Direct Torque Control of Induction Motor Employing Differential Evolution Algorithm

Transcription

1 Direct Torque Control of Inuction Motor Employing Differential Evolution Algorithm A.Gopi 1, T.Vamsee kiran 2 PG Stuent [P.E], Dept. of EEE, DVR & Dr. HS MIC College of Technology, Anhra Praesh, Inia 1 Associate professor, Dept. of EEE, DVR & Dr. HS MIC College of Technology, Anhra Praesh, Inia 2 ABSTRACT: Unesirable torque an flux ripple may occur in conventional irect torque control (DTC) of inuction motor rive. DTC can improve the system performance at low spees by continuously tuning the regulator by ajusting the Kp, Ki values. In this paper, ifferential evolution (DE) algorithm is employe to ajust the parameters (Kp, Ki) of the spee controller in orer to minimize torque ripple, flux ripple, an stator current istortion.the DE base PI controller has resulte in maintaining a constant spee of the motor irrespective of the loa torque fluctuations. Keywors: Differential Evolution, DirectTorque Control, PI controller. I. INTRODUCTION Inuction motors are the most wiely use machines in AC rives because of their rugge construction an cost. To control the torque an flux of the inuction motor ifferent strategies are available as per the literature. Direct torque control is one of the methos which are use in variable frequency rives for the control of the inuction motor. Direct torque control has emerge over the last ecae to become one possible alternative to the well-known Vector Control of Inuction Machines. In DTC, the stator flux an the torque are irectly controlle by selecting the appropriate inverter state. The output of the spee regulator (PI controller) results in generation of the reference torque. However the PI controller cannot result in perfect control if its parameters Kp, Ki are not properly chosen. The unesire torque an flux ripple may occur in conventional irect torque controlle inuction motor rive. DTC can improve the system performance at low spees by continuously tuning the regulator by ajusting the Kp, Ki values. Many artificial intelligence techniques an ranom search methos have been employe to improve the control parameters. Differential Evolution (DE) is propose to ajust the parameters (Kp, Ki) of the spee controller in orer to minimize torque ripple, flux ripple, an stator current istortion. DE is generally consiere as a reliable, accurate, robust an fast optimization technique. DE has been successfully applie to solve a wie range of numerical optimization problems. II. MATHEMATICAL MODELING OF INDUCTION MOTOR. Mathematical moelling of the inuction motor been one base on the equations (1) (). Copyright to IJAREEIE 481

2 V qs = R si qs + φ qs t (1) V s = R si s + φ s t (2) = R ri qr + φqr ωrφ r t (3) = R ri r + φr ωrφ qr t (4) 3 p T e = (φsiqs φqsi s) 2 2 () III. CONVENTIONAL DIRECT TORQUE CONTROL A. DTC STRATEGY: Fiel Oriente metho ecouples stator current vector into -q components. FOC uplicate the DC motor ynamics. Unlike FOC, DTC oes not uplicate the DC motor ynamics, but DTC metho chooses the voltage vectors accoring to the emane flux an torque in orer to keep them within hysteresis bans. The torque evelope by the inuction motor is given by 3 p Lm T e= λ s λ r sinθ (6) 22σLsLr From the above equation we can say that the torque prouce by the inuction motor epens upon the stator flux, rotor flux an phase angle between them. The inuction motor stator voltage equation is given by λs V s = - Isr s (7) t Change in flux can be expresse as Δλ s = V s t (8) This means that the voltage vector changes the flux vector. It is well know that two level inverter is capable of proucing eight voltage vectors. A switching table is generate which etermines the voltage vector that has to be applie. The selection of the voltage vector epens on the position of the stator flux an torque. Voltage vector selection table can be expane to inclue more number of voltage vectors by three level inverter. The use of PI controllers to comman a high performance DTC of inuction motor rive is often characterize by an overshoot uring start up. This is mainly cause by the fact that the high value of the PI generates a positive high torque error. This will let the DTC scheme take control of the motor spee riving it to a value corresponing to the reference stator flux. At start up, the PI controller acts only on the error torque value by riving it to the zero borers. When this borer is crosse, the PI controller takes control of the motor spee an rives it to the reference value. Another main problem of the Conventional PI controller is the correct choice of the PI gains. Traitional PI controller using fixe gains may not provie the require control performance for the reason that the inuction motor parameters are changing on ifferent operating conitions. To tune the PI controller, lots of strategies have been propose. The most famous, which is frequently use in inustrial applications, is the Ziegler-Nichols metho which oes not require a system moel an control parameters are esigne from the plant step response. Tuning using this metho is characterize by a goo isturbance rejection but on the other han, the step response has a large percentage overshoot in aition to a high control signal that is require for the aequate performance of the system. Another technique uses frequency response methos to esign an tune PI controller gains base on specifie phase an gain margins as well as crossover frequency. Furthermore, root locus an pole assignment esign techniques are also propose in aition to transient Copyright to IJAREEIE 482

