TELKOMNIKA Indonesian Journal of Electrical EngineeringVol. 12, No. 12, December 2014, pp. 8085 ~ 8091 DOI: 10.11591/telkomnika.v12i12.6718 8085 Effect of Switching Frequency in DTC Based Switched Reluctance Motor Drive P.Srinivas Dept. of Electrical Engg., University College of Engg., Osmania University, Hyderabad, India email:
[email protected] Abstract Since the magnetizing characteristics are highly non-linear in nature, the torque ripple is high in the Switched Reluctance Motor (SRM). The torque ripple can be minimized by using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux-linkage and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands. This paper analyzes performance of the DTC based drive mainly in terms of the torque ripple in MATLAB/SIMULINK environment and results are discussed elaborately. The paper also analyzes the effect of these two bands on switching frequency of the converter. Keywords: switched reluctance motor, direct torque control, switching frequency, torque ripple Copyright © 2014 Institute of Advanced Engineering and Science. All rights reserved. 1. Introduction Switched Reluctance Motor drives are considered as an alternative to the conventional motor drives in variable speed applications because of advantages such as simple mechanical structure, no winding or magnet on rotor, high speed operation, wide speed operating range etc. Because of doubly salient structure and highly non-linear magnetic characteristics, the torque ripple is high [1, 2]. The torque ripple reduction of SRM drive using Direct Torque Control is proposed in [3]. But this method requires a new winding scheme which is expensive and inconvenient. To overcome the above disadvantages, a novel DTC technique is proposed in [4, 5]. This technique clearly describes the difference between DTC applied to Induction motor and DTC as applied to SRM. This also clearly analyses the performance of SRM drive using conventional Hystersis Current Control technique and the new DTC scheme. It also proves that using DTC technique torque ripples can be minimized to a greater extend than when compared to the Hysteresis Current Control method [6-8]. The novel DTC technique presented in [4, 5] is simulated in [9, 10]. The simulation and analysis of DTC based 4 phase 8/6 SRM drive for constant torque load is analyzed in [11]. This paper analyzes the performance of DTC based drive for Fan load. Performance analysis of DTC based SRM drive using simplified Torque Equation and FEA models is discussed in [12]. This paper presents the variation of switching frequency in DTC based drive for different combinations of Flux and Torque Hysteresis bands in MATLAB/SIMULINK environment. 2. Principle of DTC The mathematical equations of DTC [4, 5] as applied to SRM are discussed here. The instantaneous voltage across the motor winding is given by: v Ri d ( , i ) dt Where (,i) is the phase flux linkages as a function of rotor position θ and stator current i. Received August 19, 2014; Revised October 22, 2014; Accepted November 8, 2014 (1) it is reduced by applying voltage vectors which are directed toward the center of the flux vector space and vice-versa [5]. No. When one switch is turned ON and other is turned OFF. eight Space Voltage Vectors that are separated by 450 are sufficient. Hence. the torque is controlled by an acceleration or deceleration of the stator flux relative to the rotor movement. by substituting (4) into (3) the expression for the instantaneous torque production of an SRM phase can be written as: T i ( . If a decrease in torque is required. When both the switches are turned OFF. i ) d i dt dt (2) The differential mechanical energy obtained [5] is shown in Equation (3) dW m i W f ( . voltage vectors that advance the stator flux-linkage in the direction of rotation are selected. Asymmetrical converter is popularly used for the SRM drives. the influence of the second term in (5) is negligible. December 2014 : 8085 – 8091 . 