Fuzzy-Expert System for Voltage Stability Monitoring and Control BY O Bodapatti Nageswararao, B .E. A thesis submitted to the School of Graduate Studies in partial fulfillment of the requirements for the degree of Master of Engineering Faculty of Engineering and Applied Science Memonal University of Newfoundland Febniary, 1998. St. John's Canada National Library Bibliothèque nationale du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395. nie Wellington OtGawaON K 1 A W OttawaON KtAON4 Canada Canada The author has granted a non- exclusive licence allowing the National Library of Canada to reproduce, loan, distribute or sel copies of this thesis in microform, paper or electronic formats. The author retains ownership of the copyright in this thesis. Neither the thesis nor substantial extracts fkom it may be printed or othexwise reproduced without the author's permission. L'auteur a accordé une licence non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la fome de microfiche/nlm, de reproduction sur papier ou sur format électronique. L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation. Abstract In recent years, electric power utilities are forced to transmit maximum possible power through existing networks due to environmental, economic and regulatory changes. Due to these constraints, voltage instability has emerged as one of the most important areas of concem to modem power utilities. Voltage instability has been responsibie for several system collapses in North America, Europe and Asia This thesis presents fùndamental concepts of voltage stabiliîy. it describes three traditionai voltage stability indices namely singular value decomposition, L index and QV curves. A simple five bus system is used to highlight the limitations of these traditional methods. A more widely accepted technique like modal analysis along with continuation power flow is studied and simulations are carried out on the IEEE 30 bus system and the New Engfand 39 bus system. The test results clearly indicate areas prone to voltage instability and also identify groups of buses and cntical bus that participate in the instability and thereby eliminate the problems associated with traditional methods. Hence, modal d y s i s technique is not only used as a benchmark tool for the developrnent of the proposed f h q - expert system, but also as an important tool for validating its accuracy. To understand this new approach, fundamental concepts of funy logic based on the theory of approximate reasoning is dealt in detail. To get fûrther insight into this altemate approach, a simple method using fùzq sets for the voltage-reactive power control to improve the system voltage level is presented. A modified IEEE 30 bus system is used as an example to illustrate this method. Simulation resuits of this simple problem is encouraging and has been a useful stamng point for the proposed fùzzy-expert system for voltage çtability evaluatioa The proposed fuay-expert system consists of two main wmponents. nie knowledge-base and the inference engine. Here, the key system variables Like load bus voltage, generator MVAR reserve and generator terminal voltage which are used to monitor the voltage stability are stored in the database. Changes in the system operating conditions are reflected in the database. The above key variables are fuzzified using the theory of uncertamty. The debase comprises a set of production d e s which fom the basis for logical reasoning conducted by the inference engine. The production d e s are expressed in the form of F-THEN type, that relates key system variables to stability. The New England 39 bus system is taken as a case study to illustrate the proposed procedure. The expert system output is compared with the simulation results of a commercially available software ( VSTAB 4.1 ) output through modal analysis. The proposed system is fast and more efficient than conventional voltage stability methods. Acknowledgments 1 would like to express my sincere gratitude and appreciation for the invaluable help and guidance given to me by Dr. Benjamin Jeyasurya during al1 stages of this work. My thanks are also to Dr. Jeyasurya, Facuity of Engineering and Applied Science and the School of Graduate Studies for the fuiancial support provided to me during my M-Eng. program. 1 acknowledge the assistance received fiom faculty members, fellow graduate midents and other staff of the Faculty of Engineering and Applied Science. Finally, I express my sincere gratitude to my family for their encouragement, support and understanding. Contents A c h o w ledgments Contents List of Figures List of Tables iv v vui IC 1 INTRODUCTION 1 2 VOLTAGE S T A B I ' ANALYSIS IN P O W R 4 SYSTEMS 2.1 Introduction 4 2.2 Voltage Stability Phenomenon 5 2.3 Voltage Collapse incidents 10 2.4 Factors Contributing to Voltage uistability/Collapse 1 1 2.5 Voltage Stabilify Analysis 12 2.5.1 S ingular value decomposition 13 2.5.2 L index 15 2.5.3 Q V c w e s 17 2.6 Simulation Resuits and Discussions 19 2.6.1 Singular value decomposition 20 2.6.2 L index 22 2.6.3 QV curves 24 2.7 Limitation of Traditional Methods in Voltage Stability 28 Anal ysis 2.8 Need for Expert Systems in Electric Power System 29 2.9 Slrmmary 3 CONTINUATION POWER FLOW AND MODAL ANALYSPS 3.1 Introduction 3.2 Continuation Power Flow Technique 3.2.1 Basic prùlciple 3.2.2 Mathematical formulation 3.3 Modal