Power System Stabilizer(PSS) Design Using ANFIS Algorithm and Comparing the Results with conventional and fuzzy PSS

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1 J. Basic. Appl. Sci. Res., () ,, TextRoad Publication IS 9-44X Journal of Basic and Applied Scientific Research Power System Stabilizer(PSS) Design Using ANFIS Algorithm and Comparing the Results with conventional and fuzzy PSS * B.Bayati Chaloshtori, S.Hoghoughi Isfahani, A.Kargar, N.R.Abjadi Department of Electrical Engineering, Faculty of Engineering, Shahrekord University, Shahrekord, Iran ABSTRACT In this paper,used fuzzy logic controller (FLC) for design power system stabilizer (PSS) for single machine infinite bus(smib). Then, the use of ANFIS algorithm for design optimization of the fuzzy controller and comparing the PSS design results based on the usage of conventional controller, FLC by the Mamdani and T-S methods and the ANFIS is addressed. The proposed initiatives in this paper can be referred to the calculations of steam turbine model and the governor in power system stabilizer design. The computer simulation results by MATLAB demonstrate the high ability of power system stabilizer design by the ANFIS Algorithm. KEY WORDS: PSS; Fuzzy logic controller; SMIB; Governor,ANFIS INTRODUCTION Low frequency oscillation in power systems is one of the difficulties that electrical engineers have been usually faced with []. In order to isolate these oscillations as soon as possible, the power system stabilizer is used []. In order to increase the dynamic stability of the power net, power system stabilizer design is needed. The basic role of a power dynamic stabilizer is to increase damping to the oscillation of generator rotor by controlling the stimulations, using auxiliary stabilizer signal. To provide damping, the stabilizer of an electronic torque element should be same-phased with the velocity deviations []. There are different methods for PSS design. One of the interesting new methods is ANFIS (Adaptive neuro-fuzzy inference system) algorithm [, 4]. In fact, the method is a combination of fuzzy method with neural networks. Sometimes, for system modeling, we are unable to recognize the membership functions through input investigation. Although it is possible to optionally determine the parameters related to the membership function, we should notice that proper choose of these parameters has a significant effect on the system operation. In such cases, we can take advantage of the adaptive neuro fuzzy inference systems (ANFIS) technique [, 4]. Modeling power system Synchronous generator model For modeling a synchronous generator connected to the infinite bus, the third machine model known as Heffron-Phillips model [5] is used, which includes three state variables. The block- diagram figure () clearly presents the Heffron-Phillips linear model and the relationship between these three state variables. Fig : Block diagram Heffron-Phillips without AVR Regarding block- diagram figure (), we obtain the following case equation: ω K D r H K K H H ω r δ = ω b H E q K 4 δ + E q T d T d K T d T L E fd *Corresponding Author: Babak Bayati Chaloshtori, Department of Electrical Engineering, Faculty of Engineering, Shahrekord University, Shahrekord, Iran. bbayati@yahoo.com 458

2 Exciter model Chaloshtori, The Thyristor exciter model is shown in figure () [6]. Fig : Block diagram thyristor exciter system In this figure, the delayt R is resulted from the terminal voltage exchanger shown ase f max, E f min.t A delay is related to AVR (Automatic Voltage Regulator) delay. Case equations: ω K D K K r H H H δ ω b ω r E = q E fd K 4 δ H T d T d K T E + V ref q T L d K AK 5 K AK 6 E fd K A T A T A T A T A The block- diagram system dominant disregarding T R are as follows Figure (): Fig : Block diagram Heffron-Phillips with AVR Turbine and governor model Figure (4) shows the simplified block-diagram model for governor and steam turbine. Fig 4: Block diagram steam turbine with governor Complete model of SMIB The Complete SMIB model including Heffron-Phillips model synchronous generator with AVR and steam turbine and the governor is shown in Figure (5). 459

