Research Article  Open Access
YangWu Shen, Ding Wang, XiangTian Deng, Qing Li, Jian Zuo, "Harmonic Modeling and Experimental Validation of the Converters of DFIGBased Wind Generation System", Complexity, vol. 2019, Article ID 7968914, 13 pages, 2019. https://doi.org/10.1155/2019/7968914
Harmonic Modeling and Experimental Validation of the Converters of DFIGBased Wind Generation System
Abstract
The doublefed induction wind generator (DFIG) based wind generation system contains power electronic converters and filter capacitor and inductor, which will bring about highfrequency harmonics under the influence of controllers. Aiming at this problem, this paper studies the relation between the output current and the harmonic source at gridside and rotorside 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 threephase voltage. Finally, the effectiveness of the proposed model is verified through the 2 MW DFIG realtime hardwareintheloop test platform by StarSim software and real test data, respectively.
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 doublefed 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 variablespeed constantfrequency operation features [1–6]. However, the doublefed 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 doublefed 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 doublefed 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 doublefed wind turbine. In [12], the harmonic characteristics of the doublefed 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 doublefed 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 gridside converter harmonic and the rotorside converter harmonic in the doublefed wind power generation system.
From the above literature studies, the gridside or rotorside converters in the doublefed 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 (pulsewidth 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 doublefed 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: Section 2 presents the harmonic source analysis of the doublefed 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 DoubleFed Wind Power Generation System
The structure of the doublefed wind power generation system is shown in Figure 1. Two backtoback PWmodulated converters are used for AC excitation through a DC link. Effective control of converters enables variablespeed constantfrequency operation and maximum wind energy tracking within a certain range [10, 19, 20].
The harmonic sources of the doublefed 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 doublefed 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 doublefed wind power generation system are studied by establishing the harmonic equivalent model.
3. Harmonic Modeling of DoubleFed Wind Power Converter
Because of the fact that the dynamics of DCside voltage is slower than the harmonic dynamics, the voltage across the capacitor between the gridside converter and the rotorside converter of the doublefed 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 gridside and rotorside converters are established to study their harmonic output characteristics and influencing factors. Note that there are subsynchronous and lowfrequency 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 DCside 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 loworder harmonic generated by the dead zone is more obvious, while the largecapacity 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 GridSide Converter
For a threephase balancing system, the system can be equivalent to a singlephase system. The command signal of the inner current loop in the gridside 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 gridside converter is obtained and shown in Figure 2. The converterside current feedback control which is more stable than the gridside current feedback current control is adopted, as shown in Figure 2 [21].
In Figure 2, K_{pwm} is the linear gain of the pulsewidth modulation (PWM) converter bridge, i_{1ref} is the reference of the current loop, u_{gh} is the harmonic voltage generated by PWM, G_{ig} is the transfer function of the current regulator which adopts the proportional resonance controller, and is the voltage at the gridconnected point. The harmonic model shown in Figure 2 considers two kinds of harmonic sources: (1) the harmonic voltage u_{gh} generated by the PWM and (2) the grid background harmonic voltage at the gridconnected point.
In the steadystate operation, the current reference i_{1ref} remains constant [22]. Thus, according to the Mason formula, the complex frequencydomain expression among i_{2}, u_{gh}, and can be obtained as follows.where s is the complex frequencydomain variable and and are expressed aswhere K_{pwm} is usually taken as 1; Z_{1} = sL_{1} + R_{1}, Z_{2} = sL_{2} + R_{2}, and , in which L_{1}, R_{1}, L_{2}, and R_{2} are the LCL filter inductance and equivalent resistance and C is the filter capacitor; and G_{ig} is expressed aswhere k_{pg} and k_{ig} are the proportional and integral coefficients of the current controller and is the fundamental frequency.
According to Figure 1 and (1), the Norton equivalent circuit of the gridside converter can be obtained, which is shown in Figure 3. In Figure 3, is the PWmodulated harmonic and is the grid background harmonic.
3.2. Harmonic Modeling of RotorSide Converter
The rotorside converter adopts the motor stator fluxoriented 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 threephase system is equivalent to a singlephase system. The current control block diagram of the rotorside converter is shown in Figure 4.
In Figure 4, is the current reference, u_{rh} is the harmonic voltage generated by PWM, and G_{ir} is the transfer function of the current controller and the proportional resonance controller is used; e_{2} is the rotorside phase electromotive force of the asynchronous machine. In Figure 4, the output current iswhere is the rotorside complex frequencydomain variable. Note that , where s_{slip} is the slip. The detailed expressions of , , and are shown as follows:where ω_{m} is the rotor speed of the asynchronous motor; , in which L_{r} and R_{r} are the rotor leakage inductance and resistance; and G_{ir} is expressed aswhere k_{pr} and k_{ir} are the proportional and integral coefficients of the current controller, respectively.
According to Figure 4 and (4) and combining with the asynchronous motor equivalent circuit [11, 12], the Norton equivalent model of the rotorside converter can be obtained, which is shown in Figure 5(a). Note that the rotorside 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 havewhere i_{s} is the statorside output current of the asynchronous motor and and are expressed aswhere and , in which L_{m} is the excitation inductance of the asynchronous motor and L_{s} and R_{s} are the stator leakage inductance and resistance.
