https://doi.org/10.6113/JPE.2019.19.5.1142

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

Reducing Current Distortion in Indirect Matrix Converters Operating in Boost Mode under Unbalanced Input Conditions

Dongho Choi^*, Yeongsu Bak^*, and Kyo-Beum Lee^†

^†,*Department of Electrical and Computer Engineering, Ajou University, Suwon, Korea

Abstract

This paper presents a control method for reducing the current distortion in an indirect matrix converter (IMC) operating in boost mode under unbalanced input conditions. IMCs operating in boost mode are useful in distributed generation (DG) systems. They are connected with renewable energy systems (RESs) and the grid to transmit the power generated by the RES. However, under unbalanced voltage conditions of the RES, which is connected with the input stage of the IMC operating in boost mode, the input-output currents are distorted. In particular, the output current distortions cause a ripple of the power, which is transferred to the grid. This aggravates the reliability and stability of the DG system. Therefore, in this paper, a control method using positive/negative sequence voltages and currents is proposed for reducing the current distortion of both side in IMCs operating in boost mode. Simulation and experimental results have been presented to validate effectiveness of the proposed control method.

Key words: Boost mode, Current distortion, Indirect matrix converter, Positive/Negative sequence voltages and currents, Unbalanced input conditions

Manuscript received Mar. 8, 2019; accepted May 14, 2019

Recommended for publication by Associate Editor Sangshin Kwak.

^†Corresponding Author: kyl@ajou.ac.kr  Tel: +82-31-219-2376, Fax: +82-31-212-9531, Ajou University

^*Dept. of Electrical and Computer Eng., Ajou University, Korea

Ⅰ. INTRODUCTION

In recent years, the gradual depletion of energy resources and environmental pollution have become important issues. Accordingly, the demand for renewable energy systems (RESs) such as wind power and solar energy generation systems has rapidly increased and research on RESs is actively progressing [1]-[9].

A RES, by connecting it to the grid, can be used to supply the power. However, since the use of devices consuming electricity has increased, the electricity from RESs is not able to sufficiently satisfy electricity demands. Additionally, the electricity supply has become saturated due to social, geographical and environmental factors. In order to satisfy the electrical demands and to overcome these problems, research on distributed generation (DG) systems is being actively pursued [10]-[13].

DG systems supply required electricity from electricity generation facilities. They represent a power generation system using a distributed arrangement surrounding an area with electricity demands and having a small scale when compared with a centralized generation (CG) system [14]- [18]. Therefore, when compared with CG systems, DG systems have a reduced burden in terms of the production of large capacity electricity and they are able to utilize RESs. RESs cannot be directly connected to the grid due to mismatch of the voltage magnitude and frequency in the DG systems. In RESs, they are variable while those of the grid are constant. Therefore, power conversion devices are required to connect RESs with the grid in DG systems. In particular, RESs with generators, AC-DC-AC or AC-AC power conversion devices are required [19], [20].

In general, AC-DC-AC power conversion devices for RESs are used such as inverter systems with diode rectifier and back-to-back (BTB) converters. A common feature of these systems is they have a DC-link capacitor. The DC-link capacitor takes up a lot more room in these systems due to its bulky size. Additionally, it has inherent drawbacks such as low durability and a short lifetime [21]-[24].

Some studies for removing DC-link capacitor have been carried out to deal with these disadvantages. An indirect matrix converter (IMC) is an AC-AC power conversion device, which can convert power without a DC-link capacitor. It is similar to the shape of a BTB converter [25]-[27]. It has advantages such as high durability and a small volume since there is no DC-link capacitor when compared with BTB converters. However, in the IMC, a maximum voltage transfer ratio is confined under 0.866. It always operates in buck mode, which is crucial drawback [28]-[34].

