# Harmonic Modeling and Experimental Validation of the Converters of DFIG-Based Wind Generation System

Authors: Yang-Wu Shen; Ding Wang; Xiang-Tian Deng; Qing Li; Jian Zuo
Journal: Complexity
 (2019)

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## Abstract

The double-fed induction wind generator- (DFIG-) based wind generation system contains power electronic converters and filter capacitor and inductor, which will bring about high-frequency harmonics under the influence of controllers. Aiming at this problem, this paper studies the relation between the output current and the harmonic source at grid-side and rotor-side converters based on their control features in the DFIG system. Furthermore, the harmonic equivalent models of these two converters are built, and the influence of different factors on harmonic features is explored from four perspectives, i.e., modulation method, altering controller parameters, altering output power, and the unbalance of three-phase voltage. Finally, the effectiveness of the proposed model is verified through the 2 MW DFIG real-time hardware-in-the-loop test platform by StarSim software and real test data, respectively.


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## Body

## 1. Introduction

New energy power generation technologies have become hot spots as the energy and environmental issues obtained prominent attention. Wind energy has been widely applied in power systems because of its clean, harmless, and abundant nature in natural resources. The double-fed wind power generation system has become the mainstream in wind power generation systems because of its small capacity in the field converter, low cost, and variable-speed constant-frequency operation features [1–6]. However, the double-fed wind power generation system contains a power electronic converter, in which the interactions among converters and passive components of the filter can lead to harmonic resonances, thus causing serious harmonic pollution and reducing the power quality [7–10].With regard to the harmonic problem in the double-fed wind power generation system, relevant researches and analyses have been carried out [11–14]. In the literature [11], the source of stator harmonic current of the double-fed wind turbine is analyzed. It is pointed out that the harmonic modulation of the converter, the cogging harmonic of the motor itself, and the grid background harmonic affect the stator output harmonics of the double-fed wind turbine. In [12], the harmonic characteristics of the double-fed wind turbine converter are analyzed, and the effect of the converter harmonic on the system overall output harmonic is analyzed by establishing the equivalent circuit of the asynchronous motor. Based on the mathematically electromagnetic relationship of the asynchronous motor, literature [13] proposes a harmonic equivalent circuit of the double-fed asynchronous motor and studies the influence of harmonics generated by the wind turbine on the power grid. According to the characteristics of the asynchronous motor, literature [14] analyzes the interaction between the grid-side converter harmonic and the rotor-side converter harmonic in 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 generation system are viewed as a simple harmonic voltage source when modeling and analyzing the converter output harmonic characteristics, while the influence of converter control factors on system harmonic output characteristics is not considered.Literature studies [15, 16] point out that the harmonics generated by PWM (pulse-width modulation) are mainly distributed near the double switching frequency. Reference [17] studies the harmonic resonance characteristics of the photovoltaic power generation system by establishing the Norton equivalent model of the photovoltaic converter. Considering the control characteristics of different types of converters [18], Wang et al. establish the converter equivalent model of voltage source control and current source control, respectively.However, there is little literature on the harmonic characteristics of the double-fed wind power generation system at present. The main contributions of this paper can be summarized as follows:(1)
Based on the existing harmonic model, the influence of component parameters and control parameters on the harmonic output of the RSC and GSC is studied, and the harmonic output characteristics of the RSC and GSC are summarized. Furthermore, a novel method for suppressing the output harmonic amplitude of the DFIG by adjusting PI control parameters is proposed, and the effectiveness of the proposed method has been verified by the simulation case.(2)
The harmonic model of the typical DFIG is established, and the parameters of the harmonic model of the DFIG are corrected by the measured data. With the correction of harmonic model parameters, the harmonic characteristics of the corrected harmonic model of the DFIG are consistent with the harmonic characteristics of the actual DFIG.The rest of this paper is organized as follows: Section2 presents the harmonic source analysis of the double-fed wind power generation system. Section 3 presents the characteristics analyses of the converter harmonic model. Case studies are presented in Section 4 to validate the proposed harmonic model of the DFIG. Conclusion is presented in Section 5.


## 2. Harmonic Source Analysis of Double-Fed Wind Power Generation System

The structure of the double-fed wind power generation system is shown in Figure1. Two back-to-back PW-modulated converters are used for AC excitation through a DC link. Effective control of converters enables variable-speed constant-frequency operation and maximum wind energy tracking within a certain range [10, 19, 20].Figure 1
Double-fed wind power generation system.The harmonic sources of the double-fed wind power generation system mainly include the harmonics caused by the asynchronous motor itself and the harmonics caused by the converter modulation [14]. In addition, the output harmonic of the double-fed wind power system may exceed the standard when there are background harmonics in the grid and irrational converter control parameters. The cogging harmonics caused by the asynchronous motor itself due to the uneven air gap can be suppressed or eliminated by rational motor structure designing. Thus, this paper mainly considers the PW modulation harmonics of the converter and the background harmonics of the power grid. The harmonic output characteristics of the double-fed wind power generation system are studied by establishing the harmonic equivalent model.


## 3. Harmonic Modeling of Double-Fed Wind Power Converter

Because of the fact that the dynamics of DC-side voltage is slower than the harmonic dynamics, the voltage across the capacitor between the grid-side converter and the rotor-side converter of the double-fed wind power system remains constant. Therefore, the two converters can be discussed separately in harmonic modeling. In this section, the harmonic equivalent models of the grid-side and rotor-side converters are established to study their harmonic output characteristics and influencing factors. Note that there are subsynchronous and low-frequency oscillations which lie below the fundamental frequency in wind power generation systems, and this paper mainly discusses the harmonics above the fundamental frequency [9].The harmonic amplitude is proportional to the switching frequency, dead time, and DC-side voltage and inversely proportional to the harmonic order. The amplitude is negligible, so the voltage generated by the dead zone effect is mainly low, such as 3, 5, 7, and 9. For a converter with a high switching frequency, the dead time is long in one switching cycle, and the low-order harmonic generated by the dead zone is more obvious, while the large-capacity converter with a lower switching frequency is generated by the dead zone effect. In this paper, the switching delay of the converter is not taken into consideration for the harmonic model of converters.