2…8. This corresponds to selection of vectors Vk+1 and Vk+2 for a stator flux-linkage in the kth zone. 5]. The eight Space Voltage Vectors that lie in the center of eight sectors N = 1. (6) the sign of the torque is directly related to the sign of . Hence.8086 ISSN: 2302-4046 Expanding Equation (1) results in Equation (2) v Ri ( . whenever the stator fluxlinkage reaches its upper limit in the hysteresis band. whereas to produce a negative torque the change in stator flux should decrease with respect to the rotor movement. 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 . As detailed previously. if the stator flux linkage lies in the kth zone. 12. 12. But in order to apply DTC to SRM. As in the conventional DTC scheme. the state is defined as ‘demagnetizing’ (state -1). The converter for one phase is shown in Figure 1 When both the switches are turned ON. The DTC technique is clearly explained in [4. In other words to produce a positive torque. voltage vectors are applied which decelerate the stator TELKOMNIKA Vol. whereas a negative value of may be defined as flux deceleration. i ) W f (5) This is a rarely used variant of conventional torque equation. from eq. the following equation for torque production may be obtained as: T i ( . the state is defined as ‘freewheeling’ (state 0). the state is defined as ‘magnetizing’ (state 1). the stator flux amplitude must increase relative to the rotor position. Therefore. by using this approximation. Due to saturation in the SRM. A positive value of may be defined as flux acceleration. i ) d d (3) The instantaneous torque equation is defined as: T dW m d (4) Thus. unipolar drives are normally used and thus the current in a motor phase is always positive. where k = 1 to 8 . Hence. i ) di ( . The 4 phase Asymmetrical converter can have a total of 81 possible Space Voltage Vectors. if an increase in torque is required. are shown in Figure 2. i ) (6) In SRM. Definition of SRM motor voltage vectors for DTC 3. One phase model Effect of Switching Frequency in DTC Based Switched Reluctance Motor Drive (P. position sensing block. Tcal mod powe rgui1 Gating Signals 4 0. Based on the output of the torque and flux hysteresis blocks.25 Flux_ref Flux_ref t Clock Fluxes 6 Theta To Workspace DTC Figure 3(a). mechanical system. This corresponds to the vectors Vk-1 and Vk-2 in the kth zone [5]. appropriate Space Voltage Vectors are selected. Internal block 1 F1 R 2 C1 -KI(A) flux K Ts 3 T1 z-1 ITBL TTBL 2 V1 1 Th1 Figure 3(c). Figure 1. A1 G11 G12 A2 G21 B1 +v - G32 B2 vm2 C1 +v - G41 C2 G42 V+ 120 V D1 V_ torque Current +v - G22 G31 Torque V1 vm1 Th1 F1 V2 1 V1 Spee d2 V3 vm3 Speed +v - C1 current Flux -K- V1 Th2 V4 Load Torque 1 Torque T2 2 V2 Theta SRM V2 F2 -K- Phase2 Th3 T3 theta 5 Load Torque C3 -K 3 V3 V3 4 Speed 5 Total Torque C2 Total Torque vm4 D2 converter 3 Flux T1 Phase1 F3 K Ts z-1 -KB K Ts Teta z-1 2 Current Phase3 -K- 1/J Th4 T4 C4 8 4 V4 T_ref T_re f V4 F3 Phase4 60 Discrete. Ts = 1e-006 s.Srinivas) . The model consists of electrical system. Asymmetrical converter and DTC block. Asymmetrical Converter Figure 2.ISSN: 2302-4046 TELKOMNIKA 8087 flux-linkage vector. The specification of the SRM is given in Appendix A. Simulation and Analysis of Direct Torque Control of SRM The complete Non-linear model of the 4-phase 8/6 SRM with Direct Torque Controller is shown in Figure 3(a). Figure 3(b) shows the internal block of SRM. Figure 3(c) shows the one phase model. Simulation model of DTC based drive Figure 3(b). The MATLAB program takes sector number. Mesh plot of flux-current-angle G22 V+ V- C1 5 B1 C2 6 B2 Br_Conv2 2 G31 G32 6 G32 V+ V+ V- C1 C2 Br_Conv3 4 V_ 7 G41 G41 G42 8 G42 V+ V- 1 V+ IGBT 1 G11 7 C1 9 D1 C2 10 D2 4 Fluxes alpha_flux flux_mag Figure 5(b). IGBT switches are used as the controllable switches in the converter. V6 = (11-1-1). C u rre n t (A ) T o rq u e (N m ) 30 20 10 10 0 -10 0 0.) 10 C Flux-linkage (Wbt) 40 60 20 60 Flux hysteresis & Torque hysteresis angle betaflux_cal fluxmag & angle Angle Sector Sector_Calculator Figure 6. flux increase or decrease signal and torque increase or decrease signal as the inputs and generates the required gate signals to the IGBTs of the converter to apply appropriate Space voltage vectorThe DTC scheme is simulated by selecting the following set of 8 Space voltage vectors. V3 = (0-101).8088 ISSN: 2302-4046 Mesh plots of two Lookup tables are shown in Figure 4(a) and Figure 4(b).1 20 0 0 Current (A) Theta (Deg. One leg of the converter 1 T_ref T_ref 2 Tcal T_cal F_BH flux_ref 3 Flux_ref alphaflux_cal MATLAB Function MATLAB Fcn T_BH flux_cal beta_flux IGBT1 2 V- Figure 5(a). 12. V5 = (10-10). Based on the angle. Torque computation block TELKOMNIKA Vol. Figure 5(a) shows the four phase Asymmetrical converter using IGBT switches. It contains Flux transformation block. The function of Flux transformation block is to convert fluxes in four phases into two phases [8]. 12. One leg of the converter is shown in Figure 5(b).3 30 0. V8 = (-111-1). the Sector selection block outputs the present sector number of the stator flux vector. Mesh plot of Torque-current-angle G11 2 G12 Br_Conv1 3 G21 0 0 E 1 G11 40 20 Theta (Deg. No. V4 = (1-1-11). V2 = (-1-111). Sector selection block and Flux magnitude and computation block. The torque computation block is shown in Figure 6.) Figure 4(a). December 2014 : 8085 – 8091 MATLAB Function pulses1 1 Gating Signals . V7 = (010-1). Asymmetrical converter Beta_flux 4 C2 D1 Br_Conv 4 flux 3 C1 2 G12 8 C2 C1 flux Alpha_flux D g G21 4 G22 1 A1 3 A2 C C2 E V+ g G12 C1 V- 5 G31 Figure 4(b). V1 = (-1010). The Sector selection block has information about the eight sectors.2 0. This combination cannot be selected as the switch is underutilized. The calculated torque ripple is 6. Figure 7(g) shows the variation of ψα with ψβ. which varies between -1800 and +1800.310 sec.15 kHz.θ) look up table and TTBL is the torque – current –angle (T.021 Wb. The performance of the DTC based SRM drive is analyzed for a Fan type load of 8 Nm and at a reference speed of 800 rpm.ISSN: 2302-4046 TELKOMNIKA 8089 The single phase model has two look up tables.87 A and 4. Table 1. Variation of Switching Frequency with Flux Hysteresis Band and Torque Hysteresis Band S. It is observed that for certain combinations where the flux and torque hysteresis bands are higher the switching frequency is low. switching frequencies are higher resulting in higher switching losses and reduced efficiency. Figure 7(a) shows the variation of stator current in all the four phases as a function of time.48 Nm as against the set band of 0.θ) look up table. Figure 7(h) shows the delta angle. It is observed that DTC leads to regularly spaced and periodic currents in all the phases. 