Since IMCs are operated in buck mode, their application is quite restricted. For example, small generation systems such as DG systems normally generate a lower voltage than the grid voltage level. This implies that an IMC is not appropriate for this system to transmit generated power to the grid. In order to sustain the advantages of an IMC and to apply it in the required voltage boost system, the IMC operating in boost mode has been researched with its configuration and control method [35], [36]. In [36], since the power direction of the RMC is opposite that of the IMC to enhance the voltage transfer ratio, an IMC operating in boost mode is a reverse matrix converter (RMC). The minimum voltage transfer ratio of the RMC is 1.155. The RMC consists of a voltage source rectifier (VSR) and a current source inverter (CSI) [37]-[39]. The input stage is connected by sources such as renewable energy systems with generator. The output stage is generally connected with the grid which has higher voltage than the input source voltage.

In the RMC, the input power quality affects the output power quality directly because the it does not have a DC-link capacitor [40]. If unbalanced conditions occur in the input voltages, negative sequence components appear in the input currents. This induces a ripple in both the output power and the input power. In addition to unbalanced input conditions, harmonic issues also exist. When harmonics are included in the source voltages, the input currents also include harmonics. These harmonic occurrences in the input currents are also reflected in the output currents. This paper presents a control method for reducing the current distortion in the RMC (IMC operating in the boost mode) under unbalanced input conditions and for improving the output power quality by reducing the current harmonics. In the preliminary conference version of this paper [41], a control method for reducing current distortion was introduced. However, in [41], there was no explanation for the produced DC-link voltage or the zero DC-link current commutation. Most importantly, the block diagrams are not specific and practical verifications obtained by experimental results are not shown in that paper. Unlike [41], in this paper, explanations for the DC-link voltage and zero DC-link current commutations are added. In addition, the block diagrams are specified and practical verifications with the experimental results are presented. The effectiveness of the proposed control method is verified by simulation and experimental results.

Ⅱ. CIRCUIT CONFIGURATION AND MODULATION STRATEGY

A. Circuit Configuration

Fig. 1 shows a circuit configuration diagram of the RMC. It consists of a VSR and a CSI. The VSR is similar in shape to a conventional three-phase two-level inverter. Each leg of the VSR is composed of 2 complementary operated switches. The CSI is composed of 12 switches which are made up of 2 bidirectional switches for the respective legs. In this system, the upper side switch of each leg is the common collector type and the lower side switch is the common emitter type. The input stage of a VSR is normally connected by an AC source with an L filter. The output stage of a CSI is connected by loads with an LC filter.

Fig. 1. Circuit configuration of the RMC.

B. Modulation of the CSI

Fig. 2 shows a space vector diagram of a CSI, which is distinguished by six sectors. In this diagram, six active states and three null states exist depending on the switching states of the CSI. However, only six active states are used for modulation. Fig. 3 shows a produced DC-link voltage, which is formed by using six active states. It is a composite of two line-to-line voltages. They are the largest and second largest magnitudes of the output stage. In the active states, the power generated from the input stage is transferred to the output stage. In the null states, unlike the active states, the DC-link voltage is shorted to zero.

Fig. 2. Space vector diagram of a CSI.

Fig. 3. Produced DC-link voltage.

In Fig. 2, when a reference current vector is located in sector 0, it is reproduced by synthesizing the nearest two vectors such as CS1 and CS6. At this time, the upper switch

of the R-phase (S_Rp) maintains the ON state during the whole switching cycle. Therefore, an upper DC-link is connected with the R-phase voltage of the output stage. Additionally, since the two lower switches (S_Sn and S_Tn) operate depending on calculated active duty ratios, a lower DC-link is alternately connected with the S-phase and T-phase voltage of the output stage depending on the switching state of the two lower switches. It is necessary to mathematically calculate the active duty ratios in order to realize the described modulation method. The respective reference phase currents of the CSI are represented as:

          (1)

where I_m is the phase current amplitude and θ_x (x = R, S, T) is the respective phase angle. From (1), by using the feature where their sum is zero, the active duty ratios (d_x and d_y) are derived as:

          (2)

In addition, it is obvious that an average fictitious DC-link voltage (V_DC(av)) must be calculated for VSR modulation. This is expressed by multiplying the active duty rations (d_x and d_y) and line-to-line voltages (V_RS and V_RT) of the output stage as:

          (3)

where V_m is a phase voltage magnitude, and ϕ_o is the power factor of the output stage. This analysis is equally applied when the current vector is placed in other sectors.

