Direct Torque Control of 4 Phase 8/6 Switched Reluctance Motor Drive for Constant Torque Load

ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 8 (2012) 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 515005, India (Received January 13 2011, Accepted January 11 2012)

Abstract. The 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. The Direct Torque Control (DTC) technique can minimize the torque ripple by regulating torque within speciﬁed hysteresis band. This paper presents the Direct Torque 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 DTC applied to ac motor, 8 Space voltage vectors are sufﬁcient to apply DTC technique to SRM. The Direct Torque Control of SRM is simulated in MATLAB/ SIMULINK for constant torque load. The 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 temper- atures and can rotate at very high speeds. The SRM achieves high torque levels at low peak currents by using small air gaps. The 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 proces- sors, the conventional variable AC/DC machines are now replaced by SRMs in applications like coal mining, electric vehicles, compressors, electric traction, washing machines etc. The main drawback of the motor is that it has highly non-linear torque-position characteristics and a torque ripple is high, which causes noise and vibrations[10]. Different techniques have been proposed in the past to minimize torque ripple. The most popular electronic method is based on the optimization of control principles, which include the supply voltage, turn-on and turn-off 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. The Neuro-Fuzzy 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. Torque 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. Torque controller is used for limiting the phase current and fuzzy logic controller for adjusting the

∗ Corresponding author. Tel.: +91-040-2709 8628. E-mail address: [email protected].

Published by World Academic Press, World Academic Union 186 S. Pratapgiri & P. Narsimha: Direct torque control

turn-on and turn-off angles. But this method is limited to low speed region. DTC proposed in [8] uses the concept of short ﬂux pattern. But it has the disadvantage of requirement of new winding topology, which is expensive and also inconvenient. In [1, 2] a novel DTC technique is applied to 3-phase 6/4 SRM in which the difference between conventional DTC applied to ac machines and the new DTC proposed to SRM has been elaborately discussed. DTC of 3 phase SRM has been also presented in [3, 11] along with simulation results. The low speed and high speed operation of 6/4 SRM drive is observed in [7] using DTC method. DTC of 4 phase 8/6 SR motor is analyzed only in [6, 14]. This paper presents DTC based 4 phase 8/6 SRM by selecting a suitable set of 8 Space voltage vectors. The DTC 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. This paper with new set of space vectors shows a signiﬁcant improvement in the torque performance of DTC based SRM compared to the DTC scheme shown in [3]. There is a considerable reduction in the torque ripple in the present study. The paper is organized as follows. Section 2 describes the mathematical equations of SRM and priniciple of DTC. The block diagram of the DTC based SRM is explained in Section 3. Simulation and analysis of results are presented in Section 4. Conclusions are presented in Section 5.

D1 D1 D1 S1 S1 S1

VDC A VDC A VDC A

D2 D2 D2 S S S 2 2 2

Fig. 1:Fig. SRM 1. SRM phase phase voltage voltage states. states Ψ N=3 β N=4 V3 N=2 V4 2 Direct torque controllerV2 Ψ The mathematical equations of DTC [2] as applied to SRM are discussedΨ2 as below The motor1 torque V5 V output N=5 can be found using the electromagnetic1 N=1 equation d ψ(θ, i) 45 v = Ri + , 0 V (1) Ψα 6 V8 dt N=6 V where ψ(θ, i) is the nonlinear7 function N=8 of phase flux linkage as a function of rotor position θ and current i. Expanding the above N=7 equation, results in Eq. (2) Ψ3 Ψ4 ∂ψ(θ, i) di ∂ψ(θ, i) dθ v = Ri + + . (2) Fig. 2: Definition of SRM motor voltage vectors∂i for DTCdt ∂θFig.d 3:t Definition of α-β axis for motor voltage Thus the equation for the power flow can be written as ∂ψ(θ, i) di ∂ψ(θ, i) dθ vi = Ri2 + i + i . (3) ∂i dt ∂θ dt Table I Now the effective power flow PeffSwitching from the Table electric of sourcespace voltage can be defined vectors as

WJMS email for contributionN: [email protected] 1 2 3 4 5 6 7 8 TQ = 1 V2 V3 V4 V5 V6 V7 V8 V1 ΨQ = 1 TQ = 0 V7 V8 V1 V2 V3 V4 V5 V6 TQ = 1 V3 V4 V5 V6 V7 V8 V1 V2 ΨQ = 0 TQ = 0 V6 V7 V8 V1 V2 V3 V4 V5