8 % flux hysteresis band and 5 % torque hysteresis band can be selected for this drive.85 A respectively. Figure 7(b) shows the magnitude of the stator flux vector. as against the set band of 0. the phase currents are nonlinear in nature.00 %. Table 1 shows the variation of switching frequency of the switching device with the flux hysteresis band and torque hysteresis band.08 8. At lower hysteresis bands.Srinivas) . The flux magnitude is maintained at the reference value of 0.49 Effect of Switching Frequency in DTC Based Switched Reluctance Motor Drive (P. For the combinations in which either flux or toque hysteresis is high cannot be selected as the switching frequency is high.29 14. The analysis is performed for 8% flux hysteresis band and 5% torque hysteresis band. 3.i . The stroke angle for 4 phase 8/6 SRM is 150. The normal operating frequency range of the device is 5 kHz . Results and Analysis The performance of the DTC based SRM drive is analyzed in Matlab/Simulink environment. The instantaneous torques of all the four phases is shown in Figure 7(e). It can be seen that the trajectory of fluxes between α and β axes is circular in nature.25 Wb by following a hysteresis band of 0.No. The settling time for steady state speed is 0.69 13. Figure 7(f) shows the speed response. It is observed the current is not directly controlled and thus due to the nonlinear motor characteristics. Figure 7 shows the simulation waveforms of the drive with DTC technique. These Lookup tables are formulated by conducting Finite Element Analysis (FEA) which is discussed clearly in [13].40 Nm. It is observed that the actual or calculated torque and flux has higher error. % Flux-linkage Hysteresis Band % Torque Hysteresis Band 1 2 3 4 5 6 10 10 8 8 5 5 10 5 8 5 10 5 Switching Frequency (kHz) 6. Figure 7(d) shows the load torque and it varies as the square of the speed. Thus. It is observed that the torque is maintained within the hysteresis band of 0.99 14. ITBL is the flux-current-angle (λ. The same is repeated for the remaining phases but each phase is displaced from one other by the stroke angle. the switching frequency of the device increases. The effect of variation of flux and torque hysteresis bands on switching frequency of the converter is analyzed.020 Wb. Figure 7(c) shows the total torque response. This can be attributed to finite iteration time of the simulation.69 7. The maximum current and the average current of each phase are 13.i . It is observed that as the hysteresis bands decreases. 364 0.364 0. The variation of flux and torque hysteresis bands on switching frequency of TELKOMNIKA Vol.5 0.366 0.1 9 9 8 8 7 7 6 5 4 3 3 1 0.368 Time (Sec) 0.3 -200 0 0.36 0.) Fluxbeta 0.374 0.25 Current (A) 10 5 0.5 (f) Speed 0.05 0 0.36 0.2 0.358 0. the torque is controlled directly through the control of magnitude of the fluxlinkage and the change in speed of the stator flux vector.15 0.2 150 100 Deltaangle (Deg.1 0 Fluxalpha 0. The DTC based 4 phase 8/6 SRM drive is analyzed.372 0 0 0. No.3 200 0.1 0.5 (h) Delta angle Figure 7.2 0.3 Time (Sec) (c) TotalTorque response 10 Ph 1 Ph 2 0.37 0.3 Time (Sec) 0. 12.1 50 0 -50 -100 -0.2 -0.2 -150 -0.2 0.3 Time (Sec) 0. Conclusion In DTC.4 5 1 0.2 0.1 0.1 (g) Flux trajectory 0. December 2014 : 8085 – 8091 .366 0.4 0 0 0.37 0.362 0.1 (e) Torque in all phases 0.374 0.8090 ISSN: 2302-4046 15 Ph 2 Ph 1 Ph 3 Ph 4 Fluxmagnitude (wb-turns) 0.1 0 -0.2 0.7 700 8 Speed (rpm) Torque (Nm) 600 6 4 2 400 300 200 100 0 0.372 0 0 0.3 Time (Sec) 0.5 6 2 0 0 0.1 0. 12.5 4 2 0.368 Time (Sec) 0.362 0.2 0.2 0.4 0.4 (b) Flux magnitude Loadtorque (Nm) Totaltorque (Nm) (a) Stator current 0.358 500 0.4342 Y: 796.3 Time (Sec) Ph 3 (d) Load torque 800 Ph 4 X: 0.4 0.1 0. Simulation waveforms of SRM drive with Direct Torque Controller 4. 26 Annual Conf. Xiang Wang. 3389-3392. th [4] AD Cheok. 2321–2325. PVN Prasad. Idris NRN. 2013. TELKOMNIKA Indonesian Journal of Electrical Engineering. Jidin A. International Conference Power Electronics & Variable Speed Drives. [8] Sutikno T. Comparative Performance Analysis of DTC based Switched Reluctance Motor Drive Using Torque Equation and FEA Models. 2014: 8(3): 509-514 [13] P Srinivas. 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