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


 Elvin Butler
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1 ISSN , England, UK World Journal of Modelling and Simulation Vol. 8 (212) No. 3, pp. 185?? Direct torque control of 4 phase 8/6 switched reluctance motor drive for constant torque load Srinivas Pratapgiri, Prasad Polaki Venkata Narsimha Department of Electrical Engg., University College of Engineering, Osmania University, Hyderabad 5155, India (Received January , Accepted January ) Abstract. he Switched Reluctance Motor (SRM) Drives have attracted the attention of many researchers in the recent past because of advantages like simple mechanical structure, adaptability to harsh environments like coal mining etc. But it has one main disadvantage of high torque ripple due to its double saliency structure. he Direct orque Control (DC) technique can minimize the torque ripple by regulating torque within specified hysteresis band. his paper presents the Direct orque Control of 4 phase 8/6 Switched Reluctance Motor fed through an asymmetrical converter. A four phase asymmetrical converter has total 81 Space voltage vectors. So like the conventional DC applied to ac motor, 8 Space voltage vectors are sufficient to apply DC technique to SRM. he Direct orque Control of SRM is simulated in MALAB/ SIMULINK for constant torque load. he performance of the drive mainly in terms of torque ripple is analyzed with new set of space vectors. Keywords: direct torque control, switched reluctance motor, torque ripple 1 Introduction Switched Reluctance Motor (SRM) has salient poles on both stator and rotor with concentrated winding on the stator and no winding on the rotor. As rotor does not have any winding, it can withstand high temperatures and can rotate at very high speeds. he SRM achieves high torque levels at low peak currents by using small air gaps. he SRM drives are inherently adjustable speed drives. SRM has attracted many researchers in the recent years because of the simple construction and low manufacturing cost. Because of the availability of low cost power electronic switches and fast computing motor specific controllers like Digital signal processors, the conventional variable AC/DC machines are now replaced by SRMs in applications like coal mining, electric vehicles, compressors, electric traction, washing machines etc. he main drawback of the motor is that it has highly nonlinear torqueposition characteristics and a torque ripple is high, which causes noise and vibrations [1]. Different techniques have been proposed in the past to minimize torque ripple. he most popular electronic method is based on the optimization of control principles, which include the supply voltage, turnon and turnoff angles of the converter and current levels. But this method has the disadvantage that it leads to reduction in the overall torque [5]. Venkatesha et al. in [9] proposed the torque ripple minimization by suitably profiling the phase currents. But the method is quite involved and the computation time required is high. he NeuroFuzzy control technique proposed by Henriques et al. in [4] adds a compensating signal to the PI controller. But the stability of this method depends on the selection of suitable value of the stopping time. orque ripple minimization of 8/6 SRM using fuzzy logic controller for constant dwell angles has been analyzed in [12]. Zhen et al. in [15] has reduced the ripples in torque by employing a torque controller and fuzzy logic controller. orque controller is used for limiting the phase current and fuzzy logic controller for adjusting the Corresponding author. el.: address: Published by World Academic Press, World Academic Union
2 186 S. Pratapgiri & P. Narsimha: Direct torque control turnon and turnoff 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 3phase 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 αβ 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 αβ of axis  axis for for motor motor voltage voltage Fig. 2: Definition of SRM motor voltage vectors for DC Fig. 3: Definition of αβ 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 = (1111), VN 3 = (11), 1V 4 = 2(1111), Q = 1 V2 V3 V4 V5 V6 V7 V8 V1 V 5 = (11), V 6 = (1111), Ψ Q = 1V 7 = (11), V 8 = (1111). 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:
5 World Journal of Modelling and Simulation, Vol. 8 (212) No. 3, pp. 185?? 189 Asymmetrical converter is popularly used for the SRM drives. Due to its structure, asymmetrical converters have more switching states than the conventional converters. As can be seen in Fig. 1, each motor phase can have three possible voltage states for a unidirectional current. Fig. 1 (a) shows that when both devices in converter are turned On. In this case positive voltage is applied to the motor phase. he voltage state for a given phase is defined as 1. When current is flowing and one device is turned Off, a zero voltage loop occurs and the state is defined as. his is shown in Fig. 1 (b). Fig. 1 (c) shows that when both devices are turned Off, the current freewheels through the diodes. In this case negative voltage is experienced by the motor phase and the state is defined as1. he 4 phase asymmetrical converter can have a total of 81 possible Space voltage vectors. However in order to apply DC to SRM, eight equal amplitude voltage vectors that are separated by π/4 radians are sufficient. he space voltage vector states are shown in Fig. 2. hese voltage state vectors are defined to lie in the center of eight zones N = 1, 2,, 8, where each zone has a width of π/4 radians. One of the eight possible states is chosen at any one time in order to keep the stator linkage and the motor torque within hysteresis bands. As