Abstract:As a typical power electronics topology, the three-phase bridge inverter circuit is widely used in motor driver, new energy grid-connected inverter, and other power electronic equipment. Current is an important parameter for the control and protection of inverter, how to obtain current information stably and accurately is the key to realize high-performance control of inverter. However, traditional control often overlooks fundamental, complex, and extensible problems caused by current parameters. Over recent years, many problems have been raised around the reliability of current detection and the improvement of accuracy, but most of the problems lack a closed-loop review of problem development. Aiming at these problems, this paper summarizes the related problems of current detection in three-phase bridge inverter, hoping to inspire follow-up research. First of all, based on the principle analysis, the current sensors that are most widely used are summarized based on operating principle, sampling accuracy, advantages and disadvantages, including Hall current sensors, fluxgate current sensors, and shunts. Different current detection circuits are directly determined from the analysis of sensor installation characteristics and the number of uses, which are mainly divided into multi-sensor detection circuits and single-sensor detection circuits, and specifically including current sensing at the high-side (AC output side) of the load using two or three current sensors; current sensing on the low side using two or three current sensors; current sensing on the DC bus using a single current sensor; multi-position coupling for current sensing using a single Hall/fluxgate current sensor detection (intermediate bridge arm coupling (IBAC), upper-lower bridge arm coupling (ULBAC), and multi-position coupling (MPC)). This paper summarizes and analyzes the different current information, advantages, and disadvantages contained in the detection circuits at different positions. However, in actual use, reliable and high-precision current sampling is caused by a combination of direct and indirect reasons. The direct reason includes long-term use of the point current sensor, or inaccurate measurement accuracy under harsh conditions. In the comprehensive use of the inverter, under different control algorithm strategies, the source (inherent error) of the current detection error occurs, so the research branch of the indirect cause of improving the current quality through PWM control strategy adjustment is derived. This paper summarizes and analyzes the influence of different control strategies such as the PWM waveform adjustment method, voltage vector synthesis method, and state observation method on the current in the case of a single current sensor, as well as the comparison of advantages and disadvantages. Finally, this paper comprehensively analyzes the direct and indirect causes of current detection. There are two types of errors in the current sampling process: one is an inherent error due to PWM; the other is sensor sampling error due to factors such as temperature or aging. Both errors are directly introduced into the measured current without correction. The inherent errors caused by PWM are divided into time-sharing errors, non-homogenous errors, and switching errors. The sampling path is composed of a Hall sensor, a conversion circuit, a filter circuit, and an analog-to-digital (A-D) conversion circuit. Affected by device tolerance, temperature