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Study and Simulation of Direct Torque Control (DTC) for a Six Phase Induction Machine (SPIM)

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Study and Simulation of Direct Torque Control (DTC) for a Six Phase Induction Machine (SPIM) INTERNATIONAL JOURNAL OF ENERGY, Issue 2, Vol. 7, 2013 Study and Simulation of Direct Torque Control (DTC) for a Six Phase Induction Machine (SPIM) Radhwane SADOUNI, Abdelkader MEROUFEL and Salim DJRIOU torque control is derived by the fact that, on the basis of the Abstract—This paper presents a performances study of a Direct errors between the reference and the estimated values of Torque and Flux Control (DTC) for a Six Phase Induction Machine torque and flux, it is possible to directly control the inverter (SPIM) dedicated to electrical drives using a two level voltage source states in order to reduce the torque and flux errors within the inverter (VSI). This method has become one of the high performance prefixed band limits [4], [5]. control strategies for AC machine to provide a very fast torque and flux control. The simulation results show the effectiveness of the This paper is organized in six sections. The SPIM model is proposed method in both dynamic and steady state response. presented in the next section. The control method by DTC will be discussed in section three and four. In the fifth and sixth Keywords— Six Phase Induction Machine (SPIM), Direct section we present the simulation results. Finally, a general Torque Control (DTC), Voltage Source Inverter (VSI), Hysteresis conclusion summaries this work. The simulation results are comparator. obtained by using Matlab/Simulink. I. INTRODUCTION II. SPIM MODEL HE power rating of an AC drive system can be increased by If A schematic of the stator and rotor windings for a using high phase order drive system (multiphase machine) T machine dual three phase is given in Fig. 1. The six stator which has more than three phases in the stator of the machine. phases are divided into two wyes-connected three phase sets High phase order drive systems possess several advantages labeled As1, Bs1, Cs1 and As2, Bs2, Cs2 whose magnetic over conventional three-phase drives, such as reducing the axes are displaced by an angle α=30°. The windings of each amplitude and increasing the frequency of torque pulsation, three phase set are uniformly distributed and have axes that reducing the rotor harmonic currents, reducing the current per are displaced 120° apart. The three phase rotor windings Ar, phase without increasing the voltage per phase, and lowering Br, Cr are also sinusoidally distributed and have axes that are the DC-Link current harmonics and high reliability. displaced apart by 120° [6], [7]. Otherwise, losing of one or more phases in a high phase order The following assumptions are made: [8], [9]: drive system does not prevent the machine from starting and -Motor windings are sinusoidally distributed; running [1]. -The two stars have same parameters; A common type of multiphase machine is the Six Phase -The magnetic saturation, the mutual leakage inductances Induction Machine (SPIM), also known as the dual star and the core losses are negligible; induction machine. This machine has been used in many Flux path is linear. applications where high reliability and high power is The voltage equations of the dual star induction machine are demanded such as aerospace applications, electric/hybrid as follow [10], [11]: vehicles, ship propulsion, rolling mills, cement mills, mine hoists … etc [1], [2]. Vsa1 d V Vsb1 R I The direct torque control (DTC) method was proposed in the s1 s1 s1 dt s1 middle of 1980 by I.Takahashi [3], this method has become Vsc1 one of the high performance control strategies for AC machine to provide a very fast torque and flux control. The name direct Vsa2 d (1) V Vsb2 R I s2 s2 s2 s2 R.Sadouni is with the Intelligent Control & Electrical Power Systems dt laboratory, Djillali Liabes University, Sidi Bel Abbes, Algeria. (E-mail: Vsc2 [email protected]). A.Meroufel is with the Intelligent Control & Electrical Power Systems Vra laboratory, Djillali Liabes University, Sidi Bel Abbes, Algeria. (E-mail: d 0 Vrb R I [email protected]). r r dt r S. DJRIOU is with Signals and systems laboratory, IGEE, M’hamed Vrc Bougara University, Boumerdes, Algeria. (E-mail: salimjr@yahoofr). 31 INTERNATIONAL JOURNAL OF ENERGY, Issue 2, Vol. 7, 2013 d Bs1 Vs1d Rs1Is1d Φs1d - ωsΦs1q dt Bs2 A r d Vs1q Rs1Is1q Φs1q ωs Φs1d As Br dt 2 As d Vs2d Rs2Is2d Φs2d ωs Φs2q 1 dt (6) d Vs2q Rs2Is2q Φs2q ωs Φs2d dt Cs dΦrd Cs 0 RrIrd ωsr Φrq 1 2 Cr dt dΦrq Fig. 1 Windings of the Six Phase Induction Machine 0 RrIrq ωsr Φrd dt The Park model of the dual star induction machine in the Where: references frame at the rotating field (d, q), is defined by the Rsa1 = Rsb1 = Rsc1 = Rs1: Stator resistance 1. following equations system (6) [6]. Rsa2 = Rsb2 = Rsc2 = Rs2: Stator resistance 2. The figure 2 represents the model of the SPIM in the Park Rra = Rrb = Rrc = Rr: Rotor resistance. frame. d Isa1 Isa2 Ira I Isb1 ; I Isb2 ; I Irb (2) is2d s1 s2 r Өr Isc1 Isc2 Irc Ar V A s2d s2 Ө Ө s1 is1d Φsa1 Φsa2 Φra As1 α (3) V s1 Φsb1 ;s2 Φsb2 ; r Φrb Өs2 s1d Φsc1 Φsc2 Φrc ird The expressions for stator and rotor flux are [10]: irq Vs1q is1qV s2q is2q [Φs1] [Ls1s1 ] [L s1s2] [L s1r] [Is1] (4) q [Φs2] [Ls2s1] [L s2s2] [L s2r] . [Is2] [Φr] [Lrs1] [L rs2] [L rr] [Ir] Fig. 2 Representation of SPIM in the Park frame Where: Where: [Ls1s1]: Inductance matrix of the star 1. [Ls2s2]: Inductance matrix of the star 2. [Lrr]: Inductance matrix of the rotor. s1d Ls1Is1d Lm (Is1d Is2d Ird) [Ls1s2]: Mutual inductance matrix between star 1and star 2. [Ls2s1]: Mutual inductance matrix between star 2and star 1. [Ls1r]: Mutual inductance matrix between star 1 and rotor. s1q Ls1Is1q Lm (Is1q Is2q Irq) [Ls2r]: Mutual inductance matrix between star 2 and rotor. [Lrs1]: Mutual inductance matrix between rotor and star 1. s2d Ls2Is2d L (Is1d Is2d Ird) [Lrs2]: Mutual inductance matrix between rotor and star 2. m (7) The expression of the electromagnetic torque is then as s2q Ls2Is2q L (Is1q Is2q Irq) follows [10],[12], [13]: m p d d rd LrIrd Lm (Is1d Is2d Ird) T .Is1 Ls1r.Ir Is2 Ls2rIr (5) em 2 dθ dθ rq r rq m s1q s2q rq L I L (I I I ) 32 INTERNATIONAL JOURNAL OF ENERGY, Issue 2, Vol. 7, 2013 Lm: Cyclic mutual inductance between stator 1, stator 2 and ccpl rotor. cflx The mechanical equation is given by: 1 1 dΩ J Tem Tr FrΩ (8) -ΔT 0 dt 0 -ΔØ ΔT s ΔØs With: -1 (b) Lm Tem p rd(Is1q Is2q) - rq(Is1d Is2d) (9) Lr Lm (a) F ig. 4 Hysteresis comparator, (a): three level hysteresis comparator III. DIRECT TORQUE CONTROL f or the torque, (b): two level hysteresis comparator for the flux The Direct Torque Control (DTC) method allows direct and For the stator flux vector laying in sector 1 (Fig.5), in order independent electromagnetic torque and flux control, selecting to increase its magnitude, the voltage vectors V1, V2, and V6 an optimal switching vector [14]. The Fig.3 shows a block can be selected. Conversely, a decrease can be obtained by diagram of the DTC scheme applied to the SPIM. The selecting V3, V4 and V5. However, to increase the reference values of flux (s*) and torque (Tem*) are electromagnetic torque the voltage vectors V2, V3 and V4 can compared to their actual values and the resultant errors are fed be selected and a decrease can be obtained by the vectors: V1, into a two level hysteresis comparator for the flux and three V5 and V6. level hysteresis comparator for the torque, who allows β controlling the motor in the two directions of rotation (Fig.4). E E - + - + isa1 isa2 Sa1 Sa2 Sb1 isb1 isb2 Sb2 V SPIM 3 V2 Øs(Te) V0 Sc1 isc2 Sc2 isc1 3 2 V4 V1 V7 Øso V5 V 4 1 6 α γ γ+ Δγ 5 6 Ør CONCORDIA Transformation Vsα1 Vsβ1 isα1 isβ1 Vsα2 Vsβ2 isα2 isβ2 Fig. 5 Voltage vector selection Flux and Torque Estimation ^ ^ ^ Øs1 Tem Øs2 The stator flux and the electromagnetic torque expression _ _ _ are given by [15]: * * + * Øs1 + Tem + Øs2 s (Te) Vs so (10) 1 1 1 0 0 0 -1 Tem Kc. s . r sin( ) (11) N1 cflx1 ccpl cflx2 N2 Kc: constant depending on the parameters of the machine. γ: Angle between the two vectors stator and rotor flux. Switching Table 1 Switching Table 2 The application of zero voltage vectors (V0 and V7) stops the rotation of the stator flux vector s. However, the rotor Fig. 3 Block diagram of Direct Torque Control for SPIM flux r continues its evolution and try to catch up the stator flux. Thus, the angle γ between stator and rotor flux will 33 INTERNATIONAL JOURNAL OF ENERGY, Issue 2, Vol. 7, 2013 decrease and the electromagnetic torque decreases slowly. 200 The switching table allows to select the appropriate inverter 150 switching state according to the state of hysteresis comparators of flux (cflx) and torque (ccpl) and the sector 100 where is the stator vector flux (s) in the plan (α, β), in order to maintain the magnitude of stator flux and electromagnetic 50 torque inside the hysteresis bands. The above consideration 0 allows construction of the switching table as presented in Table 1. (rad/s) Speed -50 Table 1: Switching table with zero voltage vectors -100 -150 -200 0 0.5 1 1.5 2 Time(s) 15 10 5 0 IV.
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