C. Modulation of the VSR

Fig. 4 shows a space vector diagram of the VSR. There are two null states (VS0 and VS7) and six active states (VS1 ~ VS6). The null states are realized by turning on either all of the upper (S_Ap, S_Bp, S_Cp) or all of the lower switches (S_An, S_Bn, S_Cn) of the VSR. In the null states, a short circuit is formed in the VSR, and power is not transmitted to the CSI from the VSR. In these states, magnetic energy is charged in the input filter inductors (L_in). Simultaneously, as shown in Fig. 5, a zero DC-link current commutation is performed in the CSI.

Fig. 4. Space vector diagram of a VSR.

Fig. 5. Zero DC-link current commutation.

During the active states, the charged power of L_in is transmitted to the output stage. As a result, the voltages of the output filter capacitors (C_out) exceed the source voltages.

VSR modulation is performed based on three-phase reference voltages, which are calculated by using d_x, d_y and V_DC(av). As a result, DC-link compensation is accomplished and sinusoidal currents can be produced. In addition, the modulation signals of each phase are divided into two modulation signals, which are represented as:

          (4)

where V_j^* (j = A, B, C) is the respective reference phase voltage, and V_offset is the offset voltage for extension of the modulation index.

Ⅲ. PROPOSED CONTROL METHOD FOR REDUCING CURRENT DISTORTION

A. Positive/Negative Sequence Voltages and Currents

The input-output currents are distorted under unbalanced input conditions of the RMC for DG systems. In particular, distorted output currents deteriorate the reliability and stability of DG systems. Therefore, an additional control method is required for reducing the output currents distortion. Distorted currents can be classified into positive/negative sequence currents. In this paper, a control method for reducing output currents distortion using them is proposed.

Fig. 6 shows a block diagrams for the classification of the positive/negative sequence voltages and currents. The positive (V_A^p, V_B^p, V_C^p) and negative sequence voltages (V_Aⁿ, V_Bⁿ, V_Cⁿ) of the input stage are classified by using a symmetrical coordinates method under unbalanced input conditions of the RMC. Additionally, this classification method can also be applied in the currents of the input stage.

Fig. 6. Block diagrams for classification. (a) Positive sequence voltages and currents. (b) Negative sequence voltages and currents.

(a)

(b)

The symmetrical coordinates method for detecting the positive/negative sequence voltages and currents was also used in [42], [43]. However, unlike the application used in this paper, the symmetrical coordinates method is used for detecting them under unbalanced grid voltage conditions in the output stage of an IMC in [42] and a wind turbine system with a doubly fed induction generator (DFIG) in [43].

B. New Reference Currents

In a RES under unbalanced input conditions, the complex power has AC components due to distorted currents with negative sequence currents. Therefore, those AC components should be removed to reduce the currents distortion. The input complex power of the RMC is expressed in the synchronous reference frame (d-q axis) as:

          (5)

where V_dq^p, V_dqⁿ, I_dq^p and I_dqⁿ are positive/negative sequence voltages and currents. The complex power consists of active and reactive power as:

          (6)

where P₀ and Q₀ are the DC components and P_cos, P_sin, Q_cos and Q_sin are the AC components oscillating to two times the input frequency. These components, excluding Q_cos and Q_sin, are represented by using V_dq^p, V_dqⁿ, I_dq^p and I_dqⁿ as:

          (7)

In (7), P₀ and Q₀ can be represented by using the input active (P_in) and reactive power (Q_in), respectively. Additionally, in order to remove the AC components of the active power, P_cos and P_sin are substituted to zero. As a result, the new reference currents for removing the AC components can be calculated as:

          (8)

Meanwhile, under balanced input conditions, each of the active and reactive reference powers of the input stage can be represented with the reference currents as:

          (9)

Finally, by substituting (9) into (8), the new reference currents for removing AC components composed of positive/ negative sequence components can be calculated as:

          (10)

As a result, the new reference currents lead to a balanced complex power that causes a reduced current distortion.