drift, aging, noise, etc., drift errors and gain errors will occur in the current sampling path. The two kinds of errors can be corrected by each other, and the suppression and compensation of sampling errors through control strategies is the current mainstream research branch of mutual errors. In the future, there will still be major challenges in current detection: with the high frequency of power electronics, the research of current sensors with high bandwidth and high response speed is still an important branch; in the face of single current sensor sampling, the current sampling that is affected by multiple factors such as the optimization of the PWM strategy and the signal processing process should be considered comprehensively; for the research on the improvement of current accuracy, attention should be paid to the closed-loop relationship between the sensor itself and the control strategy, and at the same time, new background factors such as electromagnetic interference should be introduced from the foundation to improve the current detection accuracy.
[1] 张懿, 张明明, 魏海峰, 等. 基于霍尔传感器的永磁同步电机高精度转子位置观测[J]. 电工技术学报, 2019, 34(22): 4642-4650. Zhang Yi, Zhang Mingming, Wei Haifeng, et al.High precision rotor position observation of permanent magnet synchronous motor based on hall sensors[J]. Transactions of China Electrotechnical Society, 2019, 34(22): 4642-4650. [2] 申永鹏, 郑竹风, 杨小亮, 等. 直流母线电流采样电压空间矢量脉冲宽度调制[J]. 电工技术学报, 2021, 36(8): 1617-1627. Shen Yongpeng, Zheng Zhufeng, Yang Xiaoliang, et al.A compatible SVPWM method for DC bus current sampling[J]. Transactions of China Electrotechnical Society, 2021, 36(8): 1617-1627. [3] 马铭遥, 凌峰, 孙雅蓉, 等. 三相电压型逆变器智能化故障诊断方法综述[J]. 中国电机工程学报, 2020, 40(23):7683-7698. Ma Mingyao, Ling Feng, Sun Yarong, et al.Review of intelligent fault diagnosis methods for three-phase voltage-mode inverters[J]. Proceedings of the CSEE, 2020, 40(23): 7683-7698. [4] 王文杰, 闫浩, 邹继斌, 等. 基于混合脉宽调制技术的永磁同步电机过调制区域相电流重构策略[J]. 中国电机工程学报, 2021, 41(17): 6050-6059. Wang Wenjie, Yan Hao, Zou Jibin, et al.Phase current reconstruction strategy of PMSM under over-modulation mode based on a hybrid space vector pulse width modulation technique[J]. Proceedings of the CSEE, 2021, 41(17): 6050-6059. [5] 李树成. 直流电流检测中霍尔传感器的应用[J]. 通信电源技术, 2017, 34(4): 240-241. Li Shucheng.Application of hall sensor in DC current detection[J]. Telecom Power Technology, 2017, 34(4): 240-241. [6] 刘海艳. 磁通门微电流传感器设计[J]. 自动化技术与应用, 2016, 35(9): 101-105. Liu Haiyan.Design of micro-current sensor based on the fluxgate principle[J]. Techniques of Automation and Applications, 2016, 35(9): 101-105. [7] 罗颖, 谢小军, 朱才溢, 等. 大电流检测技术探析[J]. 仪器仪表标准化与计量, 2020(3): 32-34. Luo Ying, Xie Xiaojun, Zhu Caiyi, et al.Analysis of high current detection[J]. Instrument Standardization & Metrology, 2020(3): 32-34. [8] 仪表放大器应用工程师指南(第三版)[EB/OL].仪表放大器应用工程师指南(第三版)[EB/OL]. 美国模拟器件公司, 2013. [9] Grundkötter E, Weßkamp P, Melbert J.Transient thermo-voltages on high-power shunt resistors[J]. IEEE Transactions on Instrumentation and Mea-surement, 2018, 67(2): 415-424. [10] Braudaway D W.Behavior of resistors and shunts: with today's high-precision measurement capability and a century of materials experience, what can go wrong?[J]. IEEE Transactions on Instrumentation and Measurement, 1999, 48(5): 889-893. [11] Braudaway D W.Precision resistors: a review of the techniques of measurement, advantages, disadvan-tages, and results[J]. IEEE Transactions on Instru-mentation and Measurement, 1999, 48(5): 884-888. [12] Weβkamp P, Hauβmann P, Melbert J.600-A test system for aging analysis of automotive Li-ion cells with high resolution and wide bandwidth[J]. IEEE Transactions on Instrumentation and Measurement, 2016, 65(7): 1651-1660. [13] 郑锦秀, 童欣. 一元线性回归方程在大电流分流器测量中的应用[J]. 计测技术, 2009, 29(5): 17-19. Zheng Jinxiu, Tong Xin.Application of unitary linear regression equation for measuring this great diffluent utensil[J]. Metrology & Measurement Technology, 2009, 29(5): 17-19. [14] 费继友, 梁晟铭, 李花, 等. 基于双电阻的变频控制器交流电流采样方法研究[J]. 大连交通大学学报, 2017, 38(6): 103-106. Fei Jiyou, Liang Shengming, Li Hua, et al.Research of sampling AC current with double resistance based on variable frequency controller[J]. Journal of Dalian Jiaotong University, 2017, 38(6): 103-106. [15] 王文, 罗安, 黎燕, 等. 一种新型有源电力滤波器的SVPWM算法[J]. 中国电机工程学报, 2012, 32(18): 52-58, 177. Wang Wen, Luo An, Li Yan, et al.A novel algorithm of SVPWM applied to active power filters[J]. Pro-ceedings of the CSEE, 2012, 32(18): 52-58, 177. [16] 王平, 厉虹, 王道武. 小容量变频器三电阻采样电流合成方法实现[J]. 电气自动化, 2014, 36(1): 64-66, 93. Wang Ping, Li Hong, Wang Daowu, et al.How to synthesize 3-resistor sampling current for the small-capacity converter[J]. Electrical Automation, 2014, 36(1): 64-66, 93. [17] 邓娜. 基于改进相电流重构的电流采样校正方法[J]. 电气传动, 2020, 50(8): 15-20. Deng Na.Current sampling correction method based on improved phase current reconstruction[J]. Electric Drive, 2020, 50(8): 15-20. [18] 储剑波, 胡育文, 黄文新, 等. 一种变频器相电流采样重构技术[J]. 电工技术学报, 2010, 25(1): 111-117. Chu Jianbo, Hu Yuwen, Huang Wenxin, et al.Phase current sampling reconstruction for inverter[J]. Transactions of China Electrotechnical Society, 2010, 25(1): 111-117. [19] 赵辉, 胡仁杰. SVPWM的基本原理与应用仿真[J]. 电工技术学报, 2015, 30(14): 350-353. Zhao Hui, Hu Renjie.Space-vector pulse width modulation and it's simulation based on Simulink[J]. Transactions of China Electrotechnical Society, 2015, 30(14): 350-353. [20] 王凯, 王之赟, 宗兆伦, 等. 基于霍尔位置传感器的永磁同步电机速度估计方法研究[J]. 电机与控制学报, 2019, 23(7): 46-52. Wang Kai, Wang Zhiyun, Zong Zhaolun, et al.Speed estimation method of permanent magnet synchronous motor based on Hall-effect sensor[J]. Electric Machines and Control, 2019, 23(7): 46-52. [21] 朱强, 王进城, 孙荣川. 逆变器基于电阻采样的直流分量调节电路分析[J]. 电力电子技术, 2018, 52(1): 92-93, 107. Zhu Qiang, Wang Jincheng, Sun Rongchuan.DC component regulating circuit analysis of inverter based on resistance sampling[J]. Power Electronics, 2018, 52(1): 92-93, 107. [22] 马建辉, 高佳, 周广旭, 等. 一种SVPWM简化算法的设计与实现[J/OL]. 电源学报, 2020, 1-12[2020-11-02]. https://kns.cnki.net/kcms/detail/12.1420.tm.20201030.1629.004.html. Ma Jianhui, Gao Jia, Zhou Guangxu, et al. Design and implement of a simplified SVPWM algorithm[J/OL]. Journal of Power Supply, 2020, 1-12[2020-11-02]. https://kns.cnki.net/kcms/detail/12.1420.tm.20201030.1629.004.html. [23] 王帆, 陈阳生. 不同PWM模式下交流电机单电阻三相电流采样的研究[J]. 机电工程, 2013, 30(5): 585-590, 631. Wang Fan, Chen Yangsheng.Research on phase current reconstruction for AC motor based on different PWM mode[J]. Journal of Mechanical & Electrical Engineering, 2013, 30(5): 585-590, 631. [24] Shen Yongpeng, Zheng Zhufeng, Wang Qiancheng, et al.DC bus current sensed space vector pulse width modulation for three-phase inverter[J]. IEEE Transa-ctions on Transportation Electrification, 2021, 7(2): 815-824. [25] Lu Haifeng, Cheng Xiaomeng, Qu Wenlong, et al.A three-phase current reconstruction technique using single DC current sensor based on TSPWM[J]. IEEE Transa-ctions on Power Electronics, 2014, 29(3): 1542-1550. [26] Yang S C.Initial rotor position estimation of permanent-magnet synchronous machines using square-wave voltage injection with a single current sensor[C]//Applied Power Electronics Conference & Exposition, Fort Worth, TX, USA, 2014: 2430-2437. [27] Gu Yikun, Ni Fenglei, Yang Dapeng, et al.Switching-state phase shift method for three-phase-current reconstruction with a single DC-link current sensor[J]. IEEE Transactions on Industrial Electronics, 2011, 58(11): 5186-5194. [28] Blaabjerg F, Pedersen J K.An ideal PWM-VSI inverter using only one current sensor in the DC-link[C]//International Conference on Power Elec-tronics & Variable-speed Drives, IET, London, UK, 1994: 458-464. [29] Lee W C, Lee T K, Hyun D S.Comparison of single-sensor current control in the DC link for three-phase voltage-source PWM converters[J]. IEEE Transa-ctions on Industrial Electronics, 2001, 48(3): 491-505. [30] Xu Yongxiang, Yan Hao, Zou Jibin, et al.Zero voltage vector sampling method for PMSM three-phase current reconstruction using single current sensor[J]. IEEE Transactions on Power Electronics, 2017, 32(5): 3797-3807. [31] Lai Y S, Lin Yongkai, Chen C W.New hybrid pulsewidth modulation technique to reduce current distortion and extend current reconstruction range for a three-phase inverter using only DC-link sensor[J]. IEEE Transactions on Power Electronics, 2013, 28(3): 1331-1337. [32] Kim H, Jahns T M, Integration of the measurement vector insertion method (MVIM) with discontinuous PWM for enhanced single current sensor oper-ation[C]//IEEE Industry Applications Conference Forty-First IAS Annual Meeting, Tampa, FL, USA, 2006: 2459-2465. [33] Kim H, Jahns T M.Phase current reconstruction for AC motor drives using a DC link single current sensor and measurement voltage vectors[C]//36th Power Electronics Specialists conference, 2005: 1413-1419. [34] Dusmez S, Qin Ling, Akin B.A new SVPWM technique for DC negative rail current sensing at low speeds[J]. IEEE Transactions on Industrial Elec-tronics, 2015, 62(2): 826-831. [35] Sun Kai, Wei Qing, Huang Lipei, et al.An over-modulation method for PWM-inverter-fed IPMSM drive with single current sensor[J]. IEEE Transactions on Industrial Electronics, 2010, 57(10): 3395-3404. [36] Lu Jiadong, Zhang Xiaokang, Hu Yihua, et al.Inde-pendent phase current reconstruction strategy for IPMSM sensorless control without using null switching states[J]. IEEE Transactions on Industrial Electronics, 2018, 65(6): 4492-4502. [37] Ye Haizhong, Emadi A.A six-phase current recon-struction scheme for dual traction inverters in hybrid electric vehicles with a single DC-link current sensor[J]. IEEE Transactions on Vehicular Tech-nology, 2014, 63(7): 3085-3093. [38] Cho Y, Koran A, Miwa H, et al.An active current reconstruction and balancing strategy with DC-link current sensing for a multi-phase coupled-inductor converter[J]. IEEE Transactions on Power Electronics, 2012, 27(4): 1697-1705. [39] Li Xiong, Dusmez S, Akin B, et al.A new SVPWM for the phase current reconstruction of three-phase three-level t-type converters[C]//IEEE Applied Power Electronics Conference and Exposition (APEC), Charlotte, USA, 2015: 1582-1588. [40] Shin H, Ha J I.Phase current reconstructions from DC-link currents in three-phase three-level PWM inverters[J]. IEEE Transactions on Power Electronics, 2014, 29(2): 582-593. [41] Han J, Song J H.Phase current-balance control using DC-link current sensor for multiphase converters with discontinuous current mode considered[J]. IEEE Transactions on Industrial Electronics, 2016, 63(7): 4020-4030. [42] Kim S, Ha J I, Sul S K.Single shunt current sensing technique in three-level PWM inverter[J]. 8th Inter-national Conference on Power Electronics-ECCE Asia, Jeju, Korea, 2011: 1445-1451. [43] Kovačevic H, Korošec L, Milanovič M.Single-shunt three-phase current measurement for a three-level inverter using a modified space-vector modulation[J]. Electronics, 2021, 10(14): 1734. [44] Ha J I.Current prediction in vector-controlled PWM inverters using single DC-link current sensor[J]. IEEE Transactions on Industrial Electronics, 2010, 57(2): 716-726. [45] Saritha B, Janakiraman P A.Sinusoidal three-phase current reconstruction and control using a DC-link current sensor and a curve-fitting observer[J]. IEEE Transactions on Industrial Electronics, 2007, 54(5): 2657-2664. [46] Zhao Jing, Nalakath S, Emadi A.Observer assisted current reconstruction method with single DC-link current sensor for sensorless control of interior permanent magnet synchronous machines[C]//IECON 2019-45th Annual Conference of the IEEE Industrial Electronics Society. IEEE, Lisbon, Portugal, 2019: 1228-1233. [47] Lu Jiadong, Hu Yihua, Liu Jinglin.Analysis and compensation of sampling errors in TPFS IPMSM drives with single current sensor[J]. IEEE Transa-ctions on Industrial Electronics, 2019, 66(5): 3852-3855. [48] Cheng Xiaomeng, Lu Haifeng, Qu Wenlong, et al.Single current sensor operation with fixed sampling points using a common-mode voltage reduction PWM technique[C]//2009 IEEE 6th International Power Electronics and Motion Control Conference, Wuhan, China, 2009: 479-483. [49] Wolbank T M, Macheiner P E.Current-controller with single DC link current measurement for inverter-fed AC machines based on an improved observer-structure[J]. IEEE Transactions on Power Electronics, 2004, 19(6): 1562-1567. [50] Li Pengwei, Liao Yong, Lin Hao, et al.An improved three-phase current reconstruction strategy using single current sensor with current prediction[C]//2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 2019: 1-5. [51] Marčetić D P, Adžić E M.Improved three-phase current reconstruction for induction motor drives with DC-link shunt[J]. IEEE Transactions on Industrial Electronics, 2010, 57(7): 2454-2462. [52] Zhao Jing, Nalakath S, Emadi A.A high frequency injection technique with modified current recon-struction for low-speed sensorless control of IPMSMs with a single DC-link current sensor[J]. IEEE Access, 2019, 7(99): 136137-136147. [53] Ha J I.Voltage injection method for three-phase current reconstruction in PWM inverters using a single sensor[J]. IEEE Transactions on Power Elec-tronics, 2009, 24(3): 767-775. [54] Ryu H S, Yoo H S, Ha J I.Carrier-based signal injection method for harmonic suppression in PWM inverter using single DC-link current sensor[C]//Paris, France, 2006, 2700-2705. [55] Lu Jiadong, Hu Yihua, Zhang Xiaokang, et al.High-frequency voltage injection sensorless control tech-nique for IPMSMs fed by a three-phase four-switch inverter with a single current sensor[J]. IEEE Transactions on Mechatronics, 2018, 23(2): 758-768. [56] Gan Chun, Wu Jianhua, Yang Shiyou, et al.Phase current reconstruction of switched reluctance motors from DC-link current under double high-frequency pulses injection[J]. IEEE Transactions on Industrial Electronics, 2015, 62(5): 3265-3276. [57] Yan Hao, Xu Yongxiang, Zhao Weiduo, et al.DC drift error mitigation method for three-phase current reconstruction with single hall current sensor[J]. IEEE Transactions on Magnetics, 2019, 55(2): 1-4. [58] Yan Hao, Yang Jiacheng, Zeng Fangui, et al.New three-phase current reconstruction for PMSM drive with hybrid space vector pulse width modulation technique[J]. IEEE Transactions on Power Electronics, 2022, 37(12): 15209-15220. [59] Shen Yongpeng, Wang Qiancheng, Liu Dongqi, et al.A mixed SVPWM technique for three-phase current reconstruction with single DC negative rail current sensor[J]. IEEE Transactions on Power Electronics, 2022, 37(5): 5357-5372. [60] Metidji B, Taib N, Baghli L, et al.Phase currents reconstruction using a single current sensor of three-phase AC Motors fed by SVM-controlled direct matrix converters[J]. IEEE Transactions on Industrial Electronics, 2013, 60(12): 5497-5505. [61] Cho Y, LaBella T, Lai J S. A three-phase current reconstruction strategy with online current offset compensation using a single current sensor[J]. IEEE transactions on industrial electronics, 2011, 59(7): 2924-2933. [62] Cheng He, Mi Shuai, Wang Zelu, et al.Phase current reconstruction with dual-sensor for switched relu-ctance motor drive system[J]. IEEE Access, 2021, 9: 114095-114103. [63] Sun Qingguo, Wu Jianhua, Gan Chun, et al.A new phase current reconstruction scheme for four-phase SRM drives using improved converter topology without voltage penalty[J]. IEEE Transactions on Industrial Electronics, 2018, 65(1): 133-144. [64] Zhu Lianghong, Chen Feifan, Li Binxing, et al.Phase current reconstruction error suppression method for single DC-link shunt PMSM drives at low-speed region[J]. IEEE Transactions on Power Electronics, 2022, 37(6): 7067-7081. [65] Tang Qipeng, Shen Anwen, Li Wuhua, et al.Multiple-positions-coupled sampling method for PMSM three-phase current reconstruction with a single current sensor[J]. IEEE Transactions on Power Electronics, 2020, 35(1): 699-708. [66] Salmasi F R.A self-healing induction motor drive with model free sensor tampering and sensor fault detection, isolation, and compensation[J]. IEEE Transactions on Industrial Electronics, 2017, 64(8): 6105-6115. [67] Wang Gaolin, Chen Feifan, Zhao Nannan, et al.Current reconstruction considering time-sharing sampling errors for single DC-link shunt motor drives[J]. IEEE Transactions on Power Electronics, 2021, 36(5): 5760-5770. [68] Wang Wenjie, Yan Hao, Wang Xuejiao, et al.Analysis and compensation of sampling-delay error in single current sensor method for PMSM drives[J]. IEEE Transactions on Power Electronics, 2022, 37(5): 5918-5927. [69] Im J H, Kim R Y.Improved saliency-based position sensorless control of interior permanent-magnet synchronous machines with single DC-link current sensor using current prediction method[J]. IEEE Transactions on Industrial Electronics, 2018, 65(7): 5335-5343. [70] Wang Wenjie, Yan Hao, Xu Yongxiang, et al.Improved three-phase current reconstruction techni-que for PMSM drive with current prediction[J]. IEEE Transactions on Industrial Electronics, 2022, 69(4): 3449-3459. [71] Song S H, Choi J W, Sul S K.Digitally controlled AC drives[J]. IEEE Ind. Appl. Mag, 2000, 6: 51-62. [72] Yoo M S, Park S W, Lee H J, et al.Offline compensation method for current scaling gains in AC motor drive systems with three-phase current sensors[J]. IEEE Transactions on Industrial Elec-tronics, 2021, 68(6): 4760-4768. [73] Cho K R, Seok J K.Correction on current measurement errors for accurate flux estimation of AC drives at low stator frequency[J]. IEEE Transa-ctions on Industry Applications, 2008, 44(2): 594-603. [74] Cho Y, LaBella T, Lai J S. A three-phase current reconstruction strategy with online current