Research ArticleHarmonic Modeling and Experimental Validation of theConverters of DFIG-Based Wind Generation System

Yang-Wu Shen 1 Ding Wang1 Xiang-Tian Deng 2 Qing Li3 and Jian Zuo1

1State Grid Hunan Electric Power Corporation Limited Research Institute Changsha China2School of Automation Wuhan University of Technology Wuhan China3China Electric Power Research Institute Beijing China

Correspondence should be addressed to Xiang-Tian Deng dengxtwhuteducn

Received 2 July 2019 Revised 29 August 2019 Accepted 14 September 2019 Published 3 November 2019

Guest Editor Taesic Kim

Copyright copy 2019Yang-Wu Shen et alis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e double-fed induction wind generator- (DFIG-) based wind generation system contains power electronic converters and ltercapacitor and inductor which will bring about high-frequency harmonics under the inuence of controllers Aiming at thisproblem this paper studies the relation between the output current and the harmonic source at grid-side and rotor-side convertersbased on their control features in the DFIG system Furthermore the harmonic equivalent models of these two converters arebuilt and the inuence of dierent factors on harmonic features is explored from four perspectives ie modulation methodaltering controller parameters altering output power and the unbalance of three-phase voltage Finally the eectiveness of theproposed model is veried through the 2MW DFIG real-time hardware-in-the-loop test platform by StarSim software and realtest data respectively

1 Introduction

New energy power generation technologies have become hotspots as the energy and environmental issues obtainedprominent attention Wind energy has been widely appliedin power systems because of its clean harmless andabundant nature in natural resources e double-fed windpower generation system has become the mainstream inwind power generation systems because of its small capacityin the eld converter low cost and variable-speed constant-frequency operation features [1ndash6] However the double-fedwind power generation system contains a power electronicconverter in which the interactions among converters andpassive components of the lter can lead to harmonic res-onances thus causing serious harmonic pollution and re-ducing the power quality [7ndash10]

With regard to the harmonic problem in the double-fedwind power generation system relevant researches andanalyses have been carried out [11ndash14] In the literature [11]the source of stator harmonic current of the double-fed windturbine is analyzed It is pointed out that the harmonic

modulation of the converter the cogging harmonic of themotor itself and the grid background harmonic aect thestator output harmonics of the double-fed wind turbine In[12] the harmonic characteristics of the double-fed windturbine converter are analyzed and the eect of the con-verter harmonic on the system overall output harmonic isanalyzed by establishing the equivalent circuit of theasynchronous motor Based on the mathematically elec-tromagnetic relationship of the asynchronous motor liter-ature [13] proposes a harmonic equivalent circuit of thedouble-fed asynchronous motor and studies the inuence ofharmonics generated by the wind turbine on the power gridAccording to the characteristics of the asynchronous motorliterature [14] analyzes the interaction between the grid-sideconverter harmonic and the rotor-side converter harmonicin the double-fed wind power generation system

From the above literature studies the grid-side or rotor-side converters in the double-fed wind power generationsystem are viewed as a simple harmonic voltage source whenmodeling and analyzing the converter output harmoniccharacteristics while the inuence of converter control

HindawiComplexityVolume 2019 Article ID 7968914 13 pageshttpsdoiorg10115520197968914

factors on system harmonic output characteristics is notconsidered

Literature studies [15 16] point out that the harmonicsgenerated by PWM (pulse-width modulation) are mainlydistributed near the double switching frequency Reference[17] studies the harmonic resonance characteristics of thephotovoltaic power generation system by establishing theNorton equivalent model of the photovoltaic converterConsidering the control characteristics of different types ofconverters [18] Wang et al establish the converter equiv-alent model of voltage source control and current sourcecontrol respectively

However there is little literature on the harmoniccharacteristics of the double-fed wind power generationsystem at present e main contributions of this paper canbe summarized as follows

(1) Based on the existing harmonic model the influenceof component parameters and control parameters onthe harmonic output of the RSC and GSC is studiedand the harmonic output characteristics of the RSCand GSC are summarized Furthermore a novelmethod for suppressing the output harmonic am-plitude of the DFIG by adjusting PI control param-eters is proposed and the effectiveness of the proposedmethod has been verified by the simulation case

(2) e harmonic model of the typical DFIG is estab-lished and the parameters of the harmonic model ofthe DFIG are corrected by the measured data Withthe correction of harmonic model parameters theharmonic characteristics of the corrected harmonicmodel of the DFIG are consistent with the harmoniccharacteristics of the actual DFIG

e rest of this paper is organized as follows Section 2presents the harmonic source analysis of the double-fed windpower generation system Section 3 presents the character-istics analyses of the converter harmonic model Case studiesare presented in Section 4 to validate the proposed harmonicmodel of the DFIG Conclusion is presented in Section 5

2 Harmonic Source Analysis of Double-FedWind Power Generation System

e structure of the double-fed wind power generationsystem is shown in Figure 1 Two back-to-back PW-mod-ulated converters are used for AC excitation through a DClink Effective control of converters enables variable-speedconstant-frequency operation and maximum wind energytracking within a certain range [10 19 20]

e harmonic sources of the double-fed wind powergeneration system mainly include the harmonics caused bythe asynchronous motor itself and the harmonics caused bythe converter modulation [14] In addition the outputharmonic of the double-fed wind power system may exceedthe standard when there are background harmonics in thegrid and irrational converter control parameters e cog-ging harmonics caused by the asynchronous motor itself dueto the uneven air gap can be suppressed or eliminated by

rational motor structure designing us this paper mainlyconsiders the PW modulation harmonics of the converterand the background harmonics of the power grid eharmonic output characteristics of the double-fed windpower generation system are studied by establishing theharmonic equivalent model

3 Harmonic Modeling of Double-Fed WindPower Converter

Because of the fact that the dynamics of DC-side voltage isslower than the harmonic dynamics the voltage across thecapacitor between the grid-side converter and the rotor-sideconverter of the double-fed wind power system remainsconstant erefore the two converters can be discussedseparately in harmonic modeling In this section the har-monic equivalent models of the grid-side and rotor-sideconverters are established to study their harmonic outputcharacteristics and influencing factors Note that there aresubsynchronous and low-frequency oscillations which liebelow the fundamental frequency in wind power generationsystems and this paper mainly discusses the harmonicsabove the fundamental frequency [9]

e harmonic amplitude is proportional to the switchingfrequency dead time and DC-side voltage and inverselyproportional to the harmonic order e amplitude isnegligible so the voltage generated by the dead zone effect ismainly low such as 3 5 7 and 9 For a converter with a highswitching frequency the dead time is long in one switchingcycle and the low-order harmonic generated by the deadzone is more obvious while the large-capacity converterwith a lower switching frequency is generated by the deadzone effect In this paper the switching delay of the con-verter is not taken into consideration for the harmonicmodel of converters

31 Harmonic Modeling of Grid-Side Converter For a three-phase balancing system the system can be equivalent to asingle-phase system e command signal of the innercurrent loop in the grid-side converter is given by the outervoltage loop Consider the response of the voltage loop ismuch slower than the response of the current loop us byignoring the voltage loop the control block diagram of the

DFIG

Windturbine

Rotor-sideconverter

Grid-sideconverter

Transformer

Grid

Figure 1 Double-fed wind power generation system

2 Complexity

grid-side converter is obtained and shown in Figure 2 econverter-side current feedback control which is more stablethan the grid-side current feedback current control isadopted as shown in Figure 2 [21]

In Figure 2 Kpwm is the linear gain of the pulse-widthmodulation (PWM) converter bridge i1ref is the reference ofthe current loop ugh is the harmonic voltage generated byPWM Gig is the transfer function of the current regulatorwhich adopts the proportional resonance controller anduPCC is the voltage at the grid-connected point e har-monic model shown in Figure 2 considers two kinds ofharmonic sources (1) the harmonic voltage ugh generated bythe PWM and (2) the grid background harmonic voltageuPCC at the grid-connected point

In the steady-state operation the current reference i1refremains constant [22] us according to the Mason for-mula the complex frequency-domain expression among i2ugh and uPCC can be obtained as follows

i2 Ng(s)ugh minus Yeqg(s)uPCC (1)

where s is the complex frequency-domain variable andNg(s) and Yeqg(s) are expressed as

Ng(s) ZC

Z1Z2 + Z1ZC + Z2ZC + GigKpwm Z2 + ZC( 1113857

Yeqg(s) Z1 + ZC + GigKpwm

Z1Z2 + Z1ZC + Z2ZC + GigKpwm Z2 + ZC( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

where Kpwm is usually taken as 1 Z1 sL1 +R1 Z2 sL2 +R2and ZC 1sC in which L1 R1 L2 and R2 are the LCL filterinductance and equivalent resistance and C is the filtercapacitor and Gig is expressed as

Gig kpg +skig

s2 + ω2g

(3)

where kpg and kig are the proportional and integral co-efficients of the current controller and ωg is the fundamentalfrequency

According to Figure 1 and (1) the Norton equivalentcircuit of the grid-side converter can be obtained which isshown in Figure 3 In Figure 3 Ng(s)ugh is the PW-modulated harmonic and uPCC is the grid backgroundharmonic

32 Harmonic Modeling of Rotor-Side Converter e rotor-side converter adopts the motor stator flux-orientedfeedforward decoupling control e outer control loop isthe speed control or active power control and the output ofthe outer loop controller is the reference of the innercurrent loop Similarly the response of the inner loop ismuch faster than that of the outer looperefore the outercontrol loop is neglected and the balanced three-phasesystem is equivalent to a single-phase system e currentcontrol block diagram of the rotor-side converter is shownin Figure 4

In Figure 4 irref is the current reference urh is theharmonic voltage generated by PWM and Gir is the transferfunction of the current controller and the proportionalresonance controller is used e2 is the rotor-side phaseelectromotive force of the asynchronous machine In Fig-ure 4 the output current is

ir Nr sprime( 1113857urh minus Yeqr sprime( 1113857e2 (4)

where sprime is the rotor-side complex frequency-domain var-iable Note that sprime sslip where sslip is the slip e detailedexpressions of sslip Nr(sprime) and Yeqr(sprime) are shown asfollows

sslip s minus jωm

s

Nr sprime( 1113857 1

Zr + GirKpwm

Yeqr sprime( 1113857 1

Zr + GirKpwm

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

where ωm is the rotor speed of the asynchronous motorZr sprimeLr + Rr in which Lr and Rr are the rotor leakageinductance and resistance and Gir is expressed as

1

i1refGig Kpwm

uinvr

ugh

1Z1

Z2

i1

i2

uPCC uCZC

iC

Figure 2 Current control block diagram of the grid-side converter

Ng (s)ugh

Yeqg (s)

uPCC

i2

Figure 3 Norton equivalent circuit of the grid-side converter

irref Gir Kpwmurh 1

Zr

e2

ir

Figure 4 Current control block diagram of the rotor-side converter

Complexity 3

Gir kpr +sprimekir

sprime2

+ ωg minus ωm1113872 11138732 (6)

where kpr and kir are the proportional and integral co-efficients of the current controller respectively

According to Figure 4 and (4) and combining with theasynchronous motor equivalent circuit [11 12] theNorton equivalent model of the rotor-side converter canbe obtained which is shown in Figure 5(a) Note that therotor-side variables are converted to the stator side by thegenerator conversion With the circuit conversionFigure 5(a) can be equivalent to Figure 5(b) FromFigure 5(b) we have

is Ns(s)urh minus Yeqs(s)uPCC (7)

where is is the stator-side output current of the asynchro-nous motor and Ns(s) and Yeqs(s) are expressed as

Ns(s) ZmNr sprime( 1113857

Zm + Zs + sslipYeqr sprime( 1113857ZmZs

Yeqs(s) 1 + sslipYeqr sprime( 1113857Zm

Zm + Zs + sslipYeqr sprime( 1113857ZmZs

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

where Zm sLm and Zs sLs + Rs in which Lm is the ex-citation inductance of the asynchronous motor and Ls and Rsare the stator leakage inductance and resistance

4 Characteristics Analyses of ConverterHarmonic Model

Based on the harmonic models of grid-side and rotor-side converters established in Section 3 the effects ofcomponent parameters and control parameters on har-monic characteristics are studied e detailed param-eters of the DFIG used in the simulation are shown inTable 1

41 Characteristic Analysis of Harmonic Model of Grid-SideConverter According to the Norton equivalent modelshown in Figure 3 and (1) and (2) the Bode diagram ofNg(s) and Yeqg(s) is shown in Figure 6 It can be seen fromthe figure that there are resonance peaks (magnitude greaterthan 0 dB) at a frequency of about 1450Hz in Ng(s) andYeqg(s) It indicates that the converter output current willundergo harmonic amplification when the frequency of ughand uPCC is close to the resonant frequency thus affectingthe power quality Besides it should be noted that themagnitude-frequency curves of Ng(s) and Yeqg(s) are ob-viously declining when the frequency is higher than 2000Hzindicating that the converter has a strong suppression tohigh-frequency harmonics