C. Proposed Control Method of the RMC Under Unbalanced Input Conditions

Fig. 7 shows a control block diagram of the RMC under unbalanced input conditions. The three-phase currents (I_R, I_S, I_T) of the CSI stage are transformed into the d-q axis using the phase angle (θ_out) of the loads. The d-q axis currents (I_de.out and I_qe.out) of the CSI stage are controlled to reference currents (I^*_de.out and I^*_qe.out) using a proportional-integral (PI) controller. The controller outputs (I^*_de.in and I^*_qe.in) determine the active duty ratios (d_x and d_y) for commutation of the CSI. In addition, the switches are operated by the modulation method. The three-phase currents (I_A, I_B and I_C) of the VSR stage are controlled by using the proposed control method.

Fig. 7. Control block diagram of the RMC.

Fig. 8 shows a control block diagram of the proposed control method. The classification of positive/negative sequence voltages and currents is implemented as shown in Fig. 6. Under unbalanced input conditions, the new reference currents (I_dq^p* and I_dq^n*) are calculated in (10). Finally, the positive/ negative sequence currents (I_dq^p and I_dqⁿ) are controlled to I_dq^p* and I_dq^n* with PI controllers, respectively. The outputs (V_ABC^*) of the PI controller are modulated using (4), and the switches are operated by carrier based PWM.

Fig. 8. Control block diagram of the proposed control method.

D. Control Method for Harmonics Reduction

When harmonics are included in the input currents in the RMC for DG systems, they are also indicated in the output currents. Harmonics, including the output currents, aggravate the quality of loads. Therefore, regarding the input currents, a control method for harmonics reduction is required to improve the power quality. In particular, in the input currents, the 5^th and 7^th order harmonics should be properly dealt with because they are dominant. The input currents (I_de and I_qe) in the d-q axis, including harmonics, can be expressed by using a Fourier transform as in (11). In the stationary reference frame, the 5^th and 7^th order harmonics are expressed as the 6^th order harmonics in the d-q axis.

          (11)

Therefore, the 5^th and 7^th order harmonics, including input currents, can be reduced to zero by using the control of the 6^th order harmonics in the d-q axis. As a result, the quality of the output currents can be improved.

Ⅳ. SIMULATION RESULTS

In order to validate the effectiveness of the proposed control method, PSIM simulations were carried out. the simulation parameters are listed in Table I.

TABLE I  SIMULATION PARAMETERS

Variables	Value
Input line-to-line voltage	200 Vrms/30 Hz
Output line-to-line voltage	380 Vrms/60 Hz
Input L filter	5 mH
Output LC filter	2 mH/15 μF
Control period	100 μs

Fig. 9 shows simulation results of current control without the proposed control method under unbalanced input conditions. Figs. 9(a) and 9(b) show the three-phase input voltages (V_A, V_B, V_C) and currents (I_A, I_B, I_C), and Fig. 9(c) shows the three-phase output currents (I_R, I_S, I_T). In Fig. 9, the output d-q axis currents are controlled to 0 A and 10 A depending on the output reference currents. From 0.4 s, the amplitude of the B-phase voltage (V_B) is decreased to half of the other phase voltages (V_A and V_C). In the same scenario as that of Fig. 9, Fig. 10 shows simulation results of current control with the proposed control method under unbalanced input conditions. The proposed control method is applied for reducing current distortion in Fig. 10. In Fig. 9, the input- output currents are distorted under unbalanced input conditions. Unlike Fig. 9, in Fig. 10, the distortion of the input-output currents is reduced by the proposed control method.

Fig. 9. Simulation results of current control without the proposed control method under unbalanced input conditions.

Fig. 10. Simulation results of current control with the proposed control method under unbalanced input conditions.

Fig. 11 shows simulation results of harmonics reduction in the input-output currents under balanced input conditions using the proposed control method. Fig. 11(a) shows three -phase input voltages including the 5^th and 7^th order harmonics. Figs. 11(b) and 11(c) show three-phase input-output currents, respectively. It can be seen that both currents are distorted due to harmonics of the input voltages. From 0.4 s, the proposed control method is applied in the input currents. As a result, it can be confirmed that the harmonic characteristic is improved and that the input-output currents become closer to sinusoidal waves.