(a)
(b)
4. Characteristics Analyses of Converter Harmonic Model
Based on the harmonic models of gridside and rotorside converters established in Section 3, 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.

4.1. Characteristic Analysis of Harmonic Model of GridSide Converter
According to the Norton equivalent model shown in Figure 3 and (1) and (2), the Bode diagram of and 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 and . It indicates that the converter output current will undergo harmonic amplification when the frequency of u_{gh} and is close to the resonant frequency, thus affecting the power quality. Besides, it should be noted that the magnitudefrequency curves of and are obviously declining when the frequency is higher than 2000 Hz, indicating that the converter has a strong suppression to highfrequency harmonics.
Ignoring the equivalent resistance of the filter inductor as it is usually small, and taking K_{pwm} = 1, the denominator of and shown in (2) can be expanded to
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
The resonant frequency ω_{rg} 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 5^{th}, 7^{th}, and 11^{th}. 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 frequency ω_{rg}, an approximate expression is obtained as and the capacitance of the filter capacitor is small.
It is not difficult to see from (11) that the product of k_{pg} and L_{2} provides damping for the resonance. The larger the product, the stronger the damping effect.
Since the current control parameter k_{pg} is relatively easier to change than L_{2} in practice, only the influence of k_{pg} is studied in Figure 7.
It can be seen from Figure 7 that when the parameter of the current loop controller k_{pg} is relatively small, the magnitudefrequency curve of has a resonance peak. As k_{pg} increases, the resonance peak gradually decreases to disappear. In addition, Figure 7 also shows that the controller parameter k_{pi} has less effect on the magnitudefrequency curve of since the integral term of G_{ig} is almost zero at high frequencies.
In summary, the existence of LCL filter resonance may cause harmonic amplification in the output of the gridside converter of the wind power generation system, and the resonance can be suppressed by adjusting the parameter of the current controller k_{pg}. It should be noted that k_{pg} also affects the dynamic response and stability of the converter control system, and this is beyond the scope of this paper. Therefore, the parameter k_{pg} 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 RotorSide Converter
According to (4)–(8) and Figure 5, the magnitudefrequency curves of and are obtained and shown in Figure 8. It can be seen from the curves in Figure 8 that, at higher frequencies, the rotorside converter has an effect of suppressing the higherfrequency PWM harmonics and the grid background harmonics. Since there is no capacitor in the rotorside converter and asynchronous motor, the magnitudefrequency curves of and 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 is needed for the lower secondary grid background harmonics.
As to the rotorside converter, the denominator of and in (5) can be expanded (R_{r} is ignored and K_{pwm} = 1 is considered for the same reason) to
It can be seen from (12) that when the frequency is 3 times higher than the fundamental frequency of the rotor, that is, (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 den_{r} can be approximated to
With (13), it can be found that the first and third terms form a pair of resonant poles whose resonant frequency is
Although there is no resonance in the rotorside 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 and .
From (13) and (14), the resonant frequency is related to the rotor speed ω_{m}, the rotor leakage inductance L_{r}, and the controller parameter k_{ir}. The rotor leakage inductance L_{r} 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 k_{ir} is easy to change. Similar to the gridside converter, the controller parameter k_{pr} has an effect of damping.
Figure 9 shows the magnitudefrequency curves of with different k_{ir}, k_{pr}, and ω_{m}. It can be seen from Figure 9 that, on increasing k_{ir}, the peak slope of shifts to a lower frequency and the magnitude decreases. On the contrary, the magnitudefrequency curve of declines to a large extent as k_{pr} is increased. The slip s_{slip} changes from −0.2 (corresponding to ) to −0.1 (corresponding to ), and the peak slope of shifts to a lower frequency. Considering that the actual range of slip variation is small, the parameters k_{pr} and k_{ir} are the main factors affecting the harmonic output characteristics of the rotorside converter.
4.3. Harmonic Model of DoubleFed Wind Power Generation System considering Grid Impedance
According to the equivalent harmonic models of gridside and rotorside converters shown in Figures 3 and 5, the overall equivalent harmonic model of the doublefed wind system is shown in Figure 10. In Figure 10, is the grid equivalent impedance and is the grid voltage. According to Figure 10, the current can be obtained aswhere , , and are shown as follows:
Considering the influence of grid background harmonics, the magnitudefrequency curve of 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 and , there appears similar resonant frequency in . The resonant peak of is suppressed as the parameters k_{pg}, k_{pr}, and k_{ir} are appropriately increased, which shows similar features to and 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.
5. Case Study
5.1. Simulation Verification
In order to verify the above characteristics analyses, a realtime hardwareintheloop (HIL) system from ModelingTech is built, as shown in Figure 12. Each electromagnetic transient model of the DFIG and control algorithm is constructed by StarSim software and implemented on NI FPGA board 7868R (realtime simulator). The control algorithm is implemented on the PXIe8821 controller (rapid control prototype (RCP)).
