
Y
110220
PI22D-RFCMANN2
Three-phaseGCI
MPPT
SW1
PI12D-RFCMANN1
+
P
Q
Q
PV panel
DSOGI-PLL
calculation
Active and reactive power
references calculation
P
+
SW20
+
ia ib ic
ia
ib
ic
ilowasta
ilowastq
ilowastb ilowastc
ilowastd
ab bc ca
ab
bc ca
radic31 2
Vpv
Vsag
Vsag
Cpv
Vpv
VpvI pv
100Ω
Imax
Δminus
minus
minus
minus
minus
minus
minus
e
Pre fPre f
Qlowast
++
+
+
+ Vlowastpv
Y-Δ
Figure 4 Schematic diagram of PC-based control system
119891119901119894119895119901(119873) = exp(minus
(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205902
119901119894119895119901
)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
1199102
119901119894119895119901
(119873) = 119909119901(119873) + 119903
119901119894119895119901
119891119901119894119895119901(119873 minus 1)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
(19)
where 119891119901119894119895119901
(119873) is the output of the 119895119901th block of the 119894th layer
of the 119901th input variable 119898119901119894119895119901
and 120590119901119894119895119901
are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901
represents the recurrent weight of the 119895119901th block of the
119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891
119901119894119895119901
(119873 minus 1) represents the valueof 119891119901119894119895119901
(119873) through time delay Note that the memory term119891119901119894119895119901
(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer
Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903
119901119894119895119901
119898119901119894119895119901
and 120590119901119894119895119901
Themultidimensional receptive-field function is defined as
ℎ11989411989511198952(119873) = 119891
11198941198951(119873) 11989121198941198952(119873)
= exp(minus
(1199102
11198941198951
(119873) minus 11989811198941198951
)2
1205902
11198941198951
)
times exp(minus
(1199102
21198941198952
(119873) minus 11989821198941198952
)2
1205902
21198941198952
)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(20)
where ℎ11989411989511198952
(119873) is associated with the ith layer and the 1198951th
block for input 1199091and the 119895
2th block for input 119909
2according
to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891
111119891211
119891112
119891211
and so forth are called receptive fields (or hypercube)
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
6 International Journal of Photoenergy
Input space
Fuzzification space
Receptive-fieldSpace
Recurrent unit
x1
x2
f1ij1
f2ij2
fpijp
rpijp
sum
xp
zminus1
y2pijp
Output space
y5o
h111
h121
w111
w121
hij1j2
hn119894n119895n119895
wij1j2
wn119894n119895n119895
Weight space
(a) Structure of 2D-RFCMANN
S1
S1
S2
S2
S3
S3
S4
S4
S5
S5
S6
S6
S7
S7
S8
S8
S9
S9
S10
S10
f111
f111
f211f221
f231
f121
f131
f212
f112
f212
f222
f232
f122
f132
f113
f123
f213
f223
f233
f133
f114
f214f224
f234
f124
f134
H1
H2
H3
Layer 1 Layer 1
Layer 2
Layer 2
Layer 3
Layer 3
x2
x1
(3 5)
(b) 2D-RFCMANN with 119901 = 2 119899119894= 3 and 119899
119895= 4 and its configuration of receptive-field space
activated by state (3 5)
Figure 3 Two-dimensional RFCMANN
For example a 2D-RFMANN with 119899119890
= 10 is shown as inFigure 3(b)
Space 2 (fuzzification space) According to the concept ofCMANN several elements can be accumulated as a block
In this space each block performs a Gaussian receptive-field basis function The fuzzification of the correspondingmembership function in the 2D-RFCMANN is realizedby the Gaussian basis function which can be expressedas
International Journal of Photoenergy 7
DC
AC
Current controlled
PWMPC-based control system
L SSR
Instantaneous active and
reactive power calculation
dqabc
LimiterLimiter
3-phase grid
Grid fault signal
Y
110220
PI22D-RFCMANN2
Three-phaseGCI
MPPT
SW1
PI12D-RFCMANN1
+
P
Q
Q
PV panel
DSOGI-PLL
calculation
Active and reactive power
references calculation
P
+
SW20
+
ia ib ic
ia
ib
ic
ilowasta
ilowastq
ilowastb ilowastc
ilowastd
ab bc ca
ab
bc ca
radic31 2
Vpv
Vsag
Vsag
Cpv
Vpv
VpvI pv
100Ω
Imax
Δminus
minus
minus
minus
minus
minus
minus
e
Pre fPre f
Qlowast
++
+
+
+ Vlowastpv
Y-Δ
Figure 4 Schematic diagram of PC-based control system
119891119901119894119895119901(119873) = exp(minus
(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205902
119901119894119895119901
)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
1199102
119901119894119895119901
(119873) = 119909119901(119873) + 119903
119901119894119895119901
119891119901119894119895119901(119873 minus 1)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
(19)
where 119891119901119894119895119901
(119873) is the output of the 119895119901th block of the 119894th layer
of the 119901th input variable 119898119901119894119895119901
and 120590119901119894119895119901
are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901
represents the recurrent weight of the 119895119901th block of the
119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891
119901119894119895119901
(119873 minus 1) represents the valueof 119891119901119894119895119901
(119873) through time delay Note that the memory term119891119901119894119895119901
(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer
Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903
119901119894119895119901
119898119901119894119895119901
and 120590119901119894119895119901
Themultidimensional receptive-field function is defined as
ℎ11989411989511198952(119873) = 119891
11198941198951(119873) 11989121198941198952(119873)
= exp(minus
(1199102
11198941198951
(119873) minus 11989811198941198951
)2
1205902
11198941198951
)
times exp(minus
(1199102
21198941198952
(119873) minus 11989821198941198952
)2
1205902
21198941198952
)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(20)
where ℎ11989411989511198952
(119873) is associated with the ith layer and the 1198951th
block for input 1199091and the 119895
2th block for input 119909
2according
to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891
111119891211
119891112
119891211
and so forth are called receptive fields (or hypercube)
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 7
DC
AC
Current controlled
PWMPC-based control system
L SSR
Instantaneous active and
reactive power calculation
dqabc
LimiterLimiter
3-phase grid
Grid fault signal
Y
110220
PI22D-RFCMANN2
Three-phaseGCI
MPPT
SW1
PI12D-RFCMANN1
+
P
Q
Q
PV panel
DSOGI-PLL
calculation
Active and reactive power
references calculation
P
+
SW20
+
ia ib ic
ia
ib
ic
ilowasta
ilowastq
ilowastb ilowastc
ilowastd
ab bc ca
ab
bc ca
radic31 2
Vpv
Vsag
Vsag
Cpv
Vpv
VpvI pv
100Ω
Imax
Δminus
minus
minus
minus
minus
minus
minus
e
Pre fPre f
Qlowast
++
+
+
+ Vlowastpv
Y-Δ
Figure 4 Schematic diagram of PC-based control system
119891119901119894119895119901(119873) = exp(minus
(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205902
119901119894119895119901
)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
1199102
119901119894119895119901
(119873) = 119909119901(119873) + 119903
119901119894119895119901
119891119901119894119895119901(119873 minus 1)
119901 = 1 2 119894 = 1 2 119899119894 119895119901
= 1 2 119899119895
(19)
where 119891119901119894119895119901
(119873) is the output of the 119895119901th block of the 119894th layer
of the 119901th input variable 119898119901119894119895119901
and 120590119901119894119895119901
are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901
represents the recurrent weight of the 119895119901th block of the
119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891
119901119894119895119901
(119873 minus 1) represents the valueof 119891119901119894119895119901
(119873) through time delay Note that the memory term119891119901119894119895119901
(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer
Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903
119901119894119895119901
119898119901119894119895119901
and 120590119901119894119895119901
Themultidimensional receptive-field function is defined as
ℎ11989411989511198952(119873) = 119891
11198941198951(119873) 11989121198941198952(119873)
= exp(minus
(1199102
11198941198951
(119873) minus 11989811198941198951
)2
1205902
11198941198951
)
times exp(minus
(1199102
21198941198952
(119873) minus 11989821198941198952
)2
1205902
21198941198952
)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(20)
where ℎ11989411989511198952
(119873) is associated with the ith layer and the 1198951th
block for input 1199091and the 119895
2th block for input 119909
2according
to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891
111119891211
119891112
119891211
and so forth are called receptive fields (or hypercube)
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
8 International Journal of Photoenergy
Moreover the number of receptive fields is equal to 1198992
119895in each
layer
Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as
1199104
11989411989511198952
(119873) = 11990811989411989511198952(119873)
119894 = 1 2 119899119894 1198951 1198952= 1 2 119899
119895
(21)
where 1199104
11989411989511198952
(119873) is the output of the weight memory corre-sponding to ℎ
11989411989511198952
(119873) and 11990811989411989511198952
(119873) denotes the connectingweight value of the output associated with the 119895
1th block of
1199091and the 119895
2th block of 119909
1in the ith layer
Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field
1199105
119900(119873) =
119899119894
sum
119894=1
1199105
11989411989511198952
(119873)
1199105
11989411989511198952
(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)
(22)
where 1199105
11989411989511198952
(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105
119900= 119894lowast
119902
for the active power control and1199105
119900= 119894lowast
119889for the reactive power
control in the GCIAn example is demonstrated to show the relation between
2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867
1=
119891111
119891212
1198672
= 119891122
119891222
and 1198673
= 119891132
119891233
Each hypercubeof the reception-field space is subject to the respectiveweights119908112
119908222
and 119908323
in the weight space
42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as
119864 (119873) =1
2(119910lowast
(119873) minus 119910 (119873))2
=1
21198902
(119873) (23)
where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast
(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows
Space 5The error term to be propagated is given by
1205755
119900= minus
120597119864
1205971199105119900(119873)
= minus120597119864 (119873)
120597119910
120597119910
1205971199105119900(119873)
= 119890 (119873)120597119910
1205971199105119900(119873)
(24)
The weights are updated by the amount
Δ11990811989411989511198952(119873) = minus120578
1
120597119864
12059711990811989411989511198952(119873)
= minus1205781
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
12059711990811989411989511198952(119873)
= 12057811205755
119900ℎ11989411989511198952(119873)
(25)
where the factor 1205781is the learning rate of memory weights
11990811989411989511198952
is updated according to the following equation
11990811989411989511198952(119873 + 1) = 119908
11989411989511198952(119873) + Δ119908
11989411989511198952(119873) (26)
Space 2 Applying the chain rule the update laws for 119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are
Δ119898119901119894119895119901(119873) = minus120578
2
120597119864
120597119898119901119894119895119901
= minus1205782
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119898119901119894119895119901
= 12057821205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
Δ120590119901119894119895119901(119873) = minus120578
3
120597119864
120597120590119901119894119895119901
= minus1205783
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597120590119901119894119895119901
= 12057831205755
1199001199105
11989411989511198952
(119873)
2(1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
2
1205903
119901119894119895119901
Δ119903119901119894119895119901(119873) = minus120578
4
120597119864
120597119903119901119894119895119901
= minus1205784
120597119864
1205971199105119900(119873)
1205971199105
119900(119873)
120597119903119901119894119895119901
= 12057841205755
1199001199105
11989411989511198952
(119873)
2 (1199102
119901119894119895119901
(119873) minus 119898119901119894119895119901
)
1205902
119901119894119895119901
times 1198911119894119895119901(119873 minus 1)
(27)
where the factors 1205782 1205783 and 120578
4are the learning rates
119898119901119894119895119901
120590119901119894119895119901
and 119903119901119894119895119901
are updated according to the followingequation
119898119901119894119895119901(119873 + 1) = 119898
119901119894119895119901(119873) + Δ119898
119901119894119895119901(119873)
120590119901119894119895119901(119873 + 1) = 120590
119901119894119895119901(119873) + Δ120590
119901119894119895119901(119873)
119903119901119894119895119901(119873 + 1) = 119903
119901119894119895119901(119873) + Δ119903
119901119894119895119901(119873)
(28)
Moreover the exact calculation of the Jacobian of the system120597119910120597119910
5
119900(119873) is difficult to be determined due to the unknown
dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]
1205755
119900cong (119910lowast
minus 119910) + ( 119910lowast
minus 119910) = 119890 + 119890 (29)
where 119910lowast and 119910 represent the first derivatives of 119910
lowast and 119910respectively Furthermore the selection of the values of the
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 9
0
Irradiance change
10V1A
0
Irradiance change
Irradiance change
P
Ipv
Ia
Vpv
Ppv
200W
600W
160V0A
01 s
01 s
01 s
190V3A
25A
Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller
learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows
1205781=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119908
11989411989511198952
))2
+ 120576]
1205782=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119898
119901119894119895119901
))
2
+ 120576]
1205783=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597120590
119901119894119895119901
))
2
+ 120576]
1205784=
119864 (119873)
4 [sum119899119894
119894=1((1205971198641205971199105
119900(119873)) (1205971199105
119900(119873) 120597119903
119901119894119895119901
))
2
+ 120576]
(30)
where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study
5 Experimental Results
The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579
119890is obtained byDSOGI-PLL block
The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876
lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast
119902 The
control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894
lowast
119889 Moreover since the single-
stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896
119901119899+ 119896119894119899119904 119899 = 1 2 where 119896
119901119899is
the proportional gain and 119896119894119899is the integral gain The gains
of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896
1198942are tuned to be
12 1 1 and 12 Furthermore both PI and 2D-RFCMANN
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
10 International Journal of Photoenergy
0Fault occurs
0
Fault occurs
4A
0
4A
Fault occurs
600W
02 s
02 s
02 s
Ipv
Vpv
Qlowast
Ppv
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
71A
minus71A
001 s
ia ib ic
|V+l |
(a)
4A
4A 02s
0
0
0
600W
02 s
02 sIpv
Qlowast
ia ib ic
ia ib ic
200V
P
Q
50Vrms2A
200Wvar
0
minus71A
001 s
|V+l |
Fault occurs
Fault occurs
Fault occurs
Vpv
Ppv
71A
(b)
Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers
controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879
120590for
the reference tracking are defined as follows [18]
119879119889(119873) = 119879
lowast
(119873) minus 119879 (119873)
119879MAX = max119873
(1003816100381610038161003816119879119889 (119873)
1003816100381610038161003816) 119879avg =1
119898(
119898
sum
119873=1
119879119889(119873))
119879120590
= radic1
119898(
119898
sum
119873=1
(119879119889(119873) minus 119879avg)
2
)
(31)
where 119879lowast
(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error
The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894
119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv
and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894
119886is 41 A At 119905 = 02 s the irradiance
changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894
119886reduces to 23 A From the
experimental results when the 2D-RFCMANN1 controller is
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 11
Qlowast
ia ib
ib
ic
ia ic
4A
4A
|V+l |
02 s
02 s
02 s
001 s
Q Ppv
200Wvar
50Vrms2A
Pref
P
Ipv
Vpv
Fault occurs
Fault occurs
Fault occurs
0
0
0
600W
200V
0
71A
minus71A
(a)
0
0
0
600W
200V
0
71A
minus71A
4A
4A
200Wvar PREF
02 s
02 s
02 s
Qlowast
PpvQP
Vpv
50Vrms2A
|V+l |
Ipv
ia i ic
ia i ic
b
b
001 s
Fault occurs
Fault occurs
Fault occurs
(b)
Figure 7 Experimental results of Case 2 (a) using PI controllers and (b) using 2D-RFCMANN controllers
used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition
Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled
Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881
+
119897| is 0864 pu (95Vrms) according to (13)
where 10 pu is equal to 110Vrms 119881sag and 119868lowast
119903are equal to
0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876
lowast are determined to be 794Wand 2246 var respectively Since 119875
lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
12 International Journal of Photoenergy
1009080706050403020100 Maximum Average
702
9858
147234
1102 832
Standard deviation
PI2D-RFCMANN
measuring of Q at Case1Performance
(a)
Maximum Maximum
AverageAverage
Standard deviationStandard deviation
500 300
450400350300250
250
200
200
150100500
150
100
50
0
29958
25468
minus1686minus625
47651342
PI2D-RFCMANN
PI2D-RFCMANN
minus50
45843
30091
21911868 5387 482
measuring of Q at Case2Performance
measuring of Q at Case2Performance
(b)
Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2
On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers
Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and
119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881
+
119897| and 119868
lowast
119903are equal to 0462 pu and 100
respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876
and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit
From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated
its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers
6 Conclusions
This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 13
is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing
The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001
References
[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012
[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012
[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013
[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995
[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004
[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997
[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009
[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006
[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010
[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007
[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012
[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011
[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013
[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010
[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011
[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012
[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011
[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of