advertisement

Journal of Power Electronics, Vol. ??, No. ?, pp. ?-?,MonthYear1 http://dx.doi.org/10.6113/JPE.2014.14.1.??? ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718 JPE ??-?-? Performance Evaluation of Field-Oriented Control of Star-Connected 3-Phase Induction Motor Drives under Stator Winding Open-Circuit Fault Mohammad Jannati*, Nik Rumzi Nik Idris†, and Mohd Junaidi Abdul Aziz* *† UTM-PROTON Future Drive Laboratory, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Johor Bahru, Malaysia Abstract A method for fault-tolerant vector control of star-connected 3-phase Induction Motor (IM) drive system based on Field-Oriented Control (FOC) is proposed in this paper. This method enables the control of a 3-phase IM upon an open-phase failure in one of its phases without the need of control structure changes to the conventional FOC algorithm. The proposed drive system significantly reduces the speed and torque pulsations, which are caused by an open-phase fault in the stator windings. The performance of the proposed method was verified using MATLAB (M-File) simulation as well experimental tests on a 1.5kW 3-phase IM drive system. This paper experimentally compares the operation of proposed fault-tolerant vector controller and conventional vector controller during open-phase fault. Keywords: Fault-tolerant control, Field-Oriented Control, Speed and torque pulsations, Star-connected, Stator winding open-circuit fault, 3-phase induction motor drive I. INTRODUCTION Field-Oriented Control (FOC) technique for 3-phase Induction Motors (IMs) is widely adopted by industries to obtain high performance of 3-phase IM drive systems. Conventional FOC algorithm, which is used for healthy 3-phase IM drives, cannot be used for a faulty 3-phase IM drive due to the fact that the conventional FOC is designed based on a healthy machine model [1]. Using conventional FOC for faulty 3-phase IM drives will degrade the dynamic performance of the drive system. In this regard, it is necessary to design a drive system that provides robustness against the fault conditions [1]-[5]. Generally, 3-phase IM drives are exposed to various failures; failures in the in the inverter [6], [7], failures in the mechanical or electrical sensors [5], [8] and failures related to electrical motor including faults in the stator [1], [9] and/or faults in the Manuscript received Month. Date, Year; acceptedMonth. Date, Year Recommended for publication by Associate Editor Gil-Dong Hong. CorrespondingAuthor:[email protected] Tel: +82-2-554-0185,Fax: +82-2-554-0186, Hangook University * Department of Electrical and Computer Engineering, Illinois Institute of Technology, U.S.A. ** School of Electrical Engineering, Hangook University, Seoul, Korea † Fig. 1. Classification of faults in squirrel-cage 3-phase IM drive. rotor [10], [11]. Fig. 1 shows the classification of faults in squirrel-cage 3-phase IM drives. In some critical applications, the operation of the drive system cannot be interrupted by faulty conditions mainly for safety reasons. Thus, for these applications, fault-tolerant control is essential. Based on this classification of faults, various fault-tolerant control methods have been suggested in the literature, including passive and active methods. A passive method can be ensured by conventional robust control methods such as H∞ [12], [13]. Despite the robustness of this method against disturbances, its © 2014 KIPE 2Journal of Power Electronics, Vol. ??, No. ?, Month Year performance under healthy conditions is not optimized. In an active method after fault detection and fault diagnostic, a new set of control parameters or a new control structure is applied [1]-[5] and [14]-[20]. This method has good performances under both healthy and faulty conditions. However, it requires a different control algorithm under faulty conditions. A large number of studies have been conducted on the implementation of vector control techniques for electrical machines under stator open-circuit fault [1]-[4] and [14]-[20]. Most of the pervious works have focused on developing vector control methods of faulty Permanent Magnet Synchronous Motors (PMSMs) and multi-phase IMs (five and six phases) [14]-[17]. In [18], [19] the analysis of the star-connected 3-phase IM in the open-phase fault indicates that, to compensate torque pulsations, odd