3. Block diagram of DTC Fig. 4 shows the block diagram of the proposed DTC based 4 phase 8/6 SRM drive. The flux in each phase is calculated by flux linkage computation block. The output of the flux linkage computation block is given to the α –β block where the flux in 4 phases are converted into 2 phases. The magnitude Ψs and angle δ of the flux vector are calculated by flux vector calculation block. The flux vector magnitude Ψs and the motor torque T calculated from the motor are then fed into flux and torque hysteresis blocks, together with the reference values of flux and torque. The hysteresis blocks outputs the flux and torque increase or decrease command ΨQ and TQ depending on the current flux and torque magnitudes relative to the hysteresis bands. The switching table and asymmetrical converter apply the suitable voltage vectors to the SRM windings.

D1 D1 D1 S1 S1 S1 D1 D1 D1 S1 S1 S1

VDC A VDC A VDC A VDC A VDC A VDC A

D2 D2 D2 S2 S2 S2 D2 D2 D2 S S S 2 2 2 (a) (c) (a) (b) (c) World Journal of Modelling and Simulation, Vol. 8 (2012) No. 3,(b) pp. 185-?? 187 Fig. 1: SRM phase voltage states. Ψ Fig. 1: SRM phase voltage states. β N=3 Ψβ N=4 V3 N=3 N=2 V4 N=4 V3V2 N=2 V4 V2 Ψ Ψ2 1 V5 V Ψ2 Ψ1 N=5 1 N=1 N=5 V5 V1 N=1 45 0 V 45 Ψα 6 V8 0 N=6 Ψα V6V7 V N=6 N=8 8 N=7 V7 N=8 Ψ N=7 Ψ3 4 Ψ Ψ3 4 Fig. Fig 2:. 2.DefinitionDeﬁnition of ofSRM SRM motor motor voltage voltage vectors vectors for for DTC DTC Fig.Fig 3: Definition. 3. Deﬁnition of α- ofβ axis - axis for for motor motor voltage voltage Fig. 2: Definition of SRM motor voltage vectors for DTC Fig. 3: Definition of α-β axis for motor voltage

Peff = ei, Table I Switching Table of space Table voltage I vectors where e = (v − Ri). Switching Table of space voltage vectors

Thus in a differentialN time dt, the1 differential2 3 electrical4 energy5 6 d We transferred7 8 from the source is given by T N = 1 V 1V 2V 3V 4V 5V 6V 7V 8 Ψ = 1 Q 2 3 4 5 6 7 8 1 Q T = 0T Q = V 1 VV2 VV3 VV4 VV5 VV6 VV7 VV8 V1 ΨQ = 1Q 7 8 1 2 3 4 5 6 TQ = 0 V7 V8 V1 V2 V3 V4 V5 V6 TQ = 1 V3 V4 dVW5 e =Vei6 dt.V7 V8 V1 V2 (4) ΨQ = 0 TQ = 1 V3 V4 V5 V6 V7 V8 V1 V2 Ψ =T 0Q = 0 V6 V7 V8 V1 V2 V3 V4 V5 Q T = 0 V V V V V V V V To ﬁnd an expression for the motorQ torque production,6 7 the8 energy1 equation2 3 is written4 as5

