A Fuzzy Sliding Mode Controller for AGC of Multi Area Deregulated Power System

Transcription

1 International Journal of Electronics Engineering Research. ISSN Volume 9, Number 7 (2017) pp Research India Publications A Fuzzy Sliding Mode Controller for AGC of Multi Area Deregulated Power System A. Ganga Dinesh Kumar 1, N. V. Ramana 2 1 Department of EEE, Sridevi Women s Engineering College 2 Department of EEE, JNTUH College of Engineering Abstract Two problems: Parameter uncertainty and chattering effect present in Control signal are have a great deal in performance of system with the designed controllers. This paper presents Fuzzy Sliding Mode Controller (FSMC) for Multi Area Load Frequency Control problem or Automatic Generation Control (AGC) in a De-regulated environment. The first problem is addressed by designing a sliding mode controller and the second one is dealt by designating fuzzy logic controller. The sliding surface is a function of area control error. The trajectory of surface on sliding hyper plane is controlled by well defined fuzzy rules. This affects changes in system states there by a desired dynamic response is achieved. Performance of 2-Area system with FSMC is compared with Multi Resolution Wavelet based Controller (proposed previously by the same authors) and with PI controller. Keywords: Load Frequency Control, Deregulated Power System, Wavelet based Controller, Fuzzy Sliding Mode Controller, Robust Controller and Chattering Effect. I. INTRODUCTION The Load Frequency Control (LFC) problem in a single area control is simple as there is a need for control of only one parameter i.e. changes in frequency ( f). But, in the case of deregulated system due to unbundled rules and contract violation between the

2 1080 A. Ganga Dinesh Kumar, N. V. Ramana control areas it is more difficult task [1-3]. In multi area control the control parameters are, the change in frequency of each control area and tie line power flow between the control areas. For example in two area control the control parameters are f1, f2 and Ptie12. In conventional load frequency control the task of LFC is not much difficult due to absence of contracted demand. But, in Deregulated power system frequency is a monitoring parameter to be monitored by an ISO. DISCOs can purchase the power from any GENCO and these transactions monitored by ISO [4]. The GENCOs in one control area can supply the power to other control area by using the tie lines. The DISCOs in one area can get the power from the same area or form the other area. In recent past various authors have proposed controllers for LFC problem in deregulated environment [5-17]. Using linear control theory conventional linear controllers such as PI controller, using optimal control theory optimal state feedback controllers and by using FL, ANN technique intelligent controller were proposed. Also the nonlinear controllers using sliding mode control strategy have been proposed. Linear controllers do not account the non linearities of the system. Their performance with non linear power system may be ineffective. Nonlinear controllers have the problem of model difficulties. Though such difficulties are not present with intelligent controllers but, they have the difficulties of defining universe of discourse. This paper combines the advantages of both non linear control theory and intelligent control theory to address LFC problem. For highly non linear systems such as power systems design of a controller involves linearization of non linear power system model. The linearization process if it could not be preserving the nonlinearities of the system then the effectiveness of linear controller over nonlinear system is doubtful. Researchers have been concentrating non- mathematical model techniques such as Fuzzy logic intelligent systems. Also for nonlinear power systems the effectiveness of sliding mode concepts are been already proved [18-21]. Power system model is highly nonlinear and its parameters are uncertain by nature. In addition, presence of digital equipment and minute RC parameter integrators introduces chattering effect. The control signal consisting of these two, have a great deal in performance of system. The effectiveness of controller is unpredictable and sometimes may be ineffective due to said problems. Researchers have dealt the first problem effectively by designing Sliding Mode Controllers [22-23]. However SMCs cannot control chattering effect in system dynamics as they are affected due to unaccounted model parameters [24]. This paper presents a Fuzzy Sliding Mode Controller (FSMC) which integrates the advantages of intelligent controllers and nonlinear sliding mode controller. In Section II the mathematical model of Two Area Thermal Thermal system including bilateral contracts is discussed. The design of Fuzzy Sliding Mode Controller (FSMC) is explained in Section III. The performance comparison of power system response to LFC problem with proposed and other controllers is discussed in section IV. Finally conclusions are given in section V.