### 3.1. Harmonic Modeling of Grid-Side Converter

For a three-phase balancing system, the system can be equivalent to a single-phase system. The command signal of the inner current loop in the grid-side converter is given by the outer voltage loop. Consider the response of the voltage loop is much slower than the response of the current loop. Thus, by ignoring the voltage loop, the control block diagram of the grid-side converter is obtained and shown in Figure2. The converter-side current feedback control which is more stable than the grid-side current feedback current control is adopted, as shown in Figure 2 [21].Figure 2
Current control block diagram of the grid-side converter.In Figure2, Kpwm is the linear gain of the pulse-width modulation (PWM) converter bridge, i1ref is the reference of the current loop, ugh is the harmonic voltage generated by PWM, Gig is the transfer function of the current regulator which adopts the proportional resonance controller, and uPCC is the voltage at the grid-connected point. The harmonic model shown in Figure 2 considers two kinds of harmonic sources: (1) the harmonic voltage ugh generated by the PWM and (2) the grid background harmonic voltage uPCC at the grid-connected point.In the steady-state operation, the current referencei1ref remains constant [22]. Thus, according to the Mason formula, the complex frequency-domain expression among i2, ugh, and uPCC can be obtained as follows.(1)i2=Ngsugh−YeqgsuPCC,where s is the complex frequency-domain variable and Ngs and Yeqgs are expressed as(2)Ngs=ZCZ1Z2+Z1ZC+Z2ZC+GigKpwmZ2+ZC,Yeqgs=Z1+ZC+GigKpwmZ1Z2+Z1ZC+Z2ZC+GigKpwmZ2+ZC,where Kpwm is usually taken as 1; Z1 = sL1 + R1, Z2 = sL2 + R2, and ZC=1/sC, in which L1, R1, L2, and R2 are the LCL filter inductance and equivalent resistance and C is the filter capacitor; and Gig is expressed as(3)Gig=kpg+skigs2+ωg2,where kpg and kig are the proportional and integral coefficients of the current controller and ωg is the fundamental frequency.According to Figure1 and (1), the Norton equivalent circuit of the grid-side converter can be obtained, which is shown in Figure 3. In Figure 3, Ngsugh is the PW-modulated harmonic and uPCC is the grid background harmonic.Figure 3
Norton equivalent circuit of the grid-side converter.


### 3.2. Harmonic Modeling of Rotor-Side Converter

The rotor-side converter adopts the motor stator flux-oriented feedforward decoupling control. The outer control loop is the speed control or active power control, and the output of the outer loop controller is the reference of the inner current loop. Similarly, the response of the inner loop is much faster than that of the outer loop. Therefore, the outer control loop is neglected, and the balanced three-phase system is equivalent to a single-phase system. The current control block diagram of the rotor-side converter is shown in Figure4.Figure 4
Current control block diagram of the rotor-side converter.In Figure4, irref is the current reference, urh is the harmonic voltage generated by PWM, and Gir is the transfer function of the current controller and the proportional resonance controller is used; e2 is the rotor-side phase electromotive force of the asynchronous machine. In Figure 4, the output current is(4)ir=Nrs′urh−Yeqrs′e2,where s′ is the rotor-side complex frequency-domain variable. Note that s′=sslip, where sslip is the slip. The detailed expressions of sslip, Nrs′, and Yeqrs′ are shown as follows:(5)sslip=s−jωms,Nrs′=1Zr+GirKpwm,Yeqrs′=1Zr+GirKpwm,where ωm is the rotor speed of the asynchronous motor; Zr=s′Lr+Rr, in which Lr and Rr are the rotor leakage inductance and resistance; and Gir is expressed as(6)Gir=kpr+s′kirs′2+ωg−ωm2,where kpr and kir are the proportional and integral coefficients of the current controller, respectively.According to Figure4 and (4) and combining with the asynchronous motor equivalent circuit [11, 12], the Norton equivalent model of the rotor-side converter can be obtained, which is shown in Figure 5(a). Note that the rotor-side variables are converted to the stator side by the generator conversion. With the circuit conversion, Figure 5(a) can be equivalent to Figure 5(b). From Figure 5(b), we have(7)is=Nssurh−YeqssuPCC,where is is the stator-side output current of the asynchronous motor and Nss and Yeqss are expressed as(8)Nss=ZmNrs′Zm+Zs+sslipYeqrs′ZmZs,Yeqss=1+sslipYeqrs′ZmZm+Zs+sslipYeqrs′ZmZs,where Zm=sLm and Zs=sLs+Rs, in which Lm is the excitation inductance of the asynchronous motor and Ls and Rs are the stator leakage inductance and resistance.Figure 5
Norton equivalent circuit of the rotor-side converter: (a) detailed circuit of the rotor-side converter and asynchronous machine; (b) equivalent model.
(a)
(b)


## 3.1. Harmonic Modeling of Grid-Side Converter

For a three-phase balancing system, the system can be equivalent to a single-phase system. The command signal of the inner current loop in the grid-side converter is given by the outer voltage loop. Consider the response of the voltage loop is much slower than the response of the current loop. Thus, by ignoring the voltage loop, the control block diagram of the grid-side converter is obtained and shown in Figure2. The converter-side current feedback control which is more stable than the grid-side current feedback current control is adopted, as shown in Figure 2 [21].Figure 2
Current control block diagram of the grid-side converter.In Figure2, Kpwm is the linear gain of the pulse-width modulation (PWM) converter bridge, i1ref is the reference of the current loop, ugh is the harmonic voltage generated by PWM, Gig is the transfer function of the current regulator which adopts the proportional resonance controller, and uPCC is the voltage at the grid-connected point. The harmonic model shown in Figure 2 considers two kinds of harmonic sources: (1) the harmonic voltage ugh generated by the PWM and (2) the grid background harmonic voltage uPCC at the grid-connected point.In the steady-state operation, the current referencei1ref remains constant [22]. Thus, according to the Mason formula, the complex frequency-domain expression among i2, ugh, and uPCC can be obtained as follows.(1)i2=Ngsugh−YeqgsuPCC,where s is the complex frequency-domain variable and Ngs and Yeqgs are expressed as(2)Ngs=ZCZ1Z2+Z1ZC+Z2ZC+GigKpwmZ2+ZC,Yeqgs=Z1+ZC+GigKpwmZ1Z2+Z1ZC+Z2ZC+GigKpwmZ2+ZC,where Kpwm is usually taken as 1; Z1 = sL1 + R1, Z2 = sL2 + R2, and ZC=1/sC, in which L1, R1, L2, and R2 are the LCL filter inductance and equivalent resistance and C is the filter capacitor; and Gig is expressed as(3)Gig=kpg+skigs2+ωg2,where kpg and kig are the proportional and integral coefficients of the current controller and ωg is the fundamental frequency.According to Figure1 and (1), the Norton equivalent circuit of the grid-side converter can be obtained, which is shown in Figure 3. In Figure 3, Ngsugh is the PW-modulated harmonic and uPCC is the grid background harmonic.Figure 3
Norton equivalent circuit of the grid-side converter.