Ignoring the equivalent resistance of the filter inductoras it is usually small and taking Kpwm 1 the denominatorof Ng(s) and Yeqg(s) shown in (2) can be expanded to

deng 1

sC⎡⎣s

3CL1L2 + s L1 + L2( 1113857 + s

2kpgCL2 + kpg

+s2kigCL2

s2 + ω2g

+skig

s2 + ω2g

⎤⎦

(9)

It can be seen from (9) that the cubic term and theprimary term of s in the brackets form a pair of resonantpoles whose resonant frequency is

ωrg plusmn

L1 + L2

CL1L2

1113971

(10)

e resonant frequency ωrg calculated by (10) is co-incident with the resonant frequency of the LCL filtererefore it can be inferred that the resonant peak inFigure 6 is determined by the filter inductance is meansthat choosing the right filter parameters can suppress asmany harmonics as possible in the high frequency Since thePWM harmonics are mainly concentrated near the doubleswitching frequency [15 16] the harmonic frequency ishigher and can be suppressed e range of grid backgroundharmonic frequency is wide and there are many lowerharmonics such as the 5th 7th and 11th erefore it isnecessary to further study the harmonic output character-istics of the converter affected by the grid backgroundharmonics

In the vicinity of the resonant frequency ωrg an ap-proximate expression is obtained as s2≫ωg2 and the ca-pacitance of the filter capacitor is small

deng asymp s2L1L2 +

L1 + L2

C+ skpgL2 (11)

It is not difficult to see from (11) that the product of kpgand L2 provides damping for the resonance e larger theproduct the stronger the damping effect

Since the current control parameter kpg is relativelyeasier to change than L2 in practice only the influence of kpgis studied in Figure 7

It can be seen from Figure 7 that when the parameter ofthe current loop controller kpg is relatively small themagnitude-frequency curve of Yeqg(s) has a resonance peakAs kpg increases the resonance peak gradually decreases todisappear In addition Figure 7 also shows that the con-troller parameter kpi has less effect on the magnitude-fre-quency curve of Yeqg(s) since the integral term of Gig isalmost zero at high frequencies

In summary the existence of LCL filter resonance maycause harmonic amplification in the output of the grid-sideconverter of the wind power generation system and theresonance can be suppressed by adjusting the parameter ofthe current controller kpg It should be noted that kpg alsoaffects the dynamic response and stability of the convertercontrol system and this is beyond the scope of this papererefore the parameter kpg should be increased as much aspossible to suppress the harmonic output of the converterunder the premise of meeting the dynamic performance andstability requirements of the system

4 Complexity

42 Characteristic Analysis of Harmonic Model of Rotor-SideConverter According to (4)ndash(8) and Figure 5 the magni-tude-frequency curves ofNs(s) andYeqs(s) are obtained and

shown in Figure 8 It can be seen from the curves in Figure 8that at higher frequencies the rotor-side converter has aneect of suppressing the higher-frequency PWM harmonicsand the grid background harmonics Since there is no ca-pacitor in the rotor-side converter and asynchronous motorthe magnitude-frequency curves ofNs(s) and Yeqs(s) do notshow obvious resonance peaks However it should also benoted that at lower frequencies (about 300Hz in Figure 8)there are peak slopes (magnitude exceeds 0 dB) usfurther characteristic study of Yeqs(s) is needed for the lowersecondary grid background harmonics

As to the rotor-side converter the denominator ofNr(sprime) and Yekr(sprime) in (5) can be expanded (Rr is ignoredand Kpwm 1 is considered for the same reason) to

denr sprimeLr + kpr +sprimekir

sprime2 + ωg minus ωm( )

2

s minus jωm( )Lr + kpr +s minus jωm( )kir

s minus jωm( )2 + ωg minus ωm( )2

(12)

It can be seen from (12) that when the frequency is 3times higher than the fundamental frequency of the rotorthat is s minus jωm gt 3(ωg minus ωm) (it is considered that thesmaller term can be ignored when the dierence betweentwo terms is more than 10 times in engineering application)the denominator denr can be approximated to

denr asymp s minus jωm( )Lr + kpr +kir

s minus jωm (13)

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

kpg = 05 kig = 100kpg = 10 kig = 100kpg = 05 kig = 800

Figure 7Magnitude-frequency curves ofYeqg(s)with dierent kpg

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)Yeqs(s)

Ns(s)

ndash40

ndash30

ndash20

ndash10

0

10

Figure 8 Magnitude-frequency curves of Ns(s) and Yeqs(s)

e2prime

irprime

sslipYeqr (sprime)

Zm

Zs

ndash

+is

uPCCNr (sprime)urh

(a)

ndash

+is

uPCCNs (s)urh

Yeqr (s)

(b)

Figure 5 Norton equivalent circuit of the rotor-side converter (a) detailed circuit of the rotor-side converter and asynchronous machine(b) equivalent model

Table 1 Detailed parameters of the DFIG simulation platform

Parameters ValuesLCL lter (L1) 2mHLCL lter (L2) 1mHLCL lter (C) 18 μFAsynchronous motor (Lr) 0404mHAsynchronous motor (Rr) 00079ΩAsynchronous motor (Ls) 008mHAsynchronous motor (Rs) 00025ΩAsynchronous motor (Lm) 44mHsslip minus 02

102 103 104ndash100

ndash80

ndash60

ndash40

ndash20

0

20

Frequency (Hz)

Mag

nitu

de (d

B)

Yeqg(s)

Ng(s)

Figure 6 Magnitude-frequency curves of Ng(s) and Yeqg(s)

Complexity 5

With (13) it can be found that the first and third termsform a pair of resonant poles whose resonant frequency is

ωrr ωm plusmn

kir

Lr

1113971

(14)

Although there is no resonance in the rotor-side con-verter caused by the capacitor and inductor of the LCL filter(14) shows that there will be resonance caused by the in-teraction between the controller integral term and the rotorleakage inductance Besides it can be seen from (8) that thisresonance will be finally reflected to the stator side by Ns(s)

and Yeqs(s)From (13) and (14) the resonant frequency is related to

the rotor speed ωm the rotor leakage inductance Lr and thecontroller parameter kir e rotor leakage inductance Lr isrelated to the motor parameters and is fixed after the motoris manufactured e rotor speed varies according to theactual wind speed and the range of variation is limited Onlythe controller parameter kir is easy to change Similar to thegrid-side converter the controller parameter kpr has an effectof damping

Figure 9 shows the magnitude-frequency curves ofYeqs(s) with different kir kpr and ωm It can be seen fromFigure 9 that on increasing kir the peak slope of Yeqs(s)

shifts to a lower frequency and the magnitude decreases Onthe contrary the magnitude-frequency curve of Yeqs(s)

declines to a large extent as kpr is increased e slip sslipchanges from minus 02 (corresponding to ωm 12ωg) to minus 01(corresponding to ωm 11ωg) and the peak slope ofYeqs(s) shifts to a lower frequency Considering that theactual range of slip variation is small the parameters kpr andkir are the main factors affecting the harmonic outputcharacteristics of the rotor-side converter

43 Harmonic Model of Double-Fed Wind Power GenerationSystem considering Grid Impedance According to theequivalent harmonic models of grid-side and rotor-sideconverters shown in Figures 3 and 5 the overall equivalentharmonic model of the double-fed wind system is shown inFigure 10 In Figure 10 Zg is the grid equivalent impedanceand ug is the grid voltage According to Figure 10 thecurrent ig can be obtained as

ig Ngg(s)ugh + Nsg(s)urh minus Ygg(s)ug (15)

where Ngg(s) Nsg(s) and Ygg(s) are shown as follows

Ngg(s) Ng(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Nsg(s) Ns(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Ygg(s) Yeqg(s) + Yeqs(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

Considering the influence of grid background har-monics the magnitude-frequency curve of Ygg(s) accordingto (15) and (16) is shown in Figure 11 It can be seen fromFigure 11 that when there exists significant resonance inboth Yeqg(s) and Yeqg(s) there appears similar resonantfrequency in Ygg(s) e resonant peak of Ygg(s) is sup-pressed as the parameters kpg kpr and kir are appropriatelyincreased which shows similar features to Yeqg(s) andYeqg(s) in Figures 7 and 9 erefore in the presence of thegrid impedance the grid background harmonics still can besuppressed by appropriately adjusting the controllerparameters

5 Case Study

51 Simulation Verification In order to verify the abovecharacteristics analyses a real-time hardware-in-the-loop(HIL) system from ModelingTech is built as shown inFigure 12 Each electromagnetic transient model of theDFIG and control algorithm is constructed by StarSimsoftware and implemented on NI FPGA board 7868R(real-time simulator) e control algorithm is imple-mented on the PXIe-8821 controller (rapid control pro-totype (RCP))

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash40

ndash30

ndash20

ndash10

0

10

kpr = 05 kir = 800 sslip = ndash02

kpr = 05 kir = 100 sslip = ndash02

kpr = 10 kir = 100 sslip = ndash02kpr = 05 kir = 800 sslip = ndash01

Figure 9 Magnitude-frequency curves of Yeqs(s)

ndash

+

Ng (s)ugh

Ns (s)urh

Yeqg (s)

Yeqs (s)

is

igi2

uPCC

Zg

ug

Figure 10 Norton equivalent circuit of the double-fed windgenerator

6 Complexity

e LCL filter parameters of the grid-side converter areL1 2mH L2 1mH and C 18 μF e asynchronousmotor parameters are Lr 0404mH Rr 00079ΩLs 008mH Rs 00025Ω Lm 44mH and sslip minus 02e grid equivalent inductance is L1 01mH e 5th 7th11th 13th 17th 19th 23rd 25th 29th 31st 35th and 37thharmonic sources with a magnitude of 002 pu are in serieson the grid

Figure 13 shows the grid-side converter output currentiga the asynchronous motor stator-side current isa and thegrid current ia for different control parameter cases Fig-ure 13 shows the magnitude of harmonic current measuredunder different cases e parameters in different cases areset as follows (1) case 1 kpg 05 kig 100 kpr 05 andkir 800 (2) case 2 kpg 10 kig 100 kpr 05 and kir 800(3) case 3 kpg 05 kig 100 kpr 10 and kir 100 and (4)case 4 kpg 10 kig 100 kpr 10 and kir 100

Figures 13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonancefrequency amplification due to LCL filter resonance) andlow-frequency harmonic amplification (about 5th and 7thharmonic amplification caused by improper control pa-rameters of the rotor-side converter) due to the presence of

harmonic voltages in the grid Figures 13(b) 13(d) and 14show that by appropriately increasing kpg it is possible tosuppress the high-frequency harmonic (nearby 29th har-monic current) caused by the resonance of the LCL filter

Figures 13(c) 13(d) and 14 show that a proper increase inkpr and a decrease in kir can suppress the low-frequencyharmonic (near 5th and 7th harmonic current) caused by in-appropriate rotor-side converter control parameters esimulation results are consistent with the theoretical analyses

52 Experiment Test To further verify the theory a testplatform containing the actual wind power converter is builtin the laboratory as shown in Figure 15 In the test platformthe AC servo motor is used to emulate the wind turbine andan actual wind power converter is adopted e ratedvoltages of the DFIG and the grid are 690V and 380Vrespectively which are connected by a transformer

e rated power of the converter is 20MW LC filters areutilized for the grid-side converter with the inductance offiltering being 043mH ree-phase capacitors are con-nected in a triangle shape and the capacitance is 120 μF LCfilters and the grid-side line resistances together with thetransformer equivalent impedance are combined into anLCL filter L filters are used on the rotor side with theinductance being 015mH e switch frequency of theconverter on the grid side is 3000Hz and that on the rotorside is 2000Hz and the modulation method is SVPWMeDC-side voltage is 1050V and the AC-side grid frequency is50Hz e detailed parameters of the test platform areshown in Table 2

e acquisition device is installed at PCC to obtainsamples of voltage and current signals synchronously withthe sampling rate being 6000Hz In this part the accuracy ofthe proposed harmonic modeling of the DFIG is verifiedfrom four perspectives ie modulation method alteringcontroller parameters altering output power and the un-balance of three-phase voltage

521 Modulation Method Figure 16 shows the waveformsof the voltage and current at PCC as well as their harmonicspectrums e switch frequency of the grid-side converterand rotor-side converter is 3000Hz and 2000Hz re-spectively and there are obvious harmonics with high fre-quency close to switch frequency e high-frequencyharmonic components of the voltage and current are dis-tributed at 1920 1980 2020 and 2080Hz for the grid-sideconverter and 2800 and 2900Hz for the rotor-side converter