Analysis 3.4 Simuiation Results and Discussions 3 -4.1 lEEE 30 bus system 3.4.2 New England 39 bus system 3.5 Summary 4 FUZZY-EXPERT SYSTEMS 4.1 Introduction 4.2 Expert Systern Structure 4.3 Theory of Approximate Reasoning 4.3.1 Fuay set theory 4.4 Application of Funy-Set Theory to Power Systems 4.5 sulfl~zlary 5 FUZZY CONTROL APPROACH TO VOLTAGE PROFILE ENEANCEMENT FOR POWER SYSTEMS 5.1 Introduction 5.2 Problem Statement 5.3 Fuzzy Modeling 5.3.1 Bus voltage violation level 5.3 -2 Controlling ability of controllhg devices 5.3.3 Control strategy 5.4 Methodology 5 -5 Simulation Results and Discussions 5.6 Summary 6 FUZZY-EXPERT SYSTEM FOR VOLTAGE STABItITY MONITORING AND CONTROL Introduction Expert S ystem and Design 6.2.1 The Database 6.2.2 TheRulebase Merence Engine Simulation Results and Discussions Inteption of Fuzzy-Expert Systenl into an Energy Management System s-ary 7 CONCLUSIONS 7.1 Contributions of the Research 7.2 Recommendations for Future Work REFERENCES APPENDICES A Line and Bus data for the 5 bus systern B Rules relating key variables to stability masure of the New England 39 bus system C Data used for the debase formation for the monitoring stage of the New England 39 bus system D Complete list of expert system output for the monitoring stage of the New England 39 bus system E Participation factors for the cntical case ( at the voltage stability limit ) o f the New England 39 bus system List of Figures Sample two bus power systern Vottage-Power characteristics for difEerent V1 and power factors Radial system with some of the elements that play key role in the voltage stability Line mode1 for two bus system Sample QV curve Single line diagram of the 5 bus system Singular value decomposition for 5 bus system L index of individual load buses for 5 bus system System L hdex for 5 bus system Family of QV curves for the base case of the 5 bus systern Family of QV curves near the stability Iimit of the 5 bus system Family of QV curves at the collapse point of the 5 bus system An illustration of the continuation power flow technique Single line diagram of the IEEE 30 bus system PV c u v e for bus 30 of the IEEE 30 bus system Single line diagram of New England 39 bus system PV curve for bus 12 of the New England 39 bus system Expert system structure Mernbenhip function for the fuPy set TALL The S-function The II-fûnction F u n y mode1 for bus voltage violation level Fuzzy mode1 of controlling ability of controlling device 6.1 Membership h c t i o n for the worst load bus voltage 76 6.2 Membenhip fiinction for the worst MVAR reserve 77 6.3 Membership fiindon of the generator terminal voltage 78 corresponding to the worst MVAR reserve 6.4 Voltage stability margui ( VSM ) for pre and p s t control cases 92 6.5 Funy-expert system as a part of new EMS 98 List of Tables Five smallest eigenvalues for the three loading condition of the EEE 30 bus system Participation factors for base case and critical case corresponding to the Ieast stable mode of the IEEE 30 bus system Voltage stability margin for the three loading condition of the IEEE 30 bus system Five smallest eigenvalues for different loading conditions of the New England 39 bus system Participation factors for criticai case corresponding to the least stable mode of the New England 39 bus system Voltage stability margin for the three loading condition of the New England 39 bus system Fuzzy logic operators Base case voltage profiles of the modified IEEE 30 bus system Lower and upper limits of the controllers Load bus voltage profiles of the modified IEEE 30 bus system before and after control actions Optimal fuzzy controi solution Panuneters "a" and "A" for the membership fûnction of the key variables Operating conditions for the 32 cases listed in Appendk D Expert system output - Monitoring Expert system output - control stage ( case A ) Expert system output - control stage ( case B ) Expert system output - control stage ( case C ) Voltage stability marpin ( VSM ) for pre and p s t control cases L h e &ta for the 5 bus system Bus data for the 5 bus system Rdes relating worst load bus voltage to d i l i t y measure under group 1 Rules relating key generator MVAR reserve to stability measure under group 2 Rdes relating key generator terminal voltage to stability measure under group 3 Rules relating combineci key variables to stability measure under group 4 Data used for the nilebase formation Expert systern output for various neighborhood points - Monitoring stage Bus and Generator participation factors for critical case Chapter 1 INTRODUCTION The phenornenon of voltage instability in electric power systems is characterized by a progressive decline of voltage, which can occur because of the inability of the power system to meet increasing demand for reactive power. The process of voltage instability is generally triggered by some fom of disturbance or change in operating conditions that create increased demand for reactive power in excess of w b t the system is capable of supplyuig. The dynarnic characteristics of loads, location of reactive compensatiori devices and other control actions such as those provided by load tap changing transformers, automatic voltage regulating equiprnent, speed goveming mechanism on generators are important factors which affect voltage stability. in recent years, electric power utilities are forced to transmit maximum possible power