3. Block diagram of DTC dWe = dWm + dWf , (5) 3. Block diagram of DTC Fig.where 4 shows dW theand block dW diagramare the of differential the proposed mechanical DTC based energy 4 phase and field 8/6 energySRM drive. respectively. The flux The in fieldeach energy Fig. 4 showsm the blockf diagram of the proposed DTC based 4 phase 8/6 SRM drive. The flux in each phasecan is be calculated separated by into flux its constituentlinkage computation components block. as shownThe output in Eq. of ( 6the) flux linkage computation block phase is calculated by flux linkage computation block. The output of the flux linkage computation block is given to the α –β block where the flux in 4 phases are converted into 2 phases. The magnitude Ψs and is given to the α –β block where the∂W flux in 4 phases are converted∂W into 2 phases. The magnitude Ψs and angle δ of the flux vector are calculated by fluxf vector calculationf block. The flux vector magnitude Ψs dWf = di|θ=cons tan t + dθ|i=cons tan t. (6) and theangle motor δ of torque the flux T calculatedvector are fromcalculated the∂i motor by flux are vector then fedcalculation∂ θinto flux block. and torqueThe flux hysteresis vector magnitudeblocks, Ψs and the motor torque T calculated from the motor are then fed into flux and torque hysteresis blocks, together with the reference values of flux and torque. The hysteresis blocks[13] outputs the flux and torque Fromtogether the consideration with the reference of the storedvaluesfield of flux energy and ittor canque. be The shown hysteresis that :blocks outputs the flux and torque increase or decrease command ΨQ and TQ depending on the current flux and torque magnitudes relative to increase or decrease command Ψ and T depending on the current flux and torque magnitudes relative to the hysteresis bands. The switching table∂ψQ (andθ, i )asymmetricalQ converter∂ψ(θ, apply i) the suitable voltage vectors to the hysteresis bands. ThedW switching= i table dandi| asymmetrical+ i converterdθ apply| the suitable, voltage vectors to(7) the SRM windings. e ∂i θ=cons tan t ∂θ i=cons tan t the SRM windings. ∂ψ(θ, i) dW | = i di| . (8) f θ=cons tan t ∂i θ=cons tan t

By substitution of Eq. (6) into Eq. (7) it can be found that

∂ψ(θ, i) ∂W dW = i dθ − f dθ. (9) m ∂θ ∂θ The instantaneous torque is deﬁned by

dW T = m . (10) dθ Thus by substituting Eq. (10) into Eq. (9) the expression for the instantaneous torque production of an SR motor phase can be written as

∂ψ(θ, i) ∂W T = i − f . (11) ∂θ ∂θ This 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. Therefore, by using this approximation, the following equation for torque production may be derived as

WJMS email for subscription: [email protected] 188 S. Pratapgiri & P. Narsimha: Direct torque control ∂ψ(θ, i) T ≈ i . (12) ∂θ

In SRM, unipolar drives are normally used and thus the current in a motor phase is always positive. ∂ψ Hence, from Eq. (12) the sign of the torque is directly related to the sign of ∂θ . In other words to produce a positive torque, the stator flux amplitude must increase relative to the rotor position, whereas to produce a negative torque the change in stator flux should decrease with respect to the rotor movement. A positive ∂ψ ∂ψ value of ∂θ may be defined as “flux acceleration”, whereas a negative value of ∂θ may be defined as “flux [2] deceleration”[ 2]. Hence, a new SR motor control technique is defined as follows: (i) The stator flux linkage vector of the motor is kept at constant amplitude. (ii) Torque is controlled by accelerating or decelerating the stator flux vector.

v1 ω ΨS Ψ1 α - β v2 Flux Linkage Ψ2 Transfo- Ψα Flux v SRM 3 Computation rmation Vector δ i Ψ3 v 1 Calculation 4 Ψβ i2 Ψ4 i3

Flux Ψ Q Hysteresis Ψref v 1 u1

v2 u2 Asymmetrical Torque T TQ v Converter Switching Hysteresis 3 u3 Table Tref

v4 u4 N Sector Selection

Fig.Fig. 4: 4. BlockBlock diagram diagram of of DTC DTC based based SRM SRM drive drive

4. TheSimulation objective of and control Results technique (i) is achieved similarly to the conventional DTC applied to ac ma- chinesThe DTC by selecting of 4 phase an appropriate8/6 SRM is Space modeled voltage and vector. simulated As inin conventional MATLAB /SIMULINK. ac machine DTC, Fig. the5 shows stator the ﬂux variation will have the same directional variation as the voltage vector and a change in amplitude that is pro- portionalsimulation to themodel magnitude of 8/6 ofSRM the voltagewith direct and thetorque time intervalcontroller. of application.The model Theconsists objective of 4 (ii)phase is also 8/6 achieved SRM, similarlyasymmetrical to the converter, conventional DTC ac motorcontroller DTC and because PI Contro the torqueller. In is this increased simulation or decreased test, the bymotor acceleration reference or decelerationflux is taken of as the 0.27 stator Wb ﬂux and vectora load relativetorque is to taken the rotor as 4 movement Nm. The [hysteresis2]. bands were defined to be 0.02 Wb and 0.4 Nm for the flux linkage and torque respectively. The DTC scheme is simulated by selecting the following set of 8 Space voltageTable vectors. 1. Switching Table of space voltage vectors