offset compensation using a single current sensor[J]. IEEE transactions on industrial electronics, 2011, 59(7): 2924-2933. [75] Kim M, Sul S K, Lee J.Compensation of current measurement error for current-controlled PMSM drives[J]. IEEE Transactions on Industry Applications, 2014, 50(5): 3365-3373. [76] Trinh Q N, Wang Peng, Tang Yi, et al.Compensation of DC offset and scaling errors in voltage and current measurements of three-phase AC/DC converters[J]. IEEE Transactions on Power Electronics, 2018, 33(6): 5401-5414. [77] Hu Mingjin, Hua Wei, Wu Zheng, et al.Com-pensation of current measurement offset error for permanent magnet synchronous machines[J]. IEEE Transactions on Power Electronics, 2020, 35(10): 11119-11128. [78] Jung H S, Hwang S H, Kim J M, et al.Diminution of current-measurement error for vector-controlled AC motor drives[J]. IEEE Transactions on Industry Applications, 2006, 42(5): 1249-1256. [79] Lu Jiadong, Hu Yihua, Liu Jinglin, et al.Position sensor fault detection of IPMSM using single DC-bus current sensor with accuracy uncertainty[J]. IEEE Transactions on Mechatronics, 2019, 24(2): 753-762. [80] Lee K W, Kim S J.Dynamic performance improve-ment of a current offset error compensator in current vector-controlled SPMSM drives[J]. IEEE Transa-ctions on Industrial Electronics, 2019, 66(9): 6727-6736. [81] Harke M C, Guerrero J M, Degner M W, et al.Current measurement gain tuning using high-frequency signal injection[J]. IEEE Transactions on Industry Appli-cations, 2008, 44(5): 1578-1586. [82] Kim M S, Park D H, Lee W J.Compensation of current measurement errors due to sensor scale error and non-simultaneous sampling error for three-phase inverter applications[J]. Journal of Power Electronics, 2022, 22(1): 31-39. [83] Liu Chunhua, Chau K T, Lee C H T, et al. A critical review of advanced electric machines and control strategies for electric vehicles[J]. Proceedings of the IEEE, 2021, 109(6): 1004-1028. [84] Lu Jiadong, Hu Yihua, Liu Jinglin, et al.Fixed-point sampling strategy for estimation on current mea-surement errors in IPMSM drives[J]. IEEE Transa-ctions on Power Electronics, 2021, 36(5): 5748-5759. [85] Wang Wei, Lu Zhixiang, Tian Weijie, et al.Dual-vector located model predictive control with single DC-link current sensor for permanent-magnet linear motor drives[J]. IEEE Transactions on Power Elec-tronics, 2021, 36(12): 14142-14154. [86] Hu, Yihua, Gan Chun, Cao Wenping, et al. Central-tapped node linked modular fault-tolerance topology for SRM applications[J]. IEEE Transactions on Power Electronics, 2016, 31(2): 1541-1554. [87] Zhai Qiwei, Meng Ke, Dong Zhaoyang, et al.Modeling and analysis of lithium battery operations in spot and frequency regulation service markets in Australia electricity market[J]. IEEE Transactions on Industrial Informatics, 2017, 13(5): 2576-2586. [88] Lu Jiadong, Hu Yihua, Chen Guipeng, et al.Mutual calibration of multiple current sensors with accuracy uncertainties in IPMSM drives for electric vehicles[J]. IEEE Transactions on Industrial Electronics, 2020, 67(1): 69-79. [89] Harke M C, Lorenz R D.The spatial effect and compensation of current sensor differential gains for three-phase three-wire systems[J]. IEEE Transactions on Industry Applications, 2008, 44(4): 1181-1189. [90] Yoo M S, Park S W, Choi Y Y, et al.Current-scaling gain compensation of motor drives under locked-rotor condition considering inequality of phase resi-stances[J]. IEEE Transactions on Industry Appli-cations, 2020, 56(5): 4915-4923.