522 Altering Control Parameters In order to study theinfluence of different controller parameters on the currentharmonic components at PCC different PI controllerrsquosparameters of the inner current loop are set for the DFIGrsquosgrid-side converter Specifically at first kp is set to be 023and 071 respectively when ki remains as 30 Secondly kp isset to be 21 and 45 respectively when ki remains as 045Figure 17 shows the output current harmonic spectrums ofthe DFIG converter under different PI control parameters

Host PC

Oscilloscope

RCP

Real-time simulator Junction box

Figure 12 HIL simulation platform

Frequency (Hz)

Mag

nitu

de (d

B)

102 103 104ndash100

ndash50

0

50

kpg = 05 kig = 100kpr = 05 kir = 800

kpr = 05 kir = 800

kpg = 05 kig = 100

kpg = 10 kig = 100kpr = 10 kir = 100

Yeqs(s)

Yeqg(s)

Ygg(s) Ygg(s)

Figure 11 Magnitude-frequency curves of Yeqs(s) Yeqg(s) andYgg(s)

Complexity 7

45 452 454 456 458 46

ndash05

0

05

t (s)

ia

iga

isaCu

rren

t (pu

)

(a)

t (s)45 452 454 456 458 46

ia

iga

isa

ndash05

0

05

Curr

ent (

pu)

(b)

ia

iga

isa

45 452 454 456 458 46t (s)

ndash05

0

05

Curr

ent (

pu)

(c)

iga

t (s)45 452 454 456 458 46

ia isa

ndash05

0

05

Curr

ent (

pu)

(d)

Figure 13 Currents iga isa and ia (a) case 1 (b) case 2 (c) case 3 (d) case 4

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

Harmonic order

(a)

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Harmonic order

(b)

8 Complexity

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

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Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

grid-side converter is obtained and shown in Figure 2 econverter-side current feedback control which is more stablethan the grid-side current feedback current control isadopted as shown in Figure 2 [21]

In Figure 2 Kpwm is the linear gain of the pulse-widthmodulation (PWM) converter bridge i1ref is the reference ofthe current loop ugh is the harmonic voltage generated byPWM Gig is the transfer function of the current regulatorwhich adopts the proportional resonance controller anduPCC is the voltage at the grid-connected point e har-monic model shown in Figure 2 considers two kinds ofharmonic sources (1) the harmonic voltage ugh generated bythe PWM and (2) the grid background harmonic voltageuPCC at the grid-connected point

In the steady-state operation the current reference i1refremains constant [22] us according to the Mason for-mula the complex frequency-domain expression among i2ugh and uPCC can be obtained as follows

i2 Ng(s)ugh minus Yeqg(s)uPCC (1)

where s is the complex frequency-domain variable andNg(s) and Yeqg(s) are expressed as

Ng(s) ZC

Z1Z2 + Z1ZC + Z2ZC + GigKpwm Z2 + ZC( 1113857

Yeqg(s) Z1 + ZC + GigKpwm

Z1Z2 + Z1ZC + Z2ZC + GigKpwm Z2 + ZC( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

where Kpwm is usually taken as 1 Z1 sL1 +R1 Z2 sL2 +R2and ZC 1sC in which L1 R1 L2 and R2 are the LCL filterinductance and equivalent resistance and C is the filtercapacitor and Gig is expressed as

Gig kpg +skig

s2 + ω2g

(3)

where kpg and kig are the proportional and integral co-efficients of the current controller and ωg is the fundamentalfrequency

According to Figure 1 and (1) the Norton equivalentcircuit of the grid-side converter can be obtained which isshown in Figure 3 In Figure 3 Ng(s)ugh is the PW-modulated harmonic and uPCC is the grid backgroundharmonic

32 Harmonic Modeling of Rotor-Side Converter e rotor-side converter adopts the motor stator flux-orientedfeedforward decoupling control e outer control loop isthe speed control or active power control and the output ofthe outer loop controller is the reference of the innercurrent loop Similarly the response of the inner loop ismuch faster than that of the outer looperefore the outercontrol loop is neglected and the balanced three-phasesystem is equivalent to a single-phase system e currentcontrol block diagram of the rotor-side converter is shownin Figure 4

In Figure 4 irref is the current reference urh is theharmonic voltage generated by PWM and Gir is the transferfunction of the current controller and the proportionalresonance controller is used e2 is the rotor-side phaseelectromotive force of the asynchronous machine In Fig-ure 4 the output current is

ir Nr sprime( 1113857urh minus Yeqr sprime( 1113857e2 (4)

where sprime is the rotor-side complex frequency-domain var-iable Note that sprime sslip where sslip is the slip e detailedexpressions of sslip Nr(sprime) and Yeqr(sprime) are shown asfollows

sslip s minus jωm

s

Nr sprime( 1113857 1

Zr + GirKpwm

Yeqr sprime( 1113857 1

Zr + GirKpwm

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

where ωm is the rotor speed of the asynchronous motorZr sprimeLr + Rr in which Lr and Rr are the rotor leakageinductance and resistance and Gir is expressed as

1

i1refGig Kpwm

uinvr

ugh

1Z1

Z2

i1

i2

uPCC uCZC

iC

Figure 2 Current control block diagram of the grid-side converter

Ng (s)ugh

Yeqg (s)

uPCC

i2

Figure 3 Norton equivalent circuit of the grid-side converter

irref Gir Kpwmurh 1

Zr

e2

ir

Figure 4 Current control block diagram of the rotor-side converter

Complexity 3

Gir kpr +sprimekir

sprime2

+ ωg minus ωm1113872 11138732 (6)

where kpr and kir are the proportional and integral co-efficients of the current controller respectively

According to Figure 4 and (4) and combining with theasynchronous motor equivalent circuit [11 12] theNorton equivalent model of the rotor-side converter canbe obtained which is shown in Figure 5(a) Note that therotor-side variables are converted to the stator side by thegenerator conversion With the circuit conversionFigure 5(a) can be equivalent to Figure 5(b) FromFigure 5(b) we have

is Ns(s)urh minus Yeqs(s)uPCC (7)

where is is the stator-side output current of the asynchro-nous motor and Ns(s) and Yeqs(s) are expressed as

Ns(s) ZmNr sprime( 1113857

Zm + Zs + sslipYeqr sprime( 1113857ZmZs

Yeqs(s) 1 + sslipYeqr sprime( 1113857Zm

Zm + Zs + sslipYeqr sprime( 1113857ZmZs

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

where Zm sLm and Zs sLs + Rs in which Lm is the ex-citation inductance of the asynchronous motor and Ls and Rsare the stator leakage inductance and resistance

4 Characteristics Analyses of ConverterHarmonic Model

Based on the harmonic models of grid-side and rotor-side converters established in Section 3 the effects ofcomponent parameters and control parameters on har-monic characteristics are studied e detailed param-eters of the DFIG used in the simulation are shown inTable 1

41 Characteristic Analysis of Harmonic Model of Grid-SideConverter According to the Norton equivalent modelshown in Figure 3 and (1) and (2) the Bode diagram ofNg(s) and Yeqg(s) is shown in Figure 6 It can be seen fromthe figure that there are resonance peaks (magnitude greaterthan 0 dB) at a frequency of about 1450Hz in Ng(s) andYeqg(s) It indicates that the converter output current willundergo harmonic amplification when the frequency of ughand uPCC is close to the resonant frequency thus affectingthe power quality Besides it should be noted that themagnitude-frequency curves of Ng(s) and Yeqg(s) are ob-viously declining when the frequency is higher than 2000Hzindicating that the converter has a strong suppression tohigh-frequency harmonics

Ignoring the equivalent resistance of the filter inductoras it is usually small and taking Kpwm 1 the denominatorof Ng(s) and Yeqg(s) shown in (2) can be expanded to

deng 1

sC⎡⎣s

3CL1L2 + s L1 + L2( 1113857 + s

2kpgCL2 + kpg

+s2kigCL2

s2 + ω2g

+skig

s2 + ω2g

⎤⎦

(9)

It can be seen from (9) that the cubic term and theprimary term of s in the brackets form a pair of resonantpoles whose resonant frequency is

ωrg plusmn

L1 + L2

CL1L2

1113971

(10)

e resonant frequency ωrg calculated by (10) is co-incident with the resonant frequency of the LCL filtererefore it can be inferred that the resonant peak inFigure 6 is determined by the filter inductance is meansthat choosing the right filter parameters can suppress asmany harmonics as possible in the high frequency Since thePWM harmonics are mainly concentrated near the doubleswitching frequency [15 16] the harmonic frequency ishigher and can be suppressed e range of grid backgroundharmonic frequency is wide and there are many lowerharmonics such as the 5th 7th and 11th erefore it isnecessary to further study the harmonic output character-istics of the converter affected by the grid backgroundharmonics

In the vicinity of the resonant frequency ωrg an ap-proximate expression is obtained as s2≫ωg2 and the ca-pacitance of the filter capacitor is small

deng asymp s2L1L2 +

L1 + L2

C+ skpgL2 (11)

It is not difficult to see from (11) that the product of kpgand L2 provides damping for the resonance e larger theproduct the stronger the damping effect

Since the current control parameter kpg is relativelyeasier to change than L2 in practice only the influence of kpgis studied in Figure 7

It can be seen from Figure 7 that when the parameter ofthe current loop controller kpg is relatively small themagnitude-frequency curve of Yeqg(s) has a resonance peakAs kpg increases the resonance peak gradually decreases todisappear In addition Figure 7 also shows that the con-troller parameter kpi has less effect on the magnitude-fre-quency curve of Yeqg(s) since the integral term of Gig isalmost zero at high frequencies

In summary the existence of LCL filter resonance maycause harmonic amplification in the output of the grid-sideconverter of the wind power generation system and theresonance can be suppressed by adjusting the parameter ofthe current controller kpg It should be noted that kpg alsoaffects the dynamic response and stability of the convertercontrol system and this is beyond the scope of this papererefore the parameter kpg should be increased as much aspossible to suppress the harmonic output of the converterunder the premise of meeting the dynamic performance andstability requirements of the system

4 Complexity

42 Characteristic Analysis of Harmonic Model of Rotor-SideConverter According to (4)ndash(8) and Figure 5 the magni-tude-frequency curves ofNs(s) andYeqs(s) are obtained and

shown in Figure 8 It can be seen from the curves in Figure 8that at higher frequencies the rotor-side converter has aneect of suppressing the higher-frequency PWM harmonicsand the grid background harmonics Since there is no ca-pacitor in the rotor-side converter and asynchronous motorthe magnitude-frequency curves ofNs(s) and Yeqs(s) do notshow obvious resonance peaks However it should also benoted that at lower frequencies (about 300Hz in Figure 8)there are peak slopes (magnitude exceeds 0 dB) usfurther characteristic study of Yeqs(s) is needed for the lowersecondary grid background harmonics

As to the rotor-side converter the denominator ofNr(sprime) and Yekr(sprime) in (5) can be expanded (Rr is ignoredand Kpwm 1 is considered for the same reason) to

denr sprimeLr + kpr +sprimekir

sprime2 + ωg minus ωm( )

2

s minus jωm( )Lr + kpr +s minus jωm( )kir

s minus jωm( )2 + ωg minus ωm( )2

(12)

It can be seen from (12) that when the frequency is 3times higher than the fundamental frequency of the rotorthat is s minus jωm gt 3(ωg minus ωm) (it is considered that thesmaller term can be ignored when the dierence betweentwo terms is more than 10 times in engineering application)the denominator denr can be approximated to

denr asymp s minus jωm( )Lr + kpr +kir

s minus jωm (13)

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

kpg = 05 kig = 100kpg = 10 kig = 100kpg = 05 kig = 800

Figure 7Magnitude-frequency curves ofYeqg(s)with dierent kpg

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)Yeqs(s)

Ns(s)

ndash40

ndash30

ndash20

ndash10

0

10

Figure 8 Magnitude-frequency curves of Ns(s) and Yeqs(s)

e2prime

irprime

sslipYeqr (sprime)

Zm

Zs

ndash

+is

uPCCNr (sprime)urh

(a)

ndash

+is

uPCCNs (s)urh

Yeqr (s)

(b)

Figure 5 Norton equivalent circuit of the rotor-side converter (a) detailed circuit of the rotor-side converter and asynchronous machine(b) equivalent model

Table 1 Detailed parameters of the DFIG simulation platform

Parameters ValuesLCL lter (L1) 2mHLCL lter (L2) 1mHLCL lter (C) 18 μFAsynchronous motor (Lr) 0404mHAsynchronous motor (Rr) 00079ΩAsynchronous motor (Ls) 008mHAsynchronous motor (Rs) 00025ΩAsynchronous motor (Lm) 44mHsslip minus 02

102 103 104ndash100

ndash80

ndash60

ndash40

ndash20

0

20

Frequency (Hz)