in the conventional DC scheme, if the stator linkage lies in the kth zone, the magnitude of the can be increased by using the switching vectors V k+1 and V k 1 and can be decreased by using the vectors V k+2 and V k 2. Hence, whenever the stator linkage reaches its upper limit in the hysteresis band, it is reduced by applying voltage vectors which are directed toward the center of the vector space and viceversa. As detailed previously, the torque is controlled by an acceleration or deceleration of the stator relative to the rotor movement. Hence, if an increase in torque is required, voltage vectors that advance the stator linkage in the direction of rotation are selected. his corresponds to selection of vectors V k+1 and V k+2 for a stator linkage in the kth zone. If a decrease in torque is required, voltage vectors are applied which decelerate the stator linkage vector. his corresponds to the vectors V k 1 and V k 2 in the kth zone. Hence a switching table for controlling the stator linkage and motor torque can be defined as shown in ab. 1, where Ψ Q = 1 & Ψ Q = indicate increase and decrease in the linkages respectively and Q = 1 & Q = indicate increase and decrease in torque respectively. In order to resolve the individual phase vectors into a single stator linkage vector, the vectors for the four phase SRM are transformed onto a stationary orthogonal two axis reference frame [6] as shown in Fig. 3. ψ α = ψ 1 cos 45º ψ 2 cos 45º ψ 3 cos 45º + ψ 4 cos 45º, ψ β = ψ 1 sin 45º + ψ 2 sin 45º ψ 3 sin 45º ψ 4 sin 45º, [ ] ψ s = (ψ 2 α + ψ2 β ), δ = arctan ψβ. (13) ψ α where Ψ s is the vector, δ is the angle of the vector and Ψ 1, Ψ 2, Ψ 3, Ψ 4 are the linkages of the four phases. Specifications of SRM: Aligned Inductance 11 mh Unaligned Inductance 1 mh Stator Resistance.3 Inertia.82 Kg.m2 Friction.1 N.m.s Maximum Current 3 A Voltage 12 V Maximum Fluxlinkage.3 V.s 3 Block diagram of DC Fig. 4 shows the block diagram of the proposed DC based 4 phase 8/6 SRM drive. he in each phase is calculated by linkage computation block. he output of the linkage computation block is WJMS for subscription:
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 = 1e6 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:
8 192 S. Pratapgiri & P. Narsimha: Direct torque control metrical 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 vectors. V 1 = ( 11), V 2 = ( 1 111), V 3 = ( 11), V 4 = (1 1 11), V 5 = (1 1), V 6 = (11 1 1), V 7 = (1 1), V 8 = ( 111 1). he performance of the DC based SRM drive is analyzed for a constant load torque of 4 Nm at a reference speed of 8 rpm. Actual speed is compared with the reference speed 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 hysteresis band of.41 Nm till the steady state is reached. When the steady state is reached the torque developed by the motor is maintained at the load torque by following a hysteresis band of.41 Nm. hus the torque ripple is minimized in the steady state and during acceleration period. he calculated torque ripple is 1%. Fig. 6 (b) shows the total torque response in steady state. Fig. 6 (c) shows the magnitude of the vector. he total is maintained at.27 Wb by following a set hysteresis band of.2 Wb. he current waveforms of all the four phases in the steady state are shown in Fig. 6 (d). he maximum current and average current of each phase are 8.9 A and 4.13 A respectively. Fig. 6 (e) shows speed response. he steady state speed is maintained constant at 83 rpm. Fig. 6 (f) shows the trajectory of the vector. 5 Conclusions In this paper the control of 4 phase 8/6 SRM is analyzed with Direct orque Control technique. he torque is controlled directly through the control of magnitude of the linkage and the change in speed of the stator vector. he performance of direct torque controlled SRM drive is analyzed by selecting a suitable set of 8 Space voltage vectors for constant load torque. It is observed that torque is maintained within set hysteresis band of 1% of rated torque during acceleration and in the steady state. he torque ripple is 1% in the steady state. A further study can be made on the reduction of phase current variations by maintaining the torque and within their respective bands. References [1] A. Cheok, P. Hoon. A new torque control method for switched reluctance motor drives. in: 26th Anual conference of the IEEE Industrial Electronics Society, IECON 2, 2, [2] A. Cheok, Y. Fukuda. A new torque and control method for switched reluctance motor drives. IEEE ransactions on Power Electronics, 22, 17(4): [3] H. Guo. Considerations of direct torque control for switched reluctance motors. in: Proceedings of the 26 IEEE International Symposium on Industrial Electronics, ISIE, 26, [4] L. Henriques, L. Rolim, et al. orque ripple minimization of switched reluctance drive using a neurofuzzy compensation. IEEE ransactions on Magnetics, 2, 36(5): [5] I. Husain. Minimization of torque ripple in srm drives. IEEE ransactions on Industrial Electronics, 22, 49(1): [6] B. Jeong, K. Lee, et al. Direct torque control for the 4phase switched reluctance motor drives. in: Proceedings of the 25 IEEE International Conference on Electrical Machines and Systems, ICEMS 25, 25, [7] R. Jeyabharath, P. Veena, M. Rajaram. A novel DC strategy of torque and control for switched reluctance motor drive. in: International Conference on Power Electronics, Drives and Energy Systems, PEDES 6, 26, 1 5. [8] P. Jinupun, P. Luk. Direct torque control for sensorless switched reluctance motor drives. in: Proceedings of the 7th International Conference on Power Electronics & Variable Speed Drives, 1998, WJMS for contribution:
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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