Highly Accurate Modeling of the Switched Reluctance Drive VLADAN P. VUJIČIĆ, RADOVAN D. STOJANOVIĆ Department of Electrical Engineering University of Montenegro Cetinjski put b.b. , 81000 Podgorica SERBIA AND MONTENEGRO

Abstract: - In this paper the experimentally verified, highly accurate, model of the Switched Reluctance Motor (SRM) is proposed as the PSPICE circuit model. Thus, the complex PSPICE semiconductor models can be used to analyze the realistic behavior of complete drive. As an example, the phase voltage oscillations, produced by the non-ideality of the power converter, are detected, and then eliminated by adding the appropriate snubber circuits to the power switches. This problem has not been detected when simulation was performed by MATLAB package.

Key-Words: - switched reluctance motor, PSPICE modeling.

1 Introduction The reliable nonlinear SRM model, which provides the The SRM has very simple, cost effective construction, dynamic simulation results with high accuracy, is used but the determination of its performances is difficult for the implementation by PSPICE. This model uses because of highly nonlinear relationship between the equivalent magnetic circuit of the motor as a set of torque and the excitation current [1], [2]. The SRM reluctances linked in series and in parallel. These normally works at high magnetic saturation levels, and reluctances have physical meaning and are found from the nonlinearity also is greatly affected by intense theoretical and some empirical considerations and saturation of partially overlapping stator and rotor pole knowledge. tips. Therefore, it is impossible to make simple SRM The basic model equations provide the phase current model which provides high accuracy, i.e. includes the i calculations whereas the flux linkage  and rotor most important saturation effects in the SRM. angular position  are input variables. Instantaneous The performances of SRM drive strongly depend on phase current is defined as: the applied control. The drive system, comprising signal processing, power converter and motor must be designed i( , )  io ( , )  i fe () , (1) as a whole for the specific application. Therefore, existence of a PSPICE SRM model should be of great where convenience for SRM drive design purposes, especially  2 2  for power converter design consideration. Thus, the io  co5(1 co1 )  co1co2  co1 (   co3 )  co4 , (2) complex PSPICE models of semiconductor devices   could be employed in overall design procedure for more  realistic considerations. ife = cfe1 + cfe2 . (3) Such model of the SRM is considered in this paper. The proposed approach [3] is implemented into PSPICE The coefficients cok (k=1,2,...,5) are the functions of the in the form of circuit model. The simulation is rotor position , while the cfe1, cfe2 and  are constants. performed for the case when the classic power converter The above parameters can be determined by using the [4] supplies the SRM. The PSPICE models of power motor geometry data as well as some specific points of semiconductor switches are used in the converter circuit. iron core B-H curve and unaligned phase inductance. For comparison the MATLAB model implementation is The detailed procedure of model parameters also considered. However, the idealized power switches determination is explained in [3]. of the power converter are used in this paper for The rotor position  in (1) is assumed to be a signal MATLAB simulations. The simulation results obtained from the position sensor, while the flux linkage  can by using these two packages are compared. Some unwanted phase voltage oscillations are registered by be evaluated as: t PSPICE based model only. In order to reduce such stresses on the power semiconductor devices as well as    v  Ridt , (4) EMI, the R-C snubber circuits [5] are designed and used 0 in another simulations. where v is the applied phase voltage and R is phase 2 Basic SRM Model Equations resistance. The produced torque T is determined as: W T   mo , (5)  3 PSPICE Implementation of the Model where Model equations (1), (2), (3) and (4) are used to create the PSPICE model of the SRM. Sub-circuit of the motor 1  co1 2 co1 2 2 phase is created by the PSPICE schematics, as it is Wmo  co5    co1co2  (  co3) (  co3)  co4  2 2 shown in Fig. 1. The external inputs are the applied phase voltage and the angular functions cok (k=1,2,...,5), 2 2 2  c c c c c   c  (  c )  c while the parameters R, c , c and  are defined  o1 o2 o3  o1 o4 ln( o3 o3 o4 ), (6) fe1 fe2 directly. For an existing 6/4 SRM, the functions c 2 2 co2  co3  ok  (k=1,2,...,5) are, also, completely modeled by using the motor geometry data. The schematics blocks that is a part of magnetic field energy calculated as represent these functions are shown in Fig. 2. Thus, for W  i d considered motor, the inputs are reduced to the applied mo  o with io defined by (2). phase voltage and the rotor angular speed.

Fig. 1. PSPICE schematics model for the SRM phase.

Fig. 2(a) Fig. 2(b)

Fig. 2(c)

Fig. 2. PSPICE schematics model for the input angular functions.