## 3.2. Harmonic Modeling of Rotor-Side Converter

The rotor-side converter adopts the motor stator flux-oriented feedforward decoupling control. The outer control loop is the speed control or active power control, and the output of the outer loop controller is the reference of the inner current loop. Similarly, the response of the inner loop is much faster than that of the outer loop. Therefore, the outer control loop is neglected, and the balanced three-phase system is equivalent to a single-phase system. The current control block diagram of the rotor-side converter is shown in Figure4.Figure 4
Current control block diagram of the rotor-side converter.In Figure4, irref is the current reference, urh is the harmonic voltage generated by PWM, and Gir is the transfer function of the current controller and the proportional resonance controller is used; e2 is the rotor-side phase electromotive force of the asynchronous machine. In Figure 4, the output current is(4)ir=Nrs′urh−Yeqrs′e2,where s′ is the rotor-side complex frequency-domain variable. Note that s′=sslip, where sslip is the slip. The detailed expressions of sslip, Nrs′, and Yeqrs′ are shown as follows:(5)sslip=s−jωms,Nrs′=1Zr+GirKpwm,Yeqrs′=1Zr+GirKpwm,where ωm is the rotor speed of the asynchronous motor; Zr=s′Lr+Rr, in which Lr and Rr are the rotor leakage inductance and resistance; and Gir is expressed as(6)Gir=kpr+s′kirs′2+ωg−ωm2,where kpr and kir are the proportional and integral coefficients of the current controller, respectively.According to Figure4 and (4) and combining with the asynchronous motor equivalent circuit [11, 12], the Norton equivalent model of the rotor-side converter can be obtained, which is shown in Figure 5(a). Note that the rotor-side variables are converted to the stator side by the generator conversion. With the circuit conversion, Figure 5(a) can be equivalent to Figure 5(b). From Figure 5(b), we have(7)is=Nssurh−YeqssuPCC,where is is the stator-side output current of the asynchronous motor and Nss and Yeqss are expressed as(8)Nss=ZmNrs′Zm+Zs+sslipYeqrs′ZmZs,Yeqss=1+sslipYeqrs′ZmZm+Zs+sslipYeqrs′ZmZs,where Zm=sLm and Zs=sLs+Rs, in which Lm is the excitation inductance of the asynchronous motor and Ls and Rs are the stator leakage inductance and resistance.Figure 5
Norton equivalent circuit of the rotor-side converter: (a) detailed circuit of the rotor-side converter and asynchronous machine; (b) equivalent model.
(a)
(b)


## 4. Characteristics Analyses of Converter Harmonic Model

Based on the harmonic models of grid-side and rotor-side converters established in Section3, the effects of component parameters and control parameters on harmonic characteristics are studied. The detailed parameters of the DFIG used in the simulation are shown in Table 1.Table 1
Detailed parameters of the DFIG simulation platform.
Parameters
Values
LCL filter (L1)
2 mH
LCL filter (L2)
1 mH
LCL filter (C)
18μF
Asynchronous motor (Lr)
0.404 mH
Asynchronous motor (Rr)
0.0079 Ω
Asynchronous motor (Ls)
0.08 mH
Asynchronous motor (Rs)
0.0025 Ω
Asynchronous motor (Lm)
4.4 mH
s
slip
−0.2


### 4.1. Characteristic Analysis of Harmonic Model of Grid-Side Converter

According to the Norton equivalent model shown in Figure3 and (1) and (2), the Bode diagram of Ngs and Yeqgs is shown in Figure 6. It can be seen from the figure that there are resonance peaks (magnitude greater than 0 dB) at a frequency of about 1450 Hz in Ngs and Yeqgs. It indicates that the converter output current will undergo harmonic amplification when the frequency of ugh and uPCC is close to the resonant frequency, thus affecting the power quality. Besides, it should be noted that the magnitude-frequency curves of Ngs and Yeqgs are obviously declining when the frequency is higher than 2000 Hz, indicating that the converter has a strong suppression to high-frequency harmonics.Figure 6
Magnitude-frequency curves ofNgs and Yeqgs.Ignoring the equivalent resistance of the filter inductor as it is usually small, and takingKpwm = 1, the denominator of Ngs and Yeqgs shown in (2) can be expanded to(9)deng=1sCs3CL1L2+sL1+L2+s2kpgCL2+kpg+s2kigCL2s2+ωg2+skigs2+ωg2.It can be seen from (9) that the cubic term and the primary term of s in the brackets form a pair of resonant poles whose resonant frequency is(10)ωrg=±L1+L2CL1L2.The resonant frequencyωrg calculated by (10) is coincident with the resonant frequency of the LCL filter. Therefore, it can be inferred that the resonant peak in Figure 6 is determined by the filter inductance. This means that choosing the right filter parameters can suppress as many harmonics as possible in the high frequency. Since the PWM harmonics are mainly concentrated near the double switching frequency [15, 16], the harmonic frequency is higher and can be suppressed. The range of grid background harmonic frequency is wide, and there are many lower harmonics such as the 5th, 7th, and 11th. Therefore, it is necessary to further study the harmonic output characteristics of the converter affected by the grid background harmonics.In the vicinity of the resonant frequencyωrg, an approximate expression is obtained as s2≫ωg2 and the capacitance of the filter capacitor is small.(11)deng≈s2L1L2+L1+L2C+skpgL2.It is not difficult to see from (11) that the product of kpg and L2 provides damping for the resonance. The larger the product, the stronger the damping effect.Since the current control parameterkpg is relatively easier to change than L2 in practice, only the influence of kpg is studied in Figure 7.Figure 7
Magnitude-frequency curves ofYeqgs with different kpg.It can be seen from Figure7 that when the parameter of the current loop controller kpg is relatively small, the magnitude-frequency curve of Yeqgs has a resonance peak. As kpg increases, the resonance peak gradually decreases to disappear. In addition, Figure 7 also shows that the controller parameter kpi has less effect on the magnitude-frequency curve of Yeqgs since the integral term of Gig is almost zero at high frequencies.In summary, the existence of LCL filter resonance may cause harmonic amplification in the output of the grid-side converter of the wind power generation system, and the resonance can be suppressed by adjusting the parameter of the current controllerkpg. It should be noted that kpg also affects the dynamic response and stability of the converter control system, and this is beyond the scope of this paper. Therefore, the parameter kpg should be increased as much as possible to suppress the harmonic output of the converter under the premise of meeting the dynamic performance and stability requirements of the system.