V1 = (-1010), V2 = (-1-111), VN3 = (0-101), 1V4 = 2(1-1-11), 3 4 5 6 7 8 V = (10-10), V = (11-1-1), V TQ= (010-1), = 1 V2 V = V3 (-111-1). V4 V5 V6 V7 V8 V1 5 6 ΨQ = 1 7 TQ = 0 V78 V8 V1 V2 V3 V4 V5 V6 The performance of the DTCTQ based = 1 SRMV3 V4drive V5is analyzed V6 V7 for V8a constant V1 V2load torque of 4 Nm at a Ψ = 0 reference speed of 800 rpm.Q ActualTQ =speed 0 V6 is compared V7 V8 with V1 the V2reference V3 speed V4 V5and error is given to a PI controller. The output of PI controller is the reference torque. The maximum value of PI controller output WJMSis 8 Nmemail whenever for contribution the :speed [email protected] 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 0.41 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 0.41 Nm. Thus the torque ripple is minimized in the steady state and during acceleration period. The calculated torque ripple is 10%. Fig. 6 (b) shows the total torque response in steady state. Fig. 6(c) shows the magnitude of the flux vector. The total flux is maintained at 0.27 Wb by following a set hysteresis band of 0.02 Wb. The current waveforms of all the four phases in the steady state are shown in Fig. 6(d). The maximum current and average current of each phase are 8.9 A and 4.13 A respectively. Fig. 6(e) shows speed response. The steady state speed is maintained constant at 803 rpm. Fig. 6(f) shows the trajectory of the

World Journal of Modelling and Simulation, Vol. 8 (2012) 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. The 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 0. This 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 as-1. The 4 phase asymmetrical converter can have a total of 81 possible Space voltage vectors. However in order to apply DTC to SRM, eight equal amplitude voltage vectors that are separated by π/4 radians are sufficient. The space voltage vector states are shown in Fig. 2. These 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 flux linkage and the motor torque within hysteresis bands. As in the conventional DTC scheme, if the stator flux linkage lies in the kth zone, the magnitude of the flux can be increased by using the switching vectors Vk+1 and Vk−1 and can be decreased by using the vectors Vk+2 and Vk−2. Hence, whenever the stator flux linkage reaches its upper limit in the hysteresis band, it is reduced by applying voltage vectors which are directed toward the center of the flux vector space and vice-versa. As detailed previously, the torque is controlled by an acceleration or deceleration of the stator flux relative to the rotor movement. Hence, if an increase in torque is required, voltage vectors that advance the stator flux linkage in the direction of rotation are selected. This corresponds to selection of vectors Vk+1 and Vk+2 for a stator flux linkage in the kth zone. If a decrease in torque is required, voltage vectors are applied which decelerate the stator flux linkage vector. This corresponds to the vectors Vk−1 and Vk−2 in the kth zone. Hence a switching table for controlling the stator flux linkage and motor torque can be defined as shown in Tab. 1, where ΨQ = 1 & ΨQ = 0 indicate increase and decrease in the flux-linkages respectively and TQ = 1 & TQ = 0 indicate increase and decrease in torque respectively. In order to resolve the individual phase flux vectors into a single stator flux linkage vector, the flux vectors for the four phase SRM are transformed onto a stationary orthogonal two axis reference frame [6] as shown in Fig. 3.

ψα = ψ1 cos 45º − ψ2 cos 45º − ψ3 cos 45º + ψ4 cos 45º, ψ = ψ sin 45 + ψ sin 45 − ψ sin 45 − ψ sin 45 , β 1 º 2 º 3 º 4 º q 2 2 ψβ ψs = (ψα + ψβ), δ = arctan . (13) ψα where Ψs is the flux vector, δ is the angle of the flux vector and Ψ1, Ψ2, Ψ3, Ψ4 are the flux-linkages of the four phases. Specifications of SRM:

Aligned Inductance 110 mH Unaligned Inductance 10 mH Stator Resistance 0.3 Inertia 0.0082 Kg.m2 Friction 0.001 N.m.s Maximum Current 30 A Voltage 120 V Maximum Flux-linkage 0.3 V.s

3 Block diagram of DTC

Fig. 4 shows the block diagram of the proposed DTC based 4 phase 8/6 SRM drive. The flux in each phase is calculated by flux linkage computation block. The output of the flux linkage computation block is

