# SVM-DTC OF AN INDUCTION MOTOR BASED ON VOLTAGE AND STATOR FLUX ANGLE USING FUZZY LOGIC CONTROLLER

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2 (1) Stator and rotor flux linkages in d-q reference frame (2) (3) (4) Fig-2: Equivalent circuit of induction motor in q- frame Electromagnetic torque equation where (5) (6) : Generic reference system, rotor electrical speed, rotor mechanical speed : Stator and rotor resistances : Stator, rotor and mutual inductances : The stator flux in d-q frame : Rotor flux in d-q frame : Stator and rotor currents in d-q frame P : Number of poles T and T : Motor and load torque e L B, J : Friction coefficient and inertia of the system The equivalent circuits corresponding to these equations in d-q reference frame are illustrated in Fig. 1 and Space Vector Modulation (SVM) Space vector modulation plays a pivotal and practical role in power conversion.basically it is an algorithm for the control of Pulse Width Modulation(PWM) and used for the production of Alternating Current (AC) waveforms. There are different variations of SVM that result in different quality and computational requirements. One active area of development is in the reduction of Total Harmonic Distortion in output voltages or currents in the windings of the motor load. SV PWM refers to a special method of determining the switching sequence of the upper three power transistors of a three-phase VSI. Stator voltages in αβ reference frame acts as input to SVPWM so that variable voltage and variable frequency of inverter is attained. It is using space vector concept to compute the duty cycle of the switches which is essential implementation of digital control theory of PWM modulators. Space Vector Modulation technique uses a set of vectors that are defined as instantaneous space-vectors of voltages and currents at the input and output of the converter. The instantaneous three phase voltages can be represented by a space vector in stationary reference frame. These vectors are produced by the different switching states that the converter is able of generating.the eight possible switching states of VSI are indicated as voltage space vectors in a two-level space plane as shown in Fig. 3 Fig-1: Equivalent circuit of induction motor in d- frame Fig-3 : Space vector diagram 2015, IRJET.NET- All Rights Reserved Page 1574

3 Equations for SVPWM are as follows: The three phase voltage By using Clark transformation ( ) (8) (7) Amplitude of stator voltage is controlled by PI torque and PI flux controller and then it is realized by space vector modulation approach. The conventional DTC algorithm is based on instantaneous values from hysteresis flux and torque controllers and directly intended digital control signals for the inverter.the control algorithm in DTC-SVM approach is based on average values where as the switching signals for the inverter are calculated by space vector modulator which is the main difference between conventional DTC and DTC-SVM control methods. The combined technique of Direct Torque Control(DTC) and Space Vector Modulation(SVM) is shown in Fig. 4. (9) V(t) = (10) Where, (11) (12) (13) (14) (15) (16), K = 1,2,..,6 (17) The main objective of SVM is to approximate the reference voltage by using eight switching pattern(v 0 to V 7 ). The equations(7 to 17) can be used to develop algorithm for space vector modulation. 3. DTC-SVM STRATEGY In order to overcome drawbacks in conventional DTC,Direct flux and torque control with space vector modulation scheme is proposed. In the control structure, PI controllers and space vector modulation(svm) algorithm is used. The type of DTC-SVM strategy depends on applied flux and torque control algorithm. Fig -4 : Block diagram of DTC-SVM From PI flux controller, direct axis voltage is produced and control quadrature axis voltage is from PI flux controller. These q and d axis voltages are converted into amplitude of stator voltage.stator flux angle is calculated by using rotor angular frequency and slip angular frequency.the voltages (V d,v q) and stator flux angle are used as reference signals in space vector modulation.dtc based on SVM approach can be explained in detail as follows: The output of PI torque controller is the voltage in quadrature reference frame as shown: (18) (19) From PI flux controller, voltage in direct reference frame can be expressed as shown below: (20) (21) (22) By applying cartesian to polar transformation, amplitude voltage can be obtained as shown below; 2015, IRJET.NET- All Rights Reserved Page 1575