Mag

nitu

de (d

B)

Yeqg(s)

Ng(s)

Figure 6 Magnitude-frequency curves of Ng(s) and Yeqg(s)

Complexity 5

With (13) it can be found that the first and third termsform a pair of resonant poles whose resonant frequency is

ωrr ωm plusmn

kir

Lr

1113971

(14)

Although there is no resonance in the rotor-side con-verter caused by the capacitor and inductor of the LCL filter(14) shows that there will be resonance caused by the in-teraction between the controller integral term and the rotorleakage inductance Besides it can be seen from (8) that thisresonance will be finally reflected to the stator side by Ns(s)

and Yeqs(s)From (13) and (14) the resonant frequency is related to

the rotor speed ωm the rotor leakage inductance Lr and thecontroller parameter kir e rotor leakage inductance Lr isrelated to the motor parameters and is fixed after the motoris manufactured e rotor speed varies according to theactual wind speed and the range of variation is limited Onlythe controller parameter kir is easy to change Similar to thegrid-side converter the controller parameter kpr has an effectof damping

Figure 9 shows the magnitude-frequency curves ofYeqs(s) with different kir kpr and ωm It can be seen fromFigure 9 that on increasing kir the peak slope of Yeqs(s)

shifts to a lower frequency and the magnitude decreases Onthe contrary the magnitude-frequency curve of Yeqs(s)

declines to a large extent as kpr is increased e slip sslipchanges from minus 02 (corresponding to ωm 12ωg) to minus 01(corresponding to ωm 11ωg) and the peak slope ofYeqs(s) shifts to a lower frequency Considering that theactual range of slip variation is small the parameters kpr andkir are the main factors affecting the harmonic outputcharacteristics of the rotor-side converter

43 Harmonic Model of Double-Fed Wind Power GenerationSystem considering Grid Impedance According to theequivalent harmonic models of grid-side and rotor-sideconverters shown in Figures 3 and 5 the overall equivalentharmonic model of the double-fed wind system is shown inFigure 10 In Figure 10 Zg is the grid equivalent impedanceand ug is the grid voltage According to Figure 10 thecurrent ig can be obtained as

ig Ngg(s)ugh + Nsg(s)urh minus Ygg(s)ug (15)

where Ngg(s) Nsg(s) and Ygg(s) are shown as follows

Ngg(s) Ng(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Nsg(s) Ns(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Ygg(s) Yeqg(s) + Yeqs(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

Considering the influence of grid background har-monics the magnitude-frequency curve of Ygg(s) accordingto (15) and (16) is shown in Figure 11 It can be seen fromFigure 11 that when there exists significant resonance inboth Yeqg(s) and Yeqg(s) there appears similar resonantfrequency in Ygg(s) e resonant peak of Ygg(s) is sup-pressed as the parameters kpg kpr and kir are appropriatelyincreased which shows similar features to Yeqg(s) andYeqg(s) in Figures 7 and 9 erefore in the presence of thegrid impedance the grid background harmonics still can besuppressed by appropriately adjusting the controllerparameters

5 Case Study

51 Simulation Verification In order to verify the abovecharacteristics analyses a real-time hardware-in-the-loop(HIL) system from ModelingTech is built as shown inFigure 12 Each electromagnetic transient model of theDFIG and control algorithm is constructed by StarSimsoftware and implemented on NI FPGA board 7868R(real-time simulator) e control algorithm is imple-mented on the PXIe-8821 controller (rapid control pro-totype (RCP))

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash40

ndash30

ndash20

ndash10

0

10

kpr = 05 kir = 800 sslip = ndash02

kpr = 05 kir = 100 sslip = ndash02

kpr = 10 kir = 100 sslip = ndash02kpr = 05 kir = 800 sslip = ndash01

Figure 9 Magnitude-frequency curves of Yeqs(s)

ndash

+

Ng (s)ugh

Ns (s)urh

Yeqg (s)

Yeqs (s)

is

igi2

uPCC

Zg

ug

Figure 10 Norton equivalent circuit of the double-fed windgenerator

6 Complexity

e LCL filter parameters of the grid-side converter areL1 2mH L2 1mH and C 18 μF e asynchronousmotor parameters are Lr 0404mH Rr 00079ΩLs 008mH Rs 00025Ω Lm 44mH and sslip minus 02e grid equivalent inductance is L1 01mH e 5th 7th11th 13th 17th 19th 23rd 25th 29th 31st 35th and 37thharmonic sources with a magnitude of 002 pu are in serieson the grid

Figure 13 shows the grid-side converter output currentiga the asynchronous motor stator-side current isa and thegrid current ia for different control parameter cases Fig-ure 13 shows the magnitude of harmonic current measuredunder different cases e parameters in different cases areset as follows (1) case 1 kpg 05 kig 100 kpr 05 andkir 800 (2) case 2 kpg 10 kig 100 kpr 05 and kir 800(3) case 3 kpg 05 kig 100 kpr 10 and kir 100 and (4)case 4 kpg 10 kig 100 kpr 10 and kir 100

Figures 13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonancefrequency amplification due to LCL filter resonance) andlow-frequency harmonic amplification (about 5th and 7thharmonic amplification caused by improper control pa-rameters of the rotor-side converter) due to the presence of

harmonic voltages in the grid Figures 13(b) 13(d) and 14show that by appropriately increasing kpg it is possible tosuppress the high-frequency harmonic (nearby 29th har-monic current) caused by the resonance of the LCL filter

Figures 13(c) 13(d) and 14 show that a proper increase inkpr and a decrease in kir can suppress the low-frequencyharmonic (near 5th and 7th harmonic current) caused by in-appropriate rotor-side converter control parameters esimulation results are consistent with the theoretical analyses

52 Experiment Test To further verify the theory a testplatform containing the actual wind power converter is builtin the laboratory as shown in Figure 15 In the test platformthe AC servo motor is used to emulate the wind turbine andan actual wind power converter is adopted e ratedvoltages of the DFIG and the grid are 690V and 380Vrespectively which are connected by a transformer

e rated power of the converter is 20MW LC filters areutilized for the grid-side converter with the inductance offiltering being 043mH ree-phase capacitors are con-nected in a triangle shape and the capacitance is 120 μF LCfilters and the grid-side line resistances together with thetransformer equivalent impedance are combined into anLCL filter L filters are used on the rotor side with theinductance being 015mH e switch frequency of theconverter on the grid side is 3000Hz and that on the rotorside is 2000Hz and the modulation method is SVPWMeDC-side voltage is 1050V and the AC-side grid frequency is50Hz e detailed parameters of the test platform areshown in Table 2

e acquisition device is installed at PCC to obtainsamples of voltage and current signals synchronously withthe sampling rate being 6000Hz In this part the accuracy ofthe proposed harmonic modeling of the DFIG is verifiedfrom four perspectives ie modulation method alteringcontroller parameters altering output power and the un-balance of three-phase voltage

521 Modulation Method Figure 16 shows the waveformsof the voltage and current at PCC as well as their harmonicspectrums e switch frequency of the grid-side converterand rotor-side converter is 3000Hz and 2000Hz re-spectively and there are obvious harmonics with high fre-quency close to switch frequency e high-frequencyharmonic components of the voltage and current are dis-tributed at 1920 1980 2020 and 2080Hz for the grid-sideconverter and 2800 and 2900Hz for the rotor-side converter

522 Altering Control Parameters In order to study theinfluence of different controller parameters on the currentharmonic components at PCC different PI controllerrsquosparameters of the inner current loop are set for the DFIGrsquosgrid-side converter Specifically at first kp is set to be 023and 071 respectively when ki remains as 30 Secondly kp isset to be 21 and 45 respectively when ki remains as 045Figure 17 shows the output current harmonic spectrums ofthe DFIG converter under different PI control parameters

Host PC

Oscilloscope

RCP

Real-time simulator Junction box

Figure 12 HIL simulation platform

Frequency (Hz)

Mag

nitu

de (d

B)

102 103 104ndash100

ndash50

0

50

kpg = 05 kig = 100kpr = 05 kir = 800

kpr = 05 kir = 800

kpg = 05 kig = 100

kpg = 10 kig = 100kpr = 10 kir = 100

Yeqs(s)

Yeqg(s)

Ygg(s) Ygg(s)

Figure 11 Magnitude-frequency curves of Yeqs(s) Yeqg(s) andYgg(s)

Complexity 7

45 452 454 456 458 46

ndash05

0

05

t (s)

ia

iga

isaCu

rren

t (pu

)

(a)

t (s)45 452 454 456 458 46

ia

iga

isa

ndash05

0

05

Curr

ent (

pu)

(b)

ia

iga

isa

45 452 454 456 458 46t (s)

ndash05

0

05

Curr

ent (

pu)

(c)

iga

t (s)45 452 454 456 458 46

ia isa

ndash05

0

05

Curr

ent (

pu)

(d)

Figure 13 Currents iga isa and ia (a) case 1 (b) case 2 (c) case 3 (d) case 4

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

Harmonic order

(a)

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Harmonic order

(b)

8 Complexity

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

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Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

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Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom

Gir kpr +sprimekir

sprime2

+ ωg minus ωm1113872 11138732 (6)

where kpr and kir are the proportional and integral co-efficients of the current controller respectively

According to Figure 4 and (4) and combining with theasynchronous motor equivalent circuit [11 12] theNorton equivalent model of the rotor-side converter canbe obtained which is shown in Figure 5(a) Note that therotor-side variables are converted to the stator side by thegenerator conversion With the circuit conversionFigure 5(a) can be equivalent to Figure 5(b) FromFigure 5(b) we have

is Ns(s)urh minus Yeqs(s)uPCC (7)

where is is the stator-side output current of the asynchro-nous motor and Ns(s) and Yeqs(s) are expressed as

Ns(s) ZmNr sprime( 1113857

Zm + Zs + sslipYeqr sprime( 1113857ZmZs

Yeqs(s) 1 + sslipYeqr sprime( 1113857Zm

Zm + Zs + sslipYeqr sprime( 1113857ZmZs

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

where Zm sLm and Zs sLs + Rs in which Lm is the ex-citation inductance of the asynchronous motor and Ls and Rsare the stator leakage inductance and resistance

4 Characteristics Analyses of ConverterHarmonic Model

Based on the harmonic models of grid-side and rotor-side converters established in Section 3 the effects ofcomponent parameters and control parameters on har-monic characteristics are studied e detailed param-eters of the DFIG used in the simulation are shown inTable 1

41 Characteristic Analysis of Harmonic Model of Grid-SideConverter According to the Norton equivalent modelshown in Figure 3 and (1) and (2) the Bode diagram ofNg(s) and Yeqg(s) is shown in Figure 6 It can be seen fromthe figure that there are resonance peaks (magnitude greaterthan 0 dB) at a frequency of about 1450Hz in Ng(s) andYeqg(s) It indicates that the converter output current willundergo harmonic amplification when the frequency of ughand uPCC is close to the resonant frequency thus affectingthe power quality Besides it should be noted that themagnitude-frequency curves of Ng(s) and Yeqg(s) are ob-viously declining when the frequency is higher than 2000Hzindicating that the converter has a strong suppression tohigh-frequency harmonics

Ignoring the equivalent resistance of the filter inductoras it is usually small and taking Kpwm 1 the denominatorof Ng(s) and Yeqg(s) shown in (2) can be expanded to

deng 1

sC⎡⎣s

3CL1L2 + s L1 + L2( 1113857 + s

2kpgCL2 + kpg

+s2kigCL2

s2 + ω2g

+skig

s2 + ω2g

⎤⎦

(9)

It can be seen from (9) that the cubic term and theprimary term of s in the brackets form a pair of resonantpoles whose resonant frequency is

ωrg plusmn

L1 + L2

CL1L2

1113971

(10)

e resonant frequency ωrg calculated by (10) is co-incident with the resonant frequency of the LCL filtererefore it can be inferred that the resonant peak inFigure 6 is determined by the filter inductance is meansthat choosing the right filter parameters can suppress asmany harmonics as possible in the high frequency Since thePWM harmonics are mainly concentrated near the doubleswitching frequency [15 16] the harmonic frequency ishigher and can be suppressed e range of grid backgroundharmonic frequency is wide and there are many lowerharmonics such as the 5th 7th and 11th erefore it isnecessary to further study the harmonic output character-istics of the converter affected by the grid backgroundharmonics

In the vicinity of the resonant frequency ωrg an ap-proximate expression is obtained as s2≫ωg2 and the ca-pacitance of the filter capacitor is small

deng asymp s2L1L2 +

L1 + L2

C+ skpgL2 (11)

It is not difficult to see from (11) that the product of kpgand L2 provides damping for the resonance e larger theproduct the stronger the damping effect

Since the current control parameter kpg is relativelyeasier to change than L2 in practice only the influence of kpgis studied in Figure 7

