https://doi.org/10.6113/JPE.2018.18.2.511

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718

An Improved Active Damping Method with Capacitor Current Feedback

Yi-Wen Geng^*, Ya-Wen Qi^*, Hai-Wei Liu^*, Fei Guo^*, Peng-Fei Zheng^*,Yong-Gang Li^*, and Wen-Ming Dong^†

^†,*School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China

Abstract

Proportional capacitor current feedback active damping (CCFAD) has a limited valid damping region in the discrete time domain as (0, f_s/6). However, the resonance frequency (f_r) of an LCL-type filter is usually designed to be less than half the sampling frequency (f_s) with the symmetry regular sampling method. Therefore, (f_s/6, f_s/2) becomes an invalid damping region. This paper proposes an improved CCFAD method to extend the valid damping region from (0, f_s/6) to (0, f_s/2), which covers all of the possible resonance frequencies in the design procedure. The full-valid damping region is obtained and the stability margin of the system is analyzed in the discrete time domain with the Nyquist criterion. Results show that the system can operate stably with the proposed CCFAD method when the resonance frequency is in the region (0, f_s/2). The performances at the steady and dynamic state are enhanced by the selected feedback coefficient H and controller gain K_p. Finally, the feasibility and effectiveness of the proposed CCFAD method are verified by simulation and experimental results.

Key words: Active damping, Capacitor current feedback, Damping region, LCL filter

Manuscript received Mar. 29, 2017; accepted Oct. 31, 2017

Recommended for publication by Associate Editor Seon-Hwan Hwang.

^†Corresponding Author: 13813455892@163.com Tel: +86-138-1345-5892, China University of Mining and Technology

*School of Electrical and Power Engineering, China University of Mining and Technology, China

Ⅰ. INTRODUCTION

Photovoltaic generation, as one of the most promising approaches for developing renewable energy, has been widely used. As a key piece of equipment in PV systems, the grid-connected inverter transforms DC current into AC current and injects it into the grid. A filter between the inverter and the grid is indispensable in PV grid-connected systems for attenuating the high order output current harmonics. As for the filter, an LCL-type filter provides better performance with a reduced cost and weight when compared to the traditional L-type filter [1], [2]. However, the three-order structure of the LCL filter makes it easier to resonate. Thus, it is necessary to add a damping algorithm.

Passive damping and active damping are two major alternatives of suppressing the resonance caused by an LCL filter. Passive damping is realized by adding extra resistors in series or parallel with the capacitors or inductors of LCL filters [3]-[5]. Although passive damping is easy to be realized, the power consumption on the passive components is counterproductive to the concept of energy saving. The active damping methods, such as virtual resistor algorithms [6]-[8], adopt special control strategies to achieve the same performance. When compared to passive damping methods, the absence of loss is the most obvious advantage.

Capacitor current feedback active damping (CCFAD) is extensively used due to its simple structure and easy implementation [9]-[11]. The conventional transfer function of CCFAD is analyzed and calculated in the continuous time domain [12], [13], which is inaccurate in digital control systems. In [14], the steady state characteristic of CCFAD in the discrete time domain is discussed and the optimal design of the feedback coefficient is proposed. In [15], the proportional and integral coefficients are optimized for the proportional integral (PI) controller used in CCFAD. In [16], it is indicated that a CCFAD system in the discrete time domain has a specific valid damping region. In addition, if the actual resonance frequency is higher than 1/6 of the sampling frequency f_s, the grid-connected system becomes unstable easily. In [17], the computation time of a CCFAD system is reduced to achieve high robustness against the grid impedance variations. Although the open-loop unstable poles are removed in [17], the valid damping region is still within (0, f_s/6), which causes some difficulties for parameter design. In [18], the valid damping region is extended to (0, f_s/4). However, the sampling frequency f_s needs to be twice the switching frequency f_sw, which introduces limitations on some applications. The area equivalence method is adopted in [19] to implement time delay compensation. However, its compensation time is less than 0.5T_s. The authors of [20] used capacitor current feedback through a second-order high pass filter to extend the valid damping region. However, the filter has many parameters that are difficult to design. In [21], the time delay compensation is realized by inserting a second-order lead-lag compensator into the active damping loop based on a first-order Padé approximation. However, the valid damping region is only (0, f_s/3). In addition, the compensator structure is complex.