3 A Fuzzy Sliding Mode Controller for AGC of Multi Area Deregulated Power System 1081 II. MATHEMATICAL MODELLING OF DEREGULATED POWER SYSTEM FOR LFC PROBLEM The dynamic model of two area Thermal-Thermal deregulated power system to address load frequency control problem is mentioned in Fig.1. Fig.1 Configuration of Two-Area Power System connected with AC Tie-line. As illustrated in Fig. 1, DISCO in one area can make transaction with a GENCO in another. This necessitates power flow through the tie line and frequency deviations in both the areas. The Area Control Error (ACE) is a function of frequency deviation and change in tie line power flow [5]. ACE i = B i f ierror + P tie error i = 1, 2 In deregulated power system the tie line power flow is a function of contract participation factor (cpf). [5] i=3 P Lj P tie scheduled = i=1 j=3 cpf ij P Lj j=1 cpf ij P tie error = P tie sched. P tie act. The two area deregulated power system with two plants is shown in Fig. 2. Fig.2. Restructured system for LFC in a deregulated environment connected with AC tie line.

4 1082 A. Ganga Dinesh Kumar, N. V. Ramana The transactions of DISCOMS with GENCO are given by [20] cpf 11 cpf 12 cpf 13 cpf 14 cpf DPM = [ 21 cpf 22 cpf 23 cpf 24 ] cpf 31 cpf 32 cpf 33 cpf 34 cpf 41 cpf 42 cpf 43 cpf 44 The distribution of ACE to several GENCOs is called ACE participation factor. It is represented by NGENCO j i=1 ji = 1.0 where, ji is the participation factor of the i th GENCO in the j th area number, NGENCOj is the number of GENCOs in j th area. III. DESIGN OF FUZZY SLIDING MODE CONTROLLER The main feature of this proposed Fuzzy Sliding Mode Controller (FSMC) is to obtain the desired dynamic response of the power system by adjusting the trajectory of sliding surface on hyper plane with the help of well defined fuzzy linguistic rules. The block diagram representation of the proposed FSMC with two area power system is shown in Fig. 3. The design of sliding mode control law involves two control actions to be initiated. i.e. equivalent and the reaching control. The first control law brings the parameters over the sliding surface. The second control law holds parameters on the surface. The equivalent control law is a function of Area Control Error (ACE) and differential power and deviation in frequency. The reaching control law is designed based on Fuzzy Logic System (FLS) concepts. In the design of FLS system, there are two inputs i.e. sliding surface(s) and derivative of sliding surface (s ). The sliding surface (s) is a function of Area Control Error (ACE) and sliding margin (λ). Fig.3 Block Diagram representation of FSMC

5 A Fuzzy Sliding Mode Controller for AGC of Multi Area Deregulated Power System 1083 The algorithm for the proposed FSMC and corresponding flow chart are given below. Algorithm for the design of FSMC for LFC problem 1. There is a variation in load demand. 2. This creates a mismatch between the MW output of generation and load demand of DISCOs. 3. Mismatch causes frequency deviation. 4. To achieve steady state behavior the Control action initiated by FSMC. 5. The equivalent control law is a combination of change in power and ACE (e). u eq = λe F(x); where, F(x) = [P G P D P Tie ] K p τ p ΔF(s) 1 τ p 6. The desired Reaching Control signal obtained by certain rules of FLS. Sliding surface is a scalar function varying between [-1.5, 1.5]. If s. s > 0, the fuzzy membership function of control input (u fs )has to be set in such a way that its sign is opposite to that of s. As the above multiplication is negative, the reaching condition, s. s < 0, would be satisfied. To attain the desired performance the membership function of u fs can be changed positive or negative. u r = k fs u fs 7. The complete control law is u u r u eq 8. The generated control signal, bring the system into stable operating point.

6 1084 A. Ganga Dinesh Kumar, N. V. Ramana Flowchart for FSMC

7 A Fuzzy Sliding Mode Controller for AGC of Multi Area Deregulated Power System 1085 Fig. 4. Block Diagram for Fuzzy Logic System. The input membership functions are shown in Fig. 5. Fig. 5 Membership functions for s, s The output membership function is shown in Fig. 6. Fig. 6. Membership functions for control output.

8 1086 A. Ganga Dinesh Kumar, N. V. Ramana The decision matrix is shown in Fig. 7. s NB NM Z PM PB NB NM Z PM PB PB PB PM Z Z PB PB PM Z Z PM PM Z NM NM Z Z NM NB NB Z Z NM NB NB Fig. 7. Decision Matrix IV. PERFORMANCE COMPARISON OF POWER SYSTEM RESPONSE TO LFC PROBLEM WITH PROPOSED AND OTHER CONTROLLERS. In this paper we have presented Fuzzy sliding mode controller for load frequency control problem of multi area power system in deregulated environment. The performance of the power system is tested with the proposed controller and the simulation results are presented in this section. The authors of this paper have recently presented wavelet based controller for the same system and the same problem [25]. The mathematical model and the other details can be referred in [26], however the mathematical model of the wavelet controller is briefly repeated for convenience. Wavelet transform approach is widely used in signal process, but in this paper first time wavelet transform is used for the design of a controller to encounter load