### 4.2. Characteristic Analysis of Harmonic Model of Rotor-Side Converter

According to (4)–(8) and Figure 5, the magnitude-frequency curves of Nss and Yeqss are obtained and shown in Figure 8. It can be seen from the curves in Figure 8 that, at higher frequencies, the rotor-side converter has an effect of suppressing the higher-frequency PWM harmonics and the grid background harmonics. Since there is no capacitor in the rotor-side converter and asynchronous motor, the magnitude-frequency curves of Nss and Yeqss do not show obvious resonance peaks. However, it should also be noted that, at lower frequencies (about 300 Hz in Figure 8), there are peak slopes (magnitude exceeds 0 dB). Thus, further characteristic study of Yeqss is needed for the lower secondary grid background harmonics.Figure 8
Magnitude-frequency curves ofNss and Yeqss.As to the rotor-side converter, the denominator ofNrs′ and Yekrs′ in (5) can be expanded (Rr is ignored and Kpwm = 1 is considered for the same reason) to(12)denr=s′Lr+kpr+s′kirs′2+ωg−ωm2=s−jωmLr+kpr+s−jωmkirs−jωm2+ωg−ωm2.It can be seen from (12) that when the frequency is 3 times higher than the fundamental frequency of the rotor, that is, s−jωm>3ωg−ωm (it is considered that the smaller term can be ignored when the difference between two terms is more than 10 times in engineering application), the denominator denr can be approximated to(13)denr≈s−jωmLr+kpr+kirs−jωm.With (13), it can be found that the first and third terms form a pair of resonant poles whose resonant frequency is(14)ωrr=ωm±kirLr.Although there is no resonance in the rotor-side converter caused by the capacitor and inductor of the LCL filter, (14) shows that there will be resonance caused by the interaction between the controller integral term and the rotor leakage inductance. Besides, it can be seen from (8) that this resonance will be finally reflected to the stator side by Nss and Yeqss.From (13) and (14), the resonant frequency is related to the rotor speed ωm, the rotor leakage inductance Lr, and the controller parameter kir. The rotor leakage inductance Lr is related to the motor parameters and is fixed after the motor is manufactured. The rotor speed varies according to the actual wind speed, and the range of variation is limited. Only the controller parameter kir is easy to change. Similar to the grid-side converter, the controller parameter kpr has an effect of damping.Figure9 shows the magnitude-frequency curves of Yeqss with different kir, kpr, and ωm. It can be seen from Figure 9 that, on increasing kir, the peak slope of Yeqss shifts to a lower frequency and the magnitude decreases. On the contrary, the magnitude-frequency curve of Yeqss declines to a large extent as kpr is increased. The slip sslip changes from −0.2 (corresponding to ωm=1.2ωg) to −0.1 (corresponding to ωm=1.1ωg), and the peak slope of Yeqss shifts to a lower frequency. Considering that the actual range of slip variation is small, the parameters kpr and kir are the main factors affecting the harmonic output characteristics of the rotor-side converter.Figure 9
Magnitude-frequency curves ofYeqss.


### 4.3. Harmonic Model of Double-Fed Wind Power Generation System considering Grid Impedance

According to the equivalent harmonic models of grid-side and rotor-side converters shown in Figures3 and 5, the overall equivalent harmonic model of the double-fed wind system is shown in Figure 10. In Figure 10, Zg is the grid equivalent impedance and ug is the grid voltage. According to Figure 10, the current ig can be obtained as(15)ig=Nggsugh+Nsgsurh−Yggsug,where Nggs, Nsgs, and Yggs are shown as follows:(16)Nggs=Ngs1+ZgYeqgs+Yeqss,Nsgs=Nss1+ZgYeqgs+Yeqss,Yggs=Yeqgs+Yeqss1+ZgYeqgs+Yeqss.Figure 10
Norton equivalent circuit of the double-fed wind generator.Considering the influence of grid background harmonics, the magnitude-frequency curve ofYggs according to (15) and (16) is shown in Figure 11. It can be seen from Figure 11 that when there exists significant resonance in both Yeqgs and Yeqgs, there appears similar resonant frequency in Yggs. The resonant peak of Yggs is suppressed as the parameters kpg, kpr, and kir are appropriately increased, which shows similar features to Yeqgs and Yeqgs in Figures 7 and 9. Therefore, in the presence of the grid impedance, the grid background harmonics still can be suppressed by appropriately adjusting the controller parameters.Figure 11
Magnitude-frequency curves ofYeqss, Yeqgs, and Yggs.


## 4.1. Characteristic Analysis of Harmonic Model of Grid-Side Converter

According to the Norton equivalent model shown in Figure3 and (1) and (2), the Bode diagram of Ngs and Yeqgs is shown in Figure 6. It can be seen from the figure that there are resonance peaks (magnitude greater than 0 dB) at a frequency of about 1450 Hz in Ngs and Yeqgs. It indicates that the converter output current will undergo harmonic amplification when the frequency of ugh and uPCC is close to the resonant frequency, thus affecting the power quality. Besides, it should be noted that the magnitude-frequency curves of Ngs and Yeqgs are obviously declining when the frequency is higher than 2000 Hz, indicating that the converter has a strong suppression to high-frequency harmonics.Figure 6
Magnitude-frequency curves ofNgs and Yeqgs.Ignoring the equivalent resistance of the filter inductor as it is usually small, and takingKpwm = 1, the denominator of Ngs and Yeqgs shown in (2) can be expanded to(9)deng=1sCs3CL1L2+sL1+L2+s2kpgCL2+kpg+s2kigCL2s2+ωg2+skigs2+ωg2.It can be seen from (9) that the cubic term and the primary term of s in the brackets form a pair of resonant poles whose resonant frequency is(10)ωrg=±L1+L2CL1L2.The resonant frequencyωrg calculated by (10) is coincident with the resonant frequency of the LCL filter. Therefore, it can be inferred that the resonant peak in Figure 6 is determined by the filter inductance. This means that choosing the right filter parameters can suppress as many harmonics as possible in the high frequency. Since the PWM harmonics are mainly concentrated near the double switching frequency [15, 16], the harmonic frequency is higher and can be suppressed. The range of grid background harmonic frequency is wide, and there are many lower harmonics such as the 5th, 7th, and 11th. Therefore, it is necessary to further study the harmonic output characteristics of the converter affected by the grid background harmonics.In the vicinity of the resonant frequencyωrg, an approximate expression is obtained as s2≫ωg2 and the capacitance of the filter capacitor is small.(11)deng≈s2L1L2+L1+L2C+skpgL2.It is not difficult to see from (11) that the product of kpg and L2 provides damping for the resonance. The larger the product, the stronger the damping effect.Since the current control parameterkpg is relatively easier to change than L2 in practice, only the influence of kpg is studied in Figure 7.Figure 7
Magnitude-frequency curves ofYeqgs with different kpg.It can be seen from Figure7 that when the parameter of the current loop controller kpg is relatively small, the magnitude-frequency curve of Yeqgs has a resonance peak. As kpg increases, the resonance peak gradually decreases to disappear. In addition, Figure 7 also shows that the controller parameter kpi has less effect on the magnitude-frequency curve of Yeqgs since the integral term of Gig is almost zero at high frequencies.In summary, the existence of LCL filter resonance may cause harmonic amplification in the output of the grid-side converter of the wind power generation system, and the resonance can be suppressed by adjusting the parameter of the current controllerkpg. It should be noted that kpg also affects the dynamic response and stability of the converter control system, and this is beyond the scope of this paper. Therefore, the parameter kpg should be increased as much as possible to suppress the harmonic output of the converter under the premise of meeting the dynamic performance and stability requirements of the system.