3 J. Basic. Appl. Sci. Res., () , Fig 5: Complete model single machine system with turbine and governor Conventional PSS (CPSS) In Figure (6), the power stabilizer system, which was designed by a classical controller, is shown. Fig 6: PSS designed with classical controller The CPSS block- diagram includes blocks as follows: - Phase compensation block, which provides the proper lead-phase feature for compensating the input lag-phase between the exciter input and the generator electrical torque. - Block eliminator of permanent case of signal (washout), which settles as raising filter with a stable time T w, selected large enough. - Gain block, which determines the extent of damping from the PSS. Block diagram Figure (7) presents the single machine system model with the PSS. PSS design using fuzzy controller (FLC) Fig 7: Block diagram single machine system with PSS Fuzzy controller systems Unlike the classical sets, a fuzzy set, as shown by its name, is an unspecified border set. In fact, in this kind of set, the transfer is performed from inclusion to non- inclusion. This gradual and soft transfer is organized by the membership function. This causes the fuzzy set to have a suitable flexibility for modeling the linguistic meanings [7]. 46

4 Chaloshtori, The structure of fuzzy logic controller (FLC) The structure of the fuzzy logic controller is presented in Figure (8). A fuzzy controller receives the system inputs and turns them into fuzzy forms. Then, regarding the fuzzy rules noted and on the basis of input, output, and membership functions, the controller obtains the output in a fuzzy form, and finally turns the outputs into a non-fuzzy form [8, 9]. Fig 8: Structure of FLC Fuzzy PSS design in a Mamdani form For PSS fuzzy design in a Mamdani form, two inputs and one output was used. Inputs were the rotor speed changes( ω r ), the speed changes of rotor speed( ω r ), and signal voltage output of the fuzzy controller (V PSS ). The abbreviations of input and output of membership functions are listed in Table (). Table : The abbreviations of input and output of membership functions listed Large Negative Membership functions and input and output are shown in Figures 9 to. Medium Negative Small Negative Zero Small Positive Medium Positive Large Positive Fig 9: Membership function of ω r Fig: Membership function of ω r 46

5 J. Basic. Appl. Sci. Res., () , Fig : Membership function of V PSS Considering that fuzzy controllers have two inputs and one output, for which seven membership functions have been selected, 49 rules can totally be noted for the fuzzy controller. Typical feature of the rules are as follows: If ω r is and ω r is then V PSS is The above rule indicate that if the speed change is a large negative number and the speed change coefficient or growth is a large positive number, then V PSS is approximately equal to zero, that is the PSS fuzzy will be impracticable. All the 49 rules are listed in Table (). Table : Fuzzy rules FLC (Mamdani) PSS ω r ω r Control surface of the two inputs and the output of the PSS fuzzy have been designed in the Mamdani form, as shown in Figure (). Fig : Control surface ( ω r, ω r, V PSS ), FLC(Mamdani) PSS PSS design in the T-S form We noted the fuzzy PSS design in the Mamdani form in prenominate section. In this section, the fuzzy PSS design will be settled through one of the other custom conclusion fuzzy methods, that is (T-S) (Takagi- Sugeno) method. The method which was mooted in 985 is similar to the Mamdani method in several aspects. In fact, it can be said that in this method, the st conclusion that is making and applying the fuzzy operations, are exactly the same as in the Mamdani method. The main difference between the two methods is that the Sugeno membership function outputs are as a function of input(s). The Sugeno membership function outputs are usually considered as a linear function of inputs or invariables []. In the PSS fuzzy design in the T-S form, the inputs and outputs, similar to the Mamdani method, determine ( ω r, ω r V PSS, ), respectively. The membership 46

