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Fault-Tolerant Control of Five-Phase Induction Motor Under Single-Phase Open
Fault-Tolerant Control of Five-Phase Induction Motor Under Single-Phase Open
Journal of Electrical Engineering and Technology. 2014. May, 9(3): 899-907
Copyright © 2014, The Korean Institute of Electrical Engineers
  • Received : August 27, 2013
  • Accepted : December 28, 2013
  • Published : May 01, 2014
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About the Authors
Wubin Kong
Corresponding Author: Dept. of Electrical Engineering, Zhejiang University, China. (ee_huangjin@emb.zju.edu.cn)
Jin Huang
Dept. of Electrical Engineering, Zhejiang University, China. (wubinkong@126.com)
Min Kang
Corresponding Author: Dept. of Electrical Engineering, Zhejiang University, China. (ee_huangjin@emb.zju.edu.cn)
Bingnan Li
Corresponding Author: Dept. of Electrical Engineering, Zhejiang University, China. (ee_huangjin@emb.zju.edu.cn)
Lihang Zhao
Corresponding Author: Dept. of Electrical Engineering, Zhejiang University, China. (ee_huangjin@emb.zju.edu.cn)

Abstract
This paper deals with fault-tolerant control of five-phase induction motor (IM) drives under single-phase open. By exploiting a decoupled model for five-phase IM under fault, the indirect field-oriented control ensures that electromagnetic torque oscillations are reduced by particular magnitude ratio currents. The control techniques are developed by the third harmonic current injection, in order to improve electromagnetic torque density. Furthermore, Proportional Resonant (PR) regulator is adopted to realize excellent current tracking performance in the phase frame, compared with Proportional Integral (PI) and hysteresis regulators. The analysis and experimental results confirm the validity of fault-tolerant control under single-phase open.
Keywords
1. Introduction
Multiphase drives are proper for high power application, due to their advantages over conventional three-phase drives [1 - 3] . With the addition of extra phases, the current per phase is reduced for given phase voltage and total power rating, which makes it possible to use the standard power switches on a single device [4 - 6] . Increasing the number of phases is also a solution for torque pulsation reduction [7 - 8] . More vector planes in the multiphase motor can be manipulated to optimize air-gap flux distribution and improve the torque density [9 - 11] . Another distinguished advantage is improved reliability and continuous system operation even in the fault condition [12 - 13] . This characteristic is crucial for all the applications requiring a high degree of reliability, such as Electric Vehicle (EV) or marine.
Many papers have focused on the model and control for multiphase motor under open phase condition. For the dual-three phase induction machine, a unified approach to represent the model with single-phase open has been presented by the field-oriented control strategy [13 - 15] . The resilient current control of five-phase motor with sinusoidal and non-sinusoidal current excitations under fault condition is illustrated in [16 - 18] . Fault-tolerant control techniques for five-phase PM motors with trapezoidal back electromotive forces have been discussed in [19] . The control scheme in [20] ensures the operation of a seven-phase drive under open-circuit. However, few works focus on the models of multiphase IM with concentrated winding structure under open phases, and the optimal harmonic current injection technique is rarely discussed.
Current regulator plays a key role in the high performance, and the primary goal is to track the reference current accurately during steady state and transient condition. The precise matched comparative analysis of different current regulation strategies is discussed in [21] , which is in the application of three-phase IM under healthy condition. A theoretical connection between PR and synchronous frame PI regulators is established in [22] . Hysteresis current control is widely used for its simplicity, but it results in much more harmonic current [17 - 18 , 21 - 22] . The simple PI regulator realizes the excellent dc current control. However, its performance is unsatisfactory for the ac current control [23] . Fortunately, the PR regulator can achieve virtually the same steady-state and transient performance as synchronous reference frame PI regulator under healthy condition [24] . A further significant superiority of PR controller is its application to current control in the phase frame, where synchronous reference frame control is more difficult to realize under asymmetrical condition.
The decoupled model is established for the five-phase IM under open fault, and it contains inductance parameters derivation. The proposed method is based on the simple computation of the currents in the αβ subspaces, and electromagnetic torque oscillations are reduced by particular magnitude ratio currents. Then, a set of stator currents with third harmonic injection is obtained to improve the electromagnetic torque density. Third harmonic current is also utilized to decrease the amplitude of stator current, without exceeding the rate power of inverter. Furthermore, the PR current regulator is adopted to realize excellent current tracking in the phase frame. Finally, a five-phase induction motor drive with low DC link is constructed, and experimental results verify the feasibility of the fault-tolerant control strategy under single-phase open.
2. Motor Model for Five-phase IM Under Single-phase Open
- 2.1 Voltage equations in theαβsubspace
This paper presents a four-pole five-phase induction motor with identical quasi-concentrated phase windings, and each phase winding is constituted by two adjacent concentrated winding in series. The basic equations of five-phase IM under balanced condition are discussed in [8 - 9] . Given five-phase IM with phase “a” open, the stator and rotor voltage equations can be written as
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where the current and voltage vectors are
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In Eq. (2), R s , L ss , R r , L rr , L sr and L rs are parameter matrices described in [12 - 13] .
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T 5 is transformation matrices under healthy condition contained in [9] , and the stationary transformation matrices T 4(1) and T 4(3) decomposed into α 1 β 1 and α 3 β 3 planes are given as
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where c 0 = 0.25, and γ = 2 π /5 . The electromechanical energy conversion takes place in α 1 β 1 and α 3 β 3 subspace. In (4) and (5), all the row vectors can’t realize the same norm simultaneously, while keeping the orthogonal property to each one. Additionally, the third row z 1(3) is one degree of freedom to realize the same magnitude of stator currents [12] , and the fourth row of the matrices satisfies zero sequence current equation. Then, the correlative inductance parameter sunder single-phase open can be derived, as shown in Table 1 .
Correlative inductance parameters under single phase open
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Correlative inductance parameters under single phase open
- 2.2 Electromagnetic torque ripple analysis
Reference [13] demonstrates that the electromechanical energy conversion takes place only in the α 1 β 1 plane for dual-three phase IM. The five-phase IM with concentrated winding structure has two energy conversion planes, so the currents for the dual planes can be defined as
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I α1 , I β 1 , I α 3 , I β3 are the magnitude in the α 1 β 1 and α 3 β 3 planes, respectively. The steady state is contained in the paper, and the Eq. (6) is the reference stator current. At the fault occurrence, the magnitude of Iα and Iβ are changed according to the load torque [15] .
The electromagnetic torque derivation for α 1 β 1 planes has been discussed in the reference [17] . Similarly, the electromagnetic torque for is derived as
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Eq. (8) exhibits clearly that the electromagnetic torque can be decomposed into four components: constant part
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and oscillation component
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for α 1 β 1 plane; constant part
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and oscillation component
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for α 3 β 3 plane.
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3. Indirect Field-oriented Control
In order to eliminate the torque oscillations, the current magnitude ratio is given as
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To maintain the same amplitude of stator current, the currents in the z plane are identified as i z1 = 0.236 i 1 , i z3 = 0.236 i 3 [12 , 15] . The criterion (9) can be applied in the indirect field-oriented control scheme where the dq currents are used to control electromagnetic torque. The synchronous rotating transformation matrices in d 1 q 1 and d 3 q 3 planes can be expressed as
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where
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, and
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. It is assumed that the fundamental and third harmonic rotor fluxes are attached to d axis, and no component exists on q axis. The expressions of magnetizing currents are
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To maintain a quasi-trapezoidal air-gap flux density distribution, the corresponding magnitude currents i sd3 is given by
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where m 3 =1/ 6 , as described in [10 - 11] . The slip angular speed are derived as
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Similarly, the substitution of the current from (12-13) into the torque expression (8), the electromagnetic torque can be derived as
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The torque current component in the d 3 q 3 plane can be expressed as
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According to the analysis mentioned above, the diagram of indirect field-oriented control for five-phase IM under single-phase open is shown in Fig. 1 . The current regulator in the phase frame is elaborated in the next section.
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Indirect field-oriented control for five-phase IM under single-phase open fault
4. Current Regulator Design in the Phase Frame
This section depicts the principles of three methods for current regulator [22] , and the diagram is shown in Fig. 2 .
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Diagram of current control model in the phase frame
Since Electromotive Force (EMF) is not random disturbance, its effect on the fundamental tracking error can be substantially reduced by incorporating feed forward injection of an estimated compensation. Then, the motor transfer function is described as
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where Tp = Lσs / R s . Furthermore, the current control transfer function Gc (s) is demonstrated in the following.
- 4.1 Hysteresis Current Control (Method I)
Hysteresis control operates by comparison of the reference current against the feedback current. Switching state of inverter is set to high or low, depending on its error moving outside of fixed hysteresis width [21] , according to
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This control strategy achieves a fast current response by simple programming, though it has the limitations of variable switching frequency. Another negative effect is much more harmonic current, which increases the copper loss and torque pulsation for the system drive.