3 response specifications. All these methos are consiere as moel base strategies an then the efficiency of the tuning law epens on the accuracy of the propose moel as well as the assume conitions with respect to actual operating conitions. All these techniques takes a more time fortuning the PI controller. To overcome the state problems, an aaptive PI controller has been propose to replace the classical PI controller where the proportional an integrator gains are tune by the Differential Evolution algorithm. Fig 1.Conventional DTC of Inuction motor. IV.DIFFERENTIAL EVOLUTION ALGORITHM The DE algorithm was introuce by Storn an Price in 199. It is a population base algorithm using mutation, crossover an selection that of a Genetic Algorithm. The main ifference in constructing better solutions is that Genetic Algorithm relies on crossover while DE relies on mutation operation. The DE starts by initializing the population ranomly to cover the entire search space uniformly. Each iniviual of the population is perturbe through a mutation operator an combine by using a crossover operator. These operators generate a new population consisting of the most promising solution. Each iniviual of the new population is evaluate an it was selecte into the next generation. When the best iniviual in terms of the fitness function meets the optimization criteria, or the number of iterations reaches that means maximum specifie iterations, the optimization is terminate. Fig.2 PI Controller Copyright to IJAREEIE 483

4 e(t) = W p i A. Steps in DE algorithm: Step.1: Initialization Initialize the population size(np) an generations(n). Initialize Mutant factor(f) an Crossover Rate (CR). At the early stage of DE search, i.e., t =, the problem inepenent variables are initialize somewhere in their feasible numerical range... The Population Vector (PV)=[ - - ] np,where np is the size of population. Xi(t)=X L j +ran(,1)*(x U j -X L j ) Determine the Fitness Vecor(FV) by substituting the values of variables in the objective function. ref W * e(t) = Te (k k t) Step.2:Mutation In the mutation process a new population vector was create from the initial values of population vector. For the creation of onor vector the i th member passes through the following steps. i. Three ifferent members r1 r2 r3 actual X, X, X, are chosen ranomly from the current population an not coinciing with the current member. ii. The mutation factor is multiplie with the ifference of any two members an this scale ifference ae to the thir one. V(t)=Xr 1 +F*(Xr 2 -Xr 3 ) The mutant factor is generally in the range of.4 to 1.. Step.3: Crossover Generally two types of crossover schemes are use in the DE algorithm, I. Exponential crossover an II. Binomial crossover In this paper, Binomial crossover scheme is use which can be expresse as, v(t) if ran(,1) < CR u(t) = x(t) else u(t) represents the chil that will compete with the parent X(t). u(t) having the new population, so we can etermine the new fitness function. New fitness=[ - ] np 1 Step.:Selection In the selection process comparing the ol an new fitness values. DE actually involves the Survival of the fittest principle its selection process. The selection process can be expresse as, X i(t+1) = u(t) if f(u i(t)) f(x i(t)) x i(t) if f(x i(t)) <f(u i(t)) If the new fitness value is less than the fitness value X i (t)=u i (t),else X i (t)=x i (t) Copyright to IJAREEIE 484