The LCL filter parameters of the gridside converter are L_{1} = 2 mH, L_{2} = 1 mH, and C = 18 μF. The asynchronous motor parameters are L_{r} = 0.404 mH, R_{r} = 0.0079 Ω, Ls = 0.08 mH, R_{s} = 0.0025 Ω, L_{m} = 4.4 mH, and s_{slip} = −0.2. The grid equivalent inductance is L_{1} = 0.1 mH. The 5^{th}, 7^{th}, 11^{th}, 13^{th}, 17^{th}, 19^{th}, 23^{rd}, 25^{th}, 29^{th}, 31^{st}, 35^{th}, and 37^{th} harmonic sources with a magnitude of 0.02 pu are in series on the grid.
Figure 13 shows the gridside converter output current i_{ga}, the asynchronous motor statorside current i_{sa}, and the grid current i_{a} 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: k_{pg} = 0.5, k_{ig} = 100, k_{pr} = 0.5, and k_{ir} = 800; (2) case 2: k_{pg} = 10, k_{ig} = 100, k_{pr} = 0.5, and k_{ir} = 800; (3) case 3: k_{pg} = 0.5, k_{ig} = 100, k_{pr} = 10, and k_{ir} = 100; and (4) case 4: k_{pg} = 10, k_{ig} = 100, k_{pr} = 10, and k_{ir} = 100.
(a)
(b)
(c)
(d)
Figures 13(a) and 14 show that there are both highfrequency harmonic amplification (about 29^{th} resonance frequency amplification due to LCL filter resonance) and lowfrequency harmonic amplification (about 5^{th} and 7^{th} harmonic amplification caused by improper control parameters of the rotorside converter) due to the presence of harmonic voltages in the grid. Figures 13(b), 13(d), and 14 show that, by appropriately increasing k_{pg}, it is possible to suppress the highfrequency harmonic (nearby 29^{th} harmonic current) caused by the resonance of the LCL filter.
(a)
(b)
(c)
Figures 13(c), 13(d), and 14 show that a proper increase in k_{pr} and a decrease in k_{ir} can suppress the lowfrequency harmonic (near 5^{th} and 7^{th} harmonic current) caused by inappropriate rotorside 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 Figure 15. 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.
(a)
(b)
The rated power of the converter is 2.0 MW. LC filters are utilized for the gridside converter, with the inductance of filtering being 0.43 mH. Threephase capacitors are connected in a triangle shape, and the capacitance is 120 μF. LC filters and the gridside 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 DCside voltage is 1050 V, and the ACside grid frequency is 50 Hz. The detailed parameters of the test platform are shown in Table 2.

The 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 threephase voltage.
5.2.1. Modulation Method
Figure 16 shows the waveforms of the voltage and current at PCC, as well as their harmonic spectrums. The switch frequency of the gridside converter and rotorside converter is 3000 Hz and 2000 Hz, respectively, and there are obvious harmonics with high frequency close to switch frequency. The highfrequency harmonic components of the voltage and current are distributed at 1920, 1980, 2020, and 2080 Hz for the gridside converter and 2800 and 2900 Hz for the rotorside converter.
(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 gridside converter. Specifically, at first, k_{p} is set to be 0.23 and 0.71, respectively, when k_{i} remains as 30. Secondly, k_{p} 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 k_{p} of the current inner loop PI controller of the gridside converter increases, the lower harmonic current of the DFIG below 1500 Hz is reduced, indicating that the parameter k_{p} has some damping effect. Meanwhile, when k_{i} of the current inner loop PI controller of the gridside converter changes, the harmonic current of the DFIG does not change significantly, indicating that the parameter k_{i} change has little effect on the harmonic output of the wind turbine, which is consistent with the theoretical analysis.
(a)
(b)
5.2.3. Altering Output Power
Figure 18 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.
5.2.4. ThreePhase Voltage Unbalance
In order to verify the effect of threephase voltage unbalance on the harmonic characteristics of the DFIG, the grid voltage irregularities were set to be 20% and 50%, respectively. Figure 19 shows that the larger the unbalance of the threephase voltage, the larger the amplitude of the 3^{rd} harmonic current i_{s}, which is consistent with the theoretical analysis.
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. Table 3 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.

6. Conclusion
In this paper, the harmonic equivalent models of the gridside converter and rotorside converter of the doublefed 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 gridside converter may lead to harmonic amplification in the neighboring resonace frequency, and the harmonic amplification can be suppressed by reasonably adjusting the current controller parameter k_{pg}. The integral term of the current controller in the rotorside converter resonates with the rotor leakage inductance, which may cause the lowerfrequency harmonic amplification in statorside output current of the asynchronous motor, and the harmonic can be suppressed by appropriately increasing k_{pr} and reducing k_{ir} of the rotorside current controller. The realtime 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.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This research was supported by State Grid Corporation Science and Technology Project under Grant NYB17201700081 and Hubei Natural Science Foundation under Grant 2018CFB205.
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Copyright © 2019 YangWu Shen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.