It can be seen from Figure 7 that when the parameter ofthe current loop controller kpg is relatively small themagnitude-frequency curve of Yeqg(s) has a resonance peakAs kpg increases the resonance peak gradually decreases todisappear In addition Figure 7 also shows that the con-troller parameter kpi has less effect on the magnitude-fre-quency curve of Yeqg(s) since the integral term of Gig isalmost zero at high frequencies

In summary the existence of LCL filter resonance maycause harmonic amplification in the output of the grid-sideconverter of the wind power generation system and theresonance can be suppressed by adjusting the parameter ofthe current controller kpg It should be noted that kpg alsoaffects the dynamic response and stability of the convertercontrol system and this is beyond the scope of this papererefore the parameter kpg should be increased as much aspossible to suppress the harmonic output of the converterunder the premise of meeting the dynamic performance andstability requirements of the system

4 Complexity

42 Characteristic Analysis of Harmonic Model of Rotor-SideConverter According to (4)ndash(8) and Figure 5 the magni-tude-frequency curves ofNs(s) andYeqs(s) are obtained and

shown in Figure 8 It can be seen from the curves in Figure 8that at higher frequencies the rotor-side converter has aneect of suppressing the higher-frequency PWM harmonicsand the grid background harmonics Since there is no ca-pacitor in the rotor-side converter and asynchronous motorthe magnitude-frequency curves ofNs(s) and Yeqs(s) do notshow obvious resonance peaks However it should also benoted that at lower frequencies (about 300Hz in Figure 8)there are peak slopes (magnitude exceeds 0 dB) usfurther characteristic study of Yeqs(s) is needed for the lowersecondary grid background harmonics

As to the rotor-side converter the denominator ofNr(sprime) and Yekr(sprime) in (5) can be expanded (Rr is ignoredand Kpwm 1 is considered for the same reason) to

denr sprimeLr + kpr +sprimekir

sprime2 + ωg minus ωm( )

2

s minus jωm( )Lr + kpr +s minus jωm( )kir

s minus jωm( )2 + ωg minus ωm( )2

(12)

It can be seen from (12) that when the frequency is 3times higher than the fundamental frequency of the rotorthat is s minus jωm gt 3(ωg minus ωm) (it is considered that thesmaller term can be ignored when the dierence betweentwo terms is more than 10 times in engineering application)the denominator denr can be approximated to

denr asymp s minus jωm( )Lr + kpr +kir

s minus jωm (13)

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

kpg = 05 kig = 100kpg = 10 kig = 100kpg = 05 kig = 800

Figure 7Magnitude-frequency curves ofYeqg(s)with dierent kpg

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)Yeqs(s)

Ns(s)

ndash40

ndash30

ndash20

ndash10

0

10

Figure 8 Magnitude-frequency curves of Ns(s) and Yeqs(s)

e2prime

irprime

sslipYeqr (sprime)

Zm

Zs

ndash

+is

uPCCNr (sprime)urh

(a)

ndash

+is

uPCCNs (s)urh

Yeqr (s)

(b)

Figure 5 Norton equivalent circuit of the rotor-side converter (a) detailed circuit of the rotor-side converter and asynchronous machine(b) equivalent model

Table 1 Detailed parameters of the DFIG simulation platform

Parameters ValuesLCL lter (L1) 2mHLCL lter (L2) 1mHLCL lter (C) 18 μFAsynchronous motor (Lr) 0404mHAsynchronous motor (Rr) 00079ΩAsynchronous motor (Ls) 008mHAsynchronous motor (Rs) 00025ΩAsynchronous motor (Lm) 44mHsslip minus 02

102 103 104ndash100

ndash80

ndash60

ndash40

ndash20

0

20

Frequency (Hz)

Mag

nitu

de (d

B)

Yeqg(s)

Ng(s)

Figure 6 Magnitude-frequency curves of Ng(s) and Yeqg(s)

Complexity 5

With (13) it can be found that the first and third termsform a pair of resonant poles whose resonant frequency is

ωrr ωm plusmn

kir

Lr

1113971

(14)

Although there is no resonance in the rotor-side con-verter caused by the capacitor and inductor of the LCL filter(14) shows that there will be resonance caused by the in-teraction between the controller integral term and the rotorleakage inductance Besides it can be seen from (8) that thisresonance will be finally reflected to the stator side by Ns(s)

and Yeqs(s)From (13) and (14) the resonant frequency is related to

the rotor speed ωm the rotor leakage inductance Lr and thecontroller parameter kir e rotor leakage inductance Lr isrelated to the motor parameters and is fixed after the motoris manufactured e rotor speed varies according to theactual wind speed and the range of variation is limited Onlythe controller parameter kir is easy to change Similar to thegrid-side converter the controller parameter kpr has an effectof damping

Figure 9 shows the magnitude-frequency curves ofYeqs(s) with different kir kpr and ωm It can be seen fromFigure 9 that on increasing kir the peak slope of Yeqs(s)

shifts to a lower frequency and the magnitude decreases Onthe contrary the magnitude-frequency curve of Yeqs(s)

declines to a large extent as kpr is increased e slip sslipchanges from minus 02 (corresponding to ωm 12ωg) to minus 01(corresponding to ωm 11ωg) and the peak slope ofYeqs(s) shifts to a lower frequency Considering that theactual range of slip variation is small the parameters kpr andkir are the main factors affecting the harmonic outputcharacteristics of the rotor-side converter

43 Harmonic Model of Double-Fed Wind Power GenerationSystem considering Grid Impedance According to theequivalent harmonic models of grid-side and rotor-sideconverters shown in Figures 3 and 5 the overall equivalentharmonic model of the double-fed wind system is shown inFigure 10 In Figure 10 Zg is the grid equivalent impedanceand ug is the grid voltage According to Figure 10 thecurrent ig can be obtained as

ig Ngg(s)ugh + Nsg(s)urh minus Ygg(s)ug (15)

where Ngg(s) Nsg(s) and Ygg(s) are shown as follows

Ngg(s) Ng(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Nsg(s) Ns(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Ygg(s) Yeqg(s) + Yeqs(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

Considering the influence of grid background har-monics the magnitude-frequency curve of Ygg(s) accordingto (15) and (16) is shown in Figure 11 It can be seen fromFigure 11 that when there exists significant resonance inboth Yeqg(s) and Yeqg(s) there appears similar resonantfrequency in Ygg(s) e resonant peak of Ygg(s) is sup-pressed as the parameters kpg kpr and kir are appropriatelyincreased which shows similar features to Yeqg(s) andYeqg(s) in Figures 7 and 9 erefore in the presence of thegrid impedance the grid background harmonics still can besuppressed by appropriately adjusting the controllerparameters

5 Case Study

51 Simulation Verification In order to verify the abovecharacteristics analyses a real-time hardware-in-the-loop(HIL) system from ModelingTech is built as shown inFigure 12 Each electromagnetic transient model of theDFIG and control algorithm is constructed by StarSimsoftware and implemented on NI FPGA board 7868R(real-time simulator) e control algorithm is imple-mented on the PXIe-8821 controller (rapid control pro-totype (RCP))

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash40

ndash30

ndash20

ndash10

0

10

kpr = 05 kir = 800 sslip = ndash02

kpr = 05 kir = 100 sslip = ndash02

kpr = 10 kir = 100 sslip = ndash02kpr = 05 kir = 800 sslip = ndash01

Figure 9 Magnitude-frequency curves of Yeqs(s)

ndash

+

Ng (s)ugh

Ns (s)urh

Yeqg (s)

Yeqs (s)

is

igi2

uPCC

Zg

ug

Figure 10 Norton equivalent circuit of the double-fed windgenerator

6 Complexity

e LCL filter parameters of the grid-side converter areL1 2mH L2 1mH and C 18 μF e asynchronousmotor parameters are Lr 0404mH Rr 00079ΩLs 008mH Rs 00025Ω Lm 44mH and sslip minus 02e grid equivalent inductance is L1 01mH e 5th 7th11th 13th 17th 19th 23rd 25th 29th 31st 35th and 37thharmonic sources with a magnitude of 002 pu are in serieson the grid

Figure 13 shows the grid-side converter output currentiga the asynchronous motor stator-side current isa and thegrid current ia for different control parameter cases Fig-ure 13 shows the magnitude of harmonic current measuredunder different cases e parameters in different cases areset as follows (1) case 1 kpg 05 kig 100 kpr 05 andkir 800 (2) case 2 kpg 10 kig 100 kpr 05 and kir 800(3) case 3 kpg 05 kig 100 kpr 10 and kir 100 and (4)case 4 kpg 10 kig 100 kpr 10 and kir 100

Figures 13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonancefrequency amplification due to LCL filter resonance) andlow-frequency harmonic amplification (about 5th and 7thharmonic amplification caused by improper control pa-rameters of the rotor-side converter) due to the presence of

harmonic voltages in the grid Figures 13(b) 13(d) and 14show that by appropriately increasing kpg it is possible tosuppress the high-frequency harmonic (nearby 29th har-monic current) caused by the resonance of the LCL filter

Figures 13(c) 13(d) and 14 show that a proper increase inkpr and a decrease in kir can suppress the low-frequencyharmonic (near 5th and 7th harmonic current) caused by in-appropriate rotor-side converter control parameters esimulation results are consistent with the theoretical analyses

52 Experiment Test To further verify the theory a testplatform containing the actual wind power converter is builtin the laboratory as shown in Figure 15 In the test platformthe AC servo motor is used to emulate the wind turbine andan actual wind power converter is adopted e ratedvoltages of the DFIG and the grid are 690V and 380Vrespectively which are connected by a transformer

e rated power of the converter is 20MW LC filters areutilized for the grid-side converter with the inductance offiltering being 043mH ree-phase capacitors are con-nected in a triangle shape and the capacitance is 120 μF LCfilters and the grid-side line resistances together with thetransformer equivalent impedance are combined into anLCL filter L filters are used on the rotor side with theinductance being 015mH e switch frequency of theconverter on the grid side is 3000Hz and that on the rotorside is 2000Hz and the modulation method is SVPWMeDC-side voltage is 1050V and the AC-side grid frequency is50Hz e detailed parameters of the test platform areshown in Table 2

e acquisition device is installed at PCC to obtainsamples of voltage and current signals synchronously withthe sampling rate being 6000Hz In this part the accuracy ofthe proposed harmonic modeling of the DFIG is verifiedfrom four perspectives ie modulation method alteringcontroller parameters altering output power and the un-balance of three-phase voltage

521 Modulation Method Figure 16 shows the waveformsof the voltage and current at PCC as well as their harmonicspectrums e switch frequency of the grid-side converterand rotor-side converter is 3000Hz and 2000Hz re-spectively and there are obvious harmonics with high fre-quency close to switch frequency e high-frequencyharmonic components of the voltage and current are dis-tributed at 1920 1980 2020 and 2080Hz for the grid-sideconverter and 2800 and 2900Hz for the rotor-side converter

522 Altering Control Parameters In order to study theinfluence of different controller parameters on the currentharmonic components at PCC different PI controllerrsquosparameters of the inner current loop are set for the DFIGrsquosgrid-side converter Specifically at first kp is set to be 023and 071 respectively when ki remains as 30 Secondly kp isset to be 21 and 45 respectively when ki remains as 045Figure 17 shows the output current harmonic spectrums ofthe DFIG converter under different PI control parameters

Host PC

Oscilloscope

RCP

Real-time simulator Junction box

Figure 12 HIL simulation platform

Frequency (Hz)

Mag

nitu

de (d

B)

102 103 104ndash100

ndash50

0

50

kpg = 05 kig = 100kpr = 05 kir = 800

kpr = 05 kir = 800

kpg = 05 kig = 100

kpg = 10 kig = 100kpr = 10 kir = 100

Yeqs(s)

Yeqg(s)

Ygg(s) Ygg(s)

Figure 11 Magnitude-frequency curves of Yeqs(s) Yeqg(s) andYgg(s)

Complexity 7

45 452 454 456 458 46

ndash05

0

05

t (s)

ia

iga

isaCu

rren

t (pu

)

(a)

t (s)45 452 454 456 458 46

ia

iga

isa

ndash05

0

05

Curr

ent (

pu)

(b)

ia

iga

isa

45 452 454 456 458 46t (s)

ndash05

0

05

Curr

ent (

pu)

(c)

iga

t (s)45 452 454 456 458 46

ia isa

ndash05

0

05

Curr

ent (

pu)

(d)

Figure 13 Currents iga isa and ia (a) case 1 (b) case 2 (c) case 3 (d) case 4

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

Harmonic order

(a)

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Harmonic order

(b)

8 Complexity

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

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Applied MathematicsJournal of

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Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

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Submit your manuscripts atwwwhindawicom