## 4.2. Characteristic Analysis of Harmonic Model of Rotor-Side Converter

According to (4)–(8) and Figure 5, the magnitude-frequency curves of Nss and Yeqss are obtained and shown in Figure 8. It can be seen from the curves in Figure 8 that, at higher frequencies, the rotor-side converter has an effect of suppressing the higher-frequency PWM harmonics and the grid background harmonics. Since there is no capacitor in the rotor-side converter and asynchronous motor, the magnitude-frequency curves of Nss and Yeqss do not show obvious resonance peaks. However, it should also be noted that, at lower frequencies (about 300 Hz in Figure 8), there are peak slopes (magnitude exceeds 0 dB). Thus, further characteristic study of Yeqss is needed for the lower secondary grid background harmonics.Figure 8
Magnitude-frequency curves ofNss and Yeqss.As to the rotor-side converter, the denominator ofNrs′ and Yekrs′ in (5) can be expanded (Rr is ignored and Kpwm = 1 is considered for the same reason) to(12)denr=s′Lr+kpr+s′kirs′2+ωg−ωm2=s−jωmLr+kpr+s−jωmkirs−jωm2+ωg−ωm2.It can be seen from (12) that when the frequency is 3 times higher than the fundamental frequency of the rotor, that is, s−jωm>3ωg−ωm (it is considered that the smaller term can be ignored when the difference between two terms is more than 10 times in engineering application), the denominator denr can be approximated to(13)denr≈s−jωmLr+kpr+kirs−jωm.With (13), it can be found that the first and third terms form a pair of resonant poles whose resonant frequency is(14)ωrr=ωm±kirLr.Although there is no resonance in the rotor-side converter caused by the capacitor and inductor of the LCL filter, (14) shows that there will be resonance caused by the interaction between the controller integral term and the rotor leakage inductance. Besides, it can be seen from (8) that this resonance will be finally reflected to the stator side by Nss and Yeqss.From (13) and (14), the resonant frequency is related to the rotor speed ωm, the rotor leakage inductance Lr, and the controller parameter kir. The rotor leakage inductance Lr is related to the motor parameters and is fixed after the motor is manufactured. The rotor speed varies according to the actual wind speed, and the range of variation is limited. Only the controller parameter kir is easy to change. Similar to the grid-side converter, the controller parameter kpr has an effect of damping.Figure9 shows the magnitude-frequency curves of Yeqss with different kir, kpr, and ωm. It can be seen from Figure 9 that, on increasing kir, the peak slope of Yeqss shifts to a lower frequency and the magnitude decreases. On the contrary, the magnitude-frequency curve of Yeqss declines to a large extent as kpr is increased. The slip sslip changes from −0.2 (corresponding to ωm=1.2ωg) to −0.1 (corresponding to ωm=1.1ωg), and the peak slope of Yeqss shifts to a lower frequency. Considering that the actual range of slip variation is small, the parameters kpr and kir are the main factors affecting the harmonic output characteristics of the rotor-side converter.Figure 9
Magnitude-frequency curves ofYeqss.


## 4.3. Harmonic Model of Double-Fed Wind Power Generation System considering Grid Impedance

According to the equivalent harmonic models of grid-side and rotor-side converters shown in Figures3 and 5, the overall equivalent harmonic model of the double-fed wind system is shown in Figure 10. In Figure 10, Zg is the grid equivalent impedance and ug is the grid voltage. According to Figure 10, the current ig can be obtained as(15)ig=Nggsugh+Nsgsurh−Yggsug,where Nggs, Nsgs, and Yggs are shown as follows:(16)Nggs=Ngs1+ZgYeqgs+Yeqss,Nsgs=Nss1+ZgYeqgs+Yeqss,Yggs=Yeqgs+Yeqss1+ZgYeqgs+Yeqss.Figure 10
Norton equivalent circuit of the double-fed wind generator.Considering the influence of grid background harmonics, the magnitude-frequency curve ofYggs according to (15) and (16) is shown in Figure 11. It can be seen from Figure 11 that when there exists significant resonance in both Yeqgs and Yeqgs, there appears similar resonant frequency in Yggs. The resonant peak of Yggs is suppressed as the parameters kpg, kpr, and kir are appropriately increased, which shows similar features to Yeqgs and Yeqgs in Figures 7 and 9. Therefore, in the presence of the grid impedance, the grid background harmonics still can be suppressed by appropriately adjusting the controller parameters.Figure 11
Magnitude-frequency curves ofYeqss, Yeqgs, and Yggs.