This paper proposes an improved CCFAD method that can provide a full-valid damping region, i.e., (0, f_s/2), to ensure that all of the possible frequencies are covered when designing an LCL filter. The stability margin is analyzed in the discrete time domain for selecting the proper feedback coefficient H and the controller gain K_p. Simulation and experiment results have verified the effectiveness and feasibility of the proposed method.

Ⅱ. STRUCTURE AND MODEL OF THE INVERTER

Fig. 1 shows the structure of an LCL-type three-phase voltage source inverter. L₁, L₂ and C are the inverter-side filter inductor, the grid-side filter inductor and the filter capacitor, respectively. C_dc denotes the dc-side capacitor. v_ca, v_cb, v_cc are the filter capacitor voltage. v_ga, v_gb, v_gc are the grid voltage. v_dc and i_dc represent the dc-side voltage and current.

Fig. 1. System structure of an LCL-type three-phase grid-connected inverter.

Voltage space vector pulse width modulation (SVPWM) is adopted here. In the αβ stationary frame, a proportional resonant (PR) controller is applied to track the current reference with zero steady state error. The grid-side current is sensed and fed back to obtain a high quality output current. Fig. 2 shows an equivalent diagram of the proportional CCFAD system in the continuous time domain. In Fig. 2, T_s is a sampling period. The equivalent gain of the inverter K_PWM is 1 when SVPWM is adopted. H is the proportional feedback coefficient. In addition, a sampling delay exists in the PWM modulation process, which can be described as a zero-order holder (ZOH).

Fig. 2. Diagram of the proportional CCFAD system in the continuous time domain.

The computation is implemented by a digital signal processing (DSP) chip. A computation delay is introduced because the present calculation adopts the previous beat sampling value, which can be thought of as one sampling period [22]. The transfer function of the computation delay G_d(s) can be expressed as (1).

    (1)

The transfer function of the ZOH is:

   (2)

A quasi-proportional resonant controller is adopted here for a wide bandwidth, and the transfer function is:

      (3)

Where K_p is the proportional gain, and K_r is the integral gain [23]. ω₁ and ω_c are the fundamental frequency and cut-off angular frequency.

The transfer function G_i2(s) from grid-side current to the inverter-side voltage is:

             (4)

The transfer function G_ic(s) from the capacitor current to the inverter-side voltage is:

   (5)

In (4) and (5), ω_r represents the inherent resonance angular frequency.

     (6)

Fig. 3 shows a current control diagram of the proportional CCFAD system in the discrete time domain. G_ic(s) and G_i2(s) can be rewritten as G_ic(z) and G_i2(z), which are:

           (7)

     (8)

In Fig. 3, the open-loop transfer function of the proportional CCFAD system in the discrete time domain can be derived as (9).

       (9)

Fig. 3. Diagram of the proportional CCFAD system in the discrete time domain.

Ⅲ. STABILITY ANALYSIS OF THE PROPOSED CCFAD

The condition f_r < f_s/2 is required in the parameter designing procedure when the symmetry regular sampling method is adopted [24]. Here, the designing constraint (0, f_s/2) is defined as the resonance frequency region. If the resonance frequency is designed so that it is higher than the valid damping region (0, f_s/6) in the conventional CCFAD [25], the system becomes potentially unstable due to grid impedance variations. Therefore, the parameter designing is limited to (0, f_s/6). Meanwhile, if the valid damping region is extended to (0, f_s/2), which covers the entire resonance frequency region, it becomes much easier to design the LCL parameters. In this paper, the extended valid damping region (0, f_s/2) is defined as the full-valid damping region.

A diagram of the proposed CCFAD in the discrete time domain is shown in Fig. 4, and the transfer function W(z) can be described as:

             (10)

where λ is an adjustable parameter.

Fig. 4. Diagram of the improved CCFAD in the discrete time domain.

Furthermore, in the continuous time domain, (10) can be described as:

                 (11)

A diagram of the proposed CCFAD in the continuous time domain is shown in Fig. 5. Through a series of equivalent transformations, the feedback of capacitor current can be seen as a virtual impedance Z_eq(s) paralleled with the filter capacitor, shown as the dashed box in Fig. 5. Z_eq(s) can be expressed as:

          (12)

Fig. 5. Diagram of the improved CCFAD in the continuous time domain.

A. Selection of λ

Applying s = jω to W(s) yields Z_eq(jω) as in (13). Z_eq(jω) can be regarded as a resistor paralleled with a reactor, and the paralleled impedance can be expressed as:

     (13)

     (14)

The equivalent resistance and reactance can be expressed as:

           (15)

          (16)

R_eq(ω) plays the role of damping the resonance peak. Therefore, (15) needs to be positive. In order to obtain the full-valid damping region, (17) must be satisfied.

        (17)

However, sin(0.5ωT_s) is higher than zero when ω < ω_s, which causes R_eq(ω) < 0. Therefore, the feedback in Fig. 5 is modified as a positive feedback. Accordingly, the minus sign in Fig. 5 is replaced by the plus sign shown in the bracket.

Fig. 6 shows the equivalent resistance according to (15) with different values of λ. The possible values of λ are λ = 1 and λ = 2 to satisfy (17) and to cover (0, f_s/2). Based on (9) and (10), the modified open-loop transfer function of the proposed CCFAD system can be derived as (18).

     (18)

Fig. 6. Curves of the equivalent resistance when λ= 1, 2, 4, 5.

The Nyquist stability criterion in the discrete time domain is similar to that in the continuous time domain. In order to investigate the stability of the proposed CCFAD system, the numbers of unstable open-loop poles (N) and -180^° crossings need to be discussed.

B. Stability Analysis of the  Proposed CCFAD with λ = 2

When λ = 2, the open-loop transfer function can be expressed as (19). There are five open-loop poles, and two of them are stable poles (P₁ = 1, P₂ = 0).

       (19)

Define the denominator of (19) as (20).

      (20)

The Routh-Hurwitz criterion is adopted to determine the numbers of unstable open-loop poles after a w-transformation, and the Routh array is as:

where:

                (21)

A bode diagram of the improved CCFAD system when λ = 2 is plotted as Fig. 7, and it can be discussed in the following two situations depending on H₁.

Fig. 7. Bode diagram of the improved CCFAD system when λ = 2.

(1) 0 <H < H₁, N = 1. It can be found in Fig. 7 that the phase crosses -180^° once, which makes the system unstable.

(2) H > H₁, N = 2. There is no -180^° crossing. Therefore, the system is unstable, where:

   (22)

According to the stability criterion in the discrete time domain, the proposed CCFAD system with λ = 2 always has unstable open-loop poles and the phase plot cannot meet the stability requirements as per the previous analysis. Therefore, λ = 2 is abandoned.

C. Stability Analysis of the Proposed CCFAD with λ = 1

According to (15) and (16), the paralleled equivalent resistance R_eq(ω) and reactance X_eq(ω) vary with ω as shown in Fig. 8. It can be seen that the proposed CCFAD method makes it possible for R_eq(ω) to be negative in (0, f_s/2). Thus, changing the negative feedback in the inner loop to positive feedback can make R_eq(ω) positive, as shown in Fig.5. Then the valid damping region is extended to f_s/2.

       (23)

Fig. 8. Curves of the equivalent resistance and reactance with λ= 1: (a) Equivalent resistance R_eq; (b) Equivalent reactance X_eq.

(a)

(b)

According to (18), the open-loop transfer function can be expressed as (23) when λ = 1. There are four poles in (23), and two of them are stable poles (P₁ = 1, P₂ = 0).

Similarly, define the denominator in (23) as:

     (24)

According to the Routh-Hurwitz criterion after a w-transformation, the Routh array is shown as follows.

Three conditions can be summarized as follows to investigate unstable open-loop poles by analyzing the first column of the Routh array.

(1) f_r < f_s/4 when 0 < H < H₂ or f_r > f_s/4 when 0 < H < H₃. In this case, the sign of the first column in the Routh array is positive and the numbers of unstable poles N = 0, where:

          (25)

(2) f_r < f_s/4 when H₂ < H < H₃ or f_r > f_s/4 when H₃< H < H₂. In this case, the sign of the first column in the Routh array changes once and the numbers of unstable poles N = 1.

(3) f_r < f_s/4 when H > H₃ or f_r > f_s/4 when H > H₂. In this case, the sign of the first column in the Routh array changes twice and the numbers of unstable poles N = 2.

In the second case, the numbers of unstable poles N = 1, and the system is unstable. As for the third case, a bode diagram of the open-loop system is shown in Fig. 9. As can be seen, there is no -180^° crossing in the phase plot regardless of whether or not the resonance frequency is higher than f_s/4, which makes the system unstable. Therefore, the system is stable only when the first case is satisfied. Actually, the resonance frequency shifts when the proposed CCFAD is adopted. The effect of the paralleled impedance on the resonance frequency will be discussed in the next part.

Fig. 9. Bode diagram of the third condition of the improved CCFAD system when λ = 1.

D. Effect of Paralleled Virtual Impedance on the Resonance Frequency

In the improved system, the virtual impedance algorithm changes the original resonance frequency. This part will discuss the resonance frequency shifting related to the virtual impedance.

1) LCL without Damping: the structure of an LCL without damping is shown in Fig. 10(a). The transfer impedance Z₁ can be expressed as:

           (26)

The resonance frequency of the LCL filter without damping can be obtained as (6).

Fig. 10. Structure of: (a) LCL filter without damping; (b) capacitor paralleled with a resistor; (c) capacitor paralleled with a reactor; (d) capacitor paralleled with both a resistor and a reactor.

(a)

(b)

(c)

(d)

2) LCL with a Resistor Paralleled with a Filter Capacitor: the structure of an LCL with a resistor paralleled with a filter capacitor is shown in Fig. 10(b). The transfer impedance Z₂ can be expressed as:

          (27)

The resonance frequency of the LCL with a resistor paralleled with a filter capacitor is the same as (6). Therefore, a resistor paralleled with a filter capacitor does not change the resonance frequency. Comparing (27) with (26), the real part of Z₂ is increased more than Z₁, which means that the system damping is increased.

3) LCL with a Reactor Paralleled with a Filter Capacitor: the structure of an LCL with a reactor paralleled with a filter capacitor is shown in Fig. 10(c). The transfer impedance Z₃ can be expressed as:

       (28)

The resonance frequency of the LCL with a reactor paralleled with a filter capacitor can be obtained as (29). Comparing (29) with (6), a reactor paralleled with a filter capacitor changes the resonance frequency. The resonance frequency increases when X_d > 0. Similarly, comparing (28) with (26), the imaginary part of Z₃ is higher than Z₁, which means that the system damping is increased.

    (29)

4) LCL with a Resistor and a Reactor Paralleled with a Filter Capacitor: the proposed CCFAD method can be seen as a virtual resistor and a reactor paralleled with the filter capacitor shown in Fig. 10(d). The transfer impedance Z₄ can be expressed as:

   (30)

The resonance frequency of an LCL with a resistor and a reactor paralleled with a filter capacitor is the same as (29). Comparing (30) and (29) with (26) and (6), the paralleled reactor changes the resonance frequency and when X_d > 0, and the resonance frequency shifts to the right. The resistor and reactor can both enhance the damping effect. However, the resistor plays a more important role.

In Fig. 10(d), the defined currents and through the paralleled reactor and resistor are opposite the previous currents, which corresponds to the positive feedback in Fig. 5. Despite the opposite currents, the values of the impedance and resonance frequency remain unchanged as (30) and (29). The equivalent reactor in Fig. 8 acts as an inductor in (0, f_s/4) since the reactance is positive. Thus, the actual resonance frequency decreases. It behaves as a capacitor in (f_s/4, f_s/2) since the reactance is negative. Thus, the actual resonance frequency increases.

E. Performance Evaluation of the CCFAD System with λ =1

According to the previous analysis in Section III-C, the proposed CCFAD system with λ = 1 is stable only in the following two cases, where no unstable open-loop poles exist.

1) f_r < f_s/4, 0 < H < H₂, N = 0.

2) f_r > f_s/4, 0 < H < H₃, N = 0.

Take f_r1 < f_s/4 and f_r2 > f_s/4 for example, where discrete bode diagrams are shown in Fig. 11. The parameters are displayed in Table I, where f_act1 and f_act2 are the actual resonance frequencies (f_act1 = 1.03 kHz, f_r1 = 1.04 kHz, f_act2 = 1.43 kHz and f_r2 = 1.42 kHz). The relationship of f_act1< f_r1 and f_act2> f_r2 validates the previous analysis. The magnitude and phase margin with H and K_p in Table I are 4-10dB and 45-80^°, respectively. These values meet the requirements of a stable system.

TABLE I PARAMETERS OF THE IMPROVED CCFAD

Parameters	1)	2)
Inverter-side inductance L1(mH)	1.5	1.5
Filter capacitor C(mF)	18.8	18.8
Grid-side inductance L2 (mH)	7.2	1.2
Sampling frequency fs(kHz)	5	5
Switching frequency fsw(kHz)	5	5
Feedback coefficient H	0.3	0.9
Controller gain Kp	6	6
Resonance frequency fr(kHz)	1.04	1.42
Magnitude margin Kg(dB)	9.8	4.01
Phase margin γ	76.7°	47.2°

Fig. 11. Bode diagrams of the improved capacitive current proportional feedback system.

Fig. 12 shows a closed-loop zero-pole map with the improved CCFAD method, where f_r1 < f_s/4 and f_r2 > f_s/4. As can be seen in this figure, the closed-loop poles tend to move to the center of the unit circle by properly increasing H. This improves the dynamic responses of the system.

Fig. 12. Closed-loop zero-pole map of the improved CCFAD system.

Ⅳ. SIMULATION AND EXPERIMENTAL RESULTS

A simulation model is built in MATLAB/Simulink to verify the validity and feasibility of the proposed CCFAD system. The inverter prototype in this paper uses Infineon’s BSM50GB120DLC type IGBTs. The main parameters of the IGBT, which are from its data sheet, are shown in Table II. As can be seen in Table II, the rated output rms current is 50A. To ensure that the loss of IGBT (diode) does not exceed the maximum loss, the appropriate switching frequency range is set to 0.5kHz~11kHz. The switching frequency cannot be lower than 0.5kHz. This is due to the fact that a lower switching frequency leads to increased voltage harmonics. In addition, a higher switching frequency results in a lower maximum output rms current. Therefore, the switching frequency should be lower than 5.5kHz to make sure that the maximum output rms current can be higher than 50A. Finally, in order to obtain better sinusoidal voltage waveforms, this paper selects 5kHz as the switching frequency.

TABLE II MAIN PARAMETERS OF A BSM50GB120DLC IGBT

Parameter	Value
Collector-emitter voltage UCES	1200V
Output rms current Irms	50A
Operation temperature Tvj	125˚C
Total power dissipation Ptot	460W
Turn on delay time td(on)	0.05μs
Rise time tr	0.05μs
Turn off delay time td(off)	0.25μs
Fall time tf	0.03μs

Fig. 13 shows waveforms of the voltage, current and total harmonic distortion (THD) of the grid-side current when f_r1 = 1.04 kHz and f_r2 = 1.42 kHz.

Fig. 13(a) and Fig. 13(b) are the simulation results obtained when f_r < f_s/4 and f_r > f_s/4, respectively. The values of H and K_p are consistent with Table I. The current  waveform is magnified by 10 times for easier observation in the diagram of the voltage-current. In Fig. 13(b), the system operates stably when f_r > f_s/4, which illustrates that the valid damping region is extended to (0, f_s/2) by the proposed method. The THD is 0.76% when f_r < f_s/4 and it is 1.18% when f_r > f_s/4. Therefore, the proposed CCFAD provides a satisfactory THD in both of the above occasions.

Fig. 13. Simulation results with different resonance frequencies: (a) f_r < f_s/4, f_r1 = 1.04 kHz; (b) f_r > f_s/4, f_r2 = 1.42 kHz.

(a)

(b)

A 2kW three-phase grid-connected inverter prototype is built to further validate the proposed method with the parameters shown in Table I. A FPGA and DSP together work as the controller of the system.

Fig. 14 shows the dynamic response when the damping method is changed from the proportional CCFAD to the improved CCFAD. It also shows that the system with the improved active damping method can run stably regardless of whether f_r < f_s/4 or f_r > f_s/4.

Fig. 14. Waveforms of the phase-A voltage and current with and without the proposed CCFAD: (a) f_r< f_s/4; (b) f_r > f_s/4.

(a)

(b)

Fig. 15 and Fig. 16 show waveforms of voltage and grid-side current in phase-A when f_r < f_s/4 and f_r > f_s/4, respectively. Fig. 15(a) and Fig. 16(a) indicate the steady-state performance when the reference current is 8A.