9 A Fuzzy Sliding Mode Controller for AGC of Multi Area Deregulated Power System 1087 frequency control problem [27-32]. The control law is given by u = k p g p (e) + k I δg I (e). dt Where, g p ( ), g I ( ) are linear functions. In the design of multi-resolution wavelet controller the error signal is decomposed into packets of frequency known as wavelets. The error signal is decomposed into e = i k i e i Where, ki is the control parameter. Due to this wavelet decomposition technique the noise level can be eliminated. SIMULATION RESULTS: The effectiveness of FSMC has been studied under one possible contract scenario, simulations are performed for the contact scenario under various operating conditions and larger load demands. The performance of proposed controller is compared with wavelet based controller and conventional PI controllers. Contract scenario: In this scenario, DISCO has the freedom to contract with any GENCO in there and other areas. So, the entire DISCOs contract with the GENCOs for power based on following DPM DPM = [ ] It is considered that each DISCO demands 0.1puMW total power from other GENCOs as defined by entities in DPM and these GENCOs participates in AGC based on the following apfs. apf 1 = 0.6, apf 2 = 1 apf 1 = 04 apf 3 = 0.6, apf 4 = 1 apf 3 = 04 The steady state mechanical power output in terms of cpf and change in load demand is given by j P mi = cpfij P Lj j P m1 = 0.2(0.1) + 0.3(0.1) + 0.5(0.1) + 0.0(0.1) = 0.1puMW P m2 = 0.12puMW ;

10 1088 A. Ganga Dinesh Kumar, N. V. Ramana P m3 = 0.08puMW; P m4 = 0.1puMW; The results for this case are given in the following figures. Fig. 8. represents change of frequency in CA-1, Fig. 9. represents change of frequency in CA-2. In these two figures solid line indicates frequency deviation in the respective areas with FSMC. It can be observed that, the frequency deviation is approaching quickly towards zero with FSMC as compared to other controllers. Fig.12 represents Deviation in tie-line power exchange. Table I, II gives a comparison of % overshoot and the settling time in different control areas with various controllers. Fig 8. Frequency deviation in control area 1. Fig 9. Frequency deviation in control area 2. Fig 10 illustrates tie line power deviation. The dark solid line is the tie line power deviation of the system with the proposed FSMC controller. It can be observed as compared to other controllers the power deviation is approaching quickly towards zero in accordance to frequency deviation with proposed FSMC controller.

11 A Fuzzy Sliding Mode Controller for AGC of Multi Area Deregulated Power System 1089 Chattering Effect: Fig.10. Deviation in tie-line power exchange. Though parametric uncertainties in the system are well taken care by the SMC, it could not eliminate chattering effect in the control signal. Fig.11. Illustrates area control error in CA-1 and 2 with SMC. The chattering effect can be nullified by the model free intelligent controller (FSMC) and the results were shown in Fig. 12. Fig.11. ACE in CA-1, CA_2 with Sliding Mode Control Fig.12. ACE in CA-1,CA_2 with Fuzzy Sliding Mode Control

12 1090 A. Ganga Dinesh Kumar, N. V. Ramana Table I. % shoots in frequency Deviation in CA-1 & CA-2. Type of the controller change in frequency of CA-1 change in frequency of CA-2 PI Wavelet based Controller FSMC Table II.time to Settle frequency oscillations in CA-1 & CA-2. Type of the controller CA-1 CA-2 PI 6 sec 8 sec Wavelet based Controller 5 sec 7 sec FSMC 3.5 sec 4.5 sec The results depicted in Table I illustrates the power system with wavelet controller has a shoot of 30% and 50% in CA 1 and CA-2 respectively. The proposed controller can introduce sufficient damping strength into the system as evident the % shoot of the system is recorded only 15% and 17% respectively in CA- 1 and CA-2. Also the effectiveness of the FSMC is observed to be significant as the system is settling down quickly (shown in Table II), with the proposed controller compared to others. V. CONCLUSION This paper presents a new controller based on Fuzzy logic and sliding mode concepts. Fuzzy logic system has got advantages of fine tuning and model free methodology. Sliding mode control performance is naturally robust and can take care of nonlinearities of the system inherently. By integrating the advantages of both these controllers this new algorithm is proposed. The main feature of this proposed algorithm is by properly defining Fuzzy Rules control parameters can be brought on to the sliding surface and the trajectory of the sliding surface can be adjusted for desired controller response. The performance of FSMC is evaluated on a two area Thermal-Thermal power system under deregulated environment.

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