## 5. Case Study

### 5.1. Simulation Verification

In order to verify the above characteristics analyses, a real-time hardware-in-the-loop (HIL) system from ModelingTech is built, as shown in Figure12. Each electromagnetic transient model of the DFIG and control algorithm is constructed by StarSim software and implemented on NI FPGA board 7868R (real-time simulator). The control algorithm is implemented on the PXIe-8821 controller (rapid control prototype (RCP)).Figure 12
HIL simulation platform.The LCL filter parameters of the grid-side converter areL1 = 2 mH, L2 = 1 mH, and C = 18 μF. The asynchronous motor parameters are Lr = 0.404 mH, Rr = 0.0079 Ω, Ls = 0.08 mH, Rs = 0.0025 Ω, Lm = 4.4 mH, and sslip = −0.2. The grid equivalent inductance is L1 = 0.1 mH. The 5th, 7th, 11th, 13th, 17th, 19th, 23rd, 25th, 29th, 31st, 35th, and 37th harmonic sources with a magnitude of 0.02 pu are in series on the grid.Figure13 shows the grid-side converter output current iga, the asynchronous motor stator-side current isa, and the grid current ia for different control parameter cases. Figure 13 shows the magnitude of harmonic current measured under different cases. The parameters in different cases are set as follows: (1) case 1: kpg = 0.5, kig = 100, kpr = 0.5, and kir = 800; (2) case 2: kpg = 10, kig = 100, kpr = 0.5, and kir = 800; (3) case 3: kpg = 0.5, kig = 100, kpr = 10, and kir = 100; and (4) case 4: kpg = 10, kig = 100, kpr = 10, and kir = 100.Figure 13
Currentsiga, isa, and ia: (a) case 1; (b) case 2; (c) case 3; (d) case 4.
(a)
(b)
(c)
(d)Figures13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonance frequency amplification due to LCL filter resonance) and low-frequency harmonic amplification (about 5th and 7th harmonic amplification caused by improper control parameters of the rotor-side converter) due to the presence of harmonic voltages in the grid. Figures 13(b), 13(d), and 14 show that, by appropriately increasing kpg, it is possible to suppress the high-frequency harmonic (nearby 29th harmonic current) caused by the resonance of the LCL filter.Figure 14
Harmonic current graphs of (a)iga, (b) isa, and (c) ia.
(a)
(b)
(c)Figures13(c), 13(d), and 14 show that a proper increase in kpr and a decrease in kir can suppress the low-frequency harmonic (near 5th and 7th harmonic current) caused by inappropriate rotor-side converter control parameters. The simulation results are consistent with the theoretical analyses.


### 5.2. Experiment Test

To further verify the theory, a test platform containing the actual wind power converter is built in the laboratory, as shown in Figure15. In the test platform, the AC servo motor is used to emulate the wind turbine and an actual wind power converter is adopted. The rated voltages of the DFIG and the grid are 690 V and 380 V, respectively, which are connected by a transformer.Figure 15
(a) Schematic diagram and (b) physical photograph of the experimental system.
(a)
(b)The rated power of the converter is 2.0 MW. LC filters are utilized for the grid-side converter, with the inductance of filtering being 0.43 mH. Three-phase capacitors are connected in a triangle shape, and the capacitance is 120μF. LC filters and the grid-side line resistances together with the transformer equivalent impedance are combined into an LCL filter. L filters are used on the rotor side, with the inductance being 0.15 mH. The switch frequency of the converter on the grid side is 3000 Hz and that on the rotor side is 2000 Hz, and the modulation method is SVPWM. The DC-side voltage is 1050 V, and the AC-side grid frequency is 50 Hz. The detailed parameters of the test platform are shown in Table 2.Table 2
Detailed parameters of the DFIG test platform.
Parameters
Values
Rated power (Sn)
2 MW
Rated grid frequency
50 Hz
Rated grid voltage (Ug)
380 V
Rated DFIG voltage (Ud)
690 V
Rated DC-link voltage (Udc)
1050 V
Grid-side inductance (Lg)
0.43 mH
Grid-side capacitance (Cg)
120μF
Rotor-side inductance (Lr)
0.15 mH
Modulation method
SVPWM
Switch frequency of the rotor-side converter
2 kHz
Switch frequency of the grid-side converter
3 kHzThe acquisition device is installed at PCC to obtain samples of voltage and current signals synchronously, with the sampling rate being 6000 Hz. In this part, the accuracy of the proposed harmonic modeling of the DFIG is verified from four perspectives, i.e., modulation method, altering controller parameters, altering output power, and the unbalance of three-phase voltage.


#### 5.2.1. Modulation Method

Figure16 shows the waveforms of the voltage and current at PCC, as well as their harmonic spectrums. The switch frequency of the grid-side converter and rotor-side converter is 3000 Hz and 2000 Hz, respectively, and there are obvious harmonics with high frequency close to switch frequency. The high-frequency harmonic components of the voltage and current are distributed at 1920, 1980, 2020, and 2080 Hz for the grid-side converter and 2800 and 2900 Hz for the rotor-side converter.Figure 16
(a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC.
(a)
(b)


#### 5.2.2. Altering Control Parameters

In order to study the influence of different controller parameters on the current harmonic components at PCC, different PI controller’s parameters of the inner current loop are set for the DFIG’s grid-side converter. Specifically, at first,kp is set to be 0.23 and 0.71, respectively, when ki remains as 30. Secondly, kp is set to be 21 and 45, respectively, when ki remains as 0.45. Figure 17 shows the output current harmonic spectrums of the DFIG converter under different PI control parameters. When kp of the current inner loop PI controller of the grid-side converter increases, the lower harmonic current of the DFIG below 1500 Hz is reduced, indicating that the parameter kp has some damping effect. Meanwhile, when ki of the current inner loop PI controller of the grid-side converter changes, the harmonic current of the DFIG does not change significantly, indicating that the parameter ki change has little effect on the harmonic output of the wind turbine, which is consistent with the theoretical analysis.Figure 17
(a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC.
(a)
(b)


#### 5.2.3. Altering Output Power

Figure18 shows the current harmonic diagrams under different active power conditions, i.e., when the output active power is 300 kW and 2000 kW, respectively. As shown in Figure 18, when the output active power of the wind turbine increases, the output power of the DFIG converter increases as well, and the harmonic current whose frequency is close to switch frequency also increases.Figure 18
Current waveforms and harmonic spectrum of the DFIG under different active power conditions.


#### 5.2.4. Three-Phase Voltage Unbalance

In order to verify the effect of three-phase voltage unbalance on the harmonic characteristics of the DFIG, the grid voltage irregularities were set to be 20% and 50%, respectively. Figure19 shows that the larger the unbalance of the three-phase voltage, the larger the amplitude of the 3rd harmonic current is, which is consistent with the theoretical analysis.Figure 19
Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance.