42 Characteristic Analysis of Harmonic Model of Rotor-SideConverter According to (4)ndash(8) and Figure 5 the magni-tude-frequency curves ofNs(s) andYeqs(s) are obtained and

shown in Figure 8 It can be seen from the curves in Figure 8that at higher frequencies the rotor-side converter has aneect of suppressing the higher-frequency PWM harmonicsand the grid background harmonics Since there is no ca-pacitor in the rotor-side converter and asynchronous motorthe magnitude-frequency curves ofNs(s) and Yeqs(s) do notshow obvious resonance peaks However it should also benoted that at lower frequencies (about 300Hz in Figure 8)there are peak slopes (magnitude exceeds 0 dB) usfurther characteristic study of Yeqs(s) is needed for the lowersecondary grid background harmonics

As to the rotor-side converter the denominator ofNr(sprime) and Yekr(sprime) in (5) can be expanded (Rr is ignoredand Kpwm 1 is considered for the same reason) to

denr sprimeLr + kpr +sprimekir

sprime2 + ωg minus ωm( )

2

s minus jωm( )Lr + kpr +s minus jωm( )kir

s minus jωm( )2 + ωg minus ωm( )2

(12)

It can be seen from (12) that when the frequency is 3times higher than the fundamental frequency of the rotorthat is s minus jωm gt 3(ωg minus ωm) (it is considered that thesmaller term can be ignored when the dierence betweentwo terms is more than 10 times in engineering application)the denominator denr can be approximated to

denr asymp s minus jωm( )Lr + kpr +kir

s minus jωm (13)

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

kpg = 05 kig = 100kpg = 10 kig = 100kpg = 05 kig = 800

Figure 7Magnitude-frequency curves ofYeqg(s)with dierent kpg

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)Yeqs(s)

Ns(s)

ndash40

ndash30

ndash20

ndash10

0

10

Figure 8 Magnitude-frequency curves of Ns(s) and Yeqs(s)

e2prime

irprime

sslipYeqr (sprime)

Zm

Zs

ndash

+is

uPCCNr (sprime)urh

(a)

ndash

+is

uPCCNs (s)urh

Yeqr (s)

(b)

Figure 5 Norton equivalent circuit of the rotor-side converter (a) detailed circuit of the rotor-side converter and asynchronous machine(b) equivalent model

Table 1 Detailed parameters of the DFIG simulation platform

Parameters ValuesLCL lter (L1) 2mHLCL lter (L2) 1mHLCL lter (C) 18 μFAsynchronous motor (Lr) 0404mHAsynchronous motor (Rr) 00079ΩAsynchronous motor (Ls) 008mHAsynchronous motor (Rs) 00025ΩAsynchronous motor (Lm) 44mHsslip minus 02

102 103 104ndash100

ndash80

ndash60

ndash40

ndash20

0

20

Frequency (Hz)

Mag

nitu

de (d

B)

Yeqg(s)

Ng(s)

Figure 6 Magnitude-frequency curves of Ng(s) and Yeqg(s)

Complexity 5

With (13) it can be found that the first and third termsform a pair of resonant poles whose resonant frequency is

ωrr ωm plusmn

kir

Lr

1113971

(14)

Although there is no resonance in the rotor-side con-verter caused by the capacitor and inductor of the LCL filter(14) shows that there will be resonance caused by the in-teraction between the controller integral term and the rotorleakage inductance Besides it can be seen from (8) that thisresonance will be finally reflected to the stator side by Ns(s)

and Yeqs(s)From (13) and (14) the resonant frequency is related to

the rotor speed ωm the rotor leakage inductance Lr and thecontroller parameter kir e rotor leakage inductance Lr isrelated to the motor parameters and is fixed after the motoris manufactured e rotor speed varies according to theactual wind speed and the range of variation is limited Onlythe controller parameter kir is easy to change Similar to thegrid-side converter the controller parameter kpr has an effectof damping

Figure 9 shows the magnitude-frequency curves ofYeqs(s) with different kir kpr and ωm It can be seen fromFigure 9 that on increasing kir the peak slope of Yeqs(s)

shifts to a lower frequency and the magnitude decreases Onthe contrary the magnitude-frequency curve of Yeqs(s)

declines to a large extent as kpr is increased e slip sslipchanges from minus 02 (corresponding to ωm 12ωg) to minus 01(corresponding to ωm 11ωg) and the peak slope ofYeqs(s) shifts to a lower frequency Considering that theactual range of slip variation is small the parameters kpr andkir are the main factors affecting the harmonic outputcharacteristics of the rotor-side converter

43 Harmonic Model of Double-Fed Wind Power GenerationSystem considering Grid Impedance According to theequivalent harmonic models of grid-side and rotor-sideconverters shown in Figures 3 and 5 the overall equivalentharmonic model of the double-fed wind system is shown inFigure 10 In Figure 10 Zg is the grid equivalent impedanceand ug is the grid voltage According to Figure 10 thecurrent ig can be obtained as

ig Ngg(s)ugh + Nsg(s)urh minus Ygg(s)ug (15)

where Ngg(s) Nsg(s) and Ygg(s) are shown as follows

Ngg(s) Ng(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Nsg(s) Ns(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Ygg(s) Yeqg(s) + Yeqs(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

Considering the influence of grid background har-monics the magnitude-frequency curve of Ygg(s) accordingto (15) and (16) is shown in Figure 11 It can be seen fromFigure 11 that when there exists significant resonance inboth Yeqg(s) and Yeqg(s) there appears similar resonantfrequency in Ygg(s) e resonant peak of Ygg(s) is sup-pressed as the parameters kpg kpr and kir are appropriatelyincreased which shows similar features to Yeqg(s) andYeqg(s) in Figures 7 and 9 erefore in the presence of thegrid impedance the grid background harmonics still can besuppressed by appropriately adjusting the controllerparameters

5 Case Study

51 Simulation Verification In order to verify the abovecharacteristics analyses a real-time hardware-in-the-loop(HIL) system from ModelingTech is built as shown inFigure 12 Each electromagnetic transient model of theDFIG and control algorithm is constructed by StarSimsoftware and implemented on NI FPGA board 7868R(real-time simulator) e control algorithm is imple-mented on the PXIe-8821 controller (rapid control pro-totype (RCP))

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash40

ndash30

ndash20

ndash10

0

10

kpr = 05 kir = 800 sslip = ndash02

kpr = 05 kir = 100 sslip = ndash02

kpr = 10 kir = 100 sslip = ndash02kpr = 05 kir = 800 sslip = ndash01

Figure 9 Magnitude-frequency curves of Yeqs(s)

ndash

+

Ng (s)ugh

Ns (s)urh

Yeqg (s)

Yeqs (s)

is

igi2

uPCC

Zg

ug

Figure 10 Norton equivalent circuit of the double-fed windgenerator

6 Complexity

e LCL filter parameters of the grid-side converter areL1 2mH L2 1mH and C 18 μF e asynchronousmotor parameters are Lr 0404mH Rr 00079ΩLs 008mH Rs 00025Ω Lm 44mH and sslip minus 02e grid equivalent inductance is L1 01mH e 5th 7th11th 13th 17th 19th 23rd 25th 29th 31st 35th and 37thharmonic sources with a magnitude of 002 pu are in serieson the grid

Figure 13 shows the grid-side converter output currentiga the asynchronous motor stator-side current isa and thegrid current ia for different control parameter cases Fig-ure 13 shows the magnitude of harmonic current measuredunder different cases e parameters in different cases areset as follows (1) case 1 kpg 05 kig 100 kpr 05 andkir 800 (2) case 2 kpg 10 kig 100 kpr 05 and kir 800(3) case 3 kpg 05 kig 100 kpr 10 and kir 100 and (4)case 4 kpg 10 kig 100 kpr 10 and kir 100

Figures 13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonancefrequency amplification due to LCL filter resonance) andlow-frequency harmonic amplification (about 5th and 7thharmonic amplification caused by improper control pa-rameters of the rotor-side converter) due to the presence of

harmonic voltages in the grid Figures 13(b) 13(d) and 14show that by appropriately increasing kpg it is possible tosuppress the high-frequency harmonic (nearby 29th har-monic current) caused by the resonance of the LCL filter

Figures 13(c) 13(d) and 14 show that a proper increase inkpr and a decrease in kir can suppress the low-frequencyharmonic (near 5th and 7th harmonic current) caused by in-appropriate rotor-side converter control parameters esimulation results are consistent with the theoretical analyses

52 Experiment Test To further verify the theory a testplatform containing the actual wind power converter is builtin the laboratory as shown in Figure 15 In the test platformthe AC servo motor is used to emulate the wind turbine andan actual wind power converter is adopted e ratedvoltages of the DFIG and the grid are 690V and 380Vrespectively which are connected by a transformer

e rated power of the converter is 20MW LC filters areutilized for the grid-side converter with the inductance offiltering being 043mH ree-phase capacitors are con-nected in a triangle shape and the capacitance is 120 μF LCfilters and the grid-side line resistances together with thetransformer equivalent impedance are combined into anLCL filter L filters are used on the rotor side with theinductance being 015mH e switch frequency of theconverter on the grid side is 3000Hz and that on the rotorside is 2000Hz and the modulation method is SVPWMeDC-side voltage is 1050V and the AC-side grid frequency is50Hz e detailed parameters of the test platform areshown in Table 2

e acquisition device is installed at PCC to obtainsamples of voltage and current signals synchronously withthe sampling rate being 6000Hz In this part the accuracy ofthe proposed harmonic modeling of the DFIG is verifiedfrom four perspectives ie modulation method alteringcontroller parameters altering output power and the un-balance of three-phase voltage

521 Modulation Method Figure 16 shows the waveformsof the voltage and current at PCC as well as their harmonicspectrums e switch frequency of the grid-side converterand rotor-side converter is 3000Hz and 2000Hz re-spectively and there are obvious harmonics with high fre-quency close to switch frequency e high-frequencyharmonic components of the voltage and current are dis-tributed at 1920 1980 2020 and 2080Hz for the grid-sideconverter and 2800 and 2900Hz for the rotor-side converter

522 Altering Control Parameters In order to study theinfluence of different controller parameters on the currentharmonic components at PCC different PI controllerrsquosparameters of the inner current loop are set for the DFIGrsquosgrid-side converter Specifically at first kp is set to be 023and 071 respectively when ki remains as 30 Secondly kp isset to be 21 and 45 respectively when ki remains as 045Figure 17 shows the output current harmonic spectrums ofthe DFIG converter under different PI control parameters

Host PC

Oscilloscope

RCP

Real-time simulator Junction box

Figure 12 HIL simulation platform

Frequency (Hz)

Mag

nitu

de (d

B)

102 103 104ndash100

ndash50

0

50

kpg = 05 kig = 100kpr = 05 kir = 800

kpr = 05 kir = 800

kpg = 05 kig = 100

kpg = 10 kig = 100kpr = 10 kir = 100

Yeqs(s)

Yeqg(s)

Ygg(s) Ygg(s)

Figure 11 Magnitude-frequency curves of Yeqs(s) Yeqg(s) andYgg(s)

Complexity 7

45 452 454 456 458 46

ndash05

0

05

t (s)

ia

iga

isaCu

rren

t (pu

)

(a)

t (s)45 452 454 456 458 46

ia

iga

isa

ndash05

0

05

Curr

ent (

pu)

(b)

ia

iga

isa

45 452 454 456 458 46t (s)

ndash05

0

05

Curr

ent (

pu)

(c)

iga

t (s)45 452 454 456 458 46

ia isa

ndash05

0

05

Curr

ent (

pu)

(d)

Figure 13 Currents iga isa and ia (a) case 1 (b) case 2 (c) case 3 (d) case 4

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

Harmonic order

(a)

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Harmonic order

(b)

8 Complexity

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

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Applied MathematicsJournal of

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Hindawiwwwhindawicom Volume 2018

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Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

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Engineering Mathematics

International Journal of

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Submit your manuscripts atwwwhindawicom

With (13) it can be found that the first and third termsform a pair of resonant poles whose resonant frequency is

ωrr ωm plusmn

kir

Lr

1113971

(14)

Although there is no resonance in the rotor-side con-verter caused by the capacitor and inductor of the LCL filter(14) shows that there will be resonance caused by the in-teraction between the controller integral term and the rotorleakage inductance Besides it can be seen from (8) that thisresonance will be finally reflected to the stator side by Ns(s)

and Yeqs(s)From (13) and (14) the resonant frequency is related to

the rotor speed ωm the rotor leakage inductance Lr and thecontroller parameter kir e rotor leakage inductance Lr isrelated to the motor parameters and is fixed after the motoris manufactured e rotor speed varies according to theactual wind speed and the range of variation is limited Onlythe controller parameter kir is easy to change Similar to thegrid-side converter the controller parameter kpr has an effectof damping