4 Where, : Reference and estimation flux respectively. (23) : Reference and estimation torque respectively. The stator flux angle is calculated based on the relationship between errors of torque and stator angular frequency. The slip angular frequency is the output of PI torque controller and it can be expressed as: (24) Stator angular frequency can be obtained by adding slip angular frequency with rotor angular frequency that can be expressed as : (25) Stator flux angle can be obtained by integrating stator angular frequency (26) the input of PI torque controller so that control quadrature axis voltage is determined.direct axis voltage is generated from flux calculator.by applying polar to Cartesian on amplitude voltage and stator flux angle, direct and quadrature voltages are generated. The reference stator voltages in d-q are calculated based on forcing the stator voltage error to zero at next sampling period. Stator voltages in αβ frame are generated by applying inverse park transformation on d-q voltages in Eq. (31) and (32) and apply to SVM. From the output of SVM, motor control signal is generated and speed of the induction motor is regulated towards rated speed. 4. FUZZY LOGIC SVM-DTC FOR IM Fig. 5 shows basic fuzzy logic control strategy. The classical PI regulators of flux and torque were replaced by two fuzzy logic controllers.the stator flux and torque references are compared with the values calculated in flux and torque estimator and the corresponding errors are sent to the Direct Torque Fuzzy Controllers of the voltage inverter stage control system.error and change in error acts as inputs to fuzzy logic controllers. By applying polar to Cartesian on both amplitude voltages in Eq. (23) and stator fux angle in Eq. (26),stator voltages in direct and quadrature reference frame are generated as : = (27) (28) By substracting the voltages of stator flux estimation from the voltages above in Eq. (27) and (28),the error voltages in d-q reference frame can be derived. (29) (30) (31) (32) Here, the control system is based on Space Vector Modulation(SVM), amplitude of voltage in directquadrature reference frame and angle of stator flux. Reference torque and the estimated torque is applied to Fig.-5: Fuzzy basic model Fuzzy set comprises from a membership function which could be defined by parameters. The value between 0 and 1 reveals a degree of membership to the fuzzy set. The process of converting the crisp input to a fuzzy value is called fuzzification.the output of fuzzifier module is interfaced with the rules. The basic operation of Fuzzy Logic Controller (FLC) is constructed from fuzzy control rules utilizing the values of fuzzy sets in general for the error and the change of error and control action. The results are combined to give a crisp output controlling the output variable and this process is called as DEFUZZIFICATION. The proposed fuzzy based SVM-DTC method consists of fuzzy logic torque and flux controllers that produces optimum control vector by using instantaneous flux and torque errors. On this calculation, fuzzy logic controllers keep tracking of flux and torque 2015, IRJET.NET- All Rights Reserved Page 1576

5 errors and produce necessary change in stator flux vector angle for next step.linguistic terms for error are defined in Table 1. Then, calculated optimum vector angle is applied to space vector pulse width modulation block(sv-pwm) and generates switching signals. Table-1:Linguistic variables for error Linguistic Variable Negative Big Negative Medium Negative Small Zero Error Positive Small Positive Medium Positive Big Symbol NB NM NS ZE PS PM PB Fuzzy logic control rules are defined in Table 2 that produces output from fuzzy logic flux and torque controllers used as the reference stator voltage components that are delivered to inverter stage SVM. Table-2: Rules of Fuzzy logic controller Δe(t)/e(t) NB NM NS ZE PS PM PB NB NB NB NM NM NS NS ZE NM NB NM NM NS NS ZE PS NS NM NM NS NS ZE PS PS ZE NM NS NS ZE PS PS PM PS NS NS ZE PS PS PM PM PM NS ZE PS PS PM PM PB PB ZE PS PS PM PM PB PB output of speed regulator with sampling time period of 50 μs and reference flux is 0.9Wb. The parameters are listed in Table-3. Table-3:Induction Motor simulation parameters Parameter Reference Value Frequency 50 Hz Stator resistance(rs) 2.5 ohms Rotor resistance(rr) 2.4 ohms Flux 0.9 wb Mutual inductance(lm) mh Power 2.2 kw Voltage 420 v current 5.2 A Speed 150 rad/sec Poles 4 The simulink model with SVM- DTC is studied. The results of both SVM- DTC and proposed fuzzy based SVM-DTC in terms of speed, torque and flux and current are compared and is shown below. 5. SIMULATION AND RESULTS A numerical simulation has been carried out in MATLAB/SIMULINK for the proposed scheme.the flux and torque loops of the drive were designed and simulated using fuzzy logic control techniques. Fig-7 : Electromagnetic torque in SVM-DTC Fig-6 : Simulink model of Fuzzy based SVM-DTC For the simulation, 3-phase Y-connected, 2.2 kw, 4-pole, 420V, 50Hz, 150 rad/sec and 5.2A induction motor AC drive system is used. Reference torque is the Fig-8 : Electromagnetic torque in Fuzzy based SVM-DTC 2015, IRJET.NET- All Rights Reserved Page 1577

6 From Fig. 7 and 8, it can be noted that the ripple of torque in proposed method at low speed (50 rad/sec) is reduced with fast response and reaches steady state with in 0.1 sec when compared with fuzzy based SVM- DTC. Fig-11 : Stator flux in SVM-DTC. Fig-12 : Stator flux in Fuzzy based SVM-DTC Fig-9 : Rotor speed in SVM-DTC Stator flux in SVM-DTC as shown in Fig. 11 maintains circular orbit but with high ripple but the ripple of flux in fuzzy based SVM-DTC is reduced as shown in Fig. 12. Fig-10 : Rotor speed in Fuzzy based SVM-DTC In SVM-DTC, the rotor speed reaches the steady state within 60ms as shown in Fig. 9 but the rotor speed in fuzzy based SVM-DTC reaches the steady state value within 30 ms as shown in Fig. 10. The control of speed gives fast dynamic response with no overshoot by using fuzzy logic control technique. Fig-13 : Stator current in SVM-DTC Fig-14 : Stator current in Fuzzy based SVM-DTC 2015, IRJET.NET- All Rights Reserved Page 1578

7 The stator current of combined SVM-DTC suffers from distortion which cause increasing harmonics that degrade the system performance comparing with fuzzy based SVM-DTC as shown above(fig. 13 and 14).Total Harmonic Distortion(%THD) is significantly reduced to 25% in fuzzy based SVM-DTC when compared with 75% of SVM-DTC. Finally, the transient and steady state response of an induction motor can be greatly improved by using fuzzy logic flux and torque controllers. 6. CONCLUSION In this paper, the design of a fuzzy logic based s pace vector modulation technique is proposed for the DTC controlled induction motor drive. The results are analysed, designed and the system performance was studied extensively. Results prove that it is the efficient method to provide torque and flux control without changing motor parameters. The simulation results showed that the proposed method procures good performance in presence of load disturbances as it combines space vector modulation and fuzzy logic control techniques; the advantages of this combination are fast response,reduced ripples in flux and constant switching frequency.this technique can be applied for AC drives where high dynamic performance is required and can be done practically by using Digital Signal processing(dsp) board. REFERENCES [1] Kennel R., A. EI-rafaei, F. Elkady, S. Mahmoud and E. Elkholy, Torque ripple minimization for induction motor drives with direct torque control. Proceedings of 5 th Internatonal Conference on Power Electronics and Drive Systems, 1: [2] Domenico, C., G. Serra and T. Angelo, Implementation of a direct torque control algorithm for induction motors based on discrete space vector. Modulation IEEE T. Power Electr., 15: [3] Morales-Caporal, R. and M., Pacas Encoderless predictive direct torque control for synchronous reluctance machines at very low and zero speed. IEEE T. Ind.Electron., 55: [4] Qu, X., B. Song and H. Li, DTC with adaptive stator flux observer and stator resistance estimator for induction motors. Paper Presented at the 8th World Congress on Intelligent Control and Automation, pp: [5] Yen, S.L. and H.C. Jian,2001. A new approach to direct torque control of induction motor drives for constant inverter switching frequency and torque ripple reduction. IEEE T. Energy Converter, 16 : [6] Bacha F., Dhifaoui, R., Buyse, H., Real time implementation of direct torque conrol of an induction machine by fuzzy logic controller, International conference on Electrical Machines and Systems (ICEMS), vol. 2, P [7] Brahim, M., T. Farid. A. Ahmed, T. Nabil and R.Toufik, A new fuzzy direct control strategy for induction machine based on indirect matrix converter. Int. J. Res. Rev. Comput. Eng., 1: [8] Khanna, R., M. Singla and G. Kaur, Fuzzy logic based direct torque control of induction motor. Conference of Power and Energy Society General Meeting, Calgary, AB, pp: 1-6. [9] Jia-Qiang Yang, Jin Huang, Direct torque control system for induction motors with fuzzy speed PI regulator, IEEE Proceeding of the fourth international conference on machines learning and cybernatics, Guangzhou, August 2005, pp , IRJET.NET- All Rights Reserved Page 1579

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