#### 5.2.5. Correction of the Harmonic Model Based on Measured Data

The harmonic model is corrected based on the harmonic test data of the test platform for the DFIG. Table3 shows the precorrected and corrected parameters of the DFIG converter model. The simulated results shown in Figure 20 illustrate the harmonic current of the DFIG converter before and after correction under the rated operation condition. As can be seen from Figure 20, when the parameters of the simulation model are the same as those in the real test platform, the simulation results of harmonic current are much greater than what have been measured in practice. When correcting the simulation model using the data in Table 3, the value of harmonic current whose frequency is close to the switch frequency (which is 2000 and 3000 Hz) in simulation is close to the data in the real test. Therefore, the modified model can be used to emulate the harmonic characteristics of the actual wind turbine.Figure 20
Comparison before and after harmonic model correction of the DFIG.Table 3
Model parameter correction.
Parameter type
Precorrected parameter
Corrected parameter
Filter parameter
L
1
0.43 mH
0.5 mH
C
120μF
120μF
Grid equivalent inductance
L
g
—
0.18 mH
Current loop’s PI control parameter of the grid-side converter
k
pg
1
5.0
k
ig
13
100
Current loop’s PI control parameter of the rotor-side converter
k
pr
0.5
1.5
k
ir
2.5
100


## 5.1. Simulation Verification

In order to verify the above characteristics analyses, a real-time hardware-in-the-loop (HIL) system from ModelingTech is built, as shown in Figure12. Each electromagnetic transient model of the DFIG and control algorithm is constructed by StarSim software and implemented on NI FPGA board 7868R (real-time simulator). The control algorithm is implemented on the PXIe-8821 controller (rapid control prototype (RCP)).Figure 12
HIL simulation platform.The LCL filter parameters of the grid-side converter areL1 = 2 mH, L2 = 1 mH, and C = 18 μF. The asynchronous motor parameters are Lr = 0.404 mH, Rr = 0.0079 Ω, Ls = 0.08 mH, Rs = 0.0025 Ω, Lm = 4.4 mH, and sslip = −0.2. The grid equivalent inductance is L1 = 0.1 mH. The 5th, 7th, 11th, 13th, 17th, 19th, 23rd, 25th, 29th, 31st, 35th, and 37th harmonic sources with a magnitude of 0.02 pu are in series on the grid.Figure13 shows the grid-side converter output current iga, the asynchronous motor stator-side current isa, and the grid current ia for different control parameter cases. Figure 13 shows the magnitude of harmonic current measured under different cases. The parameters in different cases are set as follows: (1) case 1: kpg = 0.5, kig = 100, kpr = 0.5, and kir = 800; (2) case 2: kpg = 10, kig = 100, kpr = 0.5, and kir = 800; (3) case 3: kpg = 0.5, kig = 100, kpr = 10, and kir = 100; and (4) case 4: kpg = 10, kig = 100, kpr = 10, and kir = 100.Figure 13
Currentsiga, isa, and ia: (a) case 1; (b) case 2; (c) case 3; (d) case 4.
(a)
(b)
(c)
(d)Figures13(a) and 14 show that there are both high-frequency harmonic amplification (about 29th resonance frequency amplification due to LCL filter resonance) and low-frequency harmonic amplification (about 5th and 7th harmonic amplification caused by improper control parameters of the rotor-side converter) due to the presence of harmonic voltages in the grid. Figures 13(b), 13(d), and 14 show that, by appropriately increasing kpg, it is possible to suppress the high-frequency harmonic (nearby 29th harmonic current) caused by the resonance of the LCL filter.Figure 14
Harmonic current graphs of (a)iga, (b) isa, and (c) ia.
(a)
(b)
(c)Figures13(c), 13(d), and 14 show that a proper increase in kpr and a decrease in kir can suppress the low-frequency harmonic (near 5th and 7th harmonic current) caused by inappropriate rotor-side converter control parameters. The simulation results are consistent with the theoretical analyses.


## 5.2. Experiment Test

To further verify the theory, a test platform containing the actual wind power converter is built in the laboratory, as shown in Figure15. In the test platform, the AC servo motor is used to emulate the wind turbine and an actual wind power converter is adopted. The rated voltages of the DFIG and the grid are 690 V and 380 V, respectively, which are connected by a transformer.Figure 15
(a) Schematic diagram and (b) physical photograph of the experimental system.
(a)
(b)The rated power of the converter is 2.0 MW. LC filters are utilized for the grid-side converter, with the inductance of filtering being 0.43 mH. Three-phase capacitors are connected in a triangle shape, and the capacitance is 120μF. LC filters and the grid-side line resistances together with the transformer equivalent impedance are combined into an LCL filter. L filters are used on the rotor side, with the inductance being 0.15 mH. The switch frequency of the converter on the grid side is 3000 Hz and that on the rotor side is 2000 Hz, and the modulation method is SVPWM. The DC-side voltage is 1050 V, and the AC-side grid frequency is 50 Hz. The detailed parameters of the test platform are shown in Table 2.Table 2
Detailed parameters of the DFIG test platform.
Parameters
Values
Rated power (Sn)
2 MW
Rated grid frequency
50 Hz
Rated grid voltage (Ug)
380 V
Rated DFIG voltage (Ud)
690 V
Rated DC-link voltage (Udc)
1050 V
Grid-side inductance (Lg)
0.43 mH
Grid-side capacitance (Cg)
120μF
Rotor-side inductance (Lr)
0.15 mH
Modulation method
SVPWM
Switch frequency of the rotor-side converter
2 kHz
Switch frequency of the grid-side converter
3 kHzThe acquisition device is installed at PCC to obtain samples of voltage and current signals synchronously, with the sampling rate being 6000 Hz. In this part, the accuracy of the proposed harmonic modeling of the DFIG is verified from four perspectives, i.e., modulation method, altering controller parameters, altering output power, and the unbalance of three-phase voltage.


### 5.2.1. Modulation Method

Figure16 shows the waveforms of the voltage and current at PCC, as well as their harmonic spectrums. The switch frequency of the grid-side converter and rotor-side converter is 3000 Hz and 2000 Hz, respectively, and there are obvious harmonics with high frequency close to switch frequency. The high-frequency harmonic components of the voltage and current are distributed at 1920, 1980, 2020, and 2080 Hz for the grid-side converter and 2800 and 2900 Hz for the rotor-side converter.Figure 16
(a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC.
(a)
(b)


### 5.2.2. Altering Control Parameters

In order to study the influence of different controller parameters on the current harmonic components at PCC, different PI controller’s parameters of the inner current loop are set for the DFIG’s grid-side converter. Specifically, at first,kp is set to be 0.23 and 0.71, respectively, when ki remains as 30. Secondly, kp is set to be 21 and 45, respectively, when ki remains as 0.45. Figure 17 shows the output current harmonic spectrums of the DFIG converter under different PI control parameters. When kp of the current inner loop PI controller of the grid-side converter increases, the lower harmonic current of the DFIG below 1500 Hz is reduced, indicating that the parameter kp has some damping effect. Meanwhile, when ki of the current inner loop PI controller of the grid-side converter changes, the harmonic current of the DFIG does not change significantly, indicating that the parameter ki change has little effect on the harmonic output of the wind turbine, which is consistent with the theoretical analysis.Figure 17
(a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC.
(a)
(b)


### 5.2.3. Altering Output Power

Figure18 shows the current harmonic diagrams under different active power conditions, i.e., when the output active power is 300 kW and 2000 kW, respectively. As shown in Figure 18, when the output active power of the wind turbine increases, the output power of the DFIG converter increases as well, and the harmonic current whose frequency is close to switch frequency also increases.Figure 18
Current waveforms and harmonic spectrum of the DFIG under different active power conditions.


