POWER SYSTEM STABILITY ENHANCEMENT WITH FUZZY TCSC CONTROLLER

Abstract

Due to various reasons such as population growth, industrialization, improvement of life style etc., the demand for electrical power is ever increasing. However, the development of new infrastructure for power generation and dispatch (transmission and distribution) is often restricted due to various economic and environmental constraints. Under this scenario, it is imperative to enhance the power transfer capability ofthe existing transmission corridors up to their thermal limits. Now, the power transfer limit over any transmission corridor is often restricted by the stability considerations. Therefore, the power transfer capability ofany transmission system can be improved by enhancing the system stability through dynamic control of various systems parameters such as line impedance, bus voltage magnitudes and angles etc. As is well established in the literature, real time, dynamic control of various network parameters can be achieved by using Flexible AC Transmission System (FACTS) controllers. Use of these controllers, which are essentially high speed power electronic controllers, results in enhanced utilization ofthe existing transmission system, allowing - flexible control of power, so that flow is on established transmission routes - secure loading (but not overloading) of transmission lines to levels nearer their thermal limits - greater ability to transfer power between controlled areas, with consequent generation reserve margin - prevention ofcascading outages by limiting the effects offaults and equipment failures - damping of power system oscillations Among various FACTS devices, one of the most important controllers is Thyristor controlled series capacitor (TCSC). TCSC is a series connected device, which modifies the line impedance by inserting a variable reactance in series with the line, thereby controlling the power flow over the line. This provides an opportunity to i) relieve heavily loaded lines, ii) prevent congestion and iii) enhance steady state power flow over a transmission line. Moreover, a TCSC can also enhance the power system stability significantly by dynamically changing the line impedance through a properly designed control system. Traditionally control systems are designed through mathematical analysis and synthesis technique. Awealth ofcontrol design techniques through mathematical approaches are available in the literature. Now, the first step for control system design through mathematical techniques is to obtain a proper model of the process to be controlled. However, for ahighly non-linear system like power system, it is often quite difficult to obtain an accurate mathematical model. Because of the inaccurate model, it is often quite an arduous task to design a control system which would be effective over a wide range of operating conditions. Under these conditions, Fuzzy Logic Controllers (FLCs) can be used quite effectively for controlling the process. Fuzzy logic controllers are essentially 'model free' controllers, which try to control a process, based on the experience of a skilled human operator without requiring a detailed model of the process to be controlled. In many cases, application offuzzy logic approach makes it possible to design a control system that is more robust, cost effective and easier to design as compared to a controller developed based on mathematical techniques. Motivated by the above features of FLC, in this thesis an attempt has been made to design fuzzy logic TCSC controllers to improve power system stability. Specifically, in this thesis, fuzzy PI controllers (FPIC) have been used in which the inputs to the fuzzy controllers are error (e) and charge in error (Ae) while the output ofFPIC is the incremental change in the control output (Au). The error (e) is defined as e=Pref- Pact where Pref is the steady state power flowing through the line (in which TCSC is installed) and Pact is the actual power flowing through that particular line following adisturbance. From these two inputs, the FPIC generates the incremental change in TCSC reactance as its output (Au = AxTcsc)-The main components of any FLC are fuzzification unit, fuzzy inference unit, fuzzy rule base and defuzzification unit. The fuzzification unit maps the measured crisp inputs into the fuzzy linguistic values which are subsequently used by the fuzzy inference mechanism. It is to be noted that the actual values of the e and Ae are not submitted directly to the fuzzification unit. The quantities e and Ae are first converted to normalized quantities ew and Aew respectively by using scaling factors Ge and GAe and subsequently these normalized quantities are passed to the fuzzification unit. The fuzzy inference mechanism, utilizing the fuzzy rule base, performs fuzzy logic operations on the fuzzified inputs to infer the control action. Finally, the defuzzification unit converts the inferred fuzzy control action into crisp, normalized incremental change in control output (AuN) which, in turn, is converted into actual incremental change in control output (Au) by using the scaling factor Gu. 11 These three scaling factor (Ge, GAe and Gu) are the main parameters for tuning the FPIC because variation ofscaling factors (SFs) changes the normalized universe ofdiscourse for input and output variables and their corresponding membership functions. These SFs play arole similar to that of the gains of aconventional controller. Therefore, they are extremely important for the controller stability and performance. Generally, there is no well defined method for computing the appropriate values of SFs for FLC and as a result, the values of these SFs are sometimes decided by trial and error technique. To circumvent this trial and error procedure, in this thesis, a genetic algorithm (GA) based technique is proposed for finding the appropriate values for Ge, GAe and Gu. In Chapter 2of the thesis, the proposed GA based technique is described in details. In this work, the scaling factors have been tuned such that the power system oscillations are minimized after the occurrence of a disturbance. Specifically, the aim is to minimize the error between the Pref and Pact following a disturbance. Various performance indices can be used to represent the above goal mathematically. In this thesis, the integral ofsquared error (ISE) index has been used as it tends to place agreater penalty on large errors. After tuning these three scaling factors, the effectiveness of the developed FPIC has been validated through