5 Fig (3) Flowchart of DE algorithm V. Results an Discussions The optimize values of Kp an Ki obtaine from DE program are consiere in the DTC system an the results have been observe. To valiate the performance of DE base DTC ifferent loa torques has been applie as shown in fig 4(a), (a), 6(a) an 7(a). The motor spee waveforms relate to the DE base DTC is comparison with conventional PI base DTC are as shown in fig 4(b), (b), 6(b) an 7(b). DTC Loa torque(n-m) Loa torque(n-m) Fig.4(a) Applie loa torque spee(rpm) spee(rpm) Convenional DTC DE base DTC Fig.4(b).Spee wave forms of conventional an DE base Conventional DTC DE base DTC Fig.(a).Applie loa torque. Fig.(b).Spee waveforms of Conventional an DE base DTC. Copyright to IJAREEIE 48

6 12 Loa torque(n-m) spee(rpm) Cnventional DTC DE base DTC Fig.6(a).Applie loa torque. Fig.6(b).Spee waveforms of Conventional an DE base DTC. 12 Loa torque(n-m) spee(rpm) Conventional DTC DE base DTC Fig.6(a).Applie loa torque. Fig.6(b).Spee waveforms of Conventional an DE base DTC. VI. CONCLUSION Base on the DTC inuction motor, DE tune PI controller is propose in this paper. DE tune PI controller also improves the spee ajustment capability of the DTC system. From the simulation results of DE base DTC it has been observe that an improve torque an flux response was achieve. The comman flux optimization scheme has reuce the torque ripple. It can be conclue that DE base DTC is better compare to the conventional DTC system. REFERENCES [1] Abou El Ela AA, Abio MA, Spea SR. Optimal power flow using ifferential evolution algorithm, Electr Power Syst Res, Vol.8, pp.878 8, 2. [2] K. Ohyama, G. M. Asher, an M. Sumner, Comparative analysis of Experimental Performance an stability of sensorless inuction motor Drives, IEEE Trans. In. Electron. Vol. 3, no. 1, pp , Feb. 26. [3] Naia Salvator Anrea Caponio, Stuent, Ferrante Neri, Silvio Stasi, an Giuseppe Leonaro Cascella, Optimization of Delaye- State Kalman- Filter- Base Algorithm via Differential Evolution for Sensorless Control of Inuction Motors IEEE transactions on Inustrial Electronics, Vol. 7, No. 1, January 2. [4] C.Thanga Raj, member, IAENG, S.P.Srinivastava, an pramo Agarwal Differential Evolution Base optimal control of Inuction Motor by serving tom Textile Inustry, IAENG International Journal of Computer Science, 3:2, IJCS [] K. V. Price, Differential evolution: A practical approach to global optimization, Springer, Berlin, 2. [6] Fang Wang, Yuhui Qiu, A moifie particle swarm optimizer with Roulette selection Operator, IEEE conference proceeings of NLP-KE, 2, pp [7] Hassan Farhan Rashag,S.P.Koh, Ahme N.Aballa, Naia M.L.Tan, K.H.Chong an S.K.Tiong. DTC torque ripples minimization base on PSO-PID controller Scientific Research an Essays Vol. 7(1), pp.172,23,april,2 [8] H. M. B. Metwally, f. E. Abul-Kaer, H. M. El-Shewy, M. M.El-Kholy, Propose torque Optimize behaviour for igital spee Control of inuction motor, Energy Conversion an Management, Vl. 43, 26, pp [9] Price, K.V., Storn, R.: Differential evolution A simple evolution strategy for fast optimization. Dr. Dobb s Journal 22(4) (1997) Copyright to IJAREEIE 486

7 [] Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approachto Global Optimization. Springer-Verlag New York, Inc. (2). BIOGRAPHY A. Gopi Receive B.Tech egree in Electrical an Electronics engineering from Sri Sarathi Institute of Engineering an Technology, Nuzvi in the year 211. He is currently pursuing M.Tech(Power electronics) in DVR & Dr. HS MIC College of Technology. Inverters. T. Vamsee Kiran is grauate from Bapatla Engineering College in the year 2 an M.E in Applie Electronics from PSG College of Technology, Coimbatore in the year 22. He worke in Sir C.R. Rey College of Engineering, K.L.College of Engineering an is presently working as Associate Professor in DVR & Dr. HS MIC College of Technology, an has got 12 years of teaching experience. He has submitte his Ph.D thesis in JNTU College of Engineering, Hyeraba. He presente papers in National, international Conferences an International Journals. His research interests inclue Power Electronics Drives an Multilevel Copyright to IJAREEIE 487