Figure 9 shows the magnitude-frequency curves ofYeqs(s) with different kir kpr and ωm It can be seen fromFigure 9 that on increasing kir the peak slope of Yeqs(s)

shifts to a lower frequency and the magnitude decreases Onthe contrary the magnitude-frequency curve of Yeqs(s)

declines to a large extent as kpr is increased e slip sslipchanges from minus 02 (corresponding to ωm 12ωg) to minus 01(corresponding to ωm 11ωg) and the peak slope ofYeqs(s) shifts to a lower frequency Considering that theactual range of slip variation is small the parameters kpr andkir are the main factors affecting the harmonic outputcharacteristics of the rotor-side converter

43 Harmonic Model of Double-Fed Wind Power GenerationSystem considering Grid Impedance According to theequivalent harmonic models of grid-side and rotor-sideconverters shown in Figures 3 and 5 the overall equivalentharmonic model of the double-fed wind system is shown inFigure 10 In Figure 10 Zg is the grid equivalent impedanceand ug is the grid voltage According to Figure 10 thecurrent ig can be obtained as

ig Ngg(s)ugh + Nsg(s)urh minus Ygg(s)ug (15)

where Ngg(s) Nsg(s) and Ygg(s) are shown as follows

Ngg(s) Ng(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Nsg(s) Ns(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

Ygg(s) Yeqg(s) + Yeqs(s)

1 + Zg Yeqg(s) + Yeqs(s)1113872 1113873

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

Considering the influence of grid background har-monics the magnitude-frequency curve of Ygg(s) accordingto (15) and (16) is shown in Figure 11 It can be seen fromFigure 11 that when there exists significant resonance inboth Yeqg(s) and Yeqg(s) there appears similar resonantfrequency in Ygg(s) e resonant peak of Ygg(s) is sup-pressed as the parameters kpg kpr and kir are appropriatelyincreased which shows similar features to Yeqg(s) andYeqg(s) in Figures 7 and 9 erefore in the presence of thegrid impedance the grid background harmonics still can besuppressed by appropriately adjusting the controllerparameters

5 Case Study

51 Simulation Verification In order to verify the abovecharacteristics analyses a real-time hardware-in-the-loop(HIL) system from ModelingTech is built as shown inFigure 12 Each electromagnetic transient model of theDFIG and control algorithm is constructed by StarSimsoftware and implemented on NI FPGA board 7868R(real-time simulator) e control algorithm is imple-mented on the PXIe-8821 controller (rapid control pro-totype (RCP))

102 103 104

Frequency (Hz)

Mag

nitu

de (d

B)

ndash40

ndash30

ndash20

ndash10

0

10

kpr = 05 kir = 800 sslip = ndash02

kpr = 05 kir = 100 sslip = ndash02

kpr = 10 kir = 100 sslip = ndash02kpr = 05 kir = 800 sslip = ndash01

Figure 9 Magnitude-frequency curves of Yeqs(s)

ndash

+

Ng (s)ugh

Ns (s)urh

Yeqg (s)

Yeqs (s)

is

igi2

uPCC

Zg

ug

Figure 10 Norton equivalent circuit of the double-fed windgenerator

6 Complexity

e LCL filter parameters of the grid-side converter areL1 2mH L2 1mH and C 18 μF e asynchronousmotor parameters are Lr 0404mH Rr 00079ΩLs 008mH Rs 00025Ω Lm 44mH and sslip minus 02e grid equivalent inductance is L1 01mH e 5th 7th11th 13th 17th 19th 23rd 25th 29th 31st 35th and 37thharmonic sources with a magnitude of 002 pu are in serieson the grid

Figure 13 shows the grid-side converter output currentiga the asynchronous motor stator-side current isa and thegrid current ia for different control parameter cases Fig-ure 13 shows the magnitude of harmonic current measuredunder different cases e parameters in different cases areset as follows (1) case 1 kpg 05 kig 100 kpr 05 andkir 800 (2) case 2 kpg 10 kig 100 kpr 05 and kir 800(3) case 3 kpg 05 kig 100 kpr 10 and kir 100 and (4)case 4 kpg 10 kig 100 kpr 10 and kir 100

Figures 13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonancefrequency amplification due to LCL filter resonance) andlow-frequency harmonic amplification (about 5th and 7thharmonic amplification caused by improper control pa-rameters of the rotor-side converter) due to the presence of

harmonic voltages in the grid Figures 13(b) 13(d) and 14show that by appropriately increasing kpg it is possible tosuppress the high-frequency harmonic (nearby 29th har-monic current) caused by the resonance of the LCL filter

Figures 13(c) 13(d) and 14 show that a proper increase inkpr and a decrease in kir can suppress the low-frequencyharmonic (near 5th and 7th harmonic current) caused by in-appropriate rotor-side converter control parameters esimulation results are consistent with the theoretical analyses

52 Experiment Test To further verify the theory a testplatform containing the actual wind power converter is builtin the laboratory as shown in Figure 15 In the test platformthe AC servo motor is used to emulate the wind turbine andan actual wind power converter is adopted e ratedvoltages of the DFIG and the grid are 690V and 380Vrespectively which are connected by a transformer

e rated power of the converter is 20MW LC filters areutilized for the grid-side converter with the inductance offiltering being 043mH ree-phase capacitors are con-nected in a triangle shape and the capacitance is 120 μF LCfilters and the grid-side line resistances together with thetransformer equivalent impedance are combined into anLCL filter L filters are used on the rotor side with theinductance being 015mH e switch frequency of theconverter on the grid side is 3000Hz and that on the rotorside is 2000Hz and the modulation method is SVPWMeDC-side voltage is 1050V and the AC-side grid frequency is50Hz e detailed parameters of the test platform areshown in Table 2

e acquisition device is installed at PCC to obtainsamples of voltage and current signals synchronously withthe sampling rate being 6000Hz In this part the accuracy ofthe proposed harmonic modeling of the DFIG is verifiedfrom four perspectives ie modulation method alteringcontroller parameters altering output power and the un-balance of three-phase voltage

521 Modulation Method Figure 16 shows the waveformsof the voltage and current at PCC as well as their harmonicspectrums e switch frequency of the grid-side converterand rotor-side converter is 3000Hz and 2000Hz re-spectively and there are obvious harmonics with high fre-quency close to switch frequency e high-frequencyharmonic components of the voltage and current are dis-tributed at 1920 1980 2020 and 2080Hz for the grid-sideconverter and 2800 and 2900Hz for the rotor-side converter

522 Altering Control Parameters In order to study theinfluence of different controller parameters on the currentharmonic components at PCC different PI controllerrsquosparameters of the inner current loop are set for the DFIGrsquosgrid-side converter Specifically at first kp is set to be 023and 071 respectively when ki remains as 30 Secondly kp isset to be 21 and 45 respectively when ki remains as 045Figure 17 shows the output current harmonic spectrums ofthe DFIG converter under different PI control parameters

Host PC

Oscilloscope

RCP

Real-time simulator Junction box

Figure 12 HIL simulation platform

Frequency (Hz)

Mag

nitu

de (d

B)

102 103 104ndash100

ndash50

0

50

kpg = 05 kig = 100kpr = 05 kir = 800

kpr = 05 kir = 800

kpg = 05 kig = 100

kpg = 10 kig = 100kpr = 10 kir = 100

Yeqs(s)

Yeqg(s)

Ygg(s) Ygg(s)

Figure 11 Magnitude-frequency curves of Yeqs(s) Yeqg(s) andYgg(s)

Complexity 7

45 452 454 456 458 46

ndash05

0

05

t (s)

ia

iga

isaCu

rren

t (pu

)

(a)

t (s)45 452 454 456 458 46

ia

iga

isa

ndash05

0

05

Curr

ent (

pu)

(b)

ia

iga

isa

45 452 454 456 458 46t (s)

ndash05

0

05

Curr

ent (

pu)

(c)

iga

t (s)45 452 454 456 458 46

ia isa

ndash05

0

05

Curr

ent (

pu)

(d)

Figure 13 Currents iga isa and ia (a) case 1 (b) case 2 (c) case 3 (d) case 4

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

Harmonic order

(a)

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Harmonic order

(b)

8 Complexity

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

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MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

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Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Volume 2018

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Dierential EquationsInternational Journal of

Volume 2018

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AnalysisInternational Journal of

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

e LCL filter parameters of the grid-side converter areL1 2mH L2 1mH and C 18 μF e asynchronousmotor parameters are Lr 0404mH Rr 00079ΩLs 008mH Rs 00025Ω Lm 44mH and sslip minus 02e grid equivalent inductance is L1 01mH e 5th 7th11th 13th 17th 19th 23rd 25th 29th 31st 35th and 37thharmonic sources with a magnitude of 002 pu are in serieson the grid

Figure 13 shows the grid-side converter output currentiga the asynchronous motor stator-side current isa and thegrid current ia for different control parameter cases Fig-ure 13 shows the magnitude of harmonic current measuredunder different cases e parameters in different cases areset as follows (1) case 1 kpg 05 kig 100 kpr 05 andkir 800 (2) case 2 kpg 10 kig 100 kpr 05 and kir 800(3) case 3 kpg 05 kig 100 kpr 10 and kir 100 and (4)case 4 kpg 10 kig 100 kpr 10 and kir 100

Figures 13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonancefrequency amplification due to LCL filter resonance) andlow-frequency harmonic amplification (about 5th and 7thharmonic amplification caused by improper control pa-rameters of the rotor-side converter) due to the presence of

harmonic voltages in the grid Figures 13(b) 13(d) and 14show that by appropriately increasing kpg it is possible tosuppress the high-frequency harmonic (nearby 29th har-monic current) caused by the resonance of the LCL filter

Figures 13(c) 13(d) and 14 show that a proper increase inkpr and a decrease in kir can suppress the low-frequencyharmonic (near 5th and 7th harmonic current) caused by in-appropriate rotor-side converter control parameters esimulation results are consistent with the theoretical analyses

52 Experiment Test To further verify the theory a testplatform containing the actual wind power converter is builtin the laboratory as shown in Figure 15 In the test platformthe AC servo motor is used to emulate the wind turbine andan actual wind power converter is adopted e ratedvoltages of the DFIG and the grid are 690V and 380Vrespectively which are connected by a transformer

e rated power of the converter is 20MW LC filters areutilized for the grid-side converter with the inductance offiltering being 043mH ree-phase capacitors are con-nected in a triangle shape and the capacitance is 120 μF LCfilters and the grid-side line resistances together with thetransformer equivalent impedance are combined into anLCL filter L filters are used on the rotor side with theinductance being 015mH e switch frequency of theconverter on the grid side is 3000Hz and that on the rotorside is 2000Hz and the modulation method is SVPWMeDC-side voltage is 1050V and the AC-side grid frequency is50Hz e detailed parameters of the test platform areshown in Table 2

e acquisition device is installed at PCC to obtainsamples of voltage and current signals synchronously withthe sampling rate being 6000Hz In this part the accuracy ofthe proposed harmonic modeling of the DFIG is verifiedfrom four perspectives ie modulation method alteringcontroller parameters altering output power and the un-balance of three-phase voltage

521 Modulation Method Figure 16 shows the waveformsof the voltage and current at PCC as well as their harmonicspectrums e switch frequency of the grid-side converterand rotor-side converter is 3000Hz and 2000Hz re-spectively and there are obvious harmonics with high fre-quency close to switch frequency e high-frequencyharmonic components of the voltage and current are dis-tributed at 1920 1980 2020 and 2080Hz for the grid-sideconverter and 2800 and 2900Hz for the rotor-side converter

522 Altering Control Parameters In order to study theinfluence of different controller parameters on the currentharmonic components at PCC different PI controllerrsquosparameters of the inner current loop are set for the DFIGrsquosgrid-side converter Specifically at first kp is set to be 023and 071 respectively when ki remains as 30 Secondly kp isset to be 21 and 45 respectively when ki remains as 045Figure 17 shows the output current harmonic spectrums ofthe DFIG converter under different PI control parameters

Host PC

Oscilloscope

RCP

Real-time simulator Junction box

Figure 12 HIL simulation platform

Frequency (Hz)

Mag

nitu

de (d

B)

102 103 104ndash100

ndash50

0

50

kpg = 05 kig = 100kpr = 05 kir = 800

kpr = 05 kir = 800

kpg = 05 kig = 100

kpg = 10 kig = 100kpr = 10 kir = 100

Yeqs(s)

Yeqg(s)

Ygg(s) Ygg(s)

Figure 11 Magnitude-frequency curves of Yeqs(s) Yeqg(s) andYgg(s)

Complexity 7

45 452 454 456 458 46

ndash05

0

05

t (s)

ia

iga

isaCu

rren

t (pu

)

(a)

t (s)45 452 454 456 458 46

ia

iga

isa

ndash05

0

05

Curr

ent (

pu)