Fig. 11. Simulation results of harmonics reduction in the input- output currents.

Fig. 12 and Fig. 13 show FFT and THD analyses depending on the application of the proposed control method for harmonics reduction. Fig. 12(a) and Fig. 13(a) show a FFT of the input voltage and current in the A-phase. Fig. 12(b) and Fig. 13(b) show a THD analysis of the output current in the R-phase. In Fig. 13(a), it can be explicitly recognized that the 5^th and 7^th order harmonics, including those in the A-phase current, have been reduced due to the proposed control method. In addition, the THD of the output R-phase current, as shown in Fig. 13(b), has been improved over that of Fig. 12(b), which is reduced to 4.27 % from 16.89 %.

Fig. 12. Graphs. (a) FFT of the input voltage and current without the proposed control method for reducing harmonics. (b) THD analysis of the output current.

Fig. 13. Graphs. (a) FFT of the input voltage and current with the proposed control method for reducing harmonics. (b) THD analysis of the output current.

Ⅴ. EXPERIMENTAL RESULTS

In order to verify the effectiveness of the proposed control method, experiments have been performed by using the experimental setup shown in Fig. 14. The experimental setup is composed of a control board, a switched mode power supply (SMPS), a power board, gate driver units (GDUs), and voltage and current sensors.

Fig. 14. Experimental setup.

The control board was fabricated by a digital signal processor (DSP) based on a TMS320C28346. The proposed control method for RMC drives and reducing current distortion is programmed on the DSP. Additionally, a field programmable gate array (FPGA) has been utilized because the DSP does not support enough PWM ports for the RMC. The FPGA is responsible for the transmission of PWM signals to the GDU in accordance with signals from the DSP. In addition, the power board consists of VSRs and CSIs using silicon carbide (SiC) MOSFETs and GDUs.

All of the experiments have been carried out under R-L load conditions, and the output d-q axis currents have been controlled to 0 A and 2 A depending on the output reference currents. The experiment parameters are listed in Table II.

TABLE II  EXPERIMENT PARAMETERS

Variables	Value
Input line-to-line voltage	50 Vrms/30 Hz
Output frequency	60 Hz
Load resistor and inductor	30 Ω/2 mH
Input L filter	5 mH
Output LC filter	2 mH/15 μF
Control period	100 μs

Fig. 15 and Fig. 16 show experimental results of three-phase input-output currents under unbalanced input conditions, respectively. From the center of the waveforms, the input B-phase voltage decreases to 70 % of the other phase voltages. This induces voltage drops at the input line-to-line voltages V_AB and V_BC as indicated in the waveforms. As a result, the three-phase input-output currents are distorted.

Fig. 15. Experimental results of three-phase input currents under unbalanced input conditions.

Fig. 16. Experimental results of three-phase output currents under unbalanced input conditions.

Fig. 17 and Fig. 18 show experimental results of three- phase input-output currents with the proposed control method under unbalanced input conditions. Although the unbalanced input condition is identical to that of Fig. 15 and Fig. 16, the distortions of the three-phase input-output currents are reduced due to the proposed control method. When compared with the THD of the input B-phase current in Fig. 15, that in Fig. 17 is decreased to 4.4 % from 7.8 %. Additionally, in Figs. 16 and 18, the THDs of the output three-phase currents are similar. As can be seen in Fig. 18, the three-phase output currents are in balance, which means the output power is also the same.

Fig. 17. Experimental results of three-phase input currents with the proposed control method under unbalanced input conditions.

Fig. 18. Experimental results of three-phase output currents with the proposed control method under unbalanced input conditions.

The harmonic issues mainly come from two elements, which are the deadtime of the converters and the inherent harmonics contained in the voltages. In this experiment, the deadtime of the RMC has been configured as 1.66 μs. In addition, the 5^th and 7^th order harmonics of the input fundamental frequency have been injected into the input voltages to simulate the harmonic issue of the grid. Each of injected harmonics are 5 % and 2 % of the fundamental frequency.

Fig. 19 and Fig. 20 show experimental results of waveforms and FFT analysis of three-phase input-output currents without the proposed control method when the proposed harmonic control method is not applied. In Fig. 19, the 5^th and 7^th order harmonics are dominant in the FFT analysis, and the input phase current has deteriorated because of both harmonics. In Fig. 20, it can be noticed that the 2^nd and 4^th order harmonics of the output fundamental frequency appear in the output phase currents. This results from the input 5^th and 7^th order harmonics.

Fig. 19. Experimental results of the three-phase input currents without the proposed control method. (a) Waveforms. (b) FFT analysis.

Fig. 20. Experimental results of the three-phase output currents without the proposed control method. (a) Waveforms. (b) FFT analysis.

In the same scenarios as those of Fig. 19 and Fig. 20, the proposed harmonic control method is applied in Fig. 21 and Fig. 22. It can be seen that the 5^th and 7^th order harmonics of the input fundamental frequency have been reduced in the input phase currents. Additionally, the 2^nd and 4^th order harmonics of the output fundamental frequency have been reduced in the three-phase output currents. When compared with the THD of the input three-phase currents in Fig. 19, that in Fig. 21 is decreased to 3.7 % from 6.9 %. Additionally, in Figs. 20 and 22, the THD of the output three-phase currents is decreased to 2.7 % from 3.1 %.

Fig. 21. Experimental results of the three-phase input currents with the proposed control method. (a) Waveforms. (b) FFT analysis.

Fig. 22. Experimental results of the three-phase output currents with the proposed control method. (a) Waveforms. (b) FFT analysis.

Ⅵ. CONCLUSIONS

The input-output currents are distorted under the unbalanced input conditions of the RMC for a DG system. In particular, the output current distortion aggravates the reliability and stability of the system. Therefore, in this paper, a control method using positive/negative sequence voltages and currents is proposed for reducing the current distortion of both side in the RMC. Through the proposed control method, current distortion is reduced under unbalanced input conditions, and the output power is balanced. As a result, the reliability and stability of the DG system can be improved in that the balanced power is transferred to loads. Additionally, a proposed harmonic control method for harmonics reduction is presented to enhance the output currents quality. Simulation and experimental results have verified the effectiveness of the proposed control method.

ACKNOWLEDGMENT

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (No.20182410105160, Demonstration and Development of ESS Solution Connected with Renewable Energy against with the wheather condition of Middle East Region)

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[27] Y. Bak and K.-B. Lee, “Reducing switching losses in indirect matrix converter drives – Discontinuous PWM method,” J. Power Electron., Vol. 18, No. 5, pp. 1325-1335, Sep. 2018.

[28] M. Uddin, S. Mekhilef, M. Rivera, and J. Rodriguez, “Imposed weighting factor optimization method for torque ripple reduction of IM fed by indirect matrix converter with predictive control algorithm,” J. Electr. Eng. Technol., Vol. 10, No. 1, pp. 227-242, Jan. 2015.

[29] T. D. Nguyen and H. H. Lee, “Dual three-phase indirect matrix converter with carrier-based PWM method,” IEEE Trans. Power Electron., Vol. 29, No. 2, pp. 569-581, Feb. 2014.

[30] J. Kolar, F. Schafmeister, and S. Round, “Novel three-phase AC-AC sparse matrix converters,” IEEE Trans. Power Electron., Vol. 22, No. 5, pp. 1649-1661, Sep. 2007.

[31] D.-T. Nguyen, H.-H. Lee, and T.-W. Chun, “A carrier- based pulse width modulation method for indirect matrix converters,” J. Power Electron., Vol. 12, No. 3, pp. 448-457, May 2012.

[32] S. Li, C. Xia, Y. Yan, and T. Shi, “Space-vector overmodulation strategy for ultrasparse matrix converter based on the maximum output voltage vector,” IEEE Trans. Power Electron., Vol. 32, No. 7, pp. 5388-5397, Jul. 2017.

[33] E. Lee and K.-B. Lee, “Fault diagnosis for a sparse matrix converter using current patters,” in Proc. APEC Conf., 2012, pp. 1549-1554.