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[12] R.Jeyabharath, P.Veena, and M.Rajaram, “A novel dtc strategy of torque and flux control for switched reluctance motor drive,” in International Conference on Power Electronics, Drives and Energy Systems, PEDES 06, Dec. 2006, pp. 1–5. [13] B.H.Jeong, K.Y.Lee, J.D.Na, G.B.Cho and H.L.Baek , “Direct Torque Control for the 4-phase Switched Reluctance Motor Drives,” in Proceedings of the 2005 IEEE International Conference on Electrical Machines and Systems, ICEMS 2005, Sept. 2005,pp. 524-528. [14] Wang Mianhau, “ Four Phase Switched Reluctance Motor Direct Torque Control,” in Proceedings of the 2011 IEEE international Conference on Measuring Technology and Mechatronics Automation,2011,pp.251-254. [15] D.A.Staton, W.L.Soong and T.J.E Miller, “Unified theory of torque production in switched reluctance and synchronous reluctance motors,” IEEE Trans. on Industry Applications, vol. 31, Mar./Apr. 1995, pp.329-337.

190 S. Pratapgiri & P. Narsimha: Direct torque control

4 TL T_ref2 G11 A1 A1 G12 Scope2 A2 A2 G21 G22 B1 B1 G31 B2 B2 m G32 C1 C1 K- G41 C2 C2 G42 D1 D1 V+ 120 V V- D2 D2 CONVERTER Switched Reluctance Motor

T_ref

F_BH M ATLAB M ATLAB 800 PI T_cal Function Function M ATLAB Fcn pulses1 Discrete PI Controller 0.27 flux_ref F_ref T_BH

flux Alpha_flux alpha_flux flux_mag flux_cal Discrete, t Ts = 1e-006 s. alphaflux_cal Subsystem Clock To Workspace powergui

flux Beta_flux beta_flux angle Angle Sector

betaflux_cal Sector_Calculator fluxmag & angle

Fig. 5. Simulation model of 4 phase 8/6 SRM with DTC Fig. 5: Simulation model of 4 phase 8/6 SRM with DTC given to the α − β block where the flux in 4 phases are converted into 2 phases. The magnitude Ψs and angle δ of the flux vector are calculated by flux vector calculation block. The flux vector magnitude Ψs and the motor torque T calculated from the motor are then fed into flux and torque hysteresis blocks, together with the reference values of flux and torque. The hysteresis blocks outputs the flux and torque increase or decrease command ΨQ and TQ depending on the current flux and torque magnitudes relative to the hysteresis bands. The switching table and asymmetrical converter apply the suitable voltage vectors to the SRM windings.

4 Simulation and results

The DTC of 4 phase 8/6 SRM is modeled and simulated in MATLAB /SIMULINK. Fig. 5 shows the simulation model of 8/6 SRM with direct torque controller. The model consists of 4 phase 8/6 SRM, asym-

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World Journal of Modelling and Simulation, Vol. 8 (2012) No. 3, pp. 185-?? 191

9 5 8

7 4

5 3

4 2 3 Totaltorque (Nm)

Totaltorque (Nm) 2 1 1 0 0 0.1 0.2 0.3 0.4 0.5 0 Time (Sec) 0.31 0.315 0.32 Time (Sec) (a) (b)

0.3 10 X: 0.3159 Y: 8.892 0.25 8 0.2 6 0.15

0.1 Current (A)

Flux Magnitude (Wb) 0.05 2

0 0 0.1 0.2 0.3 0.4 0.5 0 Time (Sec) 0.31 0.315 0.32 Time (Sec) (c) (d) 900 0.3 X: 0.3036 Y: 803.9 800 0.2

700

600 0.1

500 0

400 Fluxbeta

Speed (rpm) -0.1 300

200 -0.2

100 -0.3 0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0 0.1 0.2 0.3 0.4 0.5 Fluxalpha Time (Sec) (f) (e)

Fig. 6. SimulationFig. 6: waveformsSimulation waveforms DTC based DTC SRM based (a) SRM Total (a) torqueTotal torque (b) Total (b) Total torque torque in in steady steady state state (c)(c) Flux magnitude magnitude (d) (d) Phase currents (e) Speed (f) Flux vector trajectory Phase currents (e) Speed (f) Flux vector trajectory

WJMS email for subscription: [email protected] 192 S. Pratapgiri & P. Narsimha: Direct torque control metrical converter, DTC controller and PI Controller. In this simulation test, the motor reference flux is taken as 0.27 Wb and a load torque is taken as 4 Nm. The hysteresis bands were defined to be 0.02 Wb and 0.4 Nm for the flux linkage and torque respectively. The DTC scheme is simulated by selecting the following set of 8 Space voltage vectors.