through existing networks due to environmental, economical and regulatory changes. As a result of load growth without a corresponding increase in either the generation or transmission capacity, many power systems operate close to their voltage stability boundaries. Many utilities around the world have experienced major black-outs caused by voltage instability. When a power system is operating close to its limits, it is essential for the operators to have a clear knowledge of its operating state. A number of speciai algorithms and methods have been proposed in the literature for the analysis of voltage instability. But these traditional methods require significantiy large wmputations and are not efficient enougb for reai-time use in energy management system. Hence, there is a need for an alternative approach, which cm quickiy detect potentiaily dangerous situation and alleviates the power system nom possible collapse or blackout. To meet the above challenge, this thesis proposes a new and cost-effective solution based on fby-expert system. The aim of the thesis is as follows: O To investigate three traditional methoâs of voltage stability indices with the help of a simple system. The three methods are singular value decornposition, L index and QV curves. The analysis of these methods will bnng out the bsic concepts involved in voltage stability along with their limitations. O To apply modal anaiysis along with continuation power flow for voltage stability analysis of a power system. These methods aim to overcome the limitations of the traditional methods. To review expert systems and fuzn/ logic concepts. This will lay a foundation for the understanding of the proposed fûzzy-expert system. To get M e r insight into this alternative approach, a simple method using f i n y sets for voltage-reactive power control to improve the system voltage level is investigated To design a fùzzy-expert system for voltage stability monitoring and control. The designed funy-expert system is investigated and compared with modal anaiysis output Extensive simulations are carried out to validate the usefulness of this new approach. The thesis is organued as follows. Chapter two reviews the concepts of voltage stability followed by the description of the three most widely & techniques for the analysis of voltage stability in power systems. A simple 5 bus system is used to highiight the limitations of these traditional methods. Chapter three gives a detailed description of modal analysis for voltage stability evaiuation followed by the simulation results of the IEEE 30 bus system and the New England 39 bus system. This chapter forms the basis for the development of hizzy-expert system. Chapter four presents the theory behind funy-expert systems. Ln chapter five, a simple application of ~~I.ZZY logic to power system is s h o w to emphasize the theory developed in chapter four. A moâified IEEE 30 bus system is used as an example to illustrate this m e t h d Chapter six gives a detailed description of the fùzzy-expert system for voltage stability monitoring and control. The New England 39 bus system is taken as case study to illustrate the proposed procedure. It highlights the database and nilebase design. In the database design, the key system variables that are used to monitor the voltage stability are hansformed into fuay domain to obtain their appropriate membership hctions. The rulebase comprises a set of production rules that f o m the basis for logical reasoning conducted by the inference engine. These production d e s relate key system variables to stability. To validate the proposed system, simulation results are compared with modal analysis output Finally, chapter seven concludes the thesis with sorne recommendation for friture work. Chapter 2 VOLTAGE STABILITY ANALYSIS IN POWER SYSTEMS Introduction Voltage control and stability problems are not new to the electric utility industry but are now receiving special attention. Maintaining an adequate voltage level is a major concem because many utilities are loading their bulk transmission networks to their maximum possible capacity to avoid the capital cost of building new lines and generation facilities. Load growth without a correspondhg increase in transmission capacity has brought many power systems close to their voltage stability boundaries. In this conte* the terms 'koltage stability", "voltage collapse" occur fiequently in the literature. EEE cornmittee report [l] defines the following terrninology related to voltage stability : "Voltage Stability" is the ability of a system to maintain voltage so that when load admttance is increased, load power will increase and that both power and voltage are controllable. "Voltage Collapse" is the process by which voltage instability leads to very low voltage profile in a significant part of the system. "Voltage instability" is the absence of voltage stability and results in progressive voltage decrease ( or increase ). Voltage instability is a dynamic process. A power system is a dynamic system. in contrast to rotor angle stability, the dynamics mainly involve the loads and the means for voltage control. A system enters a state of voltage instability when a disturbance, increase in load, or system change causes voltage to drop quickly or drift downward and operator, automatic system controis fail to halt the decay. The voltage decay may take just a few seconds or 10 to 20 minutes. If the decay continues unabated, steady-state angular instability or voltage collapse will occur. 