- 4.2 PI Current Regulator (Method II)
The forward transfer block Gc (s) for a simple PI controller is defined by
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The magnitude of Gc(s) is essentially infinite at the dc because of the 1/( ski ) term. However, this method can’t realize zero ac current error in the phase frame because of the limited gain in the regulator.
- 4.3 PR Current Regulator (Method Ⅲ)
In this situation, the only remaining alternative is to increase the gain of the forward controller, but this would reduce the system of stability. Fortunately, PR regulator can realize zero ac current error in the phase frame, because the resonant term has large gain at the target frequency, which can achieve good response in the fault occurrence [21 - 22] .
The forward gain block Gc(s) of a practical PR control is described by the transfer function
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From this expression, it can be seen how the term of s /( s 2 + 𝜔e 2 ) creates infinite forward controller gain at the target frequency 𝜔e , which is utilized to achieve zero error for tracking ac current.
The phase angle of forward loop at the cross over frequency 𝜔c is given by
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where øm is target phase margin, and the value is usually set to π /6 ⌷ π /4. As described in the reference [21] , the maximum cross frequency can be derived
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Then the maximum possible magnitude of kp can be derived by setting the open loop gain to unity [24] , when gives ki ≈ 10/ 𝜔 c(max) .
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Appling the approach to the test system described for the controller gains ( kp = 0.3, ki = 0.0025 s ), the bode plots of forward open loop for PI and PR regulator are shown in Fig. 3 .
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Bode plots of PR and PI control
5. Experimental Verification
In order to evaluate the capability of the indirect fieldoriented control under fault condition, experimental tests are executed for the steady state and transient response. The drive system is depicted as Fig. 4 , and the nominal parameters of five-phase IM in the healthy condition are shown as Table 2 .
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Five-phase IM drive system
Nominal parameters of five-phase IM
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Nominal parameters of five-phase IM
The performances of the drive system for three current regulators are extensively explored in the experimental tests, when the motor operates at 600 r/min with the 15N. m load. Experimental results contain the performances of steady state and transient response under phase “a” open. For the aspect of EMF compensation in the feed forward loop, the commanded ratio of V/f curve is set to 0.40.
The experimental results in Fig. 5 exhibit the current responses of drive system controlled by hysteresis regulator (method ↑). There is relatively larger steady state and transient current errors, and the maximum amplitude is about 60A shown in Fig. 5(b) . Worse still, many low order harmonic currents are contained in hysteresis control, and the THD is about 21.5% by the algorithm of FFT.
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Experimental results for method I
The performance of PI current regulator (method II) is demonstrated in the Fig. 6 , and it is can be seen that the harmonic current is reduced significantly compared with that of hysteresis regulator. However, current pulse error at the transient response is still large.
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Experimental results for method II
The results of PR current regulator (method Ⅲ) with EMF compensation are expressed in the Fig. 7 . It can be clearly seen that the stator current is sinusoidal without low order harmonic, and the current error shown in Fig. 7(b) is minimized distinctively, especially for the transient response at fault occurrence. On the other hand, the experimental for PR regulator without EMF compensation is contained in the Fig. 8 . Consequently, the current error is amplified without forward feed compensation, identifying the theoretical analysis in section 3.
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Experimental results for method Ⅲ
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Experimental results for error between reference and actual current of phase “b”
Fig. 9 depicts five stator currents and motor torque when one phase is open without any fault-tolerant control. It can be seen that torque oscillations is significantly larger, and the maximum magnitude is reach to 5N.m. Additionally, the magnitude of phase “b” increases by 65%, and it means that the load should be restricted by the inverter with same capability.
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Experimental results under no fault-tolerant control
The torque ripple is reduced significantly with faulttolerant control, and the value is less than 1.5 N.m at the bottom of Fig.10(b) . To further verify the effectiveness of the third harmonic current injection, the experiments are executed. The maximum of stator current in the Fig. 10 (a) is decreased by 15.6%, compared with that of Fig. 7 (a) . Moreover, the electromagnetic torque is increases by 11%, as shown in Fig. 10(b) .
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Experimental results under fault-tolerant control with third harmonic current injection
Fig. 11 (a) illustrates the experimental results for fundamental and third harmonic reference currents under single-phase open, which are mapped into d 1 q 1 and d 3 q 3 planes, respectively. It can be seen that i sd1 and i sd3 are constant, while i sq1 and i sq3 are approximately proportional to the electromagnetic torque illustrated in Fig. 11(b) . The flux producing current i sd1 is controlled at 25A, and i sd3 is controlled at about 9A. Fig. 11 (b) shows that the rotor speed has no disturbance under sudden load at 15 N. m, ensuring high performance for torque control under single-phase open.
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Experimental results under sudden load
6. Conclusion
A modified model for five-phase IM under open fault has been exploited to realize high performance in this paper. The control scheme is suitable for the implementation of reducing the torque ripple, allowing disturbance-free operation with particular magnitude ratio currents. To assess the effectiveness of current control, three regulators have been analyzed in detail by comparison of current magnitude error for steady-state and transient response. The third harmonic current injection technique can be used to improve the iron utilization and torque density. The experimental results demonstrate that the proposed method is valid under single-phase open fault. Moreover, the method presented in this paper can be used for up to two open stator phases for five-phase IM.
Nomenclature
- Variable
Vs Stator voltage matrices Vr Rotor voltage matrices Is Stator current matrices Ir Rotor current matrices Rs Stator resistance matrices Rr Rotor resistance matrices Lss Stator self-inductance matrices Lrr Rotor self-inductance matrices Lsr Mutual inductance matrices M Mutual inductance under fault condition L Self inductance under fault condition P Number of poles ψ Rotor flux Tem Electromagnetic torque τ Rotor time constant ωe Electrical angular speed θ Synchronous rotating angle ϕ0 Initial angle Td Sampling and transfer delay time VDC Voltage of DC link kp Proportional gain ki Integral gain T5 Transformation matrices under healthy condition T4 Transformation matrices under faulty condition
- Subscripts
1 Fundamental component 3 Third harmonic component s Stator component r Rotor component α, β Stationary frame component d, q Synchronous frame component
BIO
Wubin Kong He received a B.S. degree from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2009. He is currently working toward the Ph.D. degree. His research interests are in multiphase machines and drives.
Jin Huang He received the B.S. degree from the College of electrical engineering, Zhejiang University, Hangzhou, China, in 1982, and the Ph.D. degree in electrical engineering from the National Polytechnic Institute of Toulouse, Toulouse, France, in 1987, respectively. From 1987 to 1994, he was an associate Professor in College of Electrical Engineering, Zhejiang University, China. He is currently Professor of Zhejiang University. He is engaged in research on electrical machine, AC drives, multiphase machine and condition monitoring of electrical machines. Min Kang received the B.S. and Ph.D. degrees from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2003 and 2008, respective.
Min Kang received the B.S. and Ph.D. degrees from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2003 and 2008, respectively. From 2008 to 2011, he was a Lecturer in the College of Electrical Engineering, Zhejiang University of Science and Technology, China. He is currently associate Professor of Zhejiang of Science and Technology. His research interests are in multiphase bearingless machines and AC drives.
Bingnan Li He received the B.S. and M.S. degrees from the College of Electrical Engineering, Shenyang University of Technology, Shenyang, China, in 2006 and 2009, respectively. He is currently working toward the Ph.D. degree from the College of Electrical Engineering, Zhejiang University, Hangzhou, China. His research interests are in multiphase theory, multiphase bearingless machines and drives.
LiHang Zhao He received a B.S. degree from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2011, where he is currently working toward the Ph.D. degree. His research interests are in parameter identification of AC motor.
References
Toliyat Hamid A. 1991 “Analysis of a concentrated winding induction machine for adjustable speed drive applications,” IEEE Trans. Energy Convers 6 (4) 679 - 683    DOI : 10.1109/60.103641
Fu R. , Lipo T. A. 1994 “Disturbance-free operation of a multiphase current-regulated motor drive with an opened phase,” IEEE Trans. Ind. Appl 30 (10) 1267 - 1274    DOI : 10.1109/28.315238
Levi E. , Bojoi R. , Profumo F. 2007 “Multiphase induction motor drives - A technology status review,” IET Electr. Power Appl 1 (4) 489 - 516    DOI : 10.1049/iet-epa:20060342
Levi E. 2008 “Multiphase electric machines for variablespeed applications,” IEEE Trans. Ind. Electron 55 (5) 1893 - 1909    DOI : 10.1109/TIE.2008.918488
Levi E. , Jones M. , Vukosavic S. N. , Toliyat H. A. 2004 “A novel concept of a multiphase, multimotor vector controlled drive system supplied from a single voltage source inverter,” IEEE Trans. Power Electron 19 (2) 320 - 335    DOI : 10.1109/TPEL.2003.823241
Xu H. , Toliyat H. A. , Petersen L. J. 2002 “Five-phase induction motor drives with dsp-based control system,” IEEE Trans. Power Electron 17 (4) 524 - 533    DOI : 10.1109/TPEL.2002.800983
Parsa L. , Toliyat H. A. 2005 “Five-phase permanentmagnet motor drives,” IEEE Trans. Ind. Appl. 41 (1) 30 - 37    DOI : 10.1109/TIA.2004.841021
Xu H. , Toliyat H. A. , Petersen L. J. 2001 “Rotor field oriented control of a five-phase induction motor with the combined fundamental and third harmonic currents,” Proc. IEEE APEC Anaheim, CA 1 392 - 398
Libo Zheng , Fletcher J. E. , Williams B. W. 2008 “Dualplane vector control of a five-phase induction machine for an improved flux pattern,” IEEE Trans. Ind. Electron 55 (5) 1996 - 2005    DOI : 10.1109/TIE.2008.918464
Ayman S A-K , Shady M G , Mahmoud I M 2011 “Optimum flux distribution with harmonic injection for a multiphase induction machine using genetic algorithm,” IEEE Trans. Energy Convers 26 (2) 501 - 512    DOI : 10.1109/TEC.2010.2093139
Abdel-Khalik A S , Masoud M I , Williams Barry W 2012 “Improved flux pattern with third harmonic injection for multiphase induction machines,” IEEE Trans. Power Electron 27 (3) 1563 - 1578    DOI : 10.1109/TPEL.2011.2163320
Ryu H.-M. , Kim J.-W. , Sul S.-K. 2006 “Synchronousframe current control of multiphase synchronous motor under asymmetric fault condition due to open phases,” IEEE Trans. Ind. Appl 42 (4) 1062 - 1070    DOI : 10.1109/TIA.2006.876074
Zhao Y. , Lipo T. A. 1996 “Modeling and control of a multi-phase induction machine with structural unbalance,” Part I: Machine modeling and multidimensional current regulation,” IEEE Trans. Energy Convers. 11 (3) 570 - 577    DOI : 10.1109/60.537009
Zhao Y. , Lipo T. A. 1996 “Modeling and control of a multi-phase induction machine with structural unbalance,” Part II: Field-oriented control and experimental verification,” IEEE Trans. Energy Convers 11 (3) 578 - 584    DOI : 10.1109/60.537028
Kiani-Nezhad R. , Nahidmobarakeh B. , Baghli L. , Betin F. , Capolino G. A. 2008 “Modeling and control of six-phase symmetrical induction machines under fault condition due to open phases,” IEEE Trans. Ind. Electron 55 (5) 1966 - 1977    DOI : 10.1109/TIE.2008.918479
Bianchi N. , Bolognani S. , Pre M. D. 2007 “Strategies for the fault-tolerant current control of a five-phase permanent-magnet motor,” IEEE Trans. Ind. Appl. 43 (4) 960 - 970    DOI : 10.1109/TIA.2007.900445
Medoued A. , Lebaroud A. , Boukadoum A. , Clerc G. 2010 “On-line faults signature monitoring tool for induction motor diagnosis“ Journal of Electrical Engineering & Technology 5 (1) 140 - 145    DOI : 10.5370/JEET.2010.5.1.140
Toliyat Hamid A. , Parsa L. , Bianchi N. 2002 “Resilient current control of five-phase induction motor under asymmetrical fault,” Proc. IEEE APEC TX, USA 1 64 - 71
Dwari S. , Parsa L. 2011 “Fault-tolerant control of fivephase permanent magnet motors with trapezoidal back EMF,” IEEE Trans. Ind. Electron. 58 (2) 476 - 485    DOI : 10.1109/TIE.2010.2045322
Tani A. , Mengoni M. , Zarri L. 2012 “Control of Multiphase Induction Motors With an Odd Number of Phases Under Open-Circuit Phase Faults,” IEEE Trans. Ind. Electron 27 (2) 565 - 577
Del Blanco F. B. , Degner M. W. , Lorenz R. D. 1999 “Dynamic analysis of current regulators for AC motors using complex vectors,” IEEE Trans. Ind. Appl 35 (6) 1424 - 1432    DOI : 10.1109/28.806058
Zmood D N , Holmes D G. 2003 “Stationary frame current regulation of PWM inverters with zero steady-state error“ IEEE Trans. Power Electron 18 (3) 814 - 822    DOI : 10.1109/TPEL.2003.810852
Holmes D. G. , McGrath B. P. , Parker S. T. 2012 “Current regulation strategies for vector-controlled induction motor drives,” IEEE Trans. Ind. Electron 59 (10) 3680 - 3688    DOI : 10.1109/TIE.2011.2165455
Holmes D. G. , Lipo T. A. , McGrath B. P. 2009 “Optimized Design of Stationary Frame Three Phase AC Current Regulators,” IEEE Trans. Ind. Electron 24 (11) 2417 - 2426