3740 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 5, MAY 2018 Flux-Weakening Control for Induction Motor in Voltage Extension Region: Torque Analysis and Dynamic Performance Improvement Zhen Dong , Student Member, IEEE, Yong Yu , Wenshuang Li , Bo Wang , Student Member, IEEE, and Dianguo Xu , Fellow, IEEE Abstract—Flux-weakening control for induction motor (IM) in voltage extension region (outside the inscribed circle but in the hexagon) is meaningful to yield a further maximum torque. However, as the voltage-limit trajectory migrates out of the inscribed circle, torque ripple becomes more severe. Meanwhile, the insufficient voltage margin results in the degradation of current dynamic performance in transition period (from base speed region to flux-weakening region), especially in harsh conditions, e.g., a step speed command. To address the problems above, this paper gives a quanti- tative analysis of the torque ripple and an explicit discus- sion on the current dynamic performance. A novel “Voltage Reference Adjustable” flux-weakening controller with “Self- Locking Limit Block” (SLLB) is proposed. There are two advantages. The first is the capability to operate in any volt- age extension regions, offering a tradeoff between obtain- ing the maximum torque and suppressing the torque ripple. The second is an optimized voltage distribution, achieving a better track characteristic of d- and q-axis currents with the help of triggered SLLB in transition period. Experimental re- sults on a commercial IM control system verify the validity of the proposed scheme. Index Terms—Dynamic performance improvement, flux- weakening control, induction motor (IM), maximum torque, voltage extension. I. INTRODUCTION O WING to the limited current and voltage, the original unconstrained induction motor (IM) control system becomes constrained as the frequency enters into the flux- weakening region. Considering the definition of the “general windup problem” [1], it is reasonable to regard the flux- weakening strategy as one part of the antiwindup technique, called “condition technique.” When the voltage migrates out of the limit, the reference trajectory (or set point) should be adjusted, which is either a feedforward issue in terms of the Manuscript received June 8, 2017; revised August 16, 2017, Septem- ber 25, 2017, and October 5, 2017; accepted October 9, 2017. Date of publication October 19, 2017; date of current version January 16, 2018. This work was supported by the Research Fund for the National Sci- ence Foundation of China under Grant 51377032 and Grant 51690182. (Corresponding author: Yong Yu.) The authors are with the School of Electrical Engineering and Au- tomation, Harbin Institute of Technology, Harbin 150001, China (e-mail: dongzhen@stu.hit.edu.cn; yuyong@hit.edu.cn; liwens_hit@163.com; wangbo6222@126.com; xudiang@hit.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2017.2764853 system or a feedback issue in terms of the output voltage [2]. Hence, the objective of the particular flux-weakening methods, e.g., analytic method based upon motor model, current/voltage error method, voltage closed-loop method, and lookup table method (classified by [3]), for motor control, is to design a high-efficiency controller for the d-axis current control as well as assign an appropriate q-axis current for the required output torque. Many papers mentioned in the review [4] have addressed on it. Of particular interest, the voltage closed-loop flux-weakening scheme (VCFS) proposed by Kim and Sul [5] has been regarded as a successful method in terms of ease of implementation and low parameter sensitivity [6], [7]. Within the constrained IM control system, the subsystem, proportional-integral (PI) current regulator, also suffers from the windup problem due to the increased back electromotive force (EMF). Different structures of antiwindup controllers are investigated for a better performance. Contributions on this is- sue could be found in [7]–[9]. Further, it can be seen that the whole control system is actually a double-nesting windup sys- tem, which makes it a much more complicated system compared to other common windup systems. In such a complex system, the capability of voltage-source inverter is further explored to increase the maximum torque. The voltage-limit constraint hence migrates from the inscribed circle to the hexagon. As a result, the utilization of the dc-link voltage is extended. Methods for flux-weakening operation in voltage extension region are given in [10]–[15]. In addition, it is worthy to be noticed that the voltage-limit constraint trajectory, the voltage reference in flux-weakening controller, and the voltage saturation boundary in PI antiwindup structure mentioned above must be consistent in voltage extension region. Otherwise, the whole control system may be put into a double squeeze [16]. Even though the efforts of the aforementioned papers have rendered the whole flux-weakening control system a great im- provement, better solutions for two issues in the voltage exten- sion region are still necessary: Torque ripple caused by over modulation and dynamic performance degradation because of the insufficient voltage margin. Therefore, the contributions of this paper are listed as follows. 1) A general and quantitative torque analysis for both the inscribed circle and the hexagon circumstances is devel- oped. Series of conclusions are reached and will act as the guidance to make the tradeoff between torque max- 0278-0046 © 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.