(b)

ia

iga

isa

45 452 454 456 458 46t (s)

ndash05

0

05

Curr

ent (

pu)

(c)

iga

t (s)45 452 454 456 458 46

ia isa

ndash05

0

05

Curr

ent (

pu)

(d)

Figure 13 Currents iga isa and ia (a) case 1 (b) case 2 (c) case 3 (d) case 4

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

Harmonic order

(a)

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Harmonic order

(b)

8 Complexity

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

45 452 454 456 458 46

ndash05

0

05

t (s)

ia

iga

isaCu

rren

t (pu

)

(a)

t (s)45 452 454 456 458 46

ia

iga

isa

ndash05

0

05

Curr

ent (

pu)

(b)

ia

iga

isa

45 452 454 456 458 46t (s)

ndash05

0

05

Curr

ent (

pu)

(c)

iga

t (s)45 452 454 456 458 46

ia isa

ndash05

0

05

Curr

ent (

pu)

(d)

Figure 13 Currents iga isa and ia (a) case 1 (b) case 2 (c) case 3 (d) case 4

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

Harmonic order

(a)

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 370

001

002

003

004

Harmonic order

(b)

8 Complexity

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

When kp of the current inner loop PI controller of the grid-side converter increases the lower harmonic current of theDFIG below 1500Hz is reduced indicating that the pa-rameter kp has some damping effect Meanwhile when ki ofthe current inner loop PI controller of the grid-side con-verter changes the harmonic current of the DFIG does notchange significantly indicating that the parameter ki change

has little effect on the harmonic output of the wind turbinewhich is consistent with the theoretical analysis

523 Altering Output Power Figure 18 shows the currentharmonic diagrams under different active power condi-tions ie when the output active power is 300 kW and

Mag

nitu

de o

f har

mon

iccu

rren

t (pu

)

Case 3Case 4Case 2

Case 1

5 7 11 13 17 19 23 25 29 31 35 37Harmonic order

0

001

002

003

004

(c)

Figure 14 Harmonic current graphs of (a) iga (b) isa and (c) ia

DFIGAC servo machinery

Grid

Transformer

DFIG converter

690V 380V

Drive shaft

Data acquisition (DAQ)equipment

(a)

(b)

Figure 15 (a) Schematic diagram and (b) physical photograph of the experimental system

Complexity 9

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

2000 kW respectively As shown in Figure 18 when theoutput active power of the wind turbine increases theoutput power of the DFIG converter increases as well andthe harmonic current whose frequency is close to switchfrequency also increases

524 9ree-Phase Voltage Unbalance In order to verify theeffect of three-phase voltage unbalance on the harmoniccharacteristics of the DFIG the grid voltage irregularitieswere set to be 20 and 50 respectively Figure 19 showsthat the larger the unbalance of the three-phase voltage the

larger the amplitude of the 3rd harmonic current is which isconsistent with the theoretical analysis

525 Correction of the Harmonic Model Based on MeasuredData e harmonic model is corrected based on the har-monic test data of the test platform for the DFIG Table 3shows the precorrected and corrected parameters of theDFIG converter model e simulated results shown inFigure 20 illustrate the harmonic current of the DFIGconverter before and after correction under the rated op-eration condition As can be seen from Figure 20 when the

Table 2 Detailed parameters of the DFIG test platform

Parameters ValuesRated power (Sn) 2MWRated grid frequency 50HzRated grid voltage (Ug) 380VRated DFIG voltage (Ud) 690VRated DC-link voltage (Udc) 1050VGrid-side inductance (Lg) 043mHGrid-side capacitance (Cg) 120 μFRotor-side inductance (Lr) 015mHModulation method SVPWMSwitch frequency of the rotor-side converter 2 kHzSwitch frequency of the grid-side converter 3 kHz

898 9 902 904

ndash1000

ndash500

0

500

1000

0 1000 2000 30000

2

4

6

8

10

t (s)

Volta

ge h

arm

onic

spec

trum

(V)

Line

vol

tage

(V)

Frequency (Hz)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(a)

898 9 902 904ndash500

0

500

0 1000 2000 30000

2

4

6

8

10

Line

curr

ent (

A)

t (s) Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Harmonic component

for rotor-side converter

Harmonic component for grid-side

converter

(b)

Figure 16 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

10 Complexity

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

parameters of the simulation model are the same as those inthe real test platform the simulation results of harmoniccurrent are much greater than what have been measured in

practice When correcting the simulation model using thedata in Table 3 the value of harmonic current whose fre-quency is close to the switch frequency (which is 2000 and

0 500 1000 15000

5

10

15

20

25

30

0 500 1000 15000

5

10

15

20

25

30

kp = 023ki = 30

kp = 071ki = 30

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)

(a)

0

5

10

15

20

25

30

0

5

10

15

20

25

30kp = 045ki = 21

kp = 045ki = 45

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

0 500 1000 1500 0 500 1000 1500Frequency (Hz) Frequency (Hz)

(b)

Figure 17 (a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)1500 2000 2500 30000

2

4

6

8

10

1500 2000 2500 30000

2

4

6

8

10

P = 300kWQ = 0kVar

P = 2000kWQ = 0kVar

Figure 18 Current waveforms and harmonic spectrum of the DFIG under different active power conditions

Complexity 11

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

3000Hz) in simulation is close to the data in the real testerefore the modified model can be used to emulate theharmonic characteristics of the actual wind turbine

6 Conclusion

In this paper the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fedwind power generation system are established and theharmonic output characteristics of both converters arestudied based on the established models e researchesshow that the resonance of the LC or LCL filter in the grid-

side converter may lead to harmonic amplification in theneighboring resonace frequency and the harmonic ampli-fication can be suppressed by reasonably adjusting thecurrent controller parameter kpg e integral term of thecurrent controller in the rotor-side converter resonates withthe rotor leakage inductance which may cause the lower-frequency harmonic amplification in stator-side outputcurrent of the asynchronousmotor and the harmonic can besuppressed by appropriately increasing kpr and reducing kirof the rotor-side current controller e real-time HIL testresults verify the correctness of the theoretical analysesFurthermore the effectiveness of the proposed model is

Curr

ent h

arm

onic

spec

trum

(A)

Curr

ent h

arm

onic

spec

trum

(A)

Frequency (Hz) Frequency (Hz)100 150 200

0

5

10

15

20

100 150 2000

5

10

15

20Degree of unbalancedness is 20 Degree of unbalancedness is 50

Figure 19 Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance

Table 3 Model parameter correction

Parameter type Precorrected parameter Corrected parameter

Filter parameter L1 043mH 05mHC 120 μF 120 μF

Grid equivalent inductance Lg mdash 018mHCurrent looprsquos PI control parameter of the grid-sideconverter

kpg 1 50kig 13 100

Current looprsquos PI control parameter of the rotor-sideconverter

kpr 05 15kir 25 100

1500 2000 2500 29000

2

4

6

8

10

1500 2000 2500 2900 1500 2000 2500 2900

Measured dataPrecorrected model Corrected model

Frequency (Hz)

Curr

ent h

arm

onic

spec

trum

(A)

Figure 20 Comparison before and after harmonic model correction of the DFIG

12 Complexity

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

verified based on the actual DFIG test data which can alsoprovide guidance for the correction of the theoreticalmodel

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was supported by State Grid CorporationScience and Technology Project under GrantNYB17201700081 and Hubei Natural Science Foundationunder Grant 2018CFB205

References

[1] Y-W Shen D-P Ke Y-Z Sun D S Kirschenau W Qiaoand X-T Deng ldquoAdvanced auxiliary control of an energystorage device for transient voltage support of a doubly fedinduction generatorrdquo IEEE Transactions on Sustainable En-ergy vol 7 no 1 pp 63ndash76 2016

[2] R Tao F Li W Chen Y Fan C Liang and Y Li ldquoResearchon the protection coordination of permanent magnet syn-chronous generator based wind farms with low voltage ridethrough capabilityrdquo Protection and Control of Modern PowerSystems vol 2 no 1 pp 311ndash319 2017

[3] Y-W Shen D-P Ke W W Qiao Y-Z SunauD S Kirschenau and C Weiau ldquoTransient reconfigurationand coordinated control for power converters to enhance theLVRTof a DFIG wind turbine with an energy storage devicerdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1679ndash1690 2015

[4] S Liao J Xu Y Sun Y Bao and B Tang ldquoControl of energy-intensive load for power smoothing in wind power plantsrdquoIEEE Transactions on Power Systems vol 33 no 6pp 6142ndash6154 2018

[5] T S L V Ayyarao ldquoModified vector controlled DFIG windenergy system based on barrier function adaptive slidingmode controlrdquo Protection and Control of Modern PowerSystems vol 4 no 1 pp 34ndash41 2019

[6] W Wu Y Liu Y He H S H Chung M Liserre andF Blaabjerg ldquoDamping methods of resonances caused byLCL-filter-based current-controlled grid-tied power invertersan overviewrdquo IEEE Transactions on Industrial Electronicsvol 64 no 9 pp 7402ndash7413 2007

[7] C Wei M Benosman and T Kim ldquoOnline parameteridentification for state of power prediction of lithium-ionbatteries in electric vehicles using extremum seekingrdquo In-ternational Journal of Control Automation and Systemspp 1ndash11 2019

[8] Y-W Shen J-R Yuan F-F Shen J-Z Xu C-K Li andD Wang ldquoFinite control set model predictive control forcomplex energy system with large-scale wind powerrdquo Com-plexity vol 2019 Article ID 4358958 13 pages 2019

[9] O Noureldeen and I Hamdan ldquoA novel controllable crowbarbased on fault type protection technique for DFIG wind

energy conversion system using adaptive neuro-fuzzy in-ference systemrdquo Protection and Control of Modern PowerSystems vol 3 no 1 pp 328ndash339 2018

[10] S Boubzizi H Abid A El hajjaji and M ChaabaneldquoComparative study of three types of controllers for DFIG inwind energy conversion systemrdquo Protection and Control ofModern Power Systems vol 3 no 1 pp 214ndash225 2018

[11] Z Wang Y Z Sun G J Li et al ldquoStator current harmonicsanalysis of double-fed induction generatorrdquo Electric PowerAutomation Equipment vol 30 no 6 pp 1ndash5 2010

[12] L KWanW L Yang AW Yan et al ldquoHarmonic analysis ofconverter based on double-fed induction generatorrdquo ElectricMachines amp Control Application vol 38 no 8 pp 31ndash352011

[13] C J Zhang and Q Q Jia ldquoProbabilistic harmonic load flowcalculation containing double fed induction generatorrdquoPower Electronics vol 45 no 11 pp 108ndash111 2011

[14] M Nayeripour and M Mahdi Mansouri ldquoAn advanced an-alytical calculation and modeling of the electrical and me-chanical harmonics behavior of doubly fed inductiongenerator in wind turbinerdquo Renewable Energy vol 81pp 275ndash285 2015

[15] N Xie A Luo F J Ma et al ldquoHarmonic interaction betweenlarge-scale photovoltaic power stations and gridrdquo Proceedingsof the CSEE vol 34 pp 9ndash16 2013

[16] C Zhang XWang L Li et al ldquoStudy onmodulation functionand harmonics of SVPWMrdquo Journal of Guizhou University(Natural Sciences) vol 29 no 6 pp 63ndash67 2012

[17] J L Agorreta M Borrega J Lopez and L MarroyoldquoModeling and control of N -paralleled grid-connected in-verters with LCL filter coupled due to grid impedance in PVplantsrdquo IEEE Transactions on Power Electronics vol 26 no 3pp 770ndash785 2011

[18] X Wang F Blaabjerg M Liserre Z Chen J He and Y LildquoAn active damper for stabilizing power-electronics-based ACsystemsrdquo IEEE Transactions on Power Electronics vol 29no 7 pp 3318ndash3329 2014

[19] D Yang X Ruan and H Wu ldquoImpedance shaping of thegrid-connected inverter with LCL filter to improve itsadaptability to the weak grid conditionrdquo IEEE Transactions onPower Electronics vol 29 no 11 pp 5795ndash5805 2014

[20] Y-W Shen L-Q Liang M J Cui F Shen B Zhang andT Cui ldquoAdvanced control of DFIG to enhance the transientvoltage support capabilityrdquo Journal of Energy Engineering vol144 no 2 Article ID 04018009 2018

[21] J Rodriguez and P Cortes ldquoPredictive control of powerconverters and electrical drivesrdquo IEEE Transactions on In-dustrial Electronics vol 63 no 7 pp 4472ndash4474 2016

[22] S Rivera S Kouro B Wu et al ldquoldquoMultilevel direct powercontrolmdasha generalized approach for grid-tied multilevelconverter applicationsrdquo IEEE Trans Power Electronicsvol 29 no 10 pp 5592ndash5604 2014

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom