IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 54, NO. 2, MARCH/APRIL 2018 1425 Asymmetric Space Vector Modulation for PMSM Sensorless Drives Based on Square-Wave Voltage-Injection Method Hang Zhang , Student Member, IEEE, Weiguo Liu, Senior Member, IEEE,ZheChen , Guangzhao Luo , Jianxing Liu , and Dongdong Zhao, Member, IEEE Abstract—Square-wave voltage injection is an effective sensor- and wide speed range. Technical troubles of a position sensor less control method for permanent magnet synchronous motor attached to the traction machine often become significant is- drives to achieve zero- or low-speed operation. However, it faces sues in harsh conditions. To avoid those sensor troubles and great challenge in the case of rail transit application where the switching frequency is less than or equal to 500 Hz, which results improve durability and reliability of the traction system, a po- in rich low-order harmonics. In order to improve the performance sition sensorless technique has been attracting attentions from of high-frequency square-wave voltage-injection method over low both industry and academia [1]–[3]. switching frequency application, an asymmetric space vector mod- High-frequency (HF) signal-injection-based sensorless con- ulation (ASVM) method is proposed, and it makes comparisons trol schemes present good performance in low- and zero-speed between carrier and modulation wave in the 1/4 and 3/4 point of each switching cycle. Compared with space vector modulation, operation. According to the pattern of the injected signal, HF ASVM can significantly reduce the low-order sideband and base- voltage can be divided into two kinds: sinusoidal-wave volt- band harmonics in the bandpass filter bandwidth. As a result, the age [4]–[6] and square-wave voltage [7]–[11]. By avoiding the position estimation, which is calculated by the filtered current sig- use of low-pass filters (LPFs) in processing of HF signals, the nal, is improved. Moreover, the inverter dead-time effect has been dynamic response ability with square-wave injection is more compensated as well. With these improvements, the rotor position can be estimated without using low-pass filters and its dynamic enhanced than those with sinusoidal-wave injection. However, performance can be enhanced. The experimental results proved compared to other industrial applications, the highest inverter the effectiveness of the analysis. switching frequency of the high-speed train is less than 1 kHz Index Terms—Asymmetric space vector modulation (ASVM), because of the limitation caused by switching loss and heat dead-time effect, low switching frequency, permanent magnet dissipation. In order to make the current have better harmonic synchronous motor (PMSM), position estimation error, square- performance and symmetric characteristic, a hybrid pulse-width wave voltage injection. modulation (PWM) modulation strategy for traction inverter is widely used to meet the low switching frequency control require- ments, which adopts asynchronous modulation at low speed, I. INTRODUCTION selective harmonic eliminated (SHE) PWM at high speed and a N RAIL transit region, high-speed train like traction system square-wave modulation after rated conditions. Remarkably, the I driven by permanent magnet synchronous motor (PMSM) switching frequency is no more than 500 Hz in asynchronous is becoming increasingly popular due to its high-power density modulation region. In this case, the conventional space vector modulation (SVM) causes problems mainly including integer Manuscript received May 22, 2017; revised August 19, 2017 and October carrier-order harmonics and low-order sideband harmonics. In 22, 2017; accepted November 1, 2017. Date of publication November 12, 2017; date of current version March 19, 2018. Paper 2017-IDC-0456.R2, presented at order to make the induced HF currents have less phase de- the 2017 IEEE Applied Power Electronics Specialists Conference, Tampa, FL, lay and amplitude attenuation, the passband width of bandpass USA, Mar. 26–30, and approved for publication in the IEEE TRANSACTIONS filter (BPF) should not be too narrow. Then, the low-order har- ON INDUSTRY APPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. This work was supported in part by the National monics cannot be entirely filtered by BPF in the processing Natural Science Foundation of China under Grant 51177135, Grant 51507143, of HF signal, which leads to filtered-signal overlaps and af- and Grant 51707161, and in part by Fundamental Research Funds for the Cen- fects the position estimation precision. Moreover, the inverter tral Universities under Grant 31020170QD029 and Grant 3102017JC06004. (Corresponding author: Hang Zhang.) nonlinear effect is more severe under low switching frequency The authors are with the Department of Electrical Engineering, Northwest- and the distortion of the injected HF voltage also causes er- ern Polytechnical University, Xi’an 710072, China, and also with the Re- rors in the estimated rotor position [12]–[14]. For the above search Institute of Intelligent Control and Systems, Harbin Institute of Tech- nology, Harbin 150001, China (e-mail: [email protected]; lwglll@nwpu. reasons, the widespread application of HF signal injection- edu.cn; [email protected]; [email protected]; jx.liu@hit. based sensorless control scheme is restricted in rail transit edu.cn; [email protected]). region. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Nowadays, SVM has got wider acceptance than the SPWM in Digital Object Identifier 10.1109/TIA.2017.2772166 the case of traction inverter. Compared with SPWM, the SVM 0093-9994 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. 1426 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 54, NO. 2, MARCH/APRIL 2018 increases the efficiency of dc voltage by 15%, which reduces torque ripple and current total harmonic distortion (THD) un- der same conditions. Many efforts have been made to improve the harmonic characteristic for motor control when using SVM [15]–[17]. In [18], a synchronized SVM is presented for dual stator induction machine in high-power traction drive systems. Through the adoption of a switching strategy for transitions be- tween different modulation modes, the harmonic performance is improved in high-speed region. But, as no consideration is paid to the application of sensorless control under low switching fre- quency and the conventional SVM is still used in asynchronous Fig. 1. Injected square-wave voltage and induced triangular current. modulation, the problem of low-order sideband harmonics re- mains unsolved. Gu et al. [19] propose a multispace vector pulse width modulation strategy, which is used in position sensorless II. PRINCIPLE OF SQUARE-WAV E VOLTAGE-INJECTION BASED control of interior PMSM (IPMSM) and reduces line current rip- ON ASVM ple for high-speed operation. In addition, the complex harmonic A. Rotor Position Estimation With Square-Wave Injection components caused by low switching frequency still exist. Re- cently, optimal PWM is wildly studied in the rail transit industry IPMSM can be modeled in the rotor reference frame as [20], [21], the primary objective of these methods is to gener- ud Rs + Ld p −ωe Lq id 0 ate the optimal PWM waves and reduce the current THD in = + (1) u ω L R L p i ω ψ high-speed region, many of them focused on a switching an- q e d s + q q e f gle direct modulation, for example, SHE and lowest THD. In where udq and idq are the stator voltage and current, respectively, [22] and [23], the proposed offline optimal PWM waveform Rs is the stator resistance, Ld and Lq are the stator inductances, plays an important role in reducing the current THD but only ωe is the electrical speed, ψf is the linkage magnetic flux, and in steady state. Its application in the transient state especially p = d/dt is a derivative operator. for online position estimation is still challenging. Besides, pre- If the frequency of injected square-wave voltage is much dictive control is commonly used for low switching frequency higher than the synchronous frequency of the motor, the propor- system in [24] and [25] which have a fast-responsive ability, tion of back-electromotive force (EMF) in voltage is low and the but the process needs transforming all voltage vectors to the effect of back-EMF can be neglected. Thus, PMSM HF voltage form of rotor reference frame during every predictive process model can be approximated as and involves complex mathematical computation, which im- pose heavy computational burden on microcontroller and affect udh Ldh 0 idh real-time capability of control system. Considering the sensor- = p (2) uqh 0 Lqh iqh less control scheme needs to design an independent signal cal- culation process, the predictive control is not suitable for HF where subscript “h” means that the value is concerned with injection method before solving the problem of complicated HF signal. According to (2), the HF current induced by the operation. injected voltage can be analyzed. Both sinusoidal and square- This paper presents a HF square-wave voltage-injection- wave voltage can be utilized. based ASVM modulation strategy to reduce the low-order har- By comparing with the conventional sine-wave pulsating in- monics under low switching frequency. Section II explains the jection, the square-wave injection does not involve LPF in esti- principle of the ASVM and gives the steps of the HF square- mating the rotor position and angular velocity, which simplifies wave injection method. Based on this, analysis of position es- the signal process considerably. In the case of same carrier fre- timation error is given in Section III and the major influence quency, the square-wave injection can achieve a higher injection factors include low-order harmonics and dead-time effect of in- frequency and improve the bandwidth of the speed loop, which verters.