[34] M. A. Al-Hitmi, K. Rahman, A. Iqbal, and N. Al-Emadi, “Control and modulation of three to asymmetrical six-phase matrix converters based on space vectors,” J. Power Electron., Vol. 19, No. 2, pp. 475-486, Mar. 2019.

[35] X. Liu, P. C. Loh, P. Wang, F. Blaabjerg, Y. Tang, and E. A. Al-Ammar, “Distributed generation using indirect matrix converter in reverse power mode,” IEEE Trans. Power Electron., Vol. 28, No. 3, pp. 1072-1082, Mar. 2013.

[36] Y. Bak and K.-B. Lee, “Constant speed control of a permanent-magnet synchronous motor using a reverse matrix converter under variable generator input conditions,” IEEE J. Emerg. Sel. Topics Power Electron., Vol. 6, No. 1, pp. 315-326, Mar. 2018.

[37] Y. Bak and K.-B. Lee, “Reverse matrix converter control method for PMSM drives using DPC,” Int. J. Electron., Vol. 105, No. 5, pp. 725-740, May 2018.

[38] E. Lee and K.-B. Lee, “Fault-tolerant strategy to control a reverse matrix converter for open-switch faults in the rectifier stage,” J. Power Electron., Vol. 16, No. 1, pp. 57- 65, Jan. 2016.

[39] E. Lee and K.-B. Lee, “Design and implementation of a reverse matrix converter for permanent magnet synchronous motor drives,” J. Electr. Eng. Technol., Vol. 10, No. 6, pp. 2297-2306, Nov. 2015.

[40] K. Park, K.-B. Lee, and F. Blaabjerg, “Improving output performance of a Z-source sparse matrix converter under unbalanced input-voltage conditions,” IEEE Trans. Power Electron., Vol. 27, No. 4, pp. 2043-2054, Apr. 2012.

[41] D. Chol, Y. Bak, J.-P. Lee, T.-J. Kim, and K.-B. Lee, “Control strategy for reduction of current distortion in reverse matrix converter under unbalanced input conditions,” in Proc. APEC Conf., 2018, pp. 1299-1304.

[42] Y. Bak, J.-S. Lee, and K.-B. Lee, “Balanced current control strategy for current source rectifier stage of indirect matrix converter under unbalanced grid voltage conditions,” Energies, Vol. 10, No. 1, pp. 27-44, Jan. 2017.

[43] S.-B. Lee, K.-B. Lee, D.-C. Lee, and J.-M. Kim, “An improved control method for a DFIG in a wind turbine under an unbalanced grid voltage condition,” J. Electr. Eng. Technol., Vol. 5, No. 4, pp. 614-622, Nov. 2010.

Dongho Choi received B.S. and M.S. degrees in Electrical and Computer Engineering from Ajou University, Suwon, Korea, in 2017 and 2019, respectively. His current research interests include matrix converters and grid-connected systems.

Yeongsu Bak received B.S., M.S., and Ph.D. degrees in Electrical and Computer Engineering from Ajou University, Suwon, Korea, in 2014, 2016, and 2019, respectively. He is currently working as a Research Associate in Research Institute for Information and Electronics Technology, Ajou University, Suwon, Korea. His current research interests include grid- connected systems, electric machine drives, and matrix converter.

Kyo-Beum Lee received B.S. and M.S. degrees in Electrical and Electronic Engineering from Ajou University, Suwon, Korea, in 1997 and 1999, respectively. He received Ph.D. degree in Electrical Engineering from Korea University, Seoul, Korea, in 2003. From 2003 to 2006, he was affiliated with the Institute of Energy Technology, Aalborg University, in Aalborg, Denmark. From 2006 to 2007, he was affiliated with the Division of Electronics and Information Engineering, Chonbuk National University, Jeonju, Korea. In 2007, he joined the School of Electrical and Computer Engineering, Ajou University, Suwon, Korea. He is an Associate Editor of the IEEE Transactions on Power Electronics, Journal of Power Electronics, and Journal of Electrical Engineering & Technology. His current research interests include electric machine drives, renewable power generation, and electric vehicle applications.