4 Experimental and Simulation Results In order to verify the PSPICE model as well as to approve its convenience, the basic SRM model equations are also implemented into MATLAB program package. Thus, the same simulation results of two program packages will be compared. Firstly, the SRM model is experimentally verified by comparing the measured magnetization curves for a number of the rotor positions with the same ones calculated by MATLAB. The results are shown in Fig. 3. Good agreements of the results prove the high accuracy of the SRM model. PSPICE and MATLAB simulations are performed when the classic power converter [4] supplies the SRM. The dc link voltage was chosen to be constant in both simulation environments. The IGBTs are used as the power switches in the PSPICE model, while the idealized power switches with constant the on-state Fig. 4. PSPICE circuit used for simulations. voltage drops are used in MATLAB. The PSPICE circuit for one phase is shown in Fig. 4. The simulation results of two program packages are very similar, as it was 3 0 0 expected. However, due to the consideration of more realistic switch models, the PSPICE detects the 2 0 0 unwanted voltage oscillations on the phase endings.

Examples of the phase voltage, the phase current and the ) 1 0 0 V (

energy conversion loop, calculated by using MATLAB e g a t l and PSPICE approaches, are shown in Fig. 5 and Fig. 6. o 0 v

e

The results are obtained for 3000 rpm rotor speed using s a h the same turn on and dwell angles. p - 1 0 0

- 2 0 0

- 3 0 0 2 3 4 5 6 t i m e ( s ) x 1 0 - 3 Fig. 5(a)

4 . 5

4

3 . 5

3 ) A (

t

n 2 . 5 e r r u c

e 2 s a h

p 1 . 5

1 Fig. 3. Magnetization curves for experimental motor 0 . 5 (from unaligned to aligned position with step 5o of rotor 0 position angle). 2 3 4 5 6 -3 t i m e ( s ) x 1 0 Fig. 5(b) 0 . 5 5 5 0 mV F l u x l i n k a g e ( mV. s ) 0 . 4

) s

. 4 0 0 mV V (

e 0 . 3 g a k n i l

x 0 . 2 u l F 2 0 0 mV 0 . 1

0 0 1 2 3 4 p h a s e c u r r e n t ( A ) 0 V Ph a s e c u r r e n t

0 A 2 . 0 A 4 . 0 A Fig. 5(c) V ( HB6 . F l u x _ l i n k a g e ) - I ( HB6 . Rp h a s e ) Fig. 5. MATLAB simulation results: (a) phase voltage, (b) phase current, and (c) energy conversion loop. Fig. 6(c)

Fig. 6. PSPICE simulation results: (a) phase voltage, (b) 3 0 0 V phase current, and (c) energy conversion loop.

V o l t a g e 2 0 0 V In order to reduce voltage oscillations, the RC snubber circuits are proposed, as is shown in Fig. 7. For snubber’s parameters R10=R11=R=1K and 0 V C3=C4=C=100nF, the calculated phase voltage is given in Fig. 8. As seen, the voltage oscillations are eliminated. The positive peak of the voltage at the end of phase conducting has been eliminated by increasing snubbers - 2 0 0 V resistance R. Thus, for R=10K, the phase voltage peak is fully reduced, as is presented in Fig. 9. - 3 0 0 V 7 ms 8 ms 1 0 ms 1 2 ms 1 3 ms V ( Z 5 : E, Z 4 : C) T i me

Fig. 6(a)

4 . 0 A

Cu r r e n t

2 . 0 A

0 A

7 ms 8 ms 1 0 ms 1 2 ms - I ( HB6 . Rp h a s e ) T i me Fig. 7. PSPICE circuit with the RC snubbers. Fig. 6(b) 3 0 0 V and London: Oxford University Press, 1993. [2] T. J. E. Miller, Electronic Control of Switched V o l t a g e 2 0 0 V Reluctance Machines, Newnes Power Engineering Series, 2001. [3] V. Vujičić and S. N. Vukosavić, “A simple nonlinear model of the switched reluctance motor,” IEEE 0 V Trans. on Energy Conversion, vol. 15, no. 4, pp. 395- 400, Dec. 2000. [4] S. Vukosavić and V. R. Stefanović, "SRM inverter topologies: a comparative evaluation," IEEE Trans. - 2 0 0 V Ind. Appl., vol. 27, no. 6, pp. 1034-1047, Nov./Dec. 1991. - 3 0 0 V [5] N. Mohan, T. M. Undeland, and W. P. Robbins, 2 . 0 ms 4 . 0 ms 6 . 0 ms 7 . 0 ms V ( Z 5 : E, Z 4 : C) Power Electronics: Converters, Applications and T i me Design, John Wiley & Sons, 1995. Fig. 8. Phase voltage with added the RC snubbers (R=1K, C=100nF).

3 0 0 V

V o l t a g e 2 0 0 V

0 V

- 2 0 0 V

- 3 0 0 V 7 ms 8 ms 1 0 ms 1 2 ms 1 3 ms V ( Z5 : E , Z 4 : C) T i me

Fig. 9. Phase voltage with added the RC snubbers (R=10K, C=100nF).

5 Conclusion This paper presents the highly accurate PSPICE-based SRM model. The model is used to analyze the negative effects in the SRM drive caused by non-ideality of the power converter switches. The results show that the accurate switch models must be included for realistic simulations of the complete SRM drive. This is of the crucial importance for practical design of the SRM power converters, where a number of problems require simulations to be surpassed before fabrication.

References: [1] T. J. E. Miller, Switched reluctance motor and their control, Hillsboro, OH: Magna Physics Publishing