harmonic voltages of the magnitude and phase angle can be injected at the machine terminal. In [3], [20], vector and scalar control methods to control delta-connected 3-phase IM drive under stator winding open-phase fault based on current controller has been proposed and implemented. Modeling and FOC of a star-connected 3-phase IM under open-phase fault using current controller have also been presented in [4]. In this work, using suitable transformation matrix for stator current variables, a new model of IM is adopted during faulty conditions. This method is only verified by some simulation tests. Moreover, the use of current controller introduces problems under light load conditions, which can be an important issue for vector control of single-phase IMs. The proposed strategy in this paper not only can be used for 3-phase IMs under open-phase fault it can be also implemented for single-phase IM with main and auxiliary windings. The major contribution of this research is the development of FOC algorithm for star-connected 3-phase IM drives, which can be used for healthy and faulty (open-circuit fault) 3-phase IMs. The proposed active fault-tolerant control method in this paper does not need new FOC algorithm when a fault occurs. It is based on conventional FOC algorithm, which is modified for faulty conditions. It is shown that by switching the motor parameters and using two different unbalanced transformation matrices for stator current and voltage variables, the vector control of faulty 3-phase IM is possible. Simulation and experimental results are presented to show the main characteristics of the proposed method and to confirm the methodology and the modeling technique used in this research. II. Stator voltage equations: 0 idss Md p 0 idrs vdss rs Lds p s (1) rs Lqs p iqss 0 Mq p iqrs vqs 0 Rotor voltages equations: vdrs M d p s vqr r M d r M q idss rr Lr p r Lr idrs M q p iqss r Lr rr Lr p iqrs (2) Stator flux equations: sds Lds 0 idss Md 0 idrs s s s qs 0 Lqs iqs 0 Mq iqr Rotor flux equations: sdr M d s qr 0 0 idss Lr M q iqss 0 0 idrs Lr iqrs (4) Torque equations: pole M q iqss idrs M d idss iqrs 2 2 Jpr Br Te Tl pole Te (5) where: 3 3 Lms , M q Lms 2 2 d 1 3 Lds Lls Lms , Lqs Lls Lms , p dt 2 2 Md (6) In these equations, vsds, vsqs are the stator d-q axes voltages, are the stator d-q axes currents, isdr, isqr are the rotor d-q axes currents, λsds, λsqs are the stator d-q axes fluxes and λsdr and λsqr are the rotor d-q axes fluxes in the stationary reference frame (superscript “s”). rs and rr indicate the stator and rotor resistances. Lds, Lqs, Lr, Lms, Md and Mq denote the stator and rotor d-q axes self and mutual inductances. r is the motor speed. Te and Tl are electromagnetic torque and load torque, J and B are the moment of inertia and viscous friction coefficient respectively. As can be seen from (1)-(5), the structure of healthy and faulty 3-phase IM are the same. Actually, by replacing Md=Mq=M=3/2Lms and Lds=Lqs=Ls=Lls+3/2Lms in the faulty 3-phase IM equations, the equations of the healthy IM are obtained [1], [4]. In summary, the difference between model of healthy and faulty 3-phase IM is summarized in Table 1. isds, isqs MATHEMATICAL MODEL OF FAULTY 3-PHASE IM The d-q model of 3-phase IMs under open-phase fault can be expressed by the following equations (it can be noted that these equations are not depended on which phase of stator windings is opened; the modeling of 3-phase IM under open-phase fault is fully discussed in [1], [4]): (3) TABLE I THE DIFFERENCE BETWEEN MODEL OF HEALTHY AND FAULTY 3-PHASE IM Faulty 3-Phase IM Mq=√3/2Lms Lqs=Lls+1/2Lms Healthy 3-Phase IM Mq=M=3/2Lms Lqs=Ls=Lls+3/2Lms Preperation of Papers for Journal of Power Electronics3 TABLE II THE COMPARISON BETWEEN EQUATIONS OF FLUX, SPEED AND TORQUE FOR HEALTHY AND FAULTY 3-PHASE IM IN THE ROTATING REFERENCE FRAME Healthy IM ai cosmr , bi sinmr a i , bi , c i , d i Transformation matrix for stator current variables Flux equation Torque equation Speed equation ci sinmr , di cosmr T cos sin mr is mr r Te mr sin mr cos mr ai Faulty IM [4] Md cos mr , bi sin mr Mq ai M d / M q cos mr , bi M q / M d sin mr M ci d sin mr , d i cos mr Mq T mr is Midsmr 1 Tr p pole M r iqsmr 2 Lr mr r Faulty IM [1] Mi qsmr Tr r Md M cos mr q M d sin mr M q r Te T mr s mr is d q d r 1 Tr p Te M q iqsmr mr M d M q idsmr pole 2 mr r Tr r M q / M d sin mr M q / M d cos mr mr q M q idsmr mr r 1 Tr p MdMq Lr r iqsmr M d M q iqsmr Tr r (8) Among the various kinds of the vector control methods, FOC method is the most highly adopted method for high performance control of IM. In conventional Rotor FOC (RFOC) the equations of machine is transformed to the rotating reference frame. The transformation matrix that is used for this purpose is: sin mr cos mr T MM / /MM cos sin pole M q r iqsmr 2 Lr III. ROTOR FOC OF 3-PHASE IM UNDER OPEN-PHASE FAULT cos mr sin mr sin mr cos mr ci M d / M q sin mr , d i M q / M d cos mr (7) In (7), θmr is the angle between the stationary reference frame and the rotating reference frame (in this paper superscript “mr” indicates that the variables are in the rotating reference frame). For the unbalanced conditions used in this paper, the conventional transformation matrix can be applied to the rotor variables. However, to overcome the effect of asymmetrical stator winding structure and thus to obtain a non-pulsating torque, it is required to define an unbalanced transformation matrix for stator variables. The reason of using this transformation matrix is to obtain a model of faulty IM with balanced structure. A: Transformation matrix for stator current variables A transformation matrix for stator current variables can be considered as: It can be shown that, structure of the torque equation for the faulty IM can be obtained similar to a balanced 3-phase IM torque using two different transformation matrices as presented in [1] and [4]. In [1], the transformation matrix is given by: ai Md M cos mr , bi sin mr , ci d sin mr , d i cos mr Mq Mq (9) whereas in [4], it is given by: ai M d / M q cos mr , bi M q / M d sin mr ci M d / M q sin mr , di M q / M d cos mr (10) Based on (9) and (10), the transformation matrix, for stator current variables are obtained as (11) and (12) respectively: idsmr mr mr Tis i qs Md cos mr idss M q s M iqs d sin mr Mq idsmr idss mr mr Tis s iqs iqs M d / M q cos mr M d / M q sin mr sin mr s i dss cos mr iqs (11) M q / M d sin mr idss M q / M d cos mr iqss (12) Using (11) and (12) and after simplification, the 4Journal of Power Electronics, Vol. ??, No. ?, Month Year electromagnetic torque can be obtained as (13) and (14) respectively [1], [4]: TABLE III THE COMPARISON BETWEEN EQUATIONS OF STATOR VOLTAGES FOR HEALTHY AND FAULTY 3-PHASE IM IN THE ROTATING REFERENCE FRAME Healthy IM Stator d-axis voltage equation Stator q-axis voltage equation Te vdsmr rs idsmr ( Ls mr ( Ls M ) pidsmr Lr mr M 2 mr M Mi r )iqs ( )( ds ) Lr Lr Tr vqsmr rs iqsmr ( Ls mr ( Ls Faulty IM 2 M2 ) piqsmr Lr M 2 mr )ids mr M r Lr Lr vdsmr ( ( Mq Lr vqsmr ( rs M rs M 2 q 2 M d2 )( (13) pole M d M q (iqsmr idrmr idsmr iqrmr ) 2 (14) M q idsmr r Tr rs M q2 rs M d2 2 M d2 mr M q pole M q (iqsmr idrmr idsmr iqrmr ) 2 2 d r Lr ( )idsmr ( Lqs )( M q2 Lr ) pidsmr mr ( Lqs rs M q2 rs M d2 2 M d2 )iqsmr ( Lqs rs M q2 rs M d2 2 M d2 M q2 Lr M q2 Lr )iqsmr )(cos 2 mr idsmr sin 2 mr iqsmr ) ) piqsmr mr ( Lqs M q2 Lr )idsmr )( sin 2 mr idsmr cos 2 mr iqsmr ) and, Te As can be seen, by using (11) and (12), the torque equation of a faulty 3-phase IM becomes similar to the torque equation of a healthy 3-phase IM. The only difference between (13) and healthy 3-phase IM torque equation is that, in (13) we have: Mq=√3/2Lms but in the healthy conditions we have: M=3/2Lms. Moreover, the difference between (14) and healthy 3-phase IM torque equation is that, in (14) we have: √MdMq≈1.14Lms but in the healthy conditions we have: M=3/2Lms. In conclusion, the comparison between equations of flux, speed and torque for healthy and faulty 3-phase IMs in the rotating reference frame based on the presented transformation matrices for stator current variables (equation (11) and (12)) is summarized in Table 2 (to obtain these equations the assumptions λdrmr=|λr| and λqrmr=0 have been considered). In Table 2, Tr is the rotor time constant (Tr=Lr/rr). From the results of Table 2, it is possible to adopt the indirect field-oriented control scheme, as shown in Fig. 2, where |λr*| and Te* represent the reference flux and torque respectively. In Fig. 2, the blue blocks represent the portions of conventional FOC that require modifications under faulty conditions. Fig. 2. Current controller block diagram of Indirect RFOC for star-connected 3-phase IM under normal and open-phase fault conditions. B: Transformation matrix for stator voltage variables Like equation (8), a transformation matrix for stator voltage variables can be written as: (15) Using equation (15), the faulty 3-phase IM stator voltage equations can be written as: T vv mr vs s ds s qs 0 mr rs Lds p mr T Tvs rs Lqs p is 0 T ii 1 mr is (16) s ds s qs 0 mr 1 mr idrs M d p T Ts s Tvsmr M q p s 0 iqr In equation (16), for simplicity, (11) (rather than (12)) is used for [Tismr]. As a result, equation (16) can be written as: Preperation of Papers for Journal of Power Electronics5 Mq mr M bv q rds cos mr rds sin mr ids M Md i mr d v d rqs cos mr qs rqs sin mr Mq M mr bv q Lds cos mr Lds sin mr pids M M d piqsmr d v d sin cos L L qs mr qs mr vdsmr av mr vqs cv a v cv a mr v cv a mr v cv a v cv Mq mr Mq bv Lds sin mr Lds cos mr ids M Md i mr d v d Lqs sin mr qs Lqs cos mr bv M d sin mr M d cos mr idrmr d v M q cos mr M q sin mr iqrmr bv M d cos mr d v M q sin mr M d sin mr pidrmr M q cos mr piqrmr the faulty 3-phase IM stator voltage equations are obtained similar to the balanced 3-phase IM stator voltage equations. As a result, av, bv, cv and dv can be considered as: av cos mr , bv ( cv sin mr , d v ( Lds Lr M q M d2 M q Lqs Lr M d M d M q2 Lds Lr M q M d2 M q Lqs Lr M d M d M q2 ) sin mr (19) ) cos mr Based on (19) and by considering (Md/Mq)2=Lds/Lqs the proposed transformation matrix for stator voltage variables is obtained as (20) (in 3-phase IM under open-phase fault: Mq=√3/2Lms, Md=3/2Lms, Lqs=Lls+1/2Lms, Lds=Lls+3/2Lms, Lms˃˃Lls therefore the assumption Lqs/Lds=(Mq/Md)2 is valid). (17) TABLE IV THE COMPARISON BETWEEN CONVENTIONAL AND PROPOSED VECTOR CONTROL METHODS 3 to 2 or 2 to 2 transformation for the stator currents based on [1], [4] Rotational transformation matrix for the stator currents based on (11), [1] Conventional controller Proposed controller 1 1 1 ias idss 2 2 2 i s 3 3 bs 3 iqs 0 ics 2 2 idss 2 1 1 ias s 2 1 1 ibs iqs idsmr cos mr mr iqs sin mr Inverse of transformation matrix for the stator voltages based on (20) vdss cos mr s vqs sin mr Stator self and mutual inductance based on Table 2, Table 3 Ls Lls Stator resistance based on Table 3 sin mr idss cos mr iqss sin mr vdsmr cos mr vqsmr 3 3 Lms , M Lms 2 2 rs Md cos mr idsmr M q mr iqs M d sin mr Mq cos mr vdss s M q sin mr vqs M d sin mr s i dss cos mr iqs sin mr mr vds Mq cos mr vqsmr Md 1 3 Lms , M q Lms 2 2 rs M q2 rs M d2 2 rs 2 M d2 3 Lqs Lls Extra terms in the stator voltage equations based on Table 3 -------------------- assuming that, av bv .Z 5 . cot mr , cv d v .Z 5 . tan mr M q2 Lqs Lr Z5 Lds M q M d M q Md Lr (20) (18) It is expected using (20), the stator voltage equations of faulty motor in the rotating reference frame becomes similar to 6Journal of Power Electronics, Vol. ??, No. ?, Month Year the healthy 3-phase IMs stator voltage equations. The comparison between equations of stator voltages for healthy and faulty 3-phase IM is given in Table 3. As can be seen from Table 3, the structures of stator voltage equations for healthy and faulty 3-phase IMs are similar; the difference is in the parameters (rs→rsMq2+rsMd2/2Md2, M→Mq and Ls→Lqs). It is also noted that the stator voltage equations of faulty machine contain the extra terms: vdset ( v qset ( rs M q2 rs M d2 2 M d2 rs M q2 rs M d2 2 M d2 )(cos 2 mr idsmr sin 2 mr iqsmr ) (21) )( sin 2 mr idsmr cos 2 mr iqsmr ) (22) In summary the comparison between equations of RFOC of faulty 3-phase IM using the proposed method and the equations of RFOC for healthy 3-phase IM is summarized in Table 4. Finally, based on Table 2, Table 3 and Table 4, the proposed vector control of 3-phase IM under normal and open-phase fault conditions can be constructed as shown in Fig. 3. In this figure, the blue blocks show the required modifications needed to the conventional vector control so that it can be applied to link voltage. The reason of using M-File instead of using the IM model from SimPowerSystem provided with MATLAB is that the neutral point of the IM in SimPowerSystem is not accessible and hence cannot be used to model the faulty IM applied in this work. The parameters of simulated IM are listed in Appendix. The fourth order Runge-Kutta algorithm has been used to solve the healthy and faulty IM equations. Fig. 4 shows the results obtained from the simulation of a 3-phase IM which is directly connected to a balanced 3-phase power supply. From t=0s to t=10s, the IM runs in healthy mode and the motor is modeled using a healthy 3-phase IM equations. At t= 10s, an open-phase fault is introduced in phase “c” and hence for t 10s the motor is simulated using the faulty machine equations as given by (1)-(6). As can be seen from Fig. 4, a significant amount of oscillation in the torque, and hence speed, appears right after the open-phase fault is introduced. The oscillation in the torque is due to the unbalanced structure of the IM, mainly in its d and q inductances. Due to the connection between the neutral point of the stator and the neutral point of the supply, independent currents flow in the remaining phases as can be seen from Fig. 3. Block diagram of the proposed IRFOC for star-connected 3-phase IM under normal and open-phase fault conditions. the faulty 3-phase IM. IV. SIMULATION RESULTS To show the dynamic behavior of 3-phase IM under open-phase fault, simulations are conducted by using MATLAB (M-File) software. The model of the faulty IM (equations (1)-(6)) assumes a connection between the neutral of the star connected IM machine and the mid-point of the DC Figure 4(d). Preperation of Papers for Journal of Power Electronics7 (a) (d) (b) (e) (c) (f) Fig. 4. Simulation results of dynamic behavior of 3-phase IM under normal and open-phase fault operating conditions; (a): Stator a-axis current, (b): Stator b-axis current, (c): Zoom of stator b-axis current, (d): Zoom of stator currents, (e): Speed, (f): Torque. 8Journal of Power Electronics, Vol. ??, No. ?, Month Year V. EXPERIMENTAL RESULTS To study on the performance of the conventional and proposed methods for vector control of healthy and faulty 3-phase IM, a prototype implementation of a star-connected 3-phase IM drive was carried out. Experimental tests were carried out based on Fig. 3. The scheme used for the experimental setup is shown in Fig. 5. Fig. 5. Scheme used for experimental setup. This paper investigates the use of the scheme in Fig. 5 for feeding a 3-phase IM under open-phase fault. Two large capacitors are connected in series between the positive and negative rail of the DC link voltage in order to create a mid-point DC link voltage. When an open-phase fault occur in one of the phases, the remaining two phases can only be controlled independently if the neutral point of the IM is connected to mid-point of the DC link (as indicated in Fig. 5). During healthy mode operation, the 3-phase machine is fed with PWM voltage generated by the FOC controller. In healthy Fig. 6. Photograph of the experimental system. mode, the stator current that flows in the neutral wire is very small, which is only due to the PWM operation of the inverter [21]. This paper considers the use of the simple topology shown in Fig.5; it should be emphasized that the focused is not on the topology but on the analysis, design and implementation of the vector control strategy based FOC for a star-connected 3-phase IM drive under open-phase fault. A photograph of the developed experimental rig is shown in Fig. 6 where the 3-phase IM is supplied by a 3-phase IGBT Voltage Source Inverter (VSI). To emulate the fault condition, an electronic switch is connected in series with phase “c” and it is opened under faulty condition. The torque transient is expected to cause due to the high di/dt in phase “c” where it is cut-off. The high di/dt causes large induced voltage across the inductances and subsequently high voltage across the switches. To prevent large induced voltages due to the high di/dt at the instant of the fault, the phase can be opened at a zero crossing as used in [21]. However, in practice an open phase fault can occur at any time (and at any current level) and as a result an electrical arc will temporarily present at the instant of an open phase fault. It is not the scope of this paper to suppress this high voltage transient. In the experimental, a simple RC snubber circuits are employed for high voltage protection.A DC voltage of 240V is used for the DC link and two Hall effect sensors and an incremental encoder are used to measure the stator phase currents and rotor speed respectively. An open-phase fault is introduced in phase “c” of the stator windings therefore, the two sensors are placed