https://doi.org/10.6113/JPE.2019.19.6.1536

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

Torque Predictive Control for Permanent Magnet Synchronous Motor Drives Using Indirect Matrix Converter

Yeongsu Bak^*, Yun Jang^**, and Kyo-Beum Lee^†

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

^**LG Chem, Gwacheon, Korea

Abstract

This paper presents an improved torque predictive control (TPC) for permanent magnet synchronous motors (PMSMs) using an indirect matrix converter (IMC). The IMC has characteristics such as a high power density and sinusoidal waveforms of the input-output currents. Additionally, this configuration does not have any DC-link capacitors. Due to these advantages of the IMC, it is used in various application field such as electric vehicles and railway cars. Recently, research on various torque control methods for PMSM drives using an IMC is being actively pursued. In this paper, an improved TPC method for PMSM drives using an IMC is proposed. In the improved TPC method, the magnitudes of the voltage vectors applied to control the torque and flux of the PMSM are adjusted depending on the PMSM torque control such as the steady state and transient response. Therefore, it is able to reduce the ripples of the output current and torque in the low-speed and high-speed load ranges. Additionally, the improved TPC can improve the dynamic torque response when compared with the conventional TPC. The effectiveness of the improved TPC method is verified by experimental results.

Key words: Current source rectifier, Indirect matrix converter, Permanent magnet synchronous motor, Torque predictive control, Voltage source inverter

Manuscript received Jul. 15, 2019; accepted Aug. 20, 2019

Recommended for publication by Associate Editor Sung-Jin Choi.

^†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

Recently, interest in renewable energy systems such as wind power generation, hydroelectric power generation, and bioenergy has increased due to the depletion of fossil fuels. In renewable energy systems, a power conversion system is required to transmit the power generated by the renewable energy sources to the grid. In general, power conversion systems, such as in AC-DC-AC power conversion systems, are composed of three stages. The three stages are a rectifier stage, a DC-link, and an inverter stage. However, in the proposed system, electrolytic capacitors with a large volume are used in the DC-link for the AC-DC-AC power conversion [1]. Since electrolytic capacitors increase the volume of the system, AC-DC-AC power conversion systems are used in restricted applications. In addition, electrolytic capacitors shorten the lifetime of the system. These drawbacks can be overcome using an indirect matrix converter (IMC) [2]-[4].

IMCs do not have electrolytic capacitors in the DC-link [5]-[8]. They can overcome the disadvantages of large electrolytic capacitors in general AC-DC-AC power conversion systems. In addition, IMCs have high power density and sinusoidal input-output current characteristics [9]. Therefore, IMCs can be used in various application fields such as electric vehicles and railway cars. Various torque control methods including direct torque control (DTC) and torque predictive control (TPC) with permanent magnet synchronous motor (PMSM) drives using an IMC are being actively studied [10]-[13].

DTC as a torque control method that uses a hysteresis controller with a look-up table. It has advantages such as a simple structure in terms of the system design and fast torque response characteristics [14]. However, in DTC, because the voltage vector is always fixed by a look-up table in a given control period, the ripple components of the current and torque of PMSMs are increased [15]-[18]. Unlike DTC, TPC uses voltage vectors calculated based on the relations among the torque, flux and voltage [19], [20]. TPC also has a simple controller configuration and a fast dynamic torque response. In TPC, the ripple components of the current and torque are also increased [21], [22].

An improved TPC method for PMSM drives using an IMC is proposed in this paper. Using the proposed control method, the ripple components of the current and torque of a PMSM are decreased and the dynamic torque response can be enhanced when compared with the conventional TPC. The effectiveness of the improved TPC method is verified by experimental results.

Ⅱ. TOPOLOGY AND MODULATION METHOD OF AN IMC

A. Topology of an IMC

Fig. 1 shows the circuit configuration of an IMC for PMSM drives. The IMC consists of three stages: input stage with an AC source and an L–C filter, power-conversion stage with power semiconductor switches, and output stage with the PMSM. The L–C filter, which is composed of inductors (L_f) and capacitors (C_f) in the input stage, is used to improve the quality of the voltages and currents generated by the AC source. The IMC, the power conversion stage, consists of two sub-stages. These stages are a current source rectifier (CSR) stage and a voltage source inverter (VSI) stage. Since the IMC does not have DC-link capacitors, they are directly connected by a hypothetical DC-link. The PMSM can be controlled by the IMC.

Fig. 1. Circuit configuration of an IMC for a PMSM drive.

B. Modulation Method of the CSR Stage

By using modulation of the CSR stage, the maximum voltage of the AC source can be transferred to the DC-link. This technique guarantees the sinusoidal currents and unity power factor of the input stage. Fig. 2 shows a space vector diagram of the CSR stage with the voltage vector and current vector located in sector 1. In the space vector diagram shown in Fig. 2, θ_U is the phase angle of the current vector, and ϕ_i is the phase angle between the voltage vector and the current vector. The space vector of the CSR stage is categorized by two kinds of states, i.e., three null states and six active states. The three null states occur when the upper and lower switches in the same phase of the CSR stage are in the ON state simultaneously. The DC-link voltage is shorted to zero voltage in the null states. On the other hand, in the six active states, the power from the AC source is transferred to the output stage.

Fig. 2. Space vector diagram of the CSR stage.

In Fig. 2, the current vector located in sector 1 can be reproduced by using the nearest vectors. For example, it can be reproduced by V₁ and V₆ using the duty ratios (d_x and d_y). The duty ratios for the modulation of the CSR stage are calculated as follows. The reference three-phase currents (I^*_U, I^*_V, and I^*_W) of the CSR stage are expressed as:

                               (1)

where I_m is the amplitude of the phase current; ω_i is the angular frequency of the AC source; and θ_U, θ_V, and θ_W are the respective phase angles. Additionally, via the phase angle of the current vectors in the CSR stage, d_x and d_y are expressed as:

             (2)

The average value of the hypothetical DC-link voltage (V_DC-av) modulated by the CSR stage is calculated using the line-to-line voltage, d_x and d_y. V_DC-av is expressed as:

                                           (3)

where V_UV is the line-to-line voltage between the U-phase and the V-phase; and V_WU is the line-to-line voltage between the W-phase and the U-phase. Finally, V_DC-av is calculated in (4) by substituting d_x and d_y from (2) into V_DC-av, which is given in (3).

                  (4)

where V_m is the amplitude of the voltage vector. The other five sectors have the same interpretations. The switching states and V_DC-av, based on the six sectors in the space vector diagram of the CSR stage, are presented in Table I.

TABLE I SWITCHING STATES AND AVERAGE VALUES OF THE HYPOTHETICAL DC-LINK VOLTAGE

Sector	Range of the θU	ON Switch	Modulated Switches		VDC-av
1	-π/6 ＜ θU ＜ π/6	SUp	SVn	SWn	dxVUV – dyVWU
2	π/6 ＜ θU ＜ π/2	SWn	SUp	SVp	-dxVWU + dyVVW
3	π/2 ＜ θU ＜ 5π/6	SVp	SWn	SUn	dxVVW – dyVUV
4	5π/6 ＜ θU ＜ 7π/6	SUn	SVp	SWp	-dxVUV + dyVWU
5	7π/6 ＜ θU ＜ 9π/6	SWp	SUn	SVn	dxVWU – dyVVW
6	9π/6 ＜ θU ＜ 11π/6	SVn	SWp	SUp	-dxVVW + dyVUV

C. Modulation Method of the VSI Stage

The modulation method for the VSI stage is the same as that of a common inverter. Fig. 3 shows a space vector diagram of the VSI stage. The space vector of the VSI stage is composed of six active vectors (V₁–V₆) and two zero vectors (V₀ and V₇). The active vectors are able to apply the effective voltage to the load, and the amplitudes of the active vectors are equal to 0.667 times V_DC-av. On the other hand, the zero vectors cannot apply the effective voltage to the load. They are produced by turning ON the three upper (S_Ap, S_Bp, S_Cp) or the three lower switches (S_An, S_Bn, S_Cn) of the VSI stage.

Fig. 3. Space vector diagram of the VSI stage.

Additionally, the modulation signals (v_A-low and v_A-up) for the VSI stage, using the space vector modulation method for the A phase, can be expressed as:

                   (5)

where v_A is the reference voltage amplitude of the A phase, and v_A(MAX) and v_A(MIN) are the maximum and minimum values of the reference voltage in the A phase, respectively.

Ⅲ. TORQUE PREDICTIVE CONTROL METHOD

A. Conventional TPC

In the conventional TPC method, the voltage vectors required for the control of the torque of the PMSM are calculated using the relations among the torque, the flux, and the voltage equation. Fig. 4 shows a space vector diagram of the PMSM in different coordinate axes. d^s-q^s and d^e-q^e are the stationary and rotating reference frames synchronized to the PMSM rotor, respectively. θ_s and θ_r indicate the phase angles of the stator flux vector () and the rotor flux vector (), respectively. α is the phase angle between and the voltage vector (). β is the phase angle between and the stator flux ().

Fig. 4. Space vector diagram of a PMSM in different coordinate axes.

The electromagnetic torque is expressed using and the stator current vector () as:

                                                 (6)

where P is the number of poles of the PMSM. In addition, the rate of change of the PMSM torque (T_e) is expressed as:

                                 (7)

The voltage vector in the d^s-q^s stationary reference frame can be expressed as:

                                                  (8)

where is the stator current vector, and R_s is the stator resistance of the PMSM [23]-[29]. The rate of change of is expressed in (9), based on (8).

                                                  (9)

In (9), the stator flux vector , can be expressed as:

                                                     (10)

where L_s is the stator self-inductance. The rate of the change of is expressed in (11), based on (10).

                                           (11)

Finally, the rate of the change of T_e, as given in (7), can be rewritten as in (12) by substituting (9) and (11) into (7).

         (12)

From (12), the rate of the change of T_e can be controlled by the voltage vector , which is calculated based on , and . Based on the application time of to control the PMSM torque during a control period, the changing rate of T_e, as given in (12), can be expressed as:

               (13)

where T_s is the control period, and T_d is the duration of . From (13), α, the phase angle between and , can expressed as:

                        (14)

B. Improved TPC

In the TPC method, the voltage vector magnitude is determined by multiplying the maximum magnitude of by a constant (e), which is determined to have a value between 0 and 1. In conventional TPC methods, e is fixed at 0.7 or 1 since these values enhance the transient response of the PMSM torque control. However, in the steady state, these values result in an unnecessarily long application time of . Based on this unnecessary application time of , the ripple components of the current and torque in the PMSM are increased.

Therefore, in this paper, the improved TPC method is used to decrease the ripple components of the current and torque in a PMSM. Fig. 5 shows the determination of e in the steady state and the transient state with the improved TPC method. In the improved TPC method, e is not fixed at 0.7 or 1. Instead, it is appropriately determined as the value that decreases the unnecessary application time of in the steady state. In other words, in the steady state, e is determined to be the value that minimizes the magnitude of the voltage vector, which is required for PMSM torque control. Therefore, with an appropriate value of e, the ripple components of the current and torque in the PMSM can be decreased. Additionally, in the transient state, e is set to a value that improves the transient response of the torque control.

Fig. 5. Determination of e in the steady state and the transient state.

Fig. 6 shows the modified voltage vector () for decreasing the ripple components of the current and torque in the PMSM. is the reference voltage vector, and α^* and α^** are the phase angles of and , respectively. is obtained from the magnitude and phase angle of , which is described below.

Fig. 6. Modified voltage vector.

In (9), the voltage drop due to the stator resistance can be ignored since it is negligibly small when compared with the rate of the change of . Therefore, the rate of the change of is rewritten as in (15). From (15), the magnitude of in the stator reference frame can be calculated using the rate of the change of .

                     (15)

Finally, the magnitude of can be calculated via α^*, which is the phase angle of obtained from (14), and the magnitude of obtained from (15). In addition, the appropriate value of e that decreases the ripple components of the current and torque in the steady state or improves the transient response of the torque control in the PMSM is determined as:

                   (16)

α^** as the phase angle of , is expressed as in (17) using (14) and (16).

                                              (17)

C. Control Method for PMSM Drives Using an IMC

Fig. 7 shows a control block diagram for PMSM drives using an IMC with the improved TPC method. The IMC, which consists of the CSR stage and the VSI stage, is connected to the AC source and the PMSM. The input stage of the IMC has an L–C filter with values of L_f and C_f. The L–C filter is able to reduce the ripple components of the currents generated by the AC source.

Fig. 7. Control block diagram for PMSM drives using an IMC with the improved TPC method.

In Fig. 7, the three-phase currents (I_U, I_V, and I_W) of the input stage are transformed to the d-q axes using the phase angle (θ_i) of the AC source. Through the modulation method of the CSR stage and the d-q axes currents, the duty ratios d_x and d_y are calculated. Additionally, the average value of the hypothetical DC-link voltage V_DC-av is calculated based on d_x, d_y, and the line-to-line voltages. The three-phase currents (I_A, I_B, and I_C) of the output stage are transformed to the d-q axes using the phase angle (θ_e) of the PMSM rotor. In addition, T_e, the PMSM torque, and the stator flux vector , are calculated as in (6) and (10). The output torque error (ΔT_e) and the stator flux error (Δψ_s) are calculated using T_e, ψ_s, the reference torque (T_e^*), and the reference stator flux (ψ_s^*). The reference voltage vector () is calculated via the TPC using ΔT_e and Δψ_s. Additionally, is modified to in the improved TPC method. Finally, the VSI stage is modulated by via the space vector modulation method.

Ⅳ. EXPERIMENTAL RESULTS

Experiments were conducted to evaluate the performance of the improved TPC method for PMSM drives using an IMC. Fig. 8 shows the experiment setup. In the control board, a digital signal processor (DSP) using a TMS320C28346 is used to program the improved TPC method. The power supplied by the grid is transmitted to the PMSM by the IGBTs in both the CSR stage and the VSI stage. In addition, the parameters of the PMSM and sampling time for the control scheme are presented in Table II.

Fig. 8. Experimental setup.

TABLE II PMSM PARAMETERS

Parameters	Value
Rated power (Prated)	11 [kW]
Rated current (Irated)	19.9 [A]
Rated speed (ωrated)	1750 [rpm]
Rated torque (Trated)	60 [N·m]
Stator resistance (Rs)	0.349 [Ω]
d-axis inductance (Ld)	13.17 [mH]
q-axis inductance (Lq)	15.6 [mH]
Permanent magnet flux (λs)	0.9218 [Wb]
Number of poles (P)	6
Moment of inertia (J)	0.02 [kg·m2]

Fig. 9 shows experimental results in terms of the input line-to-line voltage (V_UV), the average value of the hypothetical DC-link voltage (V_DC-av), and the DC-link voltage (V_DC) of the IMC with a 5 N·m output torque and a load at 300 rpm. V_UV is provided by the AC source. V_DC-av can be calculated using d_x and d_y as the duty ratios. V_DC is generated by the modulation of the CSR stage.

Fig. 9. Experimental results of the input line-to-line voltages (V_UV), the average value of the hypothetical DC-link voltage (V_DC-av), and the DC-link voltage (V_DC) of the IMC.

Fig. 10 shows experiment results of the output torque (T_e) and stator flux (ψ_s) in the steady state. T_e and ψ_s are set to the reference values of 5 N·m and 0.55 Wb, respectively. The control method is switched to the improved TPC method from the conventional TPC method at 0.5 s. Comparing the performance of the conventional TPC and the improved TPC in the steady state, the ripple component of the output torque is decreased from 0.4 N·m to 0.2 N·m. In addition, the ripple component of the stator flux (ψ_s) is decreased from 0.04 Wb to 0.015 Wb.

Fig. 10. Experimental results of the output torque (T_e) and the stator flux (ψ_s) with a load at 300 rpm for different control methods.

Figs. 11(a) and 11(b) show experimental results of the dynamic torque response. The reference torque is changed from 5 N·m to 10 N·m at 0.5 s. In addition, Figs. 11(a) and 11(b) show an expanded waveform of the torque. Comparing the dynamic torque response between the conventional TPC and the improved TPC, the response time is decreased from 0.5 ms to 0.3 ms.

Fig. 11. Experimental results for the dynamic torque response. (a) Conventional TPC. (b) Improved TPC.

(a)

(b)

Ⅴ. CONCLUSIONS

This paper presents an improved TPC method for PMSM drives using an IMC. The IMC method for the control of a PMSM uses no electrolytic capacitors in the DC link. In addition, it has high power density and sinusoidal waveforms in the input-output current. In general, existing torque control methods including DTC and TPC are applied to control PMSMs. However, DTC and the conventional TPC result in ripple components in the current and torque in the PMSM. Therefore, in this paper, the improved TPC for PMSM drives using an IMC is proposed. The improved TPC decreases the ripple components of the current and torque in the PMSM. In addition, this method improves the characteristics of the dynamic torque response. Additionally, since the magnitudes of the applied voltage vectors are adjusted depending on the PMSM torque control such as the steady state and transient response in the improved TPC method, the switching loss of the improved TPC method are similar to that of the conventional TPC method. The effectiveness of the proposed control method is verified by experimental results.

ACKNOWLEDGMENT

This work was supported by “Human Resources Program in Energy Technology” of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea. (No. 20194030202370) and the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (No.20182410105160)

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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 converters.

Yun Jang received B.S. degree in Electrical Engineering from Soonchunhyang University, Asan, Korea, in 2017 and M.S. degree in Electrical and Computer Engineering from Ajou University, Suwon, Korea, in 2019.

Since 2019, he has been with the LG Chem, Gwacheon, Korea. His current research interests include motor drives and matrix converters.

Kyo-Beum Lee received the B.S. and M.S. degrees in Electrical and Electronic Engineering from Ajou University, Suwon, Korea, in 1997 and 1999, respectively. He received the Ph.D. degree in Electrical Engineering from Korea University, Seoul, Korea, in 2003. From 2003 to 2006, he was with the Institute of Energy Technology, Aalborg University, Aalborg, Denmark. From 2006 to 2007, he was 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, the Journal of Power Electronics, and the Journal of Electrical Engineering & Technology. His current research interests include electric machine drives, renewable power generation, and electric vehicle applications.