6 Chaloshtori, functions of inputs are exactly similar to those in the Mamdani method, but the output is noted invariably. In the following, a sample of the above discussed rule in the T-S method is presented: If ω r is and ω r is then V PSS is All the 49 rules applied in this method are listed in Table (). Table : Fuzzy rules FLC (T-S) PSS ω r ω r Control surface of inputs and outputs of PSS fuzzy designed shown in Figure (). Fig : Control surface ( ω r, ω r, V PSS ), FLC(T-S) PSS PSS design using ANFIS algorithm In two prenominate sections, the PSS design using classical control method and fuzzy method (Mamdani and T-S) are performed, respectively. In this part, the PSS design using the ANFIS algorithm, which is a combination of the fuzzy and neural network methods, is carried out. As noted in the introduction, in modeling a system, we are sometimes unable to determine the membership functions optionally, but attention should be paid that the proper choice of these parameters has a significant effect on the system operation. In such cases, we can take the advantage of neural conformity learning technique or ANFIS. In the fuzzy design, these cases are also dominant, i.e., by reviewing the speed changes; we cannot determine the membership functions so as the best isolation take place. So, we employ this method for the PSS design. A brief discussion about ANFIS Suppose that there is a fuzzy system in the T-S form with the following rules:. If x is A and y is B then f = p x + q y + r. If x is A and y is B then f = p x + q y + r Fuzzy membership functions sets are μ Bi, μ Ai, A i, B i ; (i =, ). Applying fuzzy conclusions and using AND operation, we will have the following calculations: W i = μ Ai (x) μ Bi (y) ; i =, F(x, y) = W (x, y)f (x, y) + W (x, y)f (x, y) f = W f + W f W (x, y) + W (x, y) W + W Defining W i in the form of W i = W i ; (i =, ) we will have: W W f = W f + W f 46

7 J. Basic. Appl. Sci. Res., () , All the above relations can be presented as structure of the neural network form, shown in Figure (4), in which a neural network has 5 layers. Fig 4: Fifth layers neuro network with T-S fuzzy In the first layer, the optional membership function parameters, in the second layer the satisfaction degree of each fuzzy rule, in the third one, normalizing the rule satisfaction degrees, in the fourth one each rule, and in the fifth layer the final output establishment will be performed [, 4]. PSS design using ANFIS For the PSS design using ANFIS in MATLAB software, the fuzzy structure T-S model designed in prenominate section will be selected as the primary sample. Then, to train the primary optional structure, we choose random inputs and download them, and start the training. In Figure (5), five layers of neural networks resulting from the ANFIS have been provided. Fig 5: ANFIS structure The results obtained from the random inputs in training, testing, and checking are presented in Figures 6, 7, and 8, respectively. Fig 6: Obtained results from the random inputs in Training 464

8 Chaloshtori, Fig 7: Obtained results from the random inputs in Testing Fig 8: Obtained results from the random inputs in Checking In Figures 9 and, the membership functions, two input systems after applying the training to the ANFIS are shown. Fig 9: Membership function of ω r after teaching Fig : Membership function of ω r after teaching 465

9 J. Basic. Appl. Sci. Res., () , In Figure (), the control structure of the input and output in the PSS, designed by the ANFIS are presented. Fig : Control surface ( ω r, ω r, V PSS ), ANFIS PSS Simulation and viewing the simulation results In all the methods applied to the PSS design, the time response of rotor speed changes for step unit changes ( pu) of the terminal voltage and the mechanical output per unit has the desirable result of simulations. (a).6 Wihtout PSS.4. delta(wr) t(sec) (b) Fig : simulation results without PSS application: a) the single machine system structure connect to infinite bus without the calculation of PSS with turbine and governer b) time response of rotor speed changes. 466

10 Chaloshtori, (a) x - With CPSS delta(wr) t(sec) (b) Fig : simulation results with classical PSS: a) the single machine system structure connect to infinite bus with calculation of classical PSS with turbine and governer b) time response of rotor speed changes. (a) 5 x - With FLC(Mamdani) PSS delta(wr) t(sec) 467

11 J. Basic. Appl. Sci. Res., () , (b) 6 x - With FLC(T-S) PSS 4 delata(wr) t(sec) 5 x - (c) With ANFIS PSS 4 delta(wr) t(sec) (d) Fig 4: simulation results with FLC: a) the single machine system structure connect to infinite bus with calculation of FLC PSS with turbine and governer; time response of rotor speed changes with b) FLC (mamdani) PSS;(c) FLC (T-S) PSS;(d) ANFIS PSS Comparison of results and conclusion In Figure (5), the result of the four methods applied for the PSS design, which are time response of rotor speed changes for changes per unit (pu), terminal voltage V ref and mechanical torque T pu L = P pu m per unit are shown. Considering the results, it can be observed that in the CPSS over shoot, and settling time was longer than that in the others and longer time was spent for ω r isolation in this method. Moreover, regarding the figures, it is clear that both design methods that are based on the use of fuzzy control for the PSS design, i.e., the Mamdani and T-S methods, yield almost the same response, except for the over shoot in the Mamdani method, which is somehow shorter than that obtained in the T-S method. In the PSS design method that is based on the ANFIS algorithm application, it is observed that the negative over shoot extent is reduced compared with the other three methods and the settling time is shorter that that calculated for the other methods and the wave form ω r was sooner damped, which indicates the high ability of a PSS designed by the ANFIS method, which in fact took the advantage of both methods simultaneously. delta(wr) x - Comparison With CPSS With FLC(Mamdani) PSS With FLC(T-S) PSS With ANFIS PSS t(sec) Fig 5: Time response of rotor speed changes applied for 4 controlly methods 468

12 Chaloshtori, REFERENCES [] P.Kundur. "Power System Stability and Control", Mc. Graw Hill,994. [] Machowiski, J., J.W.Bialek, and J.Bumby, "Power System Dynamics and Stability", st End., Wiley, England. PP:484,998. [] Jang, J.S.R., "ANFIS: Adaptive-Network-based Fuzzy Inference Systems",IEEE Transactions on Systems, Man, and Cybernetics, Vol.,No.,pp , May99. [4] Jang, J.S.R., and C.T.Sun, "Neuro-Fuzzy Modeling and Control", Proceeding of the IEEE, March 995. [5] W.G.Heffron and R.A.Phillips, "Effect of Modern Amplidyne Voltage Regulators on under Exited Operation of Large Turbine Generators", IEEE Trans. Power Appar. Syst. pp , 95. [6] "IEEE Recommended Practice for Excitiation System Models for Power System Stability Studies", IEEE Standard,pp. 4-45, 99. [7] Zadeh, L.A., "Knowledge Representation in Fuzzy Logic",IEEE Transactions on Knowledge and Data Engineering, Vol., pp. 89-, 989. [8] C.C. Lee, "Fuzzy Logic in Control Systems:Fuzzy Logic Controller-part ", IEEE Transactions on Systems,Man, and Cybernetics, pp: 44-48, 99. [9] C.C. Lee, "Fuzzy Logic in Control Systems:Fuzzy Logic Controller-part ", IEEE Transactions on Systems,Man, and Cybernetics, pp: 49-45, 99. [] Mamdani, E.H. and S. Assilian, "An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller",International Journal of Man-Machine Studies, Vol. 7, No., pp. -, 975. [] T.Takagi and M. Sugeno, "Fuzzy Identification of Systems and its Applications to Modeling and Control", IEEE Transactions on Systems, Man, and Cybernetics, pp. 6-, 985. Appendix SMIB paramrters: Synchronous generator parameters(p.u): Xls=.5, Xd=.8,Xq=.76, Xfd=.8, Xkd=.8, Xkq=.5, Xkq=.75, Rs=., Rfd=.6, Rkd=.8,Rkq=.8,Rkq=.68,ω=4.6 rad/sec, D= Exciter system parameters: KA =4 TA=.5 sec Turbine and Governer parameters: Tt=. sec TG=. sec Trancmition Line parameters: Re= Xe=.475 Operating Point parameters: P=.9 Q=. V= Generic PSS parameters: Kpss= T=. sec T=.5 sec 469