in phase “a” and “b” (in practice three sensors should be used since the faulty phase is not known).The code is automatically generated using MATLAB/SIMULINK and downloaded to dSPACE DS1104 real-time R&D Controller Board. To generate the PWM signals, a sinusoidal PWM method with a switching frequency of 10kHz with a dead time of 2μs is used. The sampling time of the control algorithm is 200μs. The conventional and proposed control strategies for both healthy and faulty 3-phase IMs, are individually tested under the same conditions and experimental setup to obtain proper comparison results (the conventional IRFOC method based voltage controller is fully discussed in [22]). The parameters for the star-connected 3-phase IM are given in Appendix. In order to verify the proposed fault-tolerant control strategy, several experiments are conducted as follows. A: No-load condition To confirm the effectiveness of the proposed control strategy under no-load condition, two tests were performed. In the first test (Fig. 7), the 3-phase IM is started under normal condition and then a phase cut-off is applied at 20.3s. In the second test (Fig. 8), the 3-phase IM started under normal condition and then a phase cut-off is applied at 21.4s. In the first test, conventional FOC is applied throughout the duration, however Preperation of Papers for Journal of Power Electronics9 for the second test, the proposed FOC (as outline in Table 4) is applied immediately after the fault (instantaneous fault detection is assumed; the fault detection in this paper is based on comparison between real speed and reference speed). In Fig. 7 and Fig. 8 the reference speed during open-phase fault is changed from 55rad/s to 60rad/s. Moreover, the reference rotor flux is kept constant at the nominal value of 1Wb. Throughout the experiment, the torque during the healthy and faulty conditions is estimated based on equations given in Table 2. As shown in Fig. 7 and Fig. 8, during fault condition, the proposed algorithm exhibits a good tracking error performances and faster response when compared to the conventional FOC. As can be seen from Fig. 8, the proposed FOC method produces smaller torque and speed ripples compared to the conventional FOC method (Fig. 7). From the zoomed torque response of Fig. 7 and Fig. 8 it can be seen that the ripple of the conventional technique is almost 4N.m, whereas for the proposed FOC, the ripple is around 2N.m (in this test the ripple of the FOC technique for healthy machine is almost 0.6N.m). Also, it is noted that using the proposed controller, the time to reach steady-state is shorter than conventional controller. As shown, the time to reach steady-state using conventional controller is about 2.5s whereas the time to reach steady-state using proposed controller is about 2s. It can be seen that in comparison with proposed controller, the conventional controller is not able to provide such a desired performance due to the unbalance structure of the faulty IM. Notice that although both conventional and proposed schemes are able to almost control star-connected 3-phase IM, in general, the proposed vector control drive system provides 10Journal of Power Electronics, Vol. ??, No. ?, Month Year Fig. 7. Experimental results of the conventional IRFO controller from top to bottom: Stator a-axis current, Zoom of stator a-axis current, Stator c-axis current, Speed, Zoom of speed, Torque, Zoom of torque. Preperation of Papers for Journal of Power Electronics11 Fig. 8. Experimental results of the proposed IRFO controller from top to bottom: Stator a-axis current, Zoom of stator a-axis current, Stator c-axis current, Speed, Zoom of speed, Torque, Zoom of torque. faster response and better steady-state performance especially in decreasing the speed and torque oscillations. 12Journal of Power Electronics, Vol. ??, No. ?, Month Year B: Load condition Fig. 9 shows the experimental results of the proposed FOC applied to the open-phase fault IM under loaded condition. The motor is operated at a steady speed of 55rad/s and a step load torque of 1.5N.m applied at 29s (the limitation of the maximum permissible torque for star-connected 3-phase IM during open-phase fault is about 38% of the rated torque [23]). Fig. 9(a) shows the reference and the actual (measured) rotor speed signals and Fig. 9(b) shows the applied load step and torque response. As can be seen from Fig. 9, the torque of faulty machine increases accordingly to applied load disturbance. Moreover, after a slight disturbance, the speed recovered to the reference speed of 55rad/s. With the proposed FOC controller, the torque oscillation of faulty machine of about 2N.m is recorded before and after the load disturbance is introduced. It can be seen that the rotor speed signal closely follows the reference speed before and after the load disturbance. significantly affect the accuracy of the proposed RFOC method and hence, the dynamics of the drive system. In this work, the gains of the PI controllers during healthy and faulty conditions are obtained based on trial-and-error process. A further investigation on the optimum selection of the gains for the PI controllers has to be carried out to improve the performance of the open-phase fault IM. VI. CONCLUSION This paper has presented a fault-tolerant control strategy based on FOC for a high performance vector control of star-connected 3-phase IM drive. It is shown that with some modifications, it is possible to apply conventional FOC algorithm to 3-phase IMs under open-phase fault. The proposed fault-tolerant control method is based on transformation matrices which are used to obtain a model of faulty IM with balanced structure. The proposed FOC of faulty 3-phase IM drive under open-phase fault can also be applied to a single-phase IM with two windings (main and auxiliary windings). In comparison with conventional FOC, the modified FOC algorithm has managed to reduce the torque and speed oscillation and at the same has improved the dynamic response. Experiments are used to validate the effectiveness of the proposed controller. APPENDIX (a) Ratings and parameters of 3-phase IM: Power: 1.5kW, V=400V, f=50Hz, poles=4, rs=5.5Ω, rr=4.51Ω, M=0.292H, Ls=Lr=0.3065H, J=0.0086kg.m2 REFERENCES [1] [2] [3] (b) Fig. 9. Experimental results of the proposed IRFO controller during load condition; (a): Speed, (b): Torque. [4] In this paper, the vector control of star-connected 3-phase IM under open-phase fault is implemented with some minor changes to the conventional FOC strategy. These changes are: transformation matrices, motor parameters and PI controller coefficients. It should be noted that PI controller coefficients [5] [6] M. Jannati et. al., “A New Method for Modeling and Vector Control of Unbalanced Induction Motors,” in Energy Conversion Congress and Exposition (ECCE), pp. 3625-3632, Sep. 2012. M. Jannati et. al., “A new method for RFOC of Induction Motor under open-phase fault,” in 39th Annual Conference on IEEE Industrial Electronics Society, IECON 2013, pp. 2530-2535, Nov. 2013. A. Sayed-Ahmed and N. A. Demerdash, “Fault-tolerant operation of delta-connected scalar-and vector-controlled AC motor drives,” IEEE Transactions on Power Electronics, Vol. 27, No. 6, pp. 3041-3049, Jun. 2012. Z. Yifan and T. A. Lipo, “An approach to modeling and field-oriented control of a three phase induction machine with structural imbalance,” in Proc. APEC, San Jose, TX, pp. 380-386, Mar. 1996. M. E. H. Benbouzid et. al., “Advanced fault-tolerant control of induction-motor drives for EV/HEV traction applications: From conventional to modern and intelligent control techniques,” IEEE Transactions on Vehicular Technology, Vol. 56, No. 2, pp. 519-528, Mar. 2007. D. Kastha and A. K. Majumdar, “An improved starting strategy for voltage-source inverter fed three-phase Preperation of Papers for Journal of Power Electronics13 [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] induction motor drives under inverter fault conditions,” IEEE Transactions on Power Electronics, Vol. 15, No. 4, pp. 726-732, Jul. 2000. F. Zidani et. al., “A fuzzy-based approach for the diagnosis of fault modes in a voltage-fed PWM inverter induction motor drive,” IEEE Transactions on Industrial Electronics, Vol. 55, No. 2, pp. 586-593, Feb. 2008. A. Raisemche et. al., “Two Active Fault Tolerant Control Schemes of Induction Motor Drive in EV or HEV,” IEEE Transactions on Vehicular Technology, Vol. 63, No. 1, pp. 19-29, Jan. 2014. C. C. Yeh and N. A. Demerdash, “Fault-Tolerant Soft Starter Control of Induction Motors With Reduced Transient Torque Pulsations,” IEEE Transactions on Energy Conversion, Vol. 24, No. 4, pp. 848-859, Dec. 2009. Z. Liu et. al., “Online rotor mixed fault diagnosis way based on spectrum analysis of instantaneous power in squirrel cage induction motors,” IEEE Transactions on Energy Conversion, Vol. 19, No. 3, pp. 485-490, Sep. 2004. J. Faiz et. al., “EMD-Based Analysis of Industrial Induction Motors with Broken Rotor Bar for Identification of Operating Point at Different Supply Modes,” IEEE Transactions on Industrial Informatics, Vol. 10, No. 2, pp. 957-966, May 2014. H. Niemann and J. Stoustrup, “Passive fault tolerant control of a double inverted pendulum–A case study,” Control Engineering Practice, Vol. 13, No. 8, pp. 1047-1059, Aug. 2005. R. Oubellil and M. Boukhnifer, “Passive fault tolerant control design of energy management system for electric vehicle,” in 23rd International Symposium on Industrial Electronics (ISIE), pp. 1402-1408, Jun. 2014. M. Salehifar et. al., “FPGA Based Robust Open Transistor Fault Diagnosis and Fault Tolerant Sliding Mode Control of Five-Phase PM Motor Drives,” Journal of Power Electronics, Vol. 15, No. 1, pp. 131-145, Jan. 2015. H. Guzman et. al., “Speed Control of Five-Phase Induction Motors with Integrated Open-Phase Fault Operation using Model-Based Predictive Current Control Techniques,” IEEE Transactions on Industrial Electronics, Vol. 61, No. 9, pp. 4474-4484, Sep. 2014. H. M. Ryu et. al., “Synchronous-frame current control of multiphase synchronous motor under asymmetric fault condition due to open phases,” IEEE Transactions on Industry Applications, Vol. 42, No. 4, pp. 1062-1070, Jul./Aug. 2006. A. Gaeta et. al., “Modeling and control of three-phase PMSMs under open-phase fault,” IEEE Transactions on Industry Applications, Vol. 49, No. 1, pp. 74-83, Jan./Feb. 2013. D. K. Kastha and B. K. Bose, “Fault mode single-phase operation of a variable frequency induction motor drive and improvement of pulsating torque characteristics,” IEEE Transactions on Industrial Electronics, Vol. 41, No. 4, pp. 426-433, Aug. 1994. D. K. Kastha and B. K. Bose, “On-line search based pulsating torque compensation of a fault mode single-phase variable frequency induction motor drive,” IEEE Transactions on Industry Applications, Vol. 31, No. 4, pp. 802-811, Jul./Aug. 2005. A. Sayed-Ahmed et. al., “Fault-tolerant technique for Δ-connected AC-motor drives,” IEEE Transactions on Energy Conversion, Vol. 26, No. 2, pp. 646-653, Jun. 2011. [21] T. H. Liu et. al., “A strategy for improving reliability of field-oriented controlled induction motor drives,” IEEE Transactions on Industry Applications, Vol. 29, No. 5, pp. 910-918, Sep. 1993. [22] P. Vas, Vector Control of AC Machines, Clarendon press Oxford, 1990. [23] A. Saleh et. al., “Fault tolerant field oriented control of the induction motor for loss of one inverter phase,” in 32nd Annual Conference on IEEE Industrial Electronics, pp. 817-822, Nov. 2006. Mohammad Jannati received the B.Sc. degree in electrical engineering from the University of Mazandaran, Iran, in 2008, the M.Sc. degree in electrical engineering from the University of Guilan, Iran, in 2010, and is currently pursuing the Ph.D. degree in electrical engineering at the Universiti Teknologi Malaysia, Malaysia. His research interests include the control of AC drives. Nik Rumzi Nik Idris received the B.Eng. degree in Electrical Engineering from the University of Wollongong, Australia, the M.Sc. degree in power electronics from Bradford University, West Yorkshire, U.K., and the Ph.D. degree from Universiti Teknologi Malaysia (UTM) in 1989, 1993, and 2000, respectively. He is an Associate Professor at the Universiti Teknologi Malaysia, and currently the Chair for the Power Electronics Chapter of IEEE Malaysia Section. His research interests include control of ac drive systems and DSP applications in power electronic systems. Mohd Junaidi Abdul Aziz was born in Kuala Terengganu, Malaysia, in 1979. He received his B.S. and M.S. in Electrical Engineering from the Universiti Teknologi Malaysia (UTM), Malaysia, in 2000 and 2002, respectively, and his Ph.D. in Electrical Engineering from The University of Nottingham, U.K, in 2008. Since 2008, he has been with the Faculty of Electrical Engineering, Universiti Teknologi Malaysia (UTM), Malaysia, where he is currently a Senior Lecturer. His research interests include power electronics and electric vehicles with a special focus on battery management systems.