2.2 Voltage Sta bility Phenornenon [2] Voltage collapse is in general caused by either load variations or contingencies. The following illustration considers voltage collapse due to load variations. The basic configuration used to explain voltage collapse is shown in Fig. 2.1. V2: receiving end load voltage X: reactance of the line V 1 : sending end voltage 6 : load angle Fig.2.1 Sample two bus power system In this circuit, a synchronous genenitor is connecteci to a load through a lossless transmission line. The load is described by its red and reactive powers P, Q and the load voltage V2 [3]. The goveming algebraic relations are Under steady-state conditions, equations (2.1) and (2.2) represent the voltage/power relation at the load end of the circuit- V I = l .O PF=0.95 laa \ // 0.2 0.4 0 - 6 0.8 1 1 . 2 1.4 Load Real Power (p.u) Fig.2.2 Voltage-Power characteristics for diEerent V1 and power factors [3] Fig. 2.2 shows the plot of load voltage versus red power for several power factors and different sending-end voltages. The graph of these equations is a parabola. In the region corresponding to the top half of the curves, the load voltage decreases as the receiving-end power increases. The nose points of these curves represents the maximum power that can theoretically be delivered to the load. If the load dernand were to increase beyond the maximum tramfer level, the amount of actual load which can be supplied as well as the receiving-end voltage will decrease. These curves Uidicate that there are two possible values of voltage for each loading. The system cannot be operated in the lower portion of the curve even though a mathematical solution exists. Consider an operating point in the lower portion of the c w e . If an additional quantity of load is added under this condition, this added Ioad wil draw additional current fkom the system. The resulting &op in voltage in this operating state would more than offset the increase in current so that the net effect is a &op in delivered pwer. If the load attempts to restore the demanded power by sorne means, such as by increasing the current, the voltage will decrease even M e r and faster. The process will eventually lead to voltage collapse or avalanche, possibly leading to l o s of synchronism of generating units and a major blackout. in a larger system, apart from load dynamics, other dynamics such as generator excitation control, on load tap changer ( OLTCs ), static var compenwitor ( SVC ) controls, thermostat controlled loads, etc, play an important role in the voltage stability of the system. The radial system shown below presents a clear picture of the voltage stability problem and its associated dynamics [l]. Genemtor to trip Residential Load 6 ~ i n e to trip Industrial not on LTC -4 Primary Capacitors LTC 7 Industrial Loat Fig.2.3 Radial system with some of the elements that play key role in the voltage stability [ 1 1 In the above system, two types of loads are considered: residential and industrial. Residential load has a relatively hi& power factor and tends to drop with voltage. On the other han4 industrial load has low power factor and does not Vary much with voltage. if this system is heavily loaded and operating near its voltage stability l e t , a mal1 increase in load ( active or reactive ), a loss of generation or shunt compensation, a drop in sending end voltage cm bring about voltage instability. Assuming that one of the above mentioned changes happen and receiving end voltage falls, several rnechanisms corne into play. As residential Ioads are voltage dependent, the active and reactive load drops with drop in voltage, while industrial active and readve loads which are dominated by induction motoa change linle. nius, the overall effect may be the stabilization of voltage at a value slightly less than the ratai value. The next action is the operation of distribution transformer load tap changers ( LTCs ) to restore distribution voltages. The residential active ioad will increase while the industrial reactive load will decrease. The increasing residential load will initially outweigh the decrease in reactive load causing the prirnary voltage to fdl further. in this scenario, the on- load tap changers ( OLTCs ) may be close to their limitç, primary voltage at around 90% and distribution voltage below normai. Industrial loads served fiom the prUnary system without LTCs will be exposed to the reduced voltage levels. This greatiy increases the stalling of induction moton. When a motor stalls, it will draw increasing reactive cunent, bringing down the voltage on the bus. This results in a cascade stalling of other induction motors resulting in a localized voltage collapse. Since, most large induction motors are controlled by magnetically held contactors, the voltage collapse would cause most motos to drop off from the system. This l o s of load will cause the voltage to recover. However, the recovered voltage will again result in the contactor closing, motor stalling and another collapse. Thus, this loss and rwvery of the load can cause aitemate collapse and recovery of voltage. From the above discussion, it is clear that voltage stability is essentially a slow dynamics and is affected by the nature and type of load and other control actions. Power systems have become more complex and are k i n g operated closer to their capability limits due to economic and environmental reasous. While these trends have contributed to angle instability, it is clear fiom a midy of recent incidents of system failures [1,4] that, it is voltage instability that is the major factor in these failures. 2.3 Voltage Collapse Incidents [4] Throughout the world, there have been disturbances involving voltage collapse over the last twenty years with the majority of these occurrences since 1982. Two typical examples of voltage collapse occurrences are the 1987 French and Tokyo power system failures. in France on January 12, 1987 at 10:30 am, one hour before the incident occurred, the voltage level was normal despite very low temperature outside. For various reasons, three themal units in one generating station failed in succession between 1055 and 1 1 :4 1 am. Thirteen seconds later, a fourth unit tripped as the result of operation of the maximum field cument protection circuit. This sudden loss in generation led to a sharp voltage &op. This &op in voltage increased thirty seconds later and spread to adjacent areas, resdting in the trippkg of other generating units on the system within a span of few minutes. As a result, 9000 MW were Iost on the French system between 11:45 and 1150 am. Normal voltage levels were restored rapidly after some load shedding took place on the system. In the same year on July 23, Tokyo's power system also experienced the voltage collapse phenornena The temperature rose to39"C and as a result, there was a sharp increase in the demand due to the extensive use of airconditionen. The 500 KV voltages began to suik ( to 460 KV ) and eventually the over current protection on the 500 KV Iines operated As a result, seven 500 KV nibstations were without supply. This resulted in the loss of 8000 MW of load for about three houn. It is interesting to note that during ail this tirne, there was no indication or abnomal operation which would have alerted the operaton to the impendlng disaster. The only indication that sornething out of the ordinary happening was that the rate of rise of the load was 400 MWhinute, which was twice as much as ever recorded before. 2.4 Factors Contributing to Voltage Instability/Colfapse [SI Based on the voltage collapse incidents described in references 1 and 4, the voltage collapse can be characterized as follows: The initiaikg event may be due to a variety of causes: smali gradua1 changes such as naturai increase in system load, or large sudden disturbances such as loss of a generating unit or a heavily loaded line. Sometimes, a seemingly uneventful initial disturbance may lead to successive events that eventually cause the system to collapse. The heart of the problem is the inability of the system to meet its reactive demands. Usually, but not dways, voltage collapse involves system conditions with heavily loaded lines. When the transport of reactive power fiom neighboring areas is difficult, any change that calls for additionai reactive power support may lead to voltage collapse. The voltage collapse generally manifests itself as a slow decay of voltage. It is the result of an accumulative process involving the actions and interactions of many devices, controls and protectïve systems. The t h e £iame of collapse in such cases could be of the order of several minutes. Thus, some of the major factors contributing to voltage instability c m be summarized as follows: sudden increase in load. O rapid on-load transformer tap changing. O level of series and shunt compensation. reactive power capability of generaton. response of various control systems. 2.5 Voltage Sta bility Analysis As incidents of voltage instability become more common and systems continue to be loaded closer to their stability limits, it becomes imperative that system operators be provided with tools that can identiS potentially dangerous situation leading to voltage collapse. A nurnber of special algorithm have been proposai in the literature [6] for the analysis of voltage instability. Few of hem are: (1) Singuiar Value Decomposition. (2) 'L' Index. (3) PV and QV c w e s . (4) Eigenvahe Decomposition. (5) V-Q Sensitivity. (6) Energy Based Measure. In ths chapter, the first three methods are discussed in detait because they are commonly used in the elecûic power industry. Whle, singular value decornposition and 'L' Ludex provide the necessary andytical tools in identifjmg voltage collapse phenornena, PV and QV curves are the more traditional methods used as voltage collapse proximity indicaton ( VCPI ) in indu- today. PV curves have already been discussed with respect to the simple two bus power systern in section 2.2. 2.5.1 Singular value decomposition In 1988, Tiranuchit and Thomas [ A proposed a global voltage stability index based on the minimum singular value of the Jacobian. They showed that a mesure of the neamess of a matnx A to singularity is its minimum singular value. An important aspect to be considered when deriving corrective control measure is the question " how close is the Jacobian to being singular? ". To examine the above question, consider the following basic problem: given a matrk A, determine conditions on perturbation matrix A such that A + AA is singular. Note that if A is non-singular, one may write A + A A = