# Direct torque control of 4 phase 8/6 switched reluctance motor drive for constant torque load

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2 186 S. Pratapgiri & P. Narsimha: Direct torque control turn-on and turn-off angles. But this method is limited to low speed region. DC proposed in [8] uses the concept of short pattern. But it has the disadvantage of requirement of new winding topology, which is expensive and also inconvenient. In [1, 2] a novel DC technique is applied to 3-phase 6/4 SRM in which the difference between conventional DC applied to ac machines and the new DC proposed to SRM has been elaborately discussed. DC of 3 phase SRM has been also presented in [3, 11] along with simulation results. he low speed and high speed operation of 6/4 SRM drive is observed in [7] using DC method. DC of 4 phase 8/6 SR motor is analyzed only in [6, 14]. his paper presents DC based 4 phase 8/6 SRM by selecting a suitable set of 8 Space voltage vectors. he DC of SRM drive is simulated for constant torque load to observe the steady state and transient performance of the drive. It is observed that the torque is maintained within the set hysteresis band. his paper with new set of space vectors shows a significant improvement in the torque performance of DC based SRM compared to the DC scheme shown in [3]. here is a considerable reduction in the torque ripple in the present study. he paper is organized as follows. Section 2 describes the mathematical equations of SRM and priniciple of DC. he block diagram of the DC based SRM is explained in Section 3. Simulation and analysis of results are presented in Section 4. Conclusions are presented in Section 5. S 1 D 1 S 1 D 1 S 1 D 1 V DC A V DC A V DC A S 2 S 2 S 2 (a) (b) (c) N=4 V 4 N=3 V 3 2 Direct torque controller V 2 Fig. 1: SRM phase voltage states. N=2 Fig. 1. SRM phase voltage states Ψ β he mathematical equations of DC [2] as applied to SRM are discussed as below he motor torque N=5 V output can 5 be found using the electromagnetic V 1 equation N=6 V 6 V 7 V 8 N=8 N=1 v = Ri + Fig. 2: Definition of SRM motor voltage vectors ifor DC dt able I Switching able of space voltage vectors N Ψ Q = 1 Q = 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 V 1 = V V V V V V V V Ψ 2 dψ(θ, i) 45, (1) dt where ψ(θ, i) is the nonlinear function of phase linkage as a function of rotor position θ and current i. Expanding the above N=7 equation, results in Eq. (2) hus the equation for the power flow can be written as di dθ v = Ri + + θ dt. (2) vi = Ri 2 di + i i dt Now the effective power flow Peff from the electric source can be defined as WJMS for contribution: Ψ 3 Fig. 3: Definition of α-β axis for motor voltage i) dθ + i ψ(θ, θ dt. (3) Ψ 1 Ψ 4 Ψ α

3 S2 S2 S2 S2 S 2 S 2 (a) (c) (a) (b) (c) World Journal of Modelling and Simulation, Vol. 8 (212) No. 3, (b) pp. 185-?? 187 Fig. 1: SRM phase voltage states. Fig. 1: SRM phase voltage states. Ψ β N=3 Ψ β N=4 V 3 N=3 N=2 V 4 N=4 N=2 N=5 V 5 N=5 N=6 V 6 V 5 V 4 V 6 V 7 N=6 N=7 V 3 V 2 V 8 V 1 V 7 N=8 N=7 V 2 V 8 P eff = ei, able I Switching able of space able voltage I vectors where e = (v Ri). Switching able of space voltage vectors hus in a differential N time dt, the 1 differential 2 3 electrical 4 energy 5 6 dw e transferred 7 8 from the source is given by N Ψ Q = 1 Q = 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 V 1 Ψ Q = 1 Q = V 1 Q = V 7 V 8 V 1 V 2 V 3 V 4 V 5 V 6 Q = V 6 Ψ Q = Q = 1 V 3 V 4 dw V 5 e = Veidt. 6 V 7 V 8 V 1 V 2 (4) Ψ Q = Q = V 2 Q = V 6 V 7 V 8 V 1 V 2 V 3 V 4 V 5 o find an expression for the motor Q = torque Vproduction, 6 V 7 Vthe 8 energy V 1 equation V 2 V 3 is written V 4 as V 5 3. Block diagram of DC 3. Block diagram of DC N=1 V 1 N=8 N=1 Fig. Fig. 2: 2. Definition Definitionof of SRM SRMmotor motor voltage voltage vectors vectors for for DC DC Fig. Fig. 3: Definition 3. Definition of α-β of axis - axis for for motor motor voltage voltage Fig. 2: Definition of SRM motor voltage vectors for DC Fig. 3: Definition of α-β axis for motor voltage Ψ 2 Ψ 3 Ψ 2 Ψ 3 dw e = dw m + dw f, (5) Fig. where 4 shows dw m the and block dw f diagram are the of differential the proposed mechanical DC based energy 4 phase and field 8/6 energy SRM drive. respectively. he he in field each energy phase Fig. 4 shows the block diagram of the proposed DC based 4 phase 8/6 SRM drive. he in each canis becalculated separated by into its constituent linkage computation components block. as shown he output in Eq. of (6) the linkage computation block is given phase to the is calculated α β block by where the linkage computation in 4 phases are block. converted he output into 2 of phases. the he linkage magnitude computation Ψ block s and angle is δ given of the to the vector α β block are calculated where the in 4 phases are converted into 2 phases. he magnitude s and angle δ of the vector are dw by vector calculation block. he vector magnitude Ψ s calculated f = W f and the motor torque calculated from the i motor di by θ=cons vector tan t + W f are then fed calculation θinto dθ i=cons block. tanhe t. vector magnitude Ψ (6) and torque hysteresis blocks, s together and with the motor the reference torque values calculated of from and torque. the motor he are hysteresis then fed blocks into outputs and the torque hysteresis and torque blocks, From together the consideration increase or decrease with the command reference of the stored Ψ values field of energy and it torque. can behe shown hysteresis that [13] : blocks outputs the and torque Q and Q depending on the current and torque magnitudes relative to the hysteresis increase bands. or decrease he switching command table Ψ Q and and asymmetrical Q depending on converter the current apply the and suitable torque voltage magnitudes vectors relative to to the SRM the hysteresis windings. bands. he dwswitching e = i table di and θ=cons asymmetrical tan t + i converter dθ apply i=cons the tan t suitable, voltage vectors to (7) i θ the SRM windings. dw f θ=cons tan t = i di θ=cons tan t. (8) i By substitution of Eq. (6) into Eq. (7) it can be found that he instantaneous torque is defined by dw m = i 45 dθ W f dθ. (9) θ θ = dw m dθ. (1) hus by substituting Eq. (1) into Eq. (9) the expression for the instantaneous torque production of an SR motor phase can be written as = i W f θ θ. (11) his is a rarely used variant of conventional torque equation. Due to saturation in the SR motor, the influence of the second term in Eq. (11) is negligible. herefore, by using this approximation, the following equation for torque production may be derived as Ψ 1 45 Ψ 4 Ψ 1 Ψ 4 Ψ α Ψ α WJMS for subscription:

4 188 S. Pratapgiri & P. Narsimha: Direct torque control i. (12) θ In SRM, unipolar drives are normally used and thus the current in a motor phase is always positive. Hence, from Eq. (12) the sign of the torque is directly related to the sign of ψ θ. In other words to produce a positive torque, the stator amplitude must increase relative to the rotor position, whereas to produce a negative torque the change in stator should decrease with respect to the rotor movement. A positive value of ψ ψ θ may be defined as acceleration, whereas a negative value of θ may be defined as deceleration [2]. Hence, a new SR motor control technique [2] is defined as follows: (i) he stator linkage vector of the motor is kept at constant amplitude. (ii) orque is controlled by accelerating or decelerating the stator vector. v 1 v 2 v 3 v 4 SRM ω i 1 i 2 i 3 Flux Linkage Computation Ψ 1 Ψ 2 Ψ 3 Ψ 4 α - β ransformation Ψα Ψ β Flux Vector Calculation Ψ S δ i 4 Ψ Q Flux Hysteresis v 1 u 1 Ψ ref v 2 v 3 Asymmetrical Converter u 2 u 3 Switching able Q orque Hysteresis ref v 4 u 4 N Sector Selection 4. Simulation and Results Fig. 4: 4. Block diagramof of DC based SRM drive he objective of control technique (i) is achieved similarly to the conventional DC applied to ac machines by selecting an appropriate Space voltage vector. As in conventional ac machine DC, the stator variation will have the same directional variation as the voltage vector and a change in amplitude that is proportional to the magnitude of the voltage and the time interval of application. he objective (ii) is also achieved similarly to the conventional ac motor DC because the torque is increased or decreased by acceleration or deceleration of the stator vector relative to the rotor movement [2]. he DC of 4 phase 8/6 SRM is modeled and simulated in MALAB /SIMULINK. Fig. 5 shows the simulation model of 8/6 SRM with direct torque controller. he model consists of 4 phase 8/6 SRM, asymmetrical converter, DC controller and PI Controller. In this simulation test, the motor reference is taken as.27 Wb and a load torque is taken as 4 Nm. he hysteresis bands were defined to be.2 Wb and.4 Nm for the linkage and torque respectively. he DC scheme is simulated by selecting the following set of 8 Space voltage able vectors. 1. Switching able of space voltage vectors V 1 = (-11), V 2 = (-1-111), VN 3 = (-11), 1V 4 = 2(1-1-11), Q = 1 V2 V3 V4 V5 V6 V7 V8 V1 V 5 = (1-1), V 6 = (11-1-1), Ψ Q = 1V 7 = (1-1), V 8 = (-111-1). Q = V7 V8 V1 V2 V3 V4 V5 V6 he performance of the DC Q based = 1 SRM V3 V4 drive V5 is analyzed V6 V7for V8 a constant V1 V2 load torque of 4 Nm at a Ψ reference speed of 8 rpm. Q = Actual Q = speed V6 is compared V7 V8with V1the V2 reference V3 speed V4 V5 and error is given to a PI controller. he output of PI controller is the reference torque. he maximum value of PI controller output is 8 Nm whenever the speed is less than the reference speed. When the speed reaches the reference value the PI controller output is equal to the load torque. Fig. 6(a) shows the total torque response over the entire simulation time. During acceleration period the torque is maintained at 8 Nm by following a WJMS for contribution:

6 19 S. Pratapgiri & P. Narsimha: Direct torque control 12 V 4 G11 _ref2 A1 G12 G21 A2 G22 B1 G31 B2 G32 C1 G41 C2 G42 V+ D1 V- D2 CONVERER L A1 A2 B1 B2 C1 C2 D1 D2 Switched Reluctance Motor m <Flux (V*s)> <I (A)> <e (N*m)> <w (rad/s)> <V (V)> K- <e (N*m)> Scope2 _ref 8 PI Discrete PI Controller.27 F_ref F_BH _cal _ref _BH MALAB Function MALAB Fcn MALAB Function pulses1 Alpha_ alpha mag _cal Clock t o Workspace Discrete, s = 1e-6 s. powergui alpha_cal Subsystem Beta_ beta_ angle Angle Sector beta_cal mag & angle Sector_Calculator Fig. 5. Simulation model of 4 phase 8/6 SRM with DC Fig. 5: Simulation model of 4 phase 8/6 SRM with DC given to the α β block where the in 4 phases are converted into 2 phases. he magnitude Ψ s and angle δ of the vector are calculated by vector calculation block. he vector magnitude Ψ s and the motor torque calculated from the motor are then fed into and torque hysteresis blocks, together with the reference values of and torque. he hysteresis blocks outputs the and torque increase or decrease command Ψ Q and Q depending on the current and torque magnitudes relative to the hysteresis bands. he switching table and asymmetrical converter apply the suitable voltage vectors to the SRM windings. 4 Simulation and results he DC of 4 phase 8/6 SRM is modeled and simulated in MALAB /SIMULINK. Fig. 5 shows the simulation model of 8/6 SRM with direct torque controller. he model consists of 4 phase 8/6 SRM, asym- WJMS for contribution:

7 World Journal of Modelling and Simulation, Vol. 8 (212) No. 3, pp. 185-?? 191 otaltorque (Nm) ime (Sec) (a) otaltorque (Nm) ime (Sec) (b) Flux Magnitude (Wb) Current (A) X:.3159 Y: Speed (rpm) ime (Sec) (c) X:.336 Y: 83.9 Fluxbeta ime (Sec) -.1 (d) ime (Sec) (e) Fluxalpha (f) Fig. 6. Simulation Fig. 6: waveforms Simulation waveforms DC based DC SRM based (a) SRM otal (a) torque otal torque (b) otal (b) otal torque torque in in steady steady state (c) Flux magnitude (d) (d) Phase currents (e) Speed (f) Flux vector trajectory Phase currents (e) Speed (f) Flux vector trajectory WJMS for subscription:

9 World Journal of Modelling and Simulation, Vol. 8 (212) No. 3, pp. 185-?? 193 [9] L.Venkatesha, V. Ramanarayanan. orque ripple minimisation in switched reluctance motor with optimal control of phase currents. in: Proceedings of the 1998 IEEE International Conference on Power Electronics Drives and Energy Systems, 2, 1998, [1]. Miller. Switched Reluctance Motors and their Control. Magna Physics & Oxford, [11] G. Song, Z. Li, et al. Direct torque control of switched reluctance motors. in: Proceedings of the 28 IEEE International Conference on Electrical Machines and Systems, ICEMS 28, 28, [12] P. Srinivas, P. Prasad. orque ripple minimization of 8/6 switched reluctance motor with fuzzy logic controller for constant dwell angles. in: Proceedings of the IEEE International Conference on Power Electronics Drives and Energy Systems, 21. [13] D. Staton, W. Soong,. Miller. Unified theory of torque production in switched reluctance and synchronous reluctance motors. IEEE ransactions on Industry Applications, 1995, 31: [14] M. Wang. Four phase switched reluctance motor direct torque control. in: Proceedings of the 211 IEEE international Conference on Measuring echnology and Mechatronics Automation, 211, [15] Z. Zhen, W. erry, C. Juan. Modeling and nonlinear control of a switched reluctance motor to minimize torque ripple. in: Proceedings of the 2 IEEE International Conference on Systems, Man and Cybernetics, vol. 5, 2, WJMS for subscription:

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