V1 = (−1010),V2 = (−1 − 111),V3 = (0 − 101),V4 = (1 − 1 − 11),

V5 = (10 − 10),V6 = (11 − 1 − 1),V7 = (010 − 1),V8 = (−111 − 1).

The performance of the DTC based SRM drive is analyzed for a constant load torque of 4 Nm at a reference speed of 800 rpm. Actual speed is compared with the reference speed and error is given to a PI controller. The output of PI controller is the reference torque. The 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 0.41 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 0.41 Nm. Thus the torque ripple is minimized in the steady state and during acceleration period. The calculated torque ripple is 10%. Fig. 6 (b) shows the total torque response in steady state. Fig. 6 (c) shows the magnitude of the flux vector. The total flux is maintained at 0.27 Wb by following a set hysteresis band of 0.02 Wb. The current waveforms of all the four phases in the steady state are shown in Fig. 6 (d). The maximum current and average current of each phase are 8.9 A and 4.13 A respectively. Fig. 6 (e) shows speed response. The steady state speed is maintained constant at 803 rpm. Fig. 6 (f) shows the trajectory of the flux vector.

5 Conclusions

In this paper the control of 4 phase 8/6 SRM is analyzed with Direct Torque Control technique. The torque is controlled directly through the control of magnitude of the flux linkage and the change in speed of the stator flux vector. The 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 10% of rated torque during acceleration and in the steady state. The torque ripple is 10% in the steady state. A further study can be made on the reduction of phase current variations by maintaining the torque and flux 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 2000, 2000, 387–392. [2] A. Cheok, Y. Fukuda. A new torque and ﬂux control method for switched reluctance motor drives. IEEE Transac- tions on Power Electronics, 2002, 17(4): 543–557. [3] H. Guo. Considerations of direct torque control for switched reluctance motors. in: Proceedings of the 2006 IEEE International Symposium on Industrial Electronics, ISIE, 2006, 2321–2325. [4] L. Henriques, L. Rolim, et al. Torque ripple minimization of switched reluctance drive using a neuro-fuzzy com- pensation. IEEE Transactions on Magnetics, 2000, 36(5): 3592–3594. [5] I. Husain. Minimization of torque ripple in srm drives. IEEE Transactions on Industrial Electronics, 2002, 49(1): 28–39. [6] B. Jeong, K. Lee, et al. Direct torque control for the 4-phase switched reluctance motor drives. in: Proceedings of the 2005 IEEE International Conference on Electrical Machines and Systems, ICEMS 2005, 2005, 524–528. [7] R. Jeyabharath, P. Veena, M. Rajaram. A novel DTC strategy of torque and ﬂux control for switched reluctance motor drive. in: International Conference on Power Electronics, Drives and Energy Systems, PEDES 06, 2006, 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, 329–334.

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[9] L.Venkatesha, V. Ramanarayanan. Torque 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, 529–534. [10] T. Miller. Switched Reluctance Motors and their Control. Magna Physics & Oxford, 1993. [11] G. Song, Z. Li, et al. Direct torque control of switched reluctance motors. in: Proceedings of the 2008 IEEE International Conference on Electrical Machines and Systems, ICEMS 2008, 2008, 3389–3392. [12] P. Srinivas, P. Prasad. Torque 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, 2010. [13] D. Staton, W. Soong, T. Miller. Uniﬁed theory of torque production in switched reluctance and synchronous reluctance motors. IEEE Transactions on Industry Applications, 1995, 31: 329–337. [14] M. Wang. Four phase switched reluctance motor direct torque control. in: Proceedings of the 2011 IEEE international Conference on Measuring Technology and Mechatronics Automation, 2011, 251–254. [15] Z. Zhen, W. Terry, C. Juan. Modeling and nonlinear control of a switched reluctance motor to minimize torque ripple. in: Proceedings of the 2000 IEEE International Conference on Systems, Man and Cybernetics, vol. 5, 2000, 3471–3448.

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Direct torque control 195