A PI-Type Sliding Mode Controller Design for PMSG...

Research ArticleA PI-Type Sliding Mode Controller Design forPMSG-Based Wind Turbine

Jun Liu Feihang Zhou Chencong Zhao and Zhuoran Wang

College of Automation Xirsquoan University of Technology China

Correspondence should be addressed to Feihang Zhou qq987102679126com

Received 2 April 2019 Revised 10 May 2019 Accepted 28 May 2019 Published 19 June 2019

Guest Editor Baltazar Aguirre-Hernandez

Copyright copy 2019 Jun Liu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Because the PMSG (permanent magnet synchronous generator)-based WECS (wind energy conversion system) has someuncertainties the conventional control strategy with poor robustness is sometimes difficult to meet the performance requirementsof control In order to ensure efficient and stability of the system this paper proposed a novel PI (proportional-integral)-typeSMC (sliding mode control) strategy for PMSG-basedWECS uncertainties and presented the detailed analysis and design processCompared with the conventional control method the PI-type SMC proposed in this paper not only can make the closed-loopsystem globally stable but also has a better robustness and slightly reduced the current ripple and distortion Finally the simulationresults verify the correctness and effectiveness of this algorithm

1 Introduction

Environment problems such air pollution and global warm-ing caused by fossil fuels have drawn the worldrsquos attention toexploration and utilization of renewable energy sources inrecent years [1ndash5] At present wind energy is the fastest grow-ing renewable energy source and is most prevalent in coastalregions spanning temperate and boreal climates [6ndash8]Thereis great potential forwind power development inChina USADenmark and other countries due to their high averagewindvelocities [9]Therefore the research on wind power genera-tion technology has a significant value nowadays Comparedwith the constant-speed constant-frequency wind turbinethe variable-speed constant-frequency wind turbines canobtain the maximum energy conversion due to its rotationalspeed could vary with wind speed to ensure that the systemhas the OTSR (optimal tip speed ratio) and maximum windenergy utilization coefficient The variable-speed constant-frequency wind energy conversion system (WECS) consistsof DFIG (doubly fed induction generator)-based WECS andPMSG (permanent magnet synchronous generator)-basedWECS The PMSG-based WECS was selected to study inthis paper due to the fact that PMSG has many superiorcharacteristics such as wider speed control range higher

reliability and more efficient performance compared withDIFG [10]

In fact the practical systems have many uncertaintiesThe uncertainties of PMSG or PMSM (permanent magnetsynchronous motor) consist of the unmodeled converterdynamics and the parameters perturbations [11ndash14] A robustcontrol scheme for PMSMuncertainties based on an adaptiveDOB (disturbance observer) was introduced in [11] Theresults indicated that the controller obtained a good controlperformance Reference [12] proposed a robust nonlinearpredictive control strategy for PMSM uncertainties The con-trol system obtained a high speed tracking precision In [13]a PFC (predictive functional control) + ESO (extended stateobserver) method was studied After that the effectivenessof this new method was verified Reference [14] proposed anovel decoupled PI current control method for the PMSG-basedWECSThismethod can successfully achieve improvedthe transient performances and the nominal performancerecovery under the model uncertainty

SMC (sliding mode control) first proposed in the early1950s has a good robustness and powerful ability to reject theplant uncertainties and disturbances [15 16] References [1516] summarized the development of SMC and examined keytechnical research issues and future perspectives Although

HindawiComplexityVolume 2019 Article ID 2538206 12 pageshttpsdoiorg10115520192538206

2 Complexity

C i sb

i sa

i sc

idc

Udc

i1 i2

igaigb

igc

1 2

Rc Lc

SVPWM

Pulse

SVPWM

Pulse

Qg_ref

Udc_ref

Udc

z

Topt

Pg Qg (P3Q3)P2 Q2P1 Q1

Usd Usqisd isq

Ugd Ugqigd igq Egd Egq

KD

TDamp

MSC DC-link GSC

Grid

FilterWind Turbine

3PMSG

Flexible Drive-Train

WECS control level

GSC controllerMSC controller

1800V

Reactive powerschedulingMPPT

Band pass filter Gain

+_

Figure 1 AWECS configuration

the SMC has been widely and extensively employed insome industrial applications for a long term it is still theresearching focus for scholars and worth studying in depthA DPC (direct power control) based on SMC for the grid-connected WECS was presented in [17] When the gridvoltage is unbalanced the controller also can regulate theinstantaneous active and reactive powers directly in statorstationary reference frame Reference [18] enhanced theexponential reaching law to improve the control efficiencyand performance of SMC used in PMSG-based WECS

An adaptive second-order SMC strategy was exploredin [19] This method can effectively deals with the pres-ence of model uncertainties intrinsic nonlinear behavior ofWECS and random wind A SMC method for mismatcheduncertainties via a nonlinear DOB was developed in [20]Meanwhile the I-SMC (integral sliding-model control) witha good steady-state precision was mentioned in [20 21]The PI-type SMC is derived by the I-SMC and FBL (feed-back linearization) approach and has been widely used inrenewable energy conversion systems and the electric motordrives [21ndash23] Furthermore compared with the I-SMC theproportional and integral parameters of the PI-type SMC areable to be adjusted to better meet the control performanceindexes such as the celerity and accuracy

Based on the above background this paper presents anovel PI-type SMC for the PMSG-based WECS Althoughthe inspiration for this paper comes from literature [20ndash23] the whole designing thought and procedure of theproposed controller are completely different from the meth-ods in [20ndash23] Furthermore [20 23] just only referred tothe control of PMSG without the consideration of grid-connected control And the study subjects in [22 23] andthis paper are different At the same time the suppressionof flexible drive-train torsional vibration also has been

regarded as a control target in this paper Then we setup a detailed 2 MW WECS simulation test platform basedon MATLABSIMULINKSimPowerSysterms to verify theeffectiveness and correctness of the proposedmethod A largenumber of existing packaging modules in SimPowerSystermsare used in the simulation test platform that is relatively closeto the real physical system Finally the simulation resultsindicate the proposed strategy has good control performance

2 PMSG-Based WECS Model

The simplified PMSG-basedWECSmainly consists of a windturbine a flexible drive-train a PMSG fully rated convertersand its control level shown in Figure 1 In order to capture themaximum wind energy the maximum power point tracking(MPPT) strategy is adopted to control the machine-sideconverter (MSC) In the loop control level the grid-sideconverter (GSC) control is to regulate the reactive power andkeepDC-link voltageUdc stable at 1800VMeanwhile in orderto suppress the torsional vibration of flexible drive-train thedamping compensation torque TDamp was introduced

21 PMSG and MSC Dynamic Model The PMSG and MSCmathematical model is [5 20ndash27]

d119894119904119889d119905 = minus 119877119904119871 119904119889 119894119904119889 + 119871 119904119902119871 119904119889 119899119901120596119894119904119902 + 1119871 119904119889119880119904119889 minus 1119871 119904119889 120576119904119889d119894119904119902d119905 = minus 119877119904119871 119904119902 119894119904119902 minus 119871 119904119889119871 119904119902 119899119901120596119894119904119889 minus 119899119901120596120595119871 119904119902 + 1119871 119904119902119880119904119902minus 1119871 119904119902 120576119904119902

(1)

Complexity 3

where Usd and Usq are the d-axis and q-axis stator armaturevoltages isd and isq are the d-axis and q-axis components ofstator currents Lsd and Lsq are the d-axis and q-axis statorinductances 120596 is the rotor speed 119899p represents magneticpole logarithms 119877s is the stator resistance 120595 represents thepermanent magnet chain And the disturbance vector 120576119904119889and 120576119904119902 represent model uncertainties including the externaldisturbances and the PWM offset 120576119904119889 and 120576119904119902 were generallyassumed to be bounded by Dsd and Dsd10038161003816100381610038161205761199041198891003816100381610038161003816 le 11986311990411988910038161003816100381610038161205761199041198891003816100381610038161003816 le 119863119904119902 (2)

where Dsd and Dsq are the boundaries of 120576119904119889 and 120576119904119902The PMSG torque is given by

119879119892 = 15119899119901 [(119871 119904119889 minus 119871 119904119902) 119894119904119889119894119904119902 + 120595119894119904119902] (3)