detailed non-linear dynamic simulation studies on two different multi-machine power systems. These study systems are: a) two area 4 machine system and b) 10 machine 39 bus system. The simulation studies have been carried out on MATLAB/SIMULINK environment. A large number of fault cases involving three phase, 5cycle, solid short circuit faults have been investigated on both these study systems for different loading conditions as well as different fault locations. From the simulation results it has been observed that the proposed FPIC for TCSC improves the system stabilitysignificantly. Even though the performance of the proposed FPIC has been found to be quite satisfactory in Chapter 2, the effectiveness of the FPIC can be further enhanced by using adaptive FPIC. In Chapter 3, such an adaptive FPIC, namely the self tuning FPIC (STFPIC) is described. In STFPIC, the output scaling factor ofFPIC is modulated on-line based on the instantaneous values ofe and Ae. Hence, the output scaling factor ofSTFPIC does not remain fixed while the controller is in operation, rather it is modified at each sampling instant by a gain updating factor 'a'. The value of 'a' is determined by afuzzy logic system, to which the normalized quantities e^ and Ae^ are given as inputs. Therefore, in a STFPIC, there are two fuzzy logic blocks, one for computing Au and other for calculating a. The effectiveness of the in developed STFPIC has been studied through detailed non-linear fault simulation studies on both the test system described in Chapter 2. The same fault cases as considered in Chapter 2 have also been studied in Chapter 3 and the performances obtained by STFPIC have been compared to those obtained by FPIC. From the comparative simulation results, it can be observed that the proposed STFPIC for TCSC improves the system damping further (as compared to the system damping obtained by FPIC). The STFPIC, which comprises of two fuzzy logic blocks, requires increased computational time and memory for implementation. Therefore, it would be advantageous to reduce the size of the rulebase so that the requirement of computational time andmemory for implementation is reduced. In Chapter 4, such a rule base reduction scheme based on the concept of singular value decomposition (SVD) is described. In the proposed rule base reduction scheme, SVD is applied on the original rule base matrix Z. The resulting singular values (obtained bySVD), convey the information regarding the importance of any particular rule within the rule base, as the rules associated with large singular values have a strong influence on the aggregated output of the rule base. Further, the number of small singular values indicates the number of insignificant rules in the original rule base. Therefore, these insignificant rules can be eliminated from the rule base retaining only the significant rules and thereby forming a reduced rule base. In Chapter 2 and 3 of this thesis, 49rules have been used for each of the two fuzzy logic blocks. After performing SVD on these two original rule bases and retaining only the largest two singular values, the number of rules in each rule base has been reduced to 9 from 49. Again, the effectiveness of the reduced rule base STFPIC has been investigated through detailed non-linear fault simulation studies onboth the test systems with the same fault conditions as considered in Chapter2 and 3. From the studies, it has been observed that when only the main FLC rule base (corresponding to Au) is reduced, the performance of STFPIC may degrade. However, when the rule base for computing a is also reduced along with that for computing Au, the performance of STFPIC is quite close to that obtained using full rule bases for both the fuzzy logic systems. Thus, the proposed rule base reduction technique reduces the total number of rules in STFPIC bymore than 80% (from 98 to 18) thereby reducing the complexity of STFPIC significantly. The performances of FPIC and STFPIC discussed in Chapter 2-4 have been tested with pre-designed scaling factors. However, in real life, the operating point in the system may vary continuously thereby making it almost impossible to pre-design the scaling factors. IV Thus, it is necessary to determine the scaling factors on-line based on some suitable measurements. In Chapter 5, such a scheme, based on functional link network (FLN), for on line determination of the scaling factors is described. From detailed non-linear fault simulation studies, it has been observed that the developed FLN based scheme helps to improve the system damping considerably. To summarize, the major contributions of this thesis are as follows: • AGA based tuning methodology for fuzzy PI controller (FPIC) has been proposed in Chapter 2. Through detailed non-linear fault simulation studies on two test systems under wide variation of operating conditions, the proposed FPIC has been found to improve the system damping significantly. • A self-tuning FPIC (STFPIC) is proposed in Chapter 3. Through detailed non-linear fault studies, it has been found that the STFPIC improves the system damping further (as compared to the damping obtained by FPIC). • ASVD based rule base reduction scheme is proposed in Chapter 4. By the proposed SVD based scheme, the total number ofrules in STFPIC has been reduced to 18 (from original 98 rules). Therefore, the size of the rule base has been reduced by more than 80%. Through detailed non-linear fault simulation studies, it has been observed that the performances obtained by using 98 rules and those obtained by using 18 rules are quite close to each other. Therefore, the proposed rule base reduction technique helps to reduce the requirement of computational time and memory significantly. • A scheme for on-line determination of scaling factors using FLN is proposed in Chapter 5. From detailed non-linear fault simulation studies, it has been observed that the proposed scheme for on-line determination ofscaling factors helps to improve the system damping significantly. The organization ofthe thesis is as follows: Chapter 1 describes the motivation of this work as well as the relevant literature review in the area of research undertaken in this thesis. Chapter 2 describes the GA based tuning mechanism of FPIC. Details of STFPIC are discussed in Chapter 3. The rule based reduction scheme is presented in Chapter 4. FLN based scheme for on-line determination of scaling factors is discussed in Chapter 5. Lastly Chapter 6 lists the major conclusions of this work as well as the future scope of work.