Fig. 15(b) and Fig. 16(b) indicate the dynamic response when the reference current changes from 8A to 12A. Fig. 15(c) and Fig. 16(c) indicate the resonance performance when K_p changes from 6 to 8.5. Comparing Fig. 15(a) and Fig. 15(c) with Fig. 16(a) and Fig. 16(c), it can be seen that a proper K_p provides a unit-power-factor performance and avoids resonance. Fig. 15(b) and Fig. 16(b) show voltage-current waveforms with the reference current changing from 8A to 12A. It shows that the current tracks the reference signal in 20ms and that the system runs stably with no stable error.

Fig. 15. Waveforms of the phase-A voltage and current with f_r< f_s/4: (a) steady-state; (b) dynamic-state; (c) resonant-state.

(a)

(b)

(c)

Fig. 16. Waveforms of the phase-A voltage and current with f_r > f_s/4: (a) steady-state; (b) dynamic-state; (c) resonant-state.

(a)

(b)

(c)

Fig. 17(a) and Fig. 17(b) show the three-phase grid-side current when f_r < f_s/4 and f_r > f_s/4, respectively. The reference current is 8A and K_p = 6. These results illustrate that the system operates stably in (0, f_s/4) and (f_s/4, f_s/2) with the proposed method.

Fig. 17. Experimental results of the three-phase grid-side current: (a) f_r< f_s/4, f_r1 = 1.04 kHz; (b) f_r > f_s/4, f_r2 = 1.42 kHz.

(a)

(b)

Ⅴ. CONCLUSIONS

This paper proposes an improved CCFAD method to obtain a full-valid damping region. When compared with the conventional proportional CCFAD, the proposed method extends the valid damping region from (0, f_s/6) to (0, f_s/2). The feedback link W(z) provides an equivalent virtual impedance to expand the valid damping region. The stability margin is analyzed with a discrete Nyquist criterion. Both simulation and experimental results show that the dynamic performance is improved and that the stability is ensured in the full-valid damping region with a proper feedback coefficient H and controller gain K_p.

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Yi-Wen Geng was born in Jiangsu Province, China, in 1977. He received his B.S., M.S. and Ph.D. degrees from the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China, in 2000, 2004 and 2014, respectively. In 2006, he became a Lecturer in the School of Electrical and Power Engineering, China University of Mining and Technology, where he has been working as an Associate Professor since 2016. His current research interests include photovoltaic inverters, harmonic mitigation, and power electronics.

Ya-Wen Qi was born in Jiangsu Province, China, in 1992. She received her B.S. degree in Electrical Engineering from the China University of Mining and Technology, Xuzhou, China, in 2016, where she is presently working towards her M.S. degree in Electrical Engineering in the School of Electrical and Power Engineering. Her current research interests include the control of converters and harmonic mitigation.

Hai-Wei Liu was born in Jiangsu Province, China, in 1994. He received his B.S. degree in Electrical Engineering from the China University of Mining and Technology, Xuzhou, China, in 2016, where he is presently working towards his M.S. degree in Electrical Engineering in the School of Electrical and Power Engineering. His current research interests include the control of current-source converters and ac machines.

Fei Guo was born in Anhui Province, China, in 1994. He received his B.S. degree in Electrical Engineering and Automation from the Anhui University, Hefei, China, in 2016. He is presently working towards his M.S. degree in Electrical Engineering in the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China. His current research interests include the drive systems of permanent magnet synchronous motors for electric vehicles.

Peng-Fei Zheng was born in Anhui Province, China, in 1993. He received his B.S. degree in Electrical Engineering and Automation from the Nanjing University of Posts and Telecommunications, Xuzhou, China, in 2016. He is presently working towards his M.S. degree in Electrical Engineering in the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China. His current research interests include bidirectional three-level LLC resonant converters and their control.

Yong-Gang Li was born in Henan Province, China, in 1994. He received his B.S. degree in Electrical Engineering from the Shanghai Institute of Technology, Shanghai, China, in 2015. He is presently working towards his M.S. degree in Electrical Engineering in the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China. His current research interests include the control of multiphase motors and electric vehicles.

Wen-Ming Dong was born in Jiangsu Province, China, in 1992. He received his B.S. degree in Electrical Engineering from the China University of Mining and Technology, Xuzhou, China, in 2015, where he is presently working towards his M.S. degree in Electrical Engineering in the School of Electrical and Power Engineering. His current research interests include the control of inverters and photovoltaic generation technologies.