### 5.2.4. Three-Phase Voltage Unbalance

In order to verify the effect of three-phase voltage unbalance on the harmonic characteristics of the DFIG, the grid voltage irregularities were set to be 20% and 50%, respectively. Figure19 shows that the larger the unbalance of the three-phase voltage, the larger the amplitude of the 3rd harmonic current is, which is consistent with the theoretical analysis.Figure 19
Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance.


### 5.2.5. Correction of the Harmonic Model Based on Measured Data

The harmonic model is corrected based on the harmonic test data of the test platform for the DFIG. Table3 shows the precorrected and corrected parameters of the DFIG converter model. The simulated results shown in Figure 20 illustrate the harmonic current of the DFIG converter before and after correction under the rated operation condition. As can be seen from Figure 20, when the parameters of the simulation model are the same as those in the real test platform, the simulation results of harmonic current are much greater than what have been measured in practice. When correcting the simulation model using the data in Table 3, the value of harmonic current whose frequency is close to the switch frequency (which is 2000 and 3000 Hz) in simulation is close to the data in the real test. Therefore, the modified model can be used to emulate the harmonic characteristics of the actual wind turbine.Figure 20
Comparison before and after harmonic model correction of the DFIG.Table 3
Model parameter correction.
Parameter type
Precorrected parameter
Corrected parameter
Filter parameter
L
1
0.43 mH
0.5 mH
C
120μF
120μF
Grid equivalent inductance
L
g
—
0.18 mH
Current loop’s PI control parameter of the grid-side converter
k
pg
1
5.0
k
ig
13
100
Current loop’s PI control parameter of the rotor-side converter
k
pr
0.5
1.5
k
ir
2.5
100


## 5.2.1. Modulation Method

Figure16 shows the waveforms of the voltage and current at PCC, as well as their harmonic spectrums. The switch frequency of the grid-side converter and rotor-side converter is 3000 Hz and 2000 Hz, respectively, and there are obvious harmonics with high frequency close to switch frequency. The high-frequency harmonic components of the voltage and current are distributed at 1920, 1980, 2020, and 2080 Hz for the grid-side converter and 2800 and 2900 Hz for the rotor-side converter.Figure 16
(a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC.
(a)
(b)


## 5.2.2. Altering Control Parameters

In order to study the influence of different controller parameters on the current harmonic components at PCC, different PI controller’s parameters of the inner current loop are set for the DFIG’s grid-side converter. Specifically, at first,kp is set to be 0.23 and 0.71, respectively, when ki remains as 30. Secondly, kp is set to be 21 and 45, respectively, when ki remains as 0.45. Figure 17 shows the output current harmonic spectrums of the DFIG converter under different PI control parameters. When kp of the current inner loop PI controller of the grid-side converter increases, the lower harmonic current of the DFIG below 1500 Hz is reduced, indicating that the parameter kp has some damping effect. Meanwhile, when ki of the current inner loop PI controller of the grid-side converter changes, the harmonic current of the DFIG does not change significantly, indicating that the parameter ki change has little effect on the harmonic output of the wind turbine, which is consistent with the theoretical analysis.Figure 17
(a) Voltage waveform and harmonic spectrum and (b) current waveform and harmonic spectrum of the DFIG at PCC.
(a)
(b)


## 5.2.3. Altering Output Power

Figure18 shows the current harmonic diagrams under different active power conditions, i.e., when the output active power is 300 kW and 2000 kW, respectively. As shown in Figure 18, when the output active power of the wind turbine increases, the output power of the DFIG converter increases as well, and the harmonic current whose frequency is close to switch frequency also increases.Figure 18
Current waveforms and harmonic spectrum of the DFIG under different active power conditions.


## 5.2.4. Three-Phase Voltage Unbalance

In order to verify the effect of three-phase voltage unbalance on the harmonic characteristics of the DFIG, the grid voltage irregularities were set to be 20% and 50%, respectively. Figure19 shows that the larger the unbalance of the three-phase voltage, the larger the amplitude of the 3rd harmonic current is, which is consistent with the theoretical analysis.Figure 19
Current waveforms and harmonic spectrum of the DFIG under three-phase voltage unbalance.


## 5.2.5. Correction of the Harmonic Model Based on Measured Data

The harmonic model is corrected based on the harmonic test data of the test platform for the DFIG. Table3 shows the precorrected and corrected parameters of the DFIG converter model. The simulated results shown in Figure 20 illustrate the harmonic current of the DFIG converter before and after correction under the rated operation condition. As can be seen from Figure 20, when the parameters of the simulation model are the same as those in the real test platform, the simulation results of harmonic current are much greater than what have been measured in practice. When correcting the simulation model using the data in Table 3, the value of harmonic current whose frequency is close to the switch frequency (which is 2000 and 3000 Hz) in simulation is close to the data in the real test. Therefore, the modified model can be used to emulate the harmonic characteristics of the actual wind turbine.Figure 20
Comparison before and after harmonic model correction of the DFIG.Table 3
Model parameter correction.
Parameter type
Precorrected parameter
Corrected parameter
Filter parameter
L
1
0.43 mH
0.5 mH
C
120μF
120μF
Grid equivalent inductance
L
g
—
0.18 mH
Current loop’s PI control parameter of the grid-side converter
k
pg
1
5.0
k
ig
13
100
Current loop’s PI control parameter of the rotor-side converter
k
pr
0.5
1.5
k
ir
2.5
100


## 6. Conclusion

In this paper, the harmonic equivalent models of the grid-side converter and rotor-side converter of the double-fed wind power generation system are established, and the harmonic output characteristics of both converters are studied based on the established models. The researches show that the resonance of the LC or LCL filter in the grid-side converter may lead to harmonic amplification in the neighboring resonace frequency, and the harmonic amplification can be suppressed by reasonably adjusting the current controller parameterkpg. The integral term of the current controller in the rotor-side converter resonates with the rotor leakage inductance, which may cause the lower-frequency harmonic amplification in stator-side output current of the asynchronous motor, and the harmonic can be suppressed by appropriately increasing kpr and reducing kir of the rotor-side current controller. The real-time HIL test results verify the correctness of the theoretical analyses. Furthermore, the effectiveness of the proposed model is verified based on the actual DFIG test data, which can also provide guidance for the correction of the theoretical model.



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*Source: 7968914-2019-11-03.xml*