22 GSC Dynamic Model The GSC dynamic model is givenby

d119894119892119889d119905 = minus119877119888119871119888 119894119892119889 + 120596119892119894119892119902 + 1119871119888119864119892119889 minus 1119871119888119880119892119889 minus 1119871119888 120576119892119889d119894119892119902d119905 = minus119877119888119871119888 119894119892119902 minus 120596119892119894119892119889 + 1119871119888119864119892119902 minus 1119871119888119880119892119902 minus 1119871119888 120576119892119902

(4)

where 119880119892119889 and 119880119892119902 are the control voltages 119894119892119889 and 119894119892119902are the components of grid-side currents 120596119892 is the powergrid frequency Lc and Rc are the filter inductance andresistance 119864119892119889 and 119864119892119902 express the d-axis and q-axis powergrid potential components (usually 119864119892119902 = 0)The 120596119892 and 119864119892119889can be gotten by the voltage phase-locked loop 120576119892119889 and 120576119892119902are also the uncertainties and meet1003816100381610038161003816100381612057611989211988910038161003816100381610038161003816 le 1198631198921198891003816100381610038161003816100381612057611989211988910038161003816100381610038161003816 le 119863119892119902 (5)

119863119892119889 and 119863119892119902 are the boundaries of 120576119892119889 and 1205761198921199023 PI-Type Sliding Mode Controller Design

31 Control Objectives If the state vector x and the referencestate vector x ref are

119909 = [119894119904119889 119894119904119902 119894119892119889 119894119892119902]T (6)

119909119903119890119891 = [119894119904119889 119903119890119891 119894119904119902 119903119890119891 119894119892119889 119903119890119891 119894119892119902 119903119890119891]T (7)

the control objectives of WECS can be expressed as

lim119905997888rarr+infin119890 = lim119905997888rarr+infin119909119903119890119891 minus 119909 = 0 (8)

where 119890 is the error vector In the above formula usually wehave 119894119904119889 119903119890119891 = 0

119894119904119902 119903119890119891 = 2119879119892 1199031198901198913119899119901120595 = 2 (119879119900119901119905 + 119879119863119886119898119901)3119899119901120595119894119892119889 119903119890119891 = (119870119875 + 119870119868119904 ) (119880119889119888 119903119890119891 minus 119880119889119888)119894119892119902 119903119890119891 = 119876119892 119903119890119891119864119892119889

(9)

where KP and KI are the PI (proportional-integral) parame-ters The optimal torque Topt in (9) meets [1 26ndash29]

119879119900119901119905 = 1198701199001199011199051205962 with 119870119900119901119905 = 1205871205881198775119862119875 max21205823119900119901119905 (10)

whereR is the wind wheel radius 120588 is the air density 119862119875 max isdefined as the maximum wind energy conversion coefficient120582opt is the OTSR (optimal tip speed ratio) and the dampingcompensation torque TDamp is given by [29ndash38]119879119863119886119898119901 = 119870119863119867(119904) 120596 (11)

where119870119863 isin 119877+ and H(s) is the transfer function of bandpassfilter shown in [29ndash38]

32 Design of Proportional-Integral (PI)-Type Sliding ModeController The PI-type sliding surface 119878 can be defined as

119878 = (119870 + 1119904 119868) 119890 (12)

where

119878 = [1198781 1198782 1198783 1198784]T (13)

119870 = diag ⟨1198701 1198702 1198703 1198704⟩ (14)

119868 = diag ⟨1198681 1198682 1198683 1198684⟩ (15)

s is Laplace variable 119870119894 isin 119877+ and 119868119894 isin 119877+ (i=1234)Obviously we also can get1198781120576119904119889 le 100381610038161003816100381611987811205761199041198891003816100381610038161003816 = 1198631199041198891198781 sgn (1198781)1198782120576119904119902 le 10038161003816100381610038161003816119878212057611990411990210038161003816100381610038161003816 = 1198631199041199021198782 sgn (1198782)1198784120576119892119889 le 10038161003816100381610038161003816119878412057611989211988910038161003816100381610038161003816 = 1198631198921198891198784 sgn (1198784)1198785120576119892119902 le 10038161003816100381610038161003816119878512057611989211990210038161003816100381610038161003816 = 1198631198921199021198785 sgn (1198785)

(16)

if the Lyapunov function is defined as

119881 = 12119878T119878 = 4sum119894=1119881119894 (17)

4 Complexity

where

119881119894 = 121198782119894 (18)

Equations (19)-(22) can be gotten by taking the derivative of(17)

1 = 1198781 1198781 = 1198781 (1198701 119890119904119889 + 1198681119890119904119889)= 11987811198701( 119894119904119889 119903119890119891 + 119877119904119871 119904119889 119894119904119889 minus 119871 119904119902119871 119904119889 119899119901120596119894119904119902minus 1119871 119904119889119880119904119889 + 1119871 119904119889 120576119904119889 )+ 1198681119890119904119889le 11987811198701( 119894119904119889 119903119890119891 + 119877119904119871 119904119889 119894119904119889 minus 119871 119904119902119871 119904119889 119899119901120596119894119904119902minus 1119871 119904119889119880119904119889 + 1119871 119904119889119863119904119889 sgn (1198781))+ 1198681119890119904119889

(19)

2 = 1198782 1198782 = 1198782 (1198702 119890119904119902 + 1198682119890119904119902)

= 11987821198702( 119894119904119902 119903119890119891 + 119877119904119871 119904119902 119894119904119902 + 119871 119904119889119871 119904119902 119899119901120596119894119904119902+119899119901120596120595119871 119904119902 minus 1119871 119904119902119880119904119902 + 1119871 119904119902 120576119904119902)+ 1198682119890119904119902le 11987821198702( 119894119904119902 119903119890119891 + 119877119904119871 119904119902 119894119904119902 + 119871 119904119889119871 119904119902 119899119901120596119894119904119902 + 119899119901120596120595119871 119904119902minus 1119871 119904119902119880119904119902 + 1119871 119904119902119863119904119902 sgn (1198782) )+ 1198682119890119904119902

(20)

3 = 1198783 1198783 = 1198783 (1198703 119890119892119889 + 1198683119890119892119889)= 11987831198703( 119894119892119889 119903119890119891 + 119877119888119871119888 119894119892119889 minus 120596119892119894119892119902minus1119871119888119864119892119889 + 1119871119888119880119892119889 + 1119871119888 120576119892119889)+ 1198683119890119892119889le 11987831198703( 119894119892119889 119903119890119891 + 119877119888119871119888 119894119892119889 minus 120596119892119894119892119902minus1119871119888119864119892119889 + 1119871119888119880119892119889 + 1119871119888119863119892119889 sgn (1198784))+ 1198683119890119892119889

(21)

4 = 1198784 1198784 = 1198784 (1198704 119890119892119902 + 1198684119890119892119902)

= 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889minus1119871119888119864119892119902 + 1119871119888119880119892119902 + 1119871119888 120576119892119902)

+ 1198684119890119892119902le 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902+ 1119871119888119880119892119902 + 1119871119888119863119892119902 sgn (1198783) )+ 1198684119890119892119902

(22)

Let

1198701 ( 119894119904119889 119903119890119891 + 119877119904119871 119904119889 119894119904119889 minus 119871 119904119902119871 119904119889 119899119901120596119894119904119902 minus 1119871 119904119889119880119904119889+ 1119871 119904119889119863119904119889 sgn (1198781)) + 1198681119890119904119889 = minus12057411198781 (23)

Complexity 5

1198702 ( 119894119904119902 119903119890119891 + 119877119904119871 119904119902 119894119904119902 + 119871 119904119889119871 119904119902 119899119901120596119894119904119902 + 119899119901120596120595119871 119904119902 minus 1119871 119904119902119880119904119902+ 1119871 119904119902119863119904119902 sgn (1198782)) + 1198682119890119904119902 = minus12057421198782 (24)

1198703 ( 119894119892119889 119903119890119891 + 119877119888119871119888 119894119892119889 minus 120596119892119894119892119902 minus 1119871119888119864119892119889 + 1119871119888119880119892119889+ 1119871119888119863119892119889 sgn (1198784)) + 1198683119890119892119889 = minus12057431198783 (25)

1198704 ( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902 + 1119871119888119880119892119902+ 1119871119888119863119892119902 sgn (1198784)) + 1198684119890119892119902 = minus12057441198784 (26)

Equation (27) can be gotten

le minus 4sum119894=1

1205741198941198782119894 le 0 (27)

where 120574119894 gt 0 Therefore the control laws are given by (28)-(31) and the control structure diagram is shown in Figure 2

119880119904119889 = 119871 1199041198891198701 (12057411198781 + 1198681119890119904119889) + 119871 119904119889 119894119904119889 119903119890119891 + 119877119904119894119904119889minus 119871 119904119902119899119901120596119894119904119902 + 119863119904119889 sgn (1198781) (28)

119880119904119902 = 119871 1199041199021198702 (12057421198782 + 1198682119890119904119902) + 119871 119904119902 119894119904119902 119903119890119891 + 119877119904119894119904119889+ 119871 119904119889119899119901120596119894119904119889 + 119899119901120596120595 + 119863119904119902 sgn (1198782) (29)

119880119892119889 = minus 1198711198881198703 (12057431198783 + 1198683119890119892119889) minus 119871119888 119894119892119889 119903119890119891 minus 119877119888119894119892119889+ 119871119888120596119892119894119892119902 + 119864119892119889 minus 119863119892119889 sgn (1198783) (30)

119880119892119902 = minus 1198711198881198704 (12057441198784 + 1198684119890119892119902) minus 119871119888 119894119892119902 119903119890119891 minus 119877119888119894119892119902minus 119871119888120596119892119894119892119889 + 119864119892119902 minus 119863119892119902 sgn (1198784) (31)

From (17) and (27) it is clear that the Lyapunov energyfunction V is greater than or equal to 0 and the derivativeof V is less than or equal to 0 Hence the whole system isasymptotically stable based on Lyapunov stability theorem

33 Tracking Accuracy Analysis In order to analyze thetracking accuracy we need to introduce Theorem 1 here

Theorem 1 For any dynamic system with state vector 119883 =[1199091 1199092 119909119899]119879 and assuming 119871 = 119891(119883) ge 0 is a Lyapunovfunction of system if le minussum119899119894=1 1198961198941199092119894 or le minussum119899119894=1 119896119894|119909119894|where119896119894 isin 119877+ then lim119905997888rarrinfin119909119894 = 0

Table 1 WECS parameters

Parameters ValueWind turbine inertia moment Jtur [kgsdotm2] 2times104Air density 120588 [kgm3] 1225Blade length R [m] 31Maximum utilization coefficient of wind energy 119862P max 0476Rated wind speed Vrate [ms] 14Rated power 119875rate [MW] 2Rated torque 119879rate [kNsdotm] 4times102Rate rotor speed 120596rate [rads] 5Generator pole logarithm 119899p 102Permanent flux 120593 [Wb] 125Stator-resistance 119877S [Ω] 0001stator-reluctance L [mH] 835DC-Link voltage [V] 1800DC-Link capacitor C [F] 022System resistance 119877119888 [Ω] 0001System inductor Lc [mH] 6Power grid potential Egd [V] 380Generator inertia moment Jgen [kgsdotm2] 700

Proof There are three casesA If 119871 equiv constant ge 0 then 0 equiv le minussum119899119894=1 1198961198941199092119894 le 0

and further 1198961198941199092119894 = 0 Due to 119896119894 = 0 thus 119909119894 = 0 This meansthat there are not continuous and stable equilibrium points119891(119883) equiv constant gt 0 such as stable limit cycle in this system

B Assuming 119871(0) = constant due to le minussum119899119894=1 1198961198941199092119894 then

119871 (0) minus 119871 (+infin) ge int+infin0

1198961198941199092119894 d119905 ge 0 (32)

forall119909119894 if lim119905997888rarrinfin119909119894 = 0 then int+infin0

1198961198941199092119894 d119905 997888rarr +infinand furthermore 119871(+infin) 997888rarr minusinfin Obviously this is incontradiction with 119871 ge 0 Thus lim119905997888rarrinfin119909119894 = 0

C Given 119871(0) 997888rarr +infin according to Lyapunov stabilitycriterion the system is stable So there must be t1 meeting119871(1199051) = constant Otherwise 119871(+infin) 997888rarr +infin This is clearlyin contradiction with system stability If we redefined t1 as 0we can get lim119905997888rarrinfin119909119894 = 0 byB

When le minussum119899119894=1 119896119894|119909119894| we have the same conclusion inthe same way

Based onTheorem 1 we have

lim119905997888rarr+infin119878 = [0 0 0 0]T (33)

From (12) and (33) we can get

lim119905997888rarr+infin119890 = lim119904997888rarr0

1199042 (119870119904 + 119868)minus1 119878 = [0 0 0 0]T (34)

The above formula shows that the steady-state error of thesystem is always 0 regardless of the input Therefore theproposed strategy can obtain a good tracking accuracy

6 Complexity

ToptTg

Topt

H(s)

MPPT

Bandpass Filter

KD TDamp

isq_ref++

0 isd_ref

2

3np

(a)

Udc_refPI

Qg_ref1Egd

+-Udc

igd_ref

igq_ref

(b)

isd_ref

i sd

+K1

esd

I1s

S1

I1

++

++

Lsd K 1

Lsds

Rs

Dsdsgn(middot)++

++

U sd

i sq Lsqnp

Lsdnp

+isq_ref esq K2

I2s

I2

Rs

S2++ +

+Lsq K2

U sq

Dsqsgn(middot)

Lsqs

+++

+

+++

dq

SVPWMPulse

MSC

Us

U s

np

2

1

(c)

K3

I3s

S 3 Lc

Lc

K3

s

Dgdsgn(middot)

3igd_ref egd

I3

Rc

Rc

Lc g

Lc g

I4

Egd

igq_ref egqK4

I4s

S4 Lc K4

Dsqsgn(middot)

4

igd

igq

s

Egq

Lc

Ugd

Ugq

dq

SVPWMPulse

GSC

Ug

Ug

(d)

Figure 2 Control structure diagram of WECS

4 Algorithm Analysis and Verification

In this section a detailed simulation test platform is con-structed to verify the correctness and effectiveness of the newalgorithm shown in Figure 3 The simulation test platformis based on the MATLABSimulink environment and thepackagedmodules in SimPowerSysterms are used in this sim-ulation test platform including the wind turbine PMSG andVSCs Meanwhile the two mass block spring damping model

mentioned in [21ndash31] is adopted to describe the dynamics offlexible drive chain Therefore the simulation test platformis relatively close to the actual physical system due tothe adoption of many packaged modules The controller ofWECS consists of MSC controller and GSC controller whichare mentioned in Figure 3 The system parameters are shownin Table 1 In general the actual wind speed is time-varyingand random however we also believe the wind speed isconstant for a short period of time Hence we assume that the

Complexity 7

a

b

c

a

b

c

A

B

C

A

B

C

A

B N

Grid GSC controller MSC controller

GSC MSC PMSG model

C

vabc2

iabc2vabc2

iabc2

Udc

vabc

iabc pulse pulse

Udc

theta

iabc1

iabc1

w

theta

theta

wtur

w

iabc

w

PWM2 PWM1

Vabc

Iabc

Rotor angleltRotor angle thetam (rad)gt

ltElectromagnetic torque Te (Nlowastm)gt

ltStator current is_c (A)gt

ltStator current is_b (A)gt

ltStator current is_a (A)gt

C-phase stator current

B-phase stator current

A-phase stator current

Electromagnetic torqueA

g+

-

+

-

+v

i

Udc

DC-link voltage

-

+-i +-

B

C

A

g

B

C

A

B

C

i_2

wtur

Wind turbine model

Mechanical torque

Flexible drive chain model

i_1

PWM1 w w

m

PWM2

Wind speed

powergui

DiscreteTs = 2e-06 s

TgWind turbine speed

Generator speed

Tg

14

13

12

11

10

9

8

7

6

N

S

Figure 3 Simulation test platform

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus2000

minus1000

0

1000

2000

3000

Time [s]

DC-

side r

ectif

ying

curr

enti

1[A

]

(a)

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus4000

minus2000

0

2000

4000

DC-

side i

nver

ter c

urre

nti 2

[A]

Time [s]

(b)

Figure 4 DC-link currents

wind speedmeets v= 12 + 04times rand(t)TheDC-link currentsi1 and i2 are shown in Figure 4 and the other response curvesof WECS are shown in Figure 5

From Figure 4 we know that the DC-link currents i1 andi2 are bidirectionalThismeans that theMSCorGSC is able toswitch between rectifier and inverter state However becauseof the mean values of i1 and i2 are positive therefore the MSCis basically working as a rectifier and the GSC is mostly in the

state of inverterThis is in accordance with the actual accidentsituation and can verify the accuracy of the model in a sense

Figure 5 shows the response curves of wind energyutilization coefficient CP DC-link voltage Udc d-axis andq-axis components of stator current and grid current Thedisturbance component of the wind speed is the main causesof CP Udc current and power fluctuations Figure 5(a)depicts the wind energy utilization coefficient CP is always

8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801

Conventional controlProposed control

Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)

Figure 5 Response curves of WECS

in the vicinity of the maximum value 119862119875 119898119886119909 (or 04763)under the proposed control strategy This implies the WECSis operating in MPPT mode to capture the maximum windenergy under the ratedwind speed It is clear that theDC-linkvoltageUdc is very close to its reference119880119889119888 119903119890119891 (or 1800V) andthe deviation does not exceed 08V by Figure 5(b) Figures5(b)ndash5(f) show that the proposed control can reduce thecurrent ripple of stator currents and grid currents comparedwith the conventional control because the uncertainty of theunmodeled dynamics is taken into account in the design ofthe proposed controller In one word the proposed controlstrategy has a better robustness than the conventional controlstrategy

The electromagnetic torque and sliding mode surfacescurves are shown in Figures 6 and 7 It is clear thatthe electromagnetic torque fluctuation under the proposedcontrol method is smaller compared with the conventionalcontrol method Meanwhile Figure 7 shows all steady-statevalues of sliding mode surfaces are tend to zero Thusthe correctness of the analysis in Section 33 is verified byFigure 7 Furthermore the proposed scheme was furtherverified for the suppression of current harmonics Here wetake the A-phase stator current of generator as an exampleThe A-phase stator current waveform is shown in Figure 8Obviously the proposed method also can reduce the currentdistortion

Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)

Figure 6 Electromagnetic torque curve

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)

Figure 7 Sliding mode surface curve

10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600

Time [s]Conventional control

Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]

Figure 8 A-phase stator current waveform

0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W

] Electromagnetic power

Grid-connected active power

times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq

(h)Figure 9 Variable wind speed and system responses

Complexity 11

To further verify the effectiveness of the proposedmethod the system responses under variable wind speedmust be observed and analyzed As Figure 9(a) showsthe wind speed varied from 10 ms to 125ms At thistime the system response curves under the variable windspeed are shown in Figures 9(b)ndash9(h) It is clear that theresults demonstrated the correctness and effectiveness of theproposed approach again Figures 9(c) and 9(f) show that thewind energy utilization coefficient CP is always maintained atits maximum value 119862119875 119898119886119909 (0476) and the DC-link voltageUdc always fluctuates around Udc ref (1800V) whether thewind speed changes From Figure 9(d) the grid-connectedactive power is always less than the electromagnetic powerdue to the copper loss

5 Conclusion

A novel PI-type SMC was proposed to ensure efficientand stability of PMSG-based WECS in this paper Thepresented strategy with a strong robustness for the uncer-tainties and disturbances of the system can make theclosed-loop system globally stable and more performantcompared with the conventional control method Finallya 2MW WECS simulation test platform which is basedon the MATLABMATLABSIMULINKSimPowerSystermsenvironmentwas built to verify thematurity and effectivenessof this presented control algorithm The simulation resultsindicated that the new method is able to reduce the currentdistortion and torque fluctuation which has important actualsignificance for the control of practical wind turbine

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research was supported by Key RampD projects in Shaanxi(Grant no 2017GY-061)

References

[1] J Liu H Meng Y Hu Z Lin and W Wang ldquoA novelMPPT method for enhancing energy conversion efficiencytaking power smoothing into accountrdquo Energy Conversion andManagement vol 101 pp 738ndash748 2015

[2] D Song J Yang X Fan et al ldquoMaximum power extraction forwind turbines through a novel yaw control solution using pre-dicted wind directionsrdquo Energy Conversion and Managementvol 157 pp 587ndash599 2018

[3] F Zhou and J Liu ldquoPitch controller design of wind turbinebased on nonlinear PIPD controlrdquo Shock and Vibration vol2018 Article ID 7859510 14 pages 2018

[4] D Song X Fan J Yang A Liu S Chen and Y H JooldquoPower extraction efficiency optimization of horizontal-axiswind turbines through optimizing control parameters of yawcontrol systems using an intelligent methodrdquo Applied Energyvol 224 pp 267ndash279 2018

[5] F Zhou and J Liu ldquoA robust control strategy research onPMSG-basedWECS considering the uncertaintiesrdquo IEEEAccess vol 6pp 51951ndash51963 2018

[6] S Li T A Haskew R P Swatloski and W Gathings ldquoOptimaland direct-current vector control of direct-driven PMSG windturbinesrdquo IEEE Transactions on Power Electronics vol 27 no 5pp 2335ndash2337 2012

[7] P Li R-X Li Y Cao D-Y Li and G Xie ldquoMulti-objectivesizing optimization for island microgrids using triangularaggregation model and levy-harmony algorithmrdquo IEEE Trans-actions on Industrial Informatics p 99 2017

[8] P Li R Dargaville Y Cao D Li and J Xia ldquoStorage aidedsystem property enhancing and hybrid robust smoothing forlarge-scale pv systemsrdquo IEEE Transactions on Smart Grid vol8 no 6 pp 2871ndash2879 2017

[9] M Little and K Pope ldquoPerformance modelling for windturbines operating in harsh conditionsrdquo International Journal ofEnergy Research vol 41 no 3 pp 417ndash428 2017

[10] J Yan H Lin Y Feng X Guo Y Huang and Z Q ZhuldquoImproved slidingmodemodel reference adaptive system speedobserver for fuzzy control of direct-drive permanent magnetsynchronous generator wind power generation systemrdquo IETRenewable Power Generation vol 7 no 1 pp 28ndash35 2013

[11] Y A-R I Mohamed ldquoDesign and implementation of a robustcurrent-control scheme for a PMSM vector drive with a simpleadaptive disturbance observerrdquo IEEE Transactions on IndustrialElectronics vol 54 no 4 pp 1981ndash1988 2007

[12] R Errouissi M Ouhrouche W-H Chen and A M Trzynad-lowski ldquoRobust nonlinear predictive controller for permanent-magnet synchronous motors with an optimized cost functionrdquoIEEE Transactions on Industrial Electronics vol 59 no 7 pp2849ndash2858 2012

[13] H Liu and S Li ldquoSpeed control for PMSM servo system usingpredictive functional control and extended state observerrdquo IEEETransactions on Industrial Electronics vol 59 no 2 pp 1171ndash1183 2012

[14] R Errouissi A Al-Durra and M Debouza ldquoA novel design ofPI current controller for PMSG-basedwind turbine consideringtransient performance specifications and control saturationrdquoIEEE Transactions on Industrial Electronics vol 65 no 11 pp8624ndash8634 2018

[15] X H Yu and O Kaynak ldquoSliding-mode control with soft com-puting a surveyrdquo IEEE Transactions on Industrial Electronicsvol 56 no 9 pp 3275ndash3285 2009

[16] O Kaynak K Erbatur and M Ertugrul ldquoThe fusion ofcomputationally intelligent methodologies and sliding-modecontrolmdasha surveyrdquo IEEE Transactions on Industrial Electronicsvol 48 no 1 pp 4ndash17 2001

[17] L Shang and J Hu ldquoSliding-mode-based direct power controlof grid-connected wind-turbine-driven doubly fed inductiongenerators under unbalanced grid voltage conditionsrdquo IEEETransactions on Energy Conversion vol 27 no 2 pp 362ndash3732012

[18] S M Mozayan M Saad H Vahedi H Fortin-Blanchette andM Soltani ldquoSliding mode control of PMSG wind turbine basedon enhanced exponential reaching lawrdquo IEEE Transactions onIndustrial Electronics vol 63 no 10 pp 6148ndash6159 2016

12 Complexity

[19] C Evangelista P Puleston F Valenciaga and L M FridmanldquoLyapunov-designed super-twisting sliding mode control forwind energy conversion optimizationrdquo IEEE Transactions onIndustrial Electronics vol 60 no 2 pp 538ndash545 2013

[20] J Yang S Li and X Yu ldquoSliding-mode control for systems withmismatched uncertainties via a disturbance observerrdquo IEEETransactions on Industrial Electronics vol 60 no 1 pp 160ndash1692013

[21] R Errouissi and A Al-Durra ldquoA novel PI-type sliding surfacefor PMSG-based wind turbine with improved transient perfor-mancerdquo IEEE Transactions on Energy Conversion vol 33 no 2pp 834ndash844 2018

[22] C Xia G Jiang W Chen and T Shi ldquoSwitching-gain adap-tation current control for brushless DC motorsrdquo IEEE Trans-actions on Industrial Electronics vol 63 no 4 pp 2044ndash20522016

[23] J Hu H Nian B Hu Y He and Z Q Zhu ldquoDirect active andreactive power regulation of DFIG using sliding-mode controlapproachrdquo IEEE Transactions on Energy Conversion vol 25 no4 pp 1028ndash1039 2010

[24] B Beltran T Ahmed-Ali and M El Hachemi BenbouzidldquoSliding mode power control of variable-speed wind energyconversion systemsrdquo IEEE Transactions on Energy Conversionvol 23 no 2 pp 551ndash558 2008

[25] C J Smith C J Crabtree and P C Matthews ldquoImpact ofwind conditions on thermal loading of PMSG wind turbinepower convertersrdquo in Proceedings of the 8th IET InternationalConference on Power Electronics Machines and Drives PEMD2016 UK April 2016

[26] J Lu Y Hu X Zhang Z Wang J Liu and C Gan ldquoHighfrequency voltage injection sensorless control technique foripmsms fed by a three-phase four-switch inverter with a singlecurrent sensorrdquo IEEEASME Transactions on Mechatronics vol99 no 1 p 1 2018

[27] J Lu X Zhang YHu J Liu CGan andZWang ldquoIndependentphase current reconstruction strategy for ipmsm sensorlesscontrol without using null switching statesrdquo IEEE Transactionson Industrial Electronics vol 99 p 1 2017

[28] F Fateh W N White and D Gruenbacher ldquoTorsionalvibrations mitigation in the drivetrain of DFIG-based grid-connected wind turbinerdquo IEEE Transactions on Industry Appli-cations vol 53 no 6 pp 5760ndash5767 2017

[29] I P Girsang J S Dhupia E MuljadiM Singh and J JonkmanldquoModeling and control to mitigate resonant load in variable-speed wind turbine drivetrainrdquo IEEE Journal of Emerging andSelected Topics in Power Electronics vol 1 no 4 pp 277ndash2862013

[30] E A Bossanyi ldquoThe design of closed loop controllers for windturbinesrdquoWind Energy vol 3 no 3 pp 149ndash163 2000

[31] E A Bossanyi ldquoWind turbine control for load reductionrdquoWindEnergy vol 6 no 3 pp 229ndash244 2003

[32] Bossanyi Ervin andDWitcher ldquoController for 5MWreferenceturbinerdquo Project UpWind Bristol England 2009

[33] F ZhangW E Leithead andO Anaya-Lara ldquoA combined con-troller design of power system stabilizer andwind turbine drive-train damping filterrdquo in Proceedings of the International Confer-ence on Sustainable Power Generation and Supply SUPERGEN2012 p 41 September 2012

[34] J Licari C E Ugalde-Loo J B Ekanayake and N JenkinsldquoDamping of torsional vibrations in a variable-speed windturbinerdquo IEEE Transactions on Energy Conversion vol 28 no1 pp 172ndash180 2013

[35] D H Anca and G Michalke ldquoModelling and control of variable-speed multi-pole permanent magnet synchronous generatorwind turbinerdquoWind Energy vol 11 pp 537ndash554 2008

[36] T Orlowska-Kowalska and K Szabat ldquoDamping of torsionalvibrations in two-mass system using adaptive sliding neuro-fuzzy approachrdquo IEEE Transactions on Industrial Informaticsvol 4 no 1 pp 47ndash57 2008

[37] R Muszynski and J Deskur ldquoDamping of torsional vibrationsin high-dynamic industrial drivesrdquo IEEE Transactions on Indus-trial Electronics vol 57 no 2 pp 544ndash552 2010

[38] A Lorenzo-Bonache A Honrubia-Escribano F Jimenez-Buendıa A Molina-Garcıa and E Gomez-Lazaro ldquoGenerictype 3 wind turbine model based on IEC 61400-27-1 Parameteranalysis and transient response under voltage dipsrdquo Energiesvol 10 no 9 2017

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Dierential EquationsInternational Journal of

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Submit your manuscripts atwwwhindawicom

2 Complexity

C i sb

i sa

i sc

idc

Udc

i1 i2

igaigb

igc

1 2

Rc Lc

SVPWM

Pulse

SVPWM

Pulse

Qg_ref

Udc_ref

Udc

z

Topt

Pg Qg (P3Q3)P2 Q2P1 Q1

Usd Usqisd isq

Ugd Ugqigd igq Egd Egq

KD

TDamp

MSC DC-link GSC

Grid

FilterWind Turbine

3PMSG

Flexible Drive-Train

WECS control level

GSC controllerMSC controller

1800V

Reactive powerschedulingMPPT

Band pass filter Gain

+_

Figure 1 AWECS configuration

the SMC has been widely and extensively employed insome industrial applications for a long term it is still theresearching focus for scholars and worth studying in depthA DPC (direct power control) based on SMC for the grid-connected WECS was presented in [17] When the gridvoltage is unbalanced the controller also can regulate theinstantaneous active and reactive powers directly in statorstationary reference frame Reference [18] enhanced theexponential reaching law to improve the control efficiencyand performance of SMC used in PMSG-based WECS

An adaptive second-order SMC strategy was exploredin [19] This method can effectively deals with the pres-ence of model uncertainties intrinsic nonlinear behavior ofWECS and random wind A SMC method for mismatcheduncertainties via a nonlinear DOB was developed in [20]Meanwhile the I-SMC (integral sliding-model control) witha good steady-state precision was mentioned in [20 21]The PI-type SMC is derived by the I-SMC and FBL (feed-back linearization) approach and has been widely used inrenewable energy conversion systems and the electric motordrives [21ndash23] Furthermore compared with the I-SMC theproportional and integral parameters of the PI-type SMC areable to be adjusted to better meet the control performanceindexes such as the celerity and accuracy

Based on the above background this paper presents anovel PI-type SMC for the PMSG-based WECS Althoughthe inspiration for this paper comes from literature [20ndash23] the whole designing thought and procedure of theproposed controller are completely different from the meth-ods in [20ndash23] Furthermore [20 23] just only referred tothe control of PMSG without the consideration of grid-connected control And the study subjects in [22 23] andthis paper are different At the same time the suppressionof flexible drive-train torsional vibration also has been

regarded as a control target in this paper Then we setup a detailed 2 MW WECS simulation test platform basedon MATLABSIMULINKSimPowerSysterms to verify theeffectiveness and correctness of the proposedmethod A largenumber of existing packaging modules in SimPowerSystermsare used in the simulation test platform that is relatively closeto the real physical system Finally the simulation resultsindicate the proposed strategy has good control performance

2 PMSG-Based WECS Model

The simplified PMSG-basedWECSmainly consists of a windturbine a flexible drive-train a PMSG fully rated convertersand its control level shown in Figure 1 In order to capture themaximum wind energy the maximum power point tracking(MPPT) strategy is adopted to control the machine-sideconverter (MSC) In the loop control level the grid-sideconverter (GSC) control is to regulate the reactive power andkeepDC-link voltageUdc stable at 1800VMeanwhile in orderto suppress the torsional vibration of flexible drive-train thedamping compensation torque TDamp was introduced

21 PMSG and MSC Dynamic Model The PMSG and MSCmathematical model is [5 20ndash27]

d119894119904119889d119905 = minus 119877119904119871 119904119889 119894119904119889 + 119871 119904119902119871 119904119889 119899119901120596119894119904119902 + 1119871 119904119889119880119904119889 minus 1119871 119904119889 120576119904119889d119894119904119902d119905 = minus 119877119904119871 119904119902 119894119904119902 minus 119871 119904119889119871 119904119902 119899119901120596119894119904119889 minus 119899119901120596120595119871 119904119902 + 1119871 119904119902119880119904119902minus 1119871 119904119902 120576119904119902

(1)

Complexity 3



119879119892 = 15119899119901 [(119871 119904119889 minus 119871 119904119902) 119894119904119889119894119904119902 + 120595119894119904119902] (3)



(4)




119909 = [119894119904119889 119894119904119902 119894119892119889 119894119892119902]T (6)

119909119903119890119891 = [119894119904119889 119903119890119891 119894119904119902 119903119890119891 119894119892119889 119903119890119891 119894119892119902 119903119890119891]T (7)




119894119904119902 119903119890119891 = 2119879119892 1199031198901198913119899119901120595 = 2 (119879119900119901119905 + 119879119863119886119898119901)3119899119901120595119894119892119889 119903119890119891 = (119870119875 + 119870119868119904 ) (119880119889119888 119903119890119891 minus 119880119889119888)119894119892119902 119903119890119891 = 119876119892 119903119890119891119864119892119889

(9)


119879119900119901119905 = 1198701199001199011199051205962 with 119870119900119901119905 = 1205871205881198775119862119875 max21205823119900119901119905 (10)




119878 = (119870 + 1119904 119868) 119890 (12)

where

119878 = [1198781 1198782 1198783 1198784]T (13)

119870 = diag ⟨1198701 1198702 1198703 1198704⟩ (14)

119868 = diag ⟨1198681 1198682 1198683 1198684⟩ (15)


(16)


119881 = 12119878T119878 = 4sum119894=1119881119894 (17)

4 Complexity

where

119881119894 = 121198782119894 (18)



(19)

2 = 1198782 1198782 = 1198782 (1198702 119890119904119902 + 1198682119890119904119902)


(20)


(21)

4 = 1198784 1198784 = 1198784 (1198704 119890119892119902 + 1198684119890119892119902)

= 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889minus1119871119888119864119892119902 + 1119871119888119880119892119902 + 1119871119888 120576119892119902)

+ 1198684119890119892119902le 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902+ 1119871119888119880119892119902 + 1119871119888119863119892119902 sgn (1198783) )+ 1198684119890119892119902

(22)

Let


Complexity 5

1198702 ( 119894119904119902 119903119890119891 + 119877119904119871 119904119902 119894119904119902 + 119871 119904119889119871 119904119902 119899119901120596119894119904119902 + 119899119901120596120595119871 119904119902 minus 1119871 119904119902119880119904119902+ 1119871 119904119902119863119904119902 sgn (1198782)) + 1198682119890119904119902 = minus12057421198782 (24)


1198704 ( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902 + 1119871119888119880119892119902+ 1119871119888119863119892119902 sgn (1198784)) + 1198684119890119892119902 = minus12057441198784 (26)



1205741198941198782119894 le 0 (27)


119880119904119889 = 119871 1199041198891198701 (12057411198781 + 1198681119890119904119889) + 119871 119904119889 119894119904119889 119903119890119891 + 119877119904119894119904119889minus 119871 119904119902119899119901120596119894119904119902 + 119863119904119889 sgn (1198781) (28)

119880119904119902 = 119871 1199041199021198702 (12057421198782 + 1198682119890119904119902) + 119871 119904119902 119894119904119902 119903119890119891 + 119877119904119894119904119889+ 119871 119904119889119899119901120596119894119904119889 + 119899119901120596120595 + 119863119904119902 sgn (1198782) (29)












1198961198941199092119894 d119905 ge 0 (32)






lim119905997888rarr+infin119878 = [0 0 0 0]T (33)



1199042 (119870119904 + 119868)minus1 119878 = [0 0 0 0]T (34)


6 Complexity

ToptTg

Topt

H(s)

MPPT

Bandpass Filter

KD TDamp

isq_ref++

0 isd_ref

2

3np

(a)

Udc_refPI

Qg_ref1Egd

+-Udc

igd_ref

igq_ref

(b)

isd_ref

i sd

+K1

esd

I1s

S1

I1

++

++

Lsd K 1

Lsds

Rs

Dsdsgn(middot)++

++

U sd

i sq Lsqnp

Lsdnp

+isq_ref esq K2

I2s

I2

Rs

S2++ +

+Lsq K2

U sq

Dsqsgn(middot)

Lsqs

+++

+

+++

dq

SVPWMPulse

MSC

Us

U s

np

2

1

(c)

K3

I3s

S 3 Lc

Lc

K3

s

Dgdsgn(middot)

3igd_ref egd

I3

Rc

Rc

Lc g

Lc g

I4

Egd

igq_ref egqK4

I4s

S4 Lc K4

Dsqsgn(middot)

4

igd

igq

s

Egq

Lc

Ugd

Ugq

dq

SVPWMPulse

GSC

Ug

Ug

(d)





Complexity 7

a

b

c

a

b

c

A

B

C

A

B

C

A

B N


GSC MSC PMSG model

C

vabc2

iabc2vabc2

iabc2

Udc

vabc

iabc pulse pulse

Udc

theta

iabc1

iabc1

w

theta

theta

wtur

w

iabc

w

PWM2 PWM1

Vabc

Iabc










g+

-

+

-

+v

i

Udc

DC-link voltage

-

+-i +-

B

C

A

g

B

C

A

B

C

i_2

wtur

Wind turbine model

Mechanical torque


i_1

PWM1 w w

m

PWM2

Wind speed

powergui



Generator speed

Tg

14

13

12

11

10

9

8

7

6

N

S


199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus2000

minus1000

0

1000

2000

3000

Time [s]

DC-

side r

ectif

ying

curr

enti

1[A

]

(a)

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus4000

minus2000

0

2000

4000

DC-

side i

nver

ter c

urre

nti 2

[A]

Time [s]

(b)






8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801


Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)




Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 3



119879119892 = 15119899119901 [(119871 119904119889 minus 119871 119904119902) 119894119904119889119894119904119902 + 120595119894119904119902] (3)



(4)




119909 = [119894119904119889 119894119904119902 119894119892119889 119894119892119902]T (6)

119909119903119890119891 = [119894119904119889 119903119890119891 119894119904119902 119903119890119891 119894119892119889 119903119890119891 119894119892119902 119903119890119891]T (7)




119894119904119902 119903119890119891 = 2119879119892 1199031198901198913119899119901120595 = 2 (119879119900119901119905 + 119879119863119886119898119901)3119899119901120595119894119892119889 119903119890119891 = (119870119875 + 119870119868119904 ) (119880119889119888 119903119890119891 minus 119880119889119888)119894119892119902 119903119890119891 = 119876119892 119903119890119891119864119892119889

(9)


119879119900119901119905 = 1198701199001199011199051205962 with 119870119900119901119905 = 1205871205881198775119862119875 max21205823119900119901119905 (10)




119878 = (119870 + 1119904 119868) 119890 (12)

where

119878 = [1198781 1198782 1198783 1198784]T (13)

119870 = diag ⟨1198701 1198702 1198703 1198704⟩ (14)

119868 = diag ⟨1198681 1198682 1198683 1198684⟩ (15)


(16)


119881 = 12119878T119878 = 4sum119894=1119881119894 (17)

4 Complexity

where

119881119894 = 121198782119894 (18)



(19)

2 = 1198782 1198782 = 1198782 (1198702 119890119904119902 + 1198682119890119904119902)


(20)


(21)

4 = 1198784 1198784 = 1198784 (1198704 119890119892119902 + 1198684119890119892119902)

= 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889minus1119871119888119864119892119902 + 1119871119888119880119892119902 + 1119871119888 120576119892119902)

+ 1198684119890119892119902le 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902+ 1119871119888119880119892119902 + 1119871119888119863119892119902 sgn (1198783) )+ 1198684119890119892119902

(22)

Let


Complexity 5

1198702 ( 119894119904119902 119903119890119891 + 119877119904119871 119904119902 119894119904119902 + 119871 119904119889119871 119904119902 119899119901120596119894119904119902 + 119899119901120596120595119871 119904119902 minus 1119871 119904119902119880119904119902+ 1119871 119904119902119863119904119902 sgn (1198782)) + 1198682119890119904119902 = minus12057421198782 (24)


1198704 ( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902 + 1119871119888119880119892119902+ 1119871119888119863119892119902 sgn (1198784)) + 1198684119890119892119902 = minus12057441198784 (26)



1205741198941198782119894 le 0 (27)


119880119904119889 = 119871 1199041198891198701 (12057411198781 + 1198681119890119904119889) + 119871 119904119889 119894119904119889 119903119890119891 + 119877119904119894119904119889minus 119871 119904119902119899119901120596119894119904119902 + 119863119904119889 sgn (1198781) (28)

119880119904119902 = 119871 1199041199021198702 (12057421198782 + 1198682119890119904119902) + 119871 119904119902 119894119904119902 119903119890119891 + 119877119904119894119904119889+ 119871 119904119889119899119901120596119894119904119889 + 119899119901120596120595 + 119863119904119902 sgn (1198782) (29)












1198961198941199092119894 d119905 ge 0 (32)






lim119905997888rarr+infin119878 = [0 0 0 0]T (33)



1199042 (119870119904 + 119868)minus1 119878 = [0 0 0 0]T (34)


6 Complexity

ToptTg

Topt

H(s)

MPPT

Bandpass Filter

KD TDamp

isq_ref++

0 isd_ref

2

3np

(a)

Udc_refPI

Qg_ref1Egd

+-Udc

igd_ref

igq_ref

(b)

isd_ref

i sd

+K1

esd

I1s

S1

I1

++

++

Lsd K 1

Lsds

Rs

Dsdsgn(middot)++

++

U sd

i sq Lsqnp

Lsdnp

+isq_ref esq K2

I2s

I2

Rs

S2++ +

+Lsq K2

U sq

Dsqsgn(middot)

Lsqs

+++

+

+++

dq

SVPWMPulse

MSC

Us

U s

np

2

1

(c)

K3

I3s

S 3 Lc

Lc

K3

s

Dgdsgn(middot)

3igd_ref egd

I3

Rc

Rc

Lc g

Lc g

I4

Egd

igq_ref egqK4

I4s

S4 Lc K4

Dsqsgn(middot)

4

igd

igq

s

Egq

Lc

Ugd

Ugq

dq

SVPWMPulse

GSC

Ug

Ug

(d)





Complexity 7

a

b

c

a

b

c

A

B

C

A

B

C

A

B N


GSC MSC PMSG model

C

vabc2

iabc2vabc2

iabc2

Udc

vabc

iabc pulse pulse

Udc

theta

iabc1

iabc1

w

theta

theta

wtur

w

iabc

w

PWM2 PWM1

Vabc

Iabc










g+

-

+

-

+v

i

Udc

DC-link voltage

-

+-i +-

B

C

A

g

B

C

A

B

C

i_2

wtur

Wind turbine model

Mechanical torque


i_1

PWM1 w w

m

PWM2

Wind speed

powergui



Generator speed

Tg

14

13

12

11

10

9

8

7

6

N

S


199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus2000

minus1000

0

1000

2000

3000

Time [s]

DC-

side r

ectif

ying

curr

enti

1[A

]

(a)

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus4000

minus2000

0

2000

4000

DC-

side i

nver

ter c

urre

nti 2

[A]

Time [s]

(b)






8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801


Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)




Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








4 Complexity

where

119881119894 = 121198782119894 (18)



(19)

2 = 1198782 1198782 = 1198782 (1198702 119890119904119902 + 1198682119890119904119902)


(20)


(21)

4 = 1198784 1198784 = 1198784 (1198704 119890119892119902 + 1198684119890119892119902)

= 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889minus1119871119888119864119892119902 + 1119871119888119880119892119902 + 1119871119888 120576119892119902)

+ 1198684119890119892119902le 11987841198704( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902+ 1119871119888119880119892119902 + 1119871119888119863119892119902 sgn (1198783) )+ 1198684119890119892119902

(22)

Let


Complexity 5

1198702 ( 119894119904119902 119903119890119891 + 119877119904119871 119904119902 119894119904119902 + 119871 119904119889119871 119904119902 119899119901120596119894119904119902 + 119899119901120596120595119871 119904119902 minus 1119871 119904119902119880119904119902+ 1119871 119904119902119863119904119902 sgn (1198782)) + 1198682119890119904119902 = minus12057421198782 (24)


1198704 ( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902 + 1119871119888119880119892119902+ 1119871119888119863119892119902 sgn (1198784)) + 1198684119890119892119902 = minus12057441198784 (26)



1205741198941198782119894 le 0 (27)


119880119904119889 = 119871 1199041198891198701 (12057411198781 + 1198681119890119904119889) + 119871 119904119889 119894119904119889 119903119890119891 + 119877119904119894119904119889minus 119871 119904119902119899119901120596119894119904119902 + 119863119904119889 sgn (1198781) (28)

119880119904119902 = 119871 1199041199021198702 (12057421198782 + 1198682119890119904119902) + 119871 119904119902 119894119904119902 119903119890119891 + 119877119904119894119904119889+ 119871 119904119889119899119901120596119894119904119889 + 119899119901120596120595 + 119863119904119902 sgn (1198782) (29)












1198961198941199092119894 d119905 ge 0 (32)






lim119905997888rarr+infin119878 = [0 0 0 0]T (33)



1199042 (119870119904 + 119868)minus1 119878 = [0 0 0 0]T (34)


6 Complexity

ToptTg

Topt

H(s)

MPPT

Bandpass Filter

KD TDamp

isq_ref++

0 isd_ref

2

3np

(a)

Udc_refPI

Qg_ref1Egd

+-Udc

igd_ref

igq_ref

(b)

isd_ref

i sd

+K1

esd

I1s

S1

I1

++

++

Lsd K 1

Lsds

Rs

Dsdsgn(middot)++

++

U sd

i sq Lsqnp

Lsdnp

+isq_ref esq K2

I2s

I2

Rs

S2++ +

+Lsq K2

U sq

Dsqsgn(middot)

Lsqs

+++

+

+++

dq

SVPWMPulse

MSC

Us

U s

np

2

1

(c)

K3

I3s

S 3 Lc

Lc

K3

s

Dgdsgn(middot)

3igd_ref egd

I3

Rc

Rc

Lc g

Lc g

I4

Egd

igq_ref egqK4

I4s

S4 Lc K4

Dsqsgn(middot)

4

igd

igq

s

Egq

Lc

Ugd

Ugq

dq

SVPWMPulse

GSC

Ug

Ug

(d)





Complexity 7

a

b

c

a

b

c

A

B

C

A

B

C

A

B N


GSC MSC PMSG model

C

vabc2

iabc2vabc2

iabc2

Udc

vabc

iabc pulse pulse

Udc

theta

iabc1

iabc1

w

theta

theta

wtur

w

iabc

w

PWM2 PWM1

Vabc

Iabc










g+

-

+

-

+v

i

Udc

DC-link voltage

-

+-i +-

B

C

A

g

B

C

A

B

C

i_2

wtur

Wind turbine model

Mechanical torque


i_1

PWM1 w w

m

PWM2

Wind speed

powergui



Generator speed

Tg

14

13

12

11

10

9

8

7

6

N

S


199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus2000

minus1000

0

1000

2000

3000

Time [s]

DC-

side r

ectif

ying

curr

enti

1[A

]

(a)

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus4000

minus2000

0

2000

4000

DC-

side i

nver

ter c

urre

nti 2

[A]

Time [s]

(b)






8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801


Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)




Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 5

1198702 ( 119894119904119902 119903119890119891 + 119877119904119871 119904119902 119894119904119902 + 119871 119904119889119871 119904119902 119899119901120596119894119904119902 + 119899119901120596120595119871 119904119902 minus 1119871 119904119902119880119904119902+ 1119871 119904119902119863119904119902 sgn (1198782)) + 1198682119890119904119902 = minus12057421198782 (24)


1198704 ( 119894119892119902 119903119890119891 + 119877119888119871119888 119894119892119902 + 120596119892119894119892119889 minus 1119871119888119864119892119902 + 1119871119888119880119892119902+ 1119871119888119863119892119902 sgn (1198784)) + 1198684119890119892119902 = minus12057441198784 (26)



1205741198941198782119894 le 0 (27)


119880119904119889 = 119871 1199041198891198701 (12057411198781 + 1198681119890119904119889) + 119871 119904119889 119894119904119889 119903119890119891 + 119877119904119894119904119889minus 119871 119904119902119899119901120596119894119904119902 + 119863119904119889 sgn (1198781) (28)

119880119904119902 = 119871 1199041199021198702 (12057421198782 + 1198682119890119904119902) + 119871 119904119902 119894119904119902 119903119890119891 + 119877119904119894119904119889+ 119871 119904119889119899119901120596119894119904119889 + 119899119901120596120595 + 119863119904119902 sgn (1198782) (29)












1198961198941199092119894 d119905 ge 0 (32)






lim119905997888rarr+infin119878 = [0 0 0 0]T (33)



1199042 (119870119904 + 119868)minus1 119878 = [0 0 0 0]T (34)


6 Complexity

ToptTg

Topt

H(s)

MPPT

Bandpass Filter

KD TDamp

isq_ref++

0 isd_ref

2

3np

(a)

Udc_refPI

Qg_ref1Egd

+-Udc

igd_ref

igq_ref

(b)

isd_ref

i sd

+K1

esd

I1s

S1

I1

++

++

Lsd K 1

Lsds

Rs

Dsdsgn(middot)++

++

U sd

i sq Lsqnp

Lsdnp

+isq_ref esq K2

I2s

I2

Rs

S2++ +

+Lsq K2

U sq

Dsqsgn(middot)

Lsqs

+++

+

+++

dq

SVPWMPulse

MSC

Us

U s

np

2

1

(c)

K3

I3s

S 3 Lc

Lc

K3

s

Dgdsgn(middot)

3igd_ref egd

I3

Rc

Rc

Lc g

Lc g

I4

Egd

igq_ref egqK4

I4s

S4 Lc K4

Dsqsgn(middot)

4

igd

igq

s

Egq

Lc

Ugd

Ugq

dq

SVPWMPulse

GSC

Ug

Ug

(d)





Complexity 7

a

b

c

a

b

c

A

B

C

A

B

C

A

B N


GSC MSC PMSG model

C

vabc2

iabc2vabc2

iabc2

Udc

vabc

iabc pulse pulse

Udc

theta

iabc1

iabc1

w

theta

theta

wtur

w

iabc

w

PWM2 PWM1

Vabc

Iabc










g+

-

+

-

+v

i

Udc

DC-link voltage

-

+-i +-

B

C

A

g

B

C

A

B

C

i_2

wtur

Wind turbine model

Mechanical torque


i_1

PWM1 w w

m

PWM2

Wind speed

powergui



Generator speed

Tg

14

13

12

11

10

9

8

7

6

N

S


199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus2000

minus1000

0

1000

2000

3000

Time [s]

DC-

side r

ectif

ying

curr

enti

1[A

]

(a)

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus4000

minus2000

0

2000

4000

DC-

side i

nver

ter c

urre

nti 2

[A]

Time [s]

(b)






8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801


Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)




Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








6 Complexity

ToptTg

Topt

H(s)

MPPT

Bandpass Filter

KD TDamp

isq_ref++

0 isd_ref

2

3np

(a)

Udc_refPI

Qg_ref1Egd

+-Udc

igd_ref

igq_ref

(b)

isd_ref

i sd

+K1

esd

I1s

S1

I1

++

++

Lsd K 1

Lsds

Rs

Dsdsgn(middot)++

++

U sd

i sq Lsqnp

Lsdnp

+isq_ref esq K2

I2s

I2

Rs

S2++ +

+Lsq K2

U sq

Dsqsgn(middot)

Lsqs

+++

+

+++

dq

SVPWMPulse

MSC

Us

U s

np

2

1

(c)

K3

I3s

S 3 Lc

Lc

K3

s

Dgdsgn(middot)

3igd_ref egd

I3

Rc

Rc

Lc g

Lc g

I4

Egd

igq_ref egqK4

I4s

S4 Lc K4

Dsqsgn(middot)

4

igd

igq

s

Egq

Lc

Ugd

Ugq

dq

SVPWMPulse

GSC

Ug

Ug

(d)





Complexity 7

a

b

c

a

b

c

A

B

C

A

B

C

A

B N


GSC MSC PMSG model

C

vabc2

iabc2vabc2

iabc2

Udc

vabc

iabc pulse pulse

Udc

theta

iabc1

iabc1

w

theta

theta

wtur

w

iabc

w

PWM2 PWM1

Vabc

Iabc










g+

-

+

-

+v

i

Udc

DC-link voltage

-

+-i +-

B

C

A

g

B

C

A

B

C

i_2

wtur

Wind turbine model

Mechanical torque


i_1

PWM1 w w

m

PWM2

Wind speed

powergui



Generator speed

Tg

14

13

12

11

10

9

8

7

6

N

S


199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus2000

minus1000

0

1000

2000

3000

Time [s]

DC-

side r

ectif

ying

curr

enti

1[A

]

(a)

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus4000

minus2000

0

2000

4000

DC-

side i

nver

ter c

urre

nti 2

[A]

Time [s]

(b)






8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801


Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)




Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 7

a

b

c

a

b

c

A

B

C

A

B

C

A

B N


GSC MSC PMSG model

C

vabc2

iabc2vabc2

iabc2

Udc

vabc

iabc pulse pulse

Udc

theta

iabc1

iabc1

w

theta

theta

wtur

w

iabc

w

PWM2 PWM1

Vabc

Iabc










g+

-

+

-

+v

i

Udc

DC-link voltage

-

+-i +-

B

C

A

g

B

C

A

B

C

i_2

wtur

Wind turbine model

Mechanical torque


i_1

PWM1 w w

m

PWM2

Wind speed

powergui



Generator speed

Tg

14

13

12

11

10

9

8

7

6

N

S


199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus2000

minus1000

0

1000

2000

3000

Time [s]

DC-

side r

ectif

ying

curr

enti

1[A

]

(a)

199 1991 1992 1993 1994 1995 1996 1997 1998 1999 2minus4000

minus2000

0

2000

4000

DC-

side i

nver

ter c

urre

nti 2

[A]

Time [s]

(b)






8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801


Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)




Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








8 Complexity

1 12 14 16 18 2 22 24 26 28 3047

0472

0474

0476

0478

Time [s]Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(a)

1 12 14 16 18 2 22 24 26 28 31799

17995

1800

18005

1801


Time [s]

DC

bus v

olta

geU

dc

[V]

(b)

1 12 14 16 18 2 22 24 26 28 3minus100

minus50

0

50

100


d ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sd[A

]

(c)

1 12 14 16 18 2 22 24 26 28 32450

2500

2550

2600

2650

2700


q ax

is co

mpo

nent

of s

tato

r

Time [s]

curr

enti

sq[A

]

(d)

1 15 2 25 33600

3700

3800

3900

4000

d ax

is co

mpo

nent

of g

rid


Time [s]

curr

enti

gd

[A]

(e)

Time [s]1 12 14 16 18 2 22 24 26 28 3

minus100

minus50

0

50

100


q ax

is co

mpo

nent

of g

rid

curr

enti

gq

[A]

(f)




Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 9

25 26 27 28 29 3475

48

485

49

495

5

Time [s]

Shown in Figure (b)

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(a)

29015 2902 29025 2903 29035483

484485486487488489

49

Time [s]

Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

] times105

(b)


1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 1

(a)

1 15 2 25 3minus5000

0

5000

Time [s]

Slid

ing

mod

e sur

face

S 2

(b)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 3

Time [s]

(c)

1 15 2 25 3minus5000

0

5000

Slid

ing

mod

e sur

face

S 4

Time [s]

(d)


10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








10 Complexity

29915 2992 29925 2993 29935 2994 29945 29952200

2300

2400

2500

2600


Proposed control

A-ph

ase s

tato

r cur

rent

I a[A

]


0 05 1 15 2 25 3 35 49510

10511

11512

12513

Win

d sp

eed [

ms

]

Time [s]

(a)

0 05 1 15 2 25 3 35 4minus1

0

1

2

3

4

Time [s]

Gen

erat

or sp

eed

[rad

s]

(b)

0 05 1 15 2 25 3 35 40

01

02

03

04

05

Time [s]

Win

d en

ergy

util

izat

ion

coeffi

cien

tCP

(c)

0 05 1 15 2 25 3 35 4minus5

0

5

10

15

20

Time [s]

Activ

e pow

er [W



times105

(d)

0 05 1 15 2 25 3 35 4minus10123456

Time [s]Elec

trom

agne

tic to

rque

Tg

[Nmiddotm

]

times105

(e)

0 05 1 15 2 25 3 35 41798

1799

1800

1801

1802

1803

Time [s]

DC-

Link

vol

tage

Udc

[V]

(f)

0 05 1 15 2 25 3 35 4minus5000

50010001500200025003000

Time [s]

d-q

axis

com

pone

nt o

f sta

tor c

urre

nts [

A]

isd

isq

(g)

0 05 1 15 2 25 3 35 4minus1000

010002000300040005000

Time [s]

d-q

axis

com

pone

nt o

f grid

curr

ents

[A]

igd

igq


Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 11


5 Conclusion


Data Availability




Acknowledgments


References



















12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018








12 Complexity




























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








A PI-Type Sliding Mode Controller Design for PMSG...

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Transcript of A PI-Type Sliding Mode Controller Design for PMSG...