MATLAB SIMULATION OF DIRECT TORQUE CONTROL OF INDUCTION MOTOR USING CONVENTIONAL METHOD AND SPACE VECTOR PULSE WIDTH MODULATION

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1 MATLAB SIMULATION OF DIRECT TORQUE CONTROL OF INDUCTION MOTOR USING CONVENTIONAL METHOD AND SPACE VECTOR PULSE WIDTH MODULATION Naveen Chander Assistant Professor, Department of Electrical and Electronics Engineering, A P Goyal Shimla University, Shimla, India. snl.naveen@gmail.com ABSTRACT This paper proposes direct torque control of induction motor simulation using conventional method and space vector pulse width modulation technique for ripple reduction. Direct Torque Control (DTC) is a control technique used in AC drive systems to obtain high performance torque control and thereby controlling the speed of induction motor. The principle is based on simultaneous decoupling of stator flux and electromagnetic torque of AC drive system. DTC drives use hysteresis comparators and they suffer from high torque ripple and variable switching frequency problem.the proposed Space Vector Pulse Width Modulation (SVPWM) baseddtc reduces torque ripples. The basis of the SVPWM-DTC methodology is the calculation of the required voltage space vector to compensate the flux and torque errors and its generation using the SVPWM at each sample period.the performance of thismethod is demonstrated by simulation using MATLAB/Simulink software. Simulation results presented in this paper show the torque,flux linkage and stator current ripple decreases with the proposed SVPWM-DTC algorithm. Keywords:Direct Torque Control, Space Vector Pulse Width modulation, Induction Motor I. INTRODUCTION Induction Motors (IM) are widely used in industrial, commercial and domestic applications as they are low- cost, rugged and easy to maintain. Induction motors demands better control platform that is precise, quick torque and flux response, large torque at low speed, wide speed range. Though DC motor provides desired performance, its maintenance is high and is unsafe in explosive environment. In 1970s, Field Oriented Control (FOC) platform proved its effectiveness for torque and speed control of induction motor. Hence the scheme proves itself superior to the DC machine. The problem faced by FOC scheme is complexity in its implementation due to dependence of machine parameters, reference frame transformation. Later DTC was introduced. 168

2 Direct torque control (DTC) method is used to control the torque (finally speed) in variable frequency drives of three-phase AC electric motors. From the measured voltage and current of the motor an estimate of the motor's magnetic flux and torque is calculated. Integrating the stator voltages, stator flux linkage is estimated. Cross product of measured motor currentvector and estimated stator flux linkage vector results in estimated torque. The estimated flux magnitude and torque are then compared with their reference values. If either the estimated flux or torque deviates from the reference more than allowed limits, the transistors of the variable frequency drive are turned OFF and ON in such a way that the flux and torque errors will return in their tolerant bands as fast as possible. Thus direct torque control is one form of the hysteresis control. The method requires only the stator resistance to estimate the stator flux and torque. The basic DTC schemeconsists of two comparators with specified bandwidth, switching table, voltage source inverter, flux and torque estimation block[1]. Like every control method has some advantages and disadvantages, DTC method has too. Some of the advantages are lower parameters dependency, making the system more robust and easier implements and the disadvantages are difficult to control flux and torque at low speed, current and torque distortion during the change of the sector, variable switching frequency, a high sampling frequency needed for digital implementation of hysteresis controllers, high torque ripple. The torque ripple generates noise and vibrations, causes errors in sensor less motor drives, and associated current ripples are in turn responsible for the EMI. The reason of the high current and torque ripple in DTC is the presence of hysteresis comparators together the limited number of available voltage vectors. If a higher number of voltage vectorsthan those used in conventional DTC is used, the favorable motor control can be obtained[2]. Because of complexity of power and control circuit, this approach is not satisfactory for low or medium power applications. This method is used in a variable-speed asynchronous motor drive. In this control scheme, a d-q coordinate s reference frame locked to the stator flux space vector is used to achieve decoupling between the motor flux and torque. They can be thus independently controlled by stator d-axis voltage and q-axis voltage. This paper proposes a novel control method of DTC based on SVPWM to give a constant torque switching frequency and reduces the torque ripple. This method is used in a variable-speed asynchronous motor drive. In this control scheme, a d-q coordinate s reference frame locked to the stator flux space vector is used to achieve decoupling between the motor flux and torque. They can be thus independently controlled by stator d-axis voltage and q-axis voltage. 169

3 II. PRINCIPLE OF DIRECT TORQUE CONTROL The basic principle of DTCis to directly select stator voltage vectors according to the torque and flux errors which are the differences between the references of torque and stator flux linkage and their actual values[3]. The basic functional blocks used to implement the DTC control platform is shown in Fig.1. The governing equation for torque for this scheme is due to the interaction of stator and rotor fields. Torque and stator flux linkage are computed from measured motor terminal quantities i.e. stator voltages and current. An optimal voltage vector for the switching of VSI is selected among the six non-zero voltage vectors and two zero voltage vectors by the hysteresis control of stator flux and torque. Fig.1 Schematic of Basic DTC A. Torque and Flux Estimator The terminal voltages and currents are used to calculate feedback flux and torque from the machine. The sector number is also calculated by the block used to compute the sector in which the flux vector lies. The phase voltage and currents in stationary reference are given by the following equations V sa =Vaand V sb = 1 3 (V a+2v b )......(1) I sa =Iaand I sb = 1 3 (I a+2i b )...(2) The stator flux components are given by Ψ sa = V sa R s I sa dt......(3) Ψ sb = V sb R s I sb dt (4) The magnitude of the stator flux can be estimated from the components of the stator flux as given by the equation 170

4 Ψ s = Ψ sa 2 + Ψ sb 2...(5) The flux components are used to obtain flux vector zone. Torquecan be calculated by using the flux components, current components and IM number of and is given by equation T e = 3 2 B. Torque and Flux Controller P 2 (Ψ sai sb Ψ sb I sa )...(6) 1) Torque Hysteresis Controller The Torque hysteresis controller is a three level controller and is shown in Fig.2. It means the torque control loop has three levels of digital outputs. The torque error ΔT e is given to the torque hysteresis controller and the output is torque error status (dt e ) which can have three values -1, 0 or 1. The width of the hysteresis band is 2ΔTe. Torque error status is given to the switching table for optimum voltage vector selection for the inverter. Fig.2 Torque Hysteresis Controller Torque error ΔT e = T eref - T e...(7) dt e = +1 if T e < T eref ΔT e : Torque to be increased dt e = - 1 if T e > T eref + ΔT e : Torque to be decreased dt e = 0 if T eref ΔT e T e T eref + ΔT e : Torque to remain unchanged. 2) Flux Hysteresis Controller The flux hysteresis controller is a two level controller and is shown in Fig.3. So the flux control loop has two digital outputs. The stator flux error ΔΨ given to the flux hysteresis controller and the output is flux error status (dψ s which can have two values 0 and 1. The width of the hysteresis band is 2ΔΨ s. Flux error status is given to the switching table for optimum voltage vector selection for the inverter. Fig. 3. Flux Hysteresis controller 171

5 Stator flux error ΔΨ s =Ψ sref - Ψ s.....(8) The flux is controlled according to the following equations dψ s = 1 if Ψ s Ψ sref ΔΨ s : flux to be increased dψ s = 0 if Ψ s Ψ sref + ΔΨ s : flux to be decreased C. Switching Selection A high performance torque control can be established due to the decoupled control of stator flux and torque in DTC. Fig.4 shows an example of stator flux located in sector-1 (S(1)) with the corresponding optimum switching voltage vectors for anti-clockwise and clockwise rotation of the shaft. Optimum switching vector selection table given by Table.1 shows the optimum selection of the switching vectors in all sectors of the stator flux plane. This table is based on the value of stator flux error status, torque error status and orientation of stator flux for counter clockwise rotation of the shaft. Fig.4 Optimum Switching Voltage Vector in Sector-1 for (a) Anti-Clockwise and (b) Clockwise Rotation Table 1 Applied Selected Voltage Vectors dψ dt e S(1) S(2) S(3) S(4) S(5) S(6) 1 1 V 2 V 3 V 4 V 5 V 6 V 1 0 V 7 V 0 V 7 V 0 V 7 V 0-1 V 6 V 1 V 2 V 3 V 4 V V 3 V 4 V 5 V 6 V 1 V 2 0 V 0 V 7 V 0 V 7 V 0 V 7-1 V 5 V 6 V 1 V 2 V 3 V 4 172

6 In stationary reference frame the stator flux equation can be written as: Ψ s = V s i s R s dt.....(9) If the stator resistance drop is neglected for simplicity, the stator flux varies along the direction of applied voltage vector and the equation is reduced to Ψ s = V s Δt.....(10) which means, by applying stator voltage vector V s for a time increment Δt, Ψ s can be changed incrementally. The command value of the stator flux Ψ s * follows a circular trajectory, the plane of stator flux is divided into six sectors as shown in Fig.5.Each sector has a different set of voltage vector to increase or decrease the stator flux. The command flux vector rotates in anticlockwise direction in a circular path and the actual stator flux vector Ψ s tracks the command flux in a zigzag path but constrained to the hysteresis band which is shown in fig.5. In general, the active forward voltage vector V s,k+1 and V s,k+2 are applied to increase or decrease the stator flux respectively when the stator flux lies in sector k. The radial voltage vectors V s,k and V s,k+3 which quickly affect the flux are generally avoided. The active reverse voltage vectors V s,k 1 and V s,k 2 are used to increase or decrease the stator flux in reverse direction. The stator flux vector change due to stator voltage vector is quick whereas change rotor flux is sluggish because of its large time constant T r. That is whyψ s movement is jerky and Ψ r moves uniformly at frequency ω e as it is more filtered. However the average speed of both remains the same in steady state condition.the flux increment vector corresponding to each of the six inverter voltage vectors are shown in Fig.5. The flux can be increased by the V 1, V 2 and V 6 vectors and it can be Fig.5 Circular Trajectory of Stator Flux decreased by the V 3, V 4 and V 5 vectors. Similarly torque is increased by the V 2, V 3 and V 4 vectors and decreased by the V 1, V 5 and V 6 vectors. The zero vector short circuits the machine terminals and keeps the flux and torque unaltered. 173

7 III. PRINCIPLE OF SPACE VECTOR MODULATED DTC SCHEME The basic functional blocks used to implement the DTC-SVM control platform is shown in Fig.6[4]. In this system, actual value of the flux linkage and torque is determined by flux and torque estimators. To determine the duration time of voltage vectors, PI controller and numeric calculation are used such that the error vector in flux and torque can be fully compensated. Since the controllers produce the voltagecommand vector, appropriate space voltage vector can be generated with SVM and fixed switching frequency can be achieved.the output of the PI flux and torquecontrollerscanbe interpreted as the reference stator voltage components in d-q coordinate system. These dc voltage commands are then transformed into stationary frame (αβ),the command valuesv α and V β are delivered to SVM block. The SVM block performs the space vector modulation of V s to obtain the gate drive pulses for driving the inverter circuit. Fig.6 Schematic of DTC-SVPWM A. Space Vector Modulation SVM techniques have several advantages such as better DC bus utilization, lower switching losses, lowertotal Harmonic Distortion (THD) in the AC motor current, lower torque ripple and easier to implement in the digital systems. At each cycle period, a preview technique is used to obtain the voltage space vector required to exactly compensate the flux and torque errors[5]. The torque ripple for this SVMDTC is significantlyimproved and switching frequency is maintained constant[6-7]. SVM switching vectors and sectors are shown in Fig. 7. SVM, based on the 174

8 Fig.8. Switching Vectors and Sectors switching between two adjacent boundary active vectors and a zero vector during one switching period, T z and for a given reference voltage vector in the first sector (0-60 o ) is shown in Fig.8(a). Fig.8. SVM in the first Sector (a) Reference Voltage Vector (b) Switching Pattern for Three-Phase Modulation. Space vector PWM can be implemented by the following steps: (i) Transform 3-phase to 2-phase quantity and determine V s and angle. (ii) Determine time duration T 0,T 1 and T 2. The reference voltage vector V s, a constant magnitude and frequency in the steady-state, is sampled at equal time intervalof T z. In this sampletime, the inverter isswitched and made to remain at different switching states for different durations of time such that the average space vector generated within sample period is equal to the sampled value of the reference vector, both in terms of magnitude and angle. The switching statesthat can be used within T z are the two zero states and the active states which are S A and S B, with vectors V 1 and V 2 respectively forming the start and the end boundaries of the sector as shown in Fig.8[8]. 175

9 The two switching states (S A and S B ) are named active switching states. S A indicates the inverter switching states (001), (100), or (010) and S B indicates the inverter switching states (101), (110) or (011). Active vector times, T A and T B, are defined as the times due to the active switching states, S A and S B respectively. Null vector times T 0 and T 7 are defined as the times due to the null switching states S 0, (000), and S 7, (111) respectively. In DTC, with the space vector PWM technique, the DTC transient performance and robustness are preserved and the steady state torque ripple is reduced. Moreover, the inverter switching frequency is constant and totally controllable. 1) Determination of space vector magnitude and angle In this modulation technique the three phase quantities can be transformed to their equivalent 2- phase quantity in stationary frame. The magnitude of reference vector used for modulating inverter output is, Vs= V a 2 + V b 2...(11) Angle is calculated as, δ = tan 1 ( V b V a )...(12) 2) Determination of time duration In Fig.7 reference space vectorvs is in sector 1 is generated as a combination of active vectors and and zero vector V 1,V 2, V 0 /V 7. T 1, T 2 and T 0 is the time duration for which vector V 0,V 1,V 2. By applying volt-sec balance, V S T Z = V 0 T 0 + V 1 T 1 +V 2 T 2....(13) V S cos δt Z = 2 3 V dct V dccos π 3 T 2...(14) V S sin δ T Z = 2 3 V dc sin π 3 T 2...(15) By solving the equations (14) and (15), time T 1, T 2 is obtained as T 0 =T Z -(T1+T2) (16) T 1 =T Z a sin (π 3 δ) sin ( π 3 ) (17) sin (δ) T 2 =T Z a sin ( π ) (18) 3 IV. SIMULATION AND RESULTS The DTC and SVM-DTC scheme for induction motor are simulated using MATLAB/Simulink and their results have been compared. Fig.8 shows the Simulink model of conventional control of induction motor and Fig.9 shows the Simulink model of SVPWM DTC of induction motor. The motor parameters used for simulation are given in Table

10 Fig.8.Simulink Model Using Conventional Method. Fig.9. Simulink Model Using DTC SVPWM Method Table 2 Motor Parameters Supply Voltage 350V Frequency 50Hz Stator Resistance, R S 1.115Q Rotor Resistance, R r Q Stator self Inductance, H Rotor self inductance, L r H Mutual Inductane, L m H Moment of Inertia, J 0.02 Kg.m 2 177

11 A. Simulation Results Both conventional control method and DTC SVPWM was simulated and stator currents, rotor speed and torque are obtained. Fig. 10 and Fig. 11 method respectivelyshows variation of stator currents with time using conventional method and DTC SVPWM. Next we compare Fig. 12 and Fig.13shows speed and torque response of induction motor using conventional method and and DTC SVPWM. It is clear that induction motor is taking 0.5 seconds time to settle to a constant speed and there are large variations in torque with time and variation is between and Nm in the conventional method. In DTCSVPWM,the transient period is very low.there isa large variation in torque which is necessary to start the induction motor as shown in Fig 13, but as the time progresses torque variations are reduced to a large extent and the motor is settling toconstant speed within no time. Fig.10. Stator Currents Using Conventional Method 178

12 Fig. 11. Stator Currents Using DTC SVPWM Method Fig.12. Speed and Torque Response Using Conventional Method 179

13 Fig. 13. Speed and Torque response Using DTC SVPWM Method V. CONCLUSION This project has reviewed control strategies for inductionmotor drives. The DTC represents avery good alternative to Field Oriented Control (FOC). For controlling the AC drivesdtc strategies have been divided into two groups: hysteresis-based switching tabledtc, and constant switching frequencyschemes operating with space vector modulator (SVM-DTC). Constant switching frequency SVM-DTCschemesimproveconsiderably the drivein terms of reduced torque and flux pulsations, reliable start up and lowspeed operation. Therefore,SVM-DTC is an excellent solution for general purpose IMdrives in a very wide powerrange. In conclusion, it is believed that the DTC principle will continue toplay a strategic role in thedevelopment of high performance drives. REFERENCES [1]Ambrozic,Buja, "Band-constrained technique for direct torque control of induction motor, pp , IEEE transaction on industrial Electronics, August [2] I. Takashi and T. Noguchi, A new quick-response and high-efficiency control of an induction motor, IEEE Trans. Industry Applications, vol. IA-22, no.5, pp , [3]AnjanaManuel and Jebin Francis, "Simulation of Direct Torque Controlled Induction Motor Drive by using Space Vector Pulse Width Modulation for Torque Ripple Reduction," 180

14 International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering,vol. 2, issue 9, pp , September,20113 [4] S.L.Kaila and H.B.jani, " Direct Torque Control for Induction Motor Using SVPWM Technique," National Conference on Recent Trends in Engineering & Technology, May [5] EmreOzkop and Halil I. Okumus, "Direct Torque Control of Induction Motor Using Space Vector Modulation (SVM-DTC)," Power System Conference, pp ,12-15 March [6] Thomas G. Habetler and Francesco Profumo, " Direct Torque Control for Induction Machines Using SVPWM Technique," IEEE transactions industry applications , vol. 28, No. 5, October [6] D. Ocean, L. Romeral, J.A. Ortega, J. Cusido, and A. Garcia, Discrete space vector modulation applied on a PMSM motor, 12th International Power Electronics and Motion Control Conference, EPE-PEMC 2006, pp , [7] H.R. Keyhani, M.R. Zolghadri, and A. Homaifar, An extended and improved discrete space vector modulation direct torque control for induction motors, 35th Annual IEEE Power Electronics Specialists Conference, Germany, pp , [8]C.Bharatiraja, Dr.S.Jeevananthan, A Novel Space Vector Pulse Width based High Performance Variable Structure Direct Torque Control Evaluation of Induction Machine Drives,International Journal of Computer Applications, pp-, vol. 3, No. 1, June