IN RECENT years, direct torque control (DTC) strategies

358 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 7, JULY 013 DTC Scheme for a Four-Switch Inverter-Fed Induction Motor Emulating the Six-Switch Inverter Operation Bassem El Badsi, Badii Bouzidi, and Ahmed Masmoudi Abstract This paper proposes a novel direct torque control (DTC) strategy for induction motor (IM) drives fed by a fourswitch three-phase inverter (FSTPI). The introduced strategy is based on the emulation of the operation of the conventional sixswitch three-phase inverter (SSTPI). This has been achieved thanks to a suitable combination of the four unbalanced voltage vectors intrinsically generated by the FSTPI, leading to the synthesis of the six balanced voltage vectors of the SSTPI. This approach has been adopted in the design of the vector selection table of the proposed DTC strategy which considers a subdivision of the Clarke plane into six sectors. Simulation results have revealed that, thanks to the proposed DTC strategy, FSTPI-fed IM drives exhibit interesting performance. These have been experimentally validated and compared to the ones yielded by the Takahashi and the basic DTC strategies dedicated to the SSTPI and to the FSTPI, respectively. Index Terms Balanced voltage vectors, direct torque control (DTC), four-switch/six-switch three-phase inverter (FSTPI/SSTPI), induction motor (IM) drive, vector selection table. I. INTRODUCTION IN RECENT years, direct torque control (DTC) strategies of induction motor (IM) drives have been widely implemented in industrial variable speed applications. Introduced in the middle of the 1980s, the first DTC strategy involves a simple control scheme which makes it possible rapid real-time implementation [1]. Since then, several investigations carried out in order to improve the performance of the original DTC strategy. The major focused features are the uncontrolled switching frequency of the inverter and the high torque ripple resulting from the use of flux and torque hysteresis controllers. Currently and more than two decades of investigation, several DTC strategies have been proposed so far [] [5]. These could be classified within four major categories: 1) strategies considering variable hysteresis band controllers []; ) strategies with space vector modulation (SVM)-based control of the switching frequency [7], [8]; 3) strategies using predictive control schemes [9] [11]; and 4) strategies built around intelligent control approaches [1], [13]. Nevertheless, the gained performance is allied to significant increase of implementation schemes. Commonly, the voltage source inverter (VSI) feeding IM under DTC is the six-switch three-phase inverter (SSTPI). This said, some applications such as electric and hybrid propulsion systems, should be as reliable as possible. Within this requirement, the reconfiguration of the SSTPI into a four-switch threephase inverter (FSTPI), in case of a switch/leg failure, is currently given an increasing attention [14] [1]. A DTC strategy dedicated to FSTPI-fed IM drives has been proposed in [17]. In spite of its simplicity, this strategy is penalized by the low dynamic and the high ripple of the torque. These drawbacks are due to the application of unbalanced voltage vectors to control flux and torque with a subdivision of the Clarke plane limited to four sectors. Recently, an attempt to discard the previously described disadvantages has been proposed in [18] where a DTC scheme using a 1-sector vector selection table has been implemented. Nevertheless, it has been noted that the drive performance remains relatively low due to the increase of the CPU time which is linked to the complexity of the involved vector selection table. In order to achieve a constant switching frequency and to decrease the torque ripple, many DTC schemes based on SVM, using the FSTPI as a VSI, dedicated to control induction and permanent-magnet synchronous motors have been reported in the literature [19], [0]. These strategies offer high performance in terms of torque ripple reduction allied to the control of the inverter switching losses. However, these performances are compromised by the complexity of their implementation schemes. This paper proposes a new DTC strategy dedicated to FSTPIfed IM drives. It is based on the emulation of the SSTPI operation thanks to the synthesis of an appropriate vector selection table, which is addressed by hysteresis controllers. The resulting simplicity of the implementation scheme makes the strategy very attractive in many applications, such as the automotive one. Manuscript received April 13, 01; revised June 5, 01; accepted October, 01. Date of current version December 4, 01. The work was supported by the Allison Transmission Division of General Motors, Indianapolis, IN. Recommended for publication by Associate Editor P. Chi-Kwong Luk. The authors are with the Department of Electromechanical Engineering, Sfax Engineering School, University of Sfax, 309 Sfax, Tunisia (e-mail: bassemelbedsi@yahoo.fr; badiibouzidi010@yahoo.fr; a.masmoudi@enis. rnu.tn). Digital Object Identifier 10.1109/TPEL.01.5449 II. DTC OF FSTPI-FED IM DRIVES: BACKGROUND A. DTC Basis DTC strategies allow a direct control of the motor variables through an appropriate selection of the inverter control signals, in order to fulfill the requirements as whether the stator flux and torque need to be increased, decreased, or maintained. These decisions are achieved according to the output c φ of the flux 0885-8993/$31.00 01 IEEE

EL BADSI et al.: DTC SCHEME FOR A FOUR-SWITCH INVERTER-FED INDUCTION MOTOR EMULATING 359 Inductio inductionn Motor motor i αs Ω m - i βs Torque Estimator Ω * m + φα s φβ s Speed Controlle r (PI) Φ s * Cl ar ke Tr ansform Stator Flux Estimator + Φ s - a c θ s Two-Level Flux Controller S V ector Selection Ta ble c φ Te * Te m Two-Level m + - Torque Controlle r Fig. 1. Implementation scheme of the DTC strategy dedicated to FSTPI-fed IM drives. b c τ S 1 Vdc Vdc o TABLE I SWITCHING STATES,STATOR PHASE VOLTAGES,THEIR Clarke COMPONENTS AND CORRESPONDING VOLTAGE VECTORS V 4 (01) (S 1 S ) V as V bs V cs V αs V βs V i (0 0) (1 0) (1 1) (0 1) II 3 0 3 3 0 3 β V 3 (11) V 4T s Ф s V 1T s V 3T s V T s I V 1 V V 3 V 4 ω + α hysteresis controller, the output c τ of the torque hysteresis controller, and the angular displacement θ s of the stator flux vector Φ s in the Clarke (αβ) plane. The dynamic of Φ s is governed by the stator voltage equation expressed in the stationary reference frame, as follows: d dt Φ s = V s r s I s (1) where V s, I s, and r s are the stator voltage vector, current vector, and resistance, respectively. Neglecting the voltage drop r s I s across the stator resistance, and taking into account that the voltage vector is constant in each sampling period T s,the variation of the stator flux vector turns to be proportional to the applied voltage vector. Maintaining the stator flux constant, the variation of the electromagnetic torque T em depends on the direction of the applied voltage vector, such that: M T em = N p l r l s M Φ s Φ s r sin δ () where Φ s r is the rotor flux vector referred to the stator, δ is the angular shift between the stator and rotor fluxes, N p is the pole pair number, and l s, l r, and M are the stator self-inductance, the rotor self-inductance, and the mutual inductance, respectively. The implementation scheme of the DTC strategy dedicated to a FSTPI-fed IM, shown in Fig. 1, has the same layout as the one of the basic DTC strategy initially proposed in [1], except that 1) the SSTPI inverter is reconfigured to a FSTPI. Such a reconfiguration is carried out by adding to the former three extra TRIACs with three fast acting fuses [1] [4], ) the three-level hysteresis controller in the torque loop is substituted by a two-level hysteresis controller. As will be depicted in Section III, this substitution is motivated by the fact that no zero voltage vector is involved in the proposed DTC scheme. Fig.. III V 1 (00) Unbalanced active voltage vectors generated by the FSTPI. IV V (10) B. Intrinsic Voltage Vectors of the FSTPI The FSTPI topology consists of a two-leg inverter as illustrated in Fig. 1. Two among the three phases of the motor are connected to the FSTPI legs, while the third one is connected to the middle point of the dc-bus voltage. Let us assume that the states of the four insulated-gate bipolar transistors (IGBTs) of the FSTPI are denoted by the binary variables S 1 to S 4, where the binary 1 corresponds to an ON state and the binary 0 indicates an OFF state. The IM stator voltages are expressed in terms of the states (S 1 and S )ofthe upper IGBTs, as follows: V 4 1 as V bs = V S 1 dc 4 1 S. (3) V cs 1 The Clarke transform applied to the stator voltages yields: [ ] Vαs = 1 1 1 V as V βs 3 V 0 3 3 bs (4) V cs Four combinations of the states of the upper IGBTs are characterized by four active voltage vectors (V 1 to V 4 )intheαβ plane, which are given in Table I. Fig. shows the four active voltage vectors represented in the αβ plane. These vectors have unbalanced amplitudes and are shifted by an angle of π. Indeed, vectors V 1 and V 3 have

3530 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 7, JULY 013 TABLE II VECTOR SELECTION TABLE OF THE BASIC DTC STRATEGY c φ +1 +1 1 1 c τ +1 1 +1 1 Sector I V 3 V V 4 V 1 Sector II V 4 V 3 V 1 V Sector III V 1 V 4 V V 3 Sector IV V V 1 V 3 V 4 an amplitude of /, while vectors V and V 4 have an amplitude of /. C. Limitations of the Basic DTC of a FSTPI-Fed IM The basic DTC of an IM fed by the FSTPI is based on the subdivision of the αβ plane into four sectors [17], limited by the four active voltage vectors as shown in Fig.. The vector selection table corresponding to the basic strategy is presented in Table II. Accounting for the symmetry of the four sectors, the following analysis of the torque and flux variations, will be limited to sector I, considering two cases: 1) the initial stator flux vector Φ s1 is held by vector V ; ) the initial stator flux vector Φ s1 is held by vector V 3. Equation (1) could be rewritten as follows: Φ i s = Φ s1 +(V i r s I s )T s (5) where V i (1 i 4) is the voltage vector generated by the FSTPI. Fig. 3 shows different phasor diagrams of (5), considering both cases previously cited with four scenarios selected from the vector selection table, for each. One can notice the following remarks which deal with the torque dynamic. 1) The application of voltage vectors V 1 or V 3 leads to a low torque dynamic if: a) Φ s1 is close to vector V due to the low amplitude of V 1 and V 3 [see Fig. 3(a1) and (a3)]; b) Φ s1 is close to vector V 3 due to the low angular shift of the flux vector [see Fig. 3(b1) and (b3)]. It is to be noted that the torque command c τ of the control combinations (c φ = 1, c τ =+1) corresponding to sector II and (c φ =+1, c τ =+1) corresponding to sector I could not be achieved by the application of vectors V 1 and V 3, respectively. ) The application of voltage vectors V or V 4 leads to a low torque dynamic if Φ s1 is close to vector V due to the low angular shift of the flux vector [see Fig. 3(a) and (a4)]. One can notice that the control combinations (c φ =+1, c τ =+1) corresponding to sector IV and (c φ = 1, c τ =+1) corresponding to sector I could not be achieved with the application of voltage vectors V and V 4, respectively. 3) The application of voltage vectors V or V 4 leads to a high torque dynamic if Φ s1 is located near vector V 3 [see Fig. 3(b) and (b4)]. Concerning the flux dynamic, one can notice the following. 1) High flux variations leading to overshoots or undershoots outside the flux hysteresis band with: a) the application of voltage vectors V 1 or V 3 if Φ s1 is close to vector V 3 [see Fig. 3(b1) and (b3)]; b) the application of voltage vectors V or V 4 if Φ s1 is close to vector V [see Fig. 3(a) and (a4)]. ) The flux command c φ is not achieved with the application of: a) vector V 1 in sector IV corresponding to the control combination (c φ =+1, c τ = 1) as illustrated in Fig. 3(a1); b) vector V in sector I corresponding to the control combination (c φ =+1, c τ = 1) as illustrated in Fig. 3(b); c) vector V 3 in sector I corresponding to the control combination (c φ =+1, c τ =+1) as illustrated in Fig. 3(a3); d) vector V 4 in sector II corresponding to the control combination (c φ =+1, c τ =+1) as illustrated in Fig. 3(b4). From the previous analysis, one can clearly notice that the basic DTC strategy presents different limitations. These could be eradicated considering the introduced DTC strategy which will be developed in the following section. III. PROPOSED DTC STRATEGY A. Approach to Generate Balanced Voltages by the FSTPI The proposed DTC strategy is based on the emulation of SSTPI operation by the FSTPI. This has been achieved through the generation of six balanced voltage vectors using the four intrinsic ones of the FSTPI. The generated vectors have the same amplitude and angular shift as those of the SSTPI. Basically, the active voltage vectors V k, with 1 k, yielded by the SSTPI have an amplitude V k equal to 3, where is the dc-bus voltage. For the same value of,the voltage vectors V i, with 1 i 4, generated by the FSTPI, present unbalanced amplitudes V i, such that: V 1 = V 3 = V dc = 1 V k V = V 4 = V () dc = 3 V k. Therefore, a dual application of the voltage vector V 1 (respectively, V 3 ) of the FSTPI, leads to the generation of the voltage vector V 11 (respectively, V 33 ), as shown in Fig. 4. It is to be noted that V 11 and V 33 are identical to two vectors among the six generated by the SSTPI. Now, let us call V ij the voltage vectors resulting from the sums of successive voltage vectors V i and V j, with 1 i 4 and 1 j 4. As far as the angular shift between two successive voltage vectors is equal to π, the amplitude V ij of vectors V ij can be expressed as follows: V ij = V i + V j = 1 + 1 = 3 = V k. (7)

EL BADSI et al.: DTC SCHEME FOR A FOUR-SWITCH INVERTER-FED INDUCTION MOTOR EMULATING 3531 Fig. 3. Phasor diagrams describing the evolution of the stator flux vector in the case where it is located in the limits of sector I. Legend: (a) initial flux vector Φ s1 held by the voltage vector V, (b) initial flux vector Φ s1 held by the voltage vector V 3. TABLE III Clarke COMPONENTS OF THE GENERATED VOLTAGE VECTORS V ij V 3 V 33 V 34 V 41 V 11 V 1 V 3 αs V dc 3 V βs 0 0 Fig. 4. Generation of the SSTPI active voltage vectors using the four unbalanced voltage ones of the FSTPI. One can notice that the voltage vectors V ij have the same amplitude as the ones generated by the SSTPI. Beyond the amplitude, the four generated vectors, named V 1, V 3, V 34, and V 41,as shown in Fig. 4, share the same phases with the four remaining active voltage vectors of the SSTPI. Table III summarizes the Clarke components of the six voltage vectors generated by the FSTPI considering the previously described approach. Following the generation of six balanced active voltage vectors (V 3, V 33, V 34, V 41, V 11, and V 1 ), the αβ plane turns to be subdivided into six symmetric sectors as illustrated in Fig. 4. Moreover, zero voltage vectors can be achieved through the application of two opposite intrinsic ones. The previously described approach represents a great control benefit so far as several DTC strategies implemented in SSTPIfed IM drives could be applied to FSTPI-fed IM ones. B. Vector Selection Table of the Proposed DTC Strategy The proposed DTC strategy is inspired from the earlier one introduced by Takahashi [1]. For the sake of reduction of the switching frequency as well as the torque ripple, the control combinations (c φ = ±1, c τ =0) are omitted using a two-level hysteresis controller in the torque loop. The synthesis of the vector selection table of the proposed DTC strategy is based on the approach described in the previous paragraph. Reaching this advanced step, one can wonder: how the control combinations (c φ = ±1, c τ = ±1) could be

353 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 7, JULY 013 Fig.. Control combinations (c φ, c τ ), desired voltage vectors per T s, equivalent voltage vectors during T s, and applied voltage vectors per T s. Fig. 5. Applied voltage vectors in the case where Φ s is located in sector I. achieved applying the generated balanced voltage vectors? To answer this question, the following approach has been adopted. 1) The application of V 1 (respectively, V 3 ) during two successive sampling periods T s allows the generation of V 11 (respectively, V 33 ), ) The application of two consecutive voltage vectors V i and V j during two successive sampling periods leads to the generation of V ij. As a result, the equivalent voltage vectors per sampling period T s generated by the FSTPI, considering the adopted approach, can be expressed as: V 11H = 1 V 11 = V 1 V 33H = 1 V 33 = V 3 (8) V ijh = 1 V ij where subscript H indicates the half of the corresponding voltage vector. In what follows, the synthesis of the vector selection table will be limited to sector I ( π θ s π ). In this case and as shown in Fig. 5, the following voltage vectors are applied during a sampling period, according to the corresponding control combinations: V 3 for (c φ =+1,c τ =+1) V 1H for (c φ =+1,c τ = 1) V 34H for (c φ = 1,c τ =+1) V 1 for (c φ = 1,c τ = 1). In order to emulate the operation of the SSTPI, each control combination (c φ, c τ ) should be maintained during two sampling periods T s, which yields the application of: V 33 for (c φ =+1,c τ =+1) V 3 then V 3 V 1 for (c φ =+1,c τ = 1) V 1 then V V 34 for (c φ = 1,c τ =+1) V 3 then V 4 V 11 for (c φ = 1,c τ = 1) V 1 then V 1. TABLE IV DESIRED VECTOR SELECTION TABLE c φ +1 +1 1 1 c τ +1 1 +1 1 Sector I V 3 V 1H V 34H V 1 Sector II V 34H V 3H V 41H V 1H Sector III V 41H V 3 V 1 V 3H Sector IV V 1 V 34H V 1H V 3 Sector V V 1H V 41H V 3H V 34H Sector VI V 3H V 1 V 3 V 41H TABLE V IMPLEMENTED VECTOR SELECTION TABLE c φ +1 +1 1 1 c τ +1 1 +1 1 Periods T s 1 st nd 1 st nd 1 st nd 1 st nd Sector I V 3 V 1 V V 3 V 4 V 1 Sector II V 3 V 4 V V 3 V 4 V 1 V 1 V Sector III V 4 V 1 V 3 V 1 V V 3 Sector IV V 1 V 3 V 4 V 1 V V 3 Sector V V 1 V V 4 V 1 V V 3 V 3 V 4 Sector VI V V 3 V 1 V 3 V 4 V 1 An illustration of the previously described control scenarios is provided in Fig.. An extension of the synthesis to the remaining sectors has led to the vector selection table given in Table IV. The inputs (c φ, c τ, and θ s ) of the vector selection table should be maintained during T s which yields the implemented vector selection table provided in Table V. It is to be noted that both intrinsic and compounded voltage vectors are involved in sectors I, III, IV, and VI, while in sectors II and V, only the compounded voltage vectors are applied. Thus, one can expect an increase of the switching frequency in sectors II and V, with respect to the one in the remaining sectors.

EL BADSI et al.: DTC SCHEME FOR A FOUR-SWITCH INVERTER-FED INDUCTION MOTOR EMULATING 3533 Stator Voltage V as (V) Stator Voltage V cs (V) Stator Currents (A) 300 00 100 0 100 00 300 300 00 100 0 100 00 300 1 0 1.84.8.88 (a).9.9.94.84.8.88 (b).9.9.94.84.8.88.9.9.94 Time (s) (c) Sectors Stator Flux (Wb) Torque (Nm) 5 4 3 1 1. 1.1 1 1 0.84.8.88.9 (d).9.94.84.8.88.9 (e).9.94.84.8.88.9.9.94 Time (s) (f) Fig. 7. Simulated steady-state variables yielded by the introduced DTC strategy for a reference speed Ω m =50rad/s and a load torque T l =1Nm. Legend: (a) stator a-phase voltage, (b) stator c-phase voltage, (c) stator phase currents, (d) sector succession described in the αβ plane, (e) stator flux amplitude and its reference, (f) electromagnetic torque. IV. SIMULATION-BASED INVESTIGATION OF PERFORMANCE OF THE DTC STRATEGY The ratings and parameters of the induction machine, used in the simulation as well as in the experimental study, are listed in Tables VII and VIII of the Appendix. The sampling period T s is equal to 100 μs, except for the flux and torque controllers as well as the function enabling the localization of Φ s in the αβ plane, where the sampling period is kept equal to T s. Considering the power invariant Clarke transformation, the amplitude of the reference stator flux is kept constant equal to 3 times its rated value. A bandwidth of the stator flux controller is equal to ±0.0 Wb which represents ±1.8% of the reference stator flux. A bandwidth of the electromagnetic torque controller is equal to ±0.04 Nm which represents ±1.% of the rated torque. For the sake of a safe operation of the inverter, the dc-bus voltage is limited to 400 V in both experimental tests and simulation works. Under this value of, it has been noticed that the maximum stator frequency is limited to 40 Hz (0.1 Hz/V) in the case of the SSTPI and to 0 Hz (0.05 Hz/V) in the case of the FSTPI. These ratio are directly linked to the amplitude of the applied voltage vectors. Indeed, the amplitude of the equivalent voltage vectors generated by the FSTPI is the half of the one of the voltage vectors generated by the SSTPI, as depicted in (8). Fig. 7 shows some features characterizing the steady-state operation of the IM under the control of the proposed DTC strategy, for a mechanical speed Ω m =50rad/s and a constant load torque T l =1Nm. Fig. 7(a) and (b) illustrates the waveforms of the stator phase voltages V as and V cs, respectively. Fig. 7(c) shows the stator phase currents. As can be noticed, the stator phase currents are almost balanced, although the stator phase voltage V cs has an amplitude lower than the one of V as. Fig. 7(d) (f) shows the sector succession, the stator flux, and the electromagnetic torque, respectively. The analysis of Fig. 7(e) with respect to Fig. 7(d) clearly highlights that a demagnetization appears at the beginning of each sector. For instance, if Φ s is located in the beginning of sector I, the corresponding control combination (c φ =+1, c τ =+1) is achieved by the application of the voltage vector V 3. This leads to a decrease of the stator flux due to the voltage drop. Such a phenomenon also occurs in the Takahashi DTC strategy implemented in SSTPI-fed IM drives [1]. Referring to Fig. 7(d), and (f), one can notice the increasing of the torque ripple frequency in sectors II and V. Indeed, during these sectors and as depicted in Table V, each control combination (c φ, c τ ) is achieved by the application of two different voltage vectors, yielding a compounded voltage vector. In order to highlight the appropriateness of the application of the compounded voltage vectors to achieve the corresponding control combinations, these have been kept unchanged during 4T s through the increase of the hysteresis bands of the torque and flux controllers. The resulting flux and torque responses are illustrated in Fig. 8 with Φ s located in sector I. Fig. 8(a) treats the case where the sequence of voltage vectors V 1 ;V is applied. One can notice an increase of the average value of the flux and a decrease of the torque one. This statement confirms the appropriateness of such a sequence to achieve the control combination (c φ =+1, c τ = 1) as synthesized in Table V. The same reasoning has been adopted in the case of the sequence of voltage vectors V 3 ;V 4. The obtained results are illustrated in Fig. 8(b) where a decrease of the average value of the flux and an increase of the torque one are noticed. Thus, the desired control combination (c φ = 1, c τ =+1) is achieved by the applied sequence.

3534 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 7, JULY 013 (a) (b) Fig. 8. Evolutions of the stator flux and the electromagnetic torque over four sampling periods in the case where Φ s is located in sector I. Legend: (a) application of the voltage vector sequence V 1 ;V ;V 1 ;V to achieve the control combination (c φ =+1, c τ = 1), (b) application of the voltage vector sequence V 3 ;V 4 ;V 3 ;V 4 to achieve the control combination (c φ = 1, c τ =+1). TABLE VI RATIO OF THE AMPLITUDES OF THE INFLUENT HARMONICS WITH RESPECT TO THE FUNDAMENTAL ONE i as Harmonic nd 3 rd 5 th nd 3 rd 5 th f s =.5Hz 8% 13.8% 9.5% 11% f s =0Hz 1% 13% 1.5% 7% 4% 8.5% i cs Fig. 9. Schematic block diagram of the developed experimental platform. V. EXPERIMENTAL VALIDATION For the sake of validation, the proposed DTC strategy has been implemented in a test bench built around a TMS30F40 DSP-based digital controller. A schematic block diagram of the experimental platform is shown in Fig. 9. The sampling period, the amplitude of the reference stator flux, the bandwidths of the controllers, and the dc-bus voltage have been kept the same as in the simulation corresponding to Fig. 7. The presented experimental results characterize the steady-state operation of the IM. A. Analysis of the Performance of the Proposed DTC Strategy In what follows is considered the operation of the IM under a low and a high values of the speed. The corresponding experimental results are presented in Fig. 10 with subscript 1 for Ω m =7rad/s (stator frequency f s =.5 Hz) and subscript for Ω m =rad/s (f s =0 Hz). The stator a-phase voltage V as and current i as are shown in Fig. 10(a). The stator c-phase voltage V cs and current i cs are shown in Fig. 10(c). From the waveforms of the stator phase voltages, one can notice the effect of the unbalanced capacitor voltages affecting the experimental results especially at high speeds. This effect is highlighted by the difference between the waveforms of i as and i cs. Obviously, this drawback does not affect simulation results as illustrated in Fig. 7. The harmonic spectra of i as and i cs are shown in Fig. 10(b) and (d), respectively. Under low-speed operation (f s =.5 Hz), the second and the third harmonics present higher amplitudes compared to the ones of the other ranks. While in the case of high-speed operation (f s =0 Hz), the second, the third, and the fifth harmonics present higher amplitudes compared to the ones of the other ranks. Table VI summarizes the ratio of the amplitudes of the influent harmonics to the fundamental one. B. Comparative Study In order to highlight the performance gained by the introduced DTC scheme, the resulting steady-state features are compared to the ones obtained following the implementation of the basic DTC strategy. Fig. 11 illustrates the waveforms of V as, i as, V cs, and i cs and the harmonic spectra of i as and i cs following the implementation of the proposed DTC strategy (subscript 1 ) and the basic DTC one (subscript ) for Ω m =50rad/s and T l =1Nm. The considered comparison criterion is the total harmonic distortion (THD) of currents i as and i cs, which is expressed as: THD = n 1 I n I 1 (9) where I 1 and I n are the amplitudes of the fundamental and the nth harmonic ranks of i as and i cs, with n =, 3, 5, and 7. From the analysis of Fig. 11(b) and (d), it has been found that the THD of i as is equal to 11% and 17.4% in the case of the proposed DTC strategy and the basic DTC one, respectively. While, the THD of i cs reaches 1.5% and 14.% in the case of the proposed DTC strategy and the basic DTC one, respectively. Now, let us consider the common-mode voltage which is defined as follows: V com = V ao + V bo + V co 3 (10)

EL BADSI et al.: DTC SCHEME FOR A FOUR-SWITCH INVERTER-FED INDUCTION MOTOR EMULATING 3535 Fig. 10. Steady-state experimental results under the proposed DTC strategy considering two values of the stator frequency f s. Legend 1: (subscript 1 ) Case of f s =.5 Hz and (subscript ) case of f s =0 Hz. Legend : (a) stator a-phase voltage V as (00 V/div) and current i as (0.5 A/div and 1 A/div), (b) harmonic spectrum of i as (10 db/div), (c) stator c-phase voltage V cs (00 V/div) and current i cs (0.5 A/div and 1 A/div), (d) harmonic spectrum of i cs (10 db/div). Fig. 11. Steady-state experimental results for a reference speed Ω m =50rad/s and a load torque T l =1Nm. Legend 1: (subscript 1 ) Case of the proposed DTC strategy and (subscript ) case of the basic DTC strategy. Legend : (a) stator a-phase voltage V as (00 V/div) and current i as (1 A/div), (b) harmonic spectrum of i as (10 db/div), (c) stator c-phase voltage V cs (00 V/div) and current i cs (1 A/div), (d) harmonic spectrum of i cs (10 db/div). where V ao, V bo, and V co denote the voltages between the inverter outputs to the middle point of the dc-bus. It is to be noted that V co is null in the case of the FSTPI. Fig. 1 shows the waveforms of V com in the case of the proposed DTC strategy [see Fig. 1(a)], in the case of the basic DTC strategy [see Fig. 1(b)] and in the case of the Takahashi DTC strategy [1] with the IM fed by a SSTPI [see Fig. 1(c)]. One can notice that V com is equal to 0 and ± 3 in the case of the FSTPI, while it is equal to ± and ± in the case of the SSTPI. The comparison study between the three DTC schemes is extended to the analysis of the sector succession, the stator flux amplitude, and locus in the αβ plane, and the electromagnetic torque. Fig. 13(a1), (b1), and (c1) illustrates the sector succession and the stator flux amplitude yielded by the proposed DTC strategy, the basic DTC scheme, and the Takahashi DTC one, respectively. Referring to Fig. 13(a1), it can be noticed that the proposed DTC strategy offers the lowest stator flux ripple which is confirmed by the locus described by the extremity of Φ s in the αβ plane shown in Fig. 13(a), (b), and (c). Fig. 13(a3), (b3), and (c3) illustrates the sector succession and the electromagnetic torque yielded by the proposed DTC strategy, the basic DTC scheme, and the Takahashi DTC one, respectively. One can clearly notice that the proposed DTC strategy exhibits a torque ripple which has the lowest amplitude and frequency. From Fig. 13(a3) and (c3), it is to be noted

353 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 7, JULY 013 Fig. 1. Steady-state experimental results corresponding to the common-mode voltage V com (100 V/div) for a reference speed Ω m =50rad/s and a load torque T l =1Nm. Legend: (a) Case of the proposed DTC strategy, (b) case of the basic DTC strategy, and (c) case of the Takahashi DTC strategy. Fig. 13. Steady-state experimental results for a reference speed Ω m =50rad/s and a load torque T l =1Nm. Legend 1: (a) Case of the proposed DTC strategy, (b) case of the basic DTC strategy, and (c) case of the TakahashiDTC strategy. Legend : (subscript 1 ) sector succession ( sectors/div) and stator flux amplitude (0. Wb/div), (subscript ) Φ s extremity-locus described in the αβ plane (0.5 Wb/div), and (subscript 3 ) sector succession ( sectors/div) and electromagnetic torque (1 Nm/div).

EL BADSI et al.: DTC SCHEME FOR A FOUR-SWITCH INVERTER-FED INDUCTION MOTOR EMULATING 3537 TABLE VII INDUCTION MACHINE RATINGS Power 0.37kW Efficiency 77% Voltage 30V/400V Current 1.7A/1A Torque.5N.m Stator flux (rms) 40mWb Speed 1380rpm Frequency 50Hz TABLE VIII INDUCTION MACHINE PARAMETERS r s =4.Ω l s = 984mH M = 914mH J =.5g.m r r =17.9Ω l r = 984mH N p = f=mn.m.s that the frequency of the torque ripple is lower in the case of the proposed DTC scheme than the one yielded by the Takahashi DTC strategy which is in full harmony with the approach adopted in the synthesis of the vector selection table treated in Section III-B. The high torque ripple noticed in Fig. 13(b3) during the sector commutations from I to II and from III to IV confirms the phasor analysis shown in Fig. 3. VI. CONCLUSION This paper dealt with a new DTC strategy dedicated to FSTPIfed IM drives. The proposed DTC strategy is based on the emulation of the operation of the conventional SSTPI. This has been achieved thanks to suitable combinations of the four unbalanced voltage vectors intrinsically generated by the FSTPI, leading to the synthesis of the six balanced voltage vectors yielded by the SSTPI. This approach has been adopted in the design of the vector selection table which is simply addressed by hysteresis controllers, considering a subdivision of the Clarke plane into six sectors. Simulation-based investigations of the IM steady-state features have revealed the high performance of the introduced DTC strategy. These performances have been the subject of an experimental validation along with a comparison against those yielded by Takahashi and the basic DTC strategies dedicated to the SSTPI and to the FSTPI, respectively. APPENDIX The ratings and parameters of the three-phase induction machine, considered in both simulation and experiments, are provided in Tables VII and VIII, respectively, at the top of the page. REFERENCES [1] I. Takahashi and T. 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3538 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 7, JULY 013 Bassem El Badsi received the B.S. degree in electromechanical engineering, and the M.S. and Ph.D. degrees both in electrical engineering from the Sfax Engineering School (SES), University of Sfax, Sfax, Tunisia, in 004, 005, and 009, respectively. Since 009, he has been an Associate Professor of power electronics and drives at SES. He is a member of the Research Unit on Renewable Energies and Electric Vehicles, University of Sfax. His major research interests include the analysis and the implementation of advanced control strategies in ac motor drives applied to automotive systems. Ahmed Masmoudi received the B.S. degree from Sfax Engineering School (SES), University of Sfax, Sfax, Tunisia, the Ph.D. degree from Pierre and Marie Curie University, Paris, France, and the Research Management Ability degree from SES in 1984, 1994, and 001, respectively, all in electrical engineering. In 1988, he joined the Tunisian University where he held different positions involved in both education and research activities. He is currently a Professor of electric power engineering at SES. He is the Manager of the Research Unit on Renewable Energies and Electric Vehicles, University of Sfax. His main research interests include the design of new topologies of ac machines allied to the implementation of advanced and efficient control strategies in drives and generators, applied to automotive as well as in renewable energy systems. Badii Bouzidi received the B.S. degree in electromechanical engineering, and the M.S. and Ph.D. degrees in electrical engineering from the Sfax Engineering School (SES), University of Sfax, Sfax, Tunisia, in 005, 00, and 011, respectively. He is currently an Associate Professor of power electronics and drives at the Department of Electromechanical Engineering, SES. He is a member of the Research Unit on Renewable Energies and Electric Vehicles, University of Sfax. His research interests include the analysis and the implementation of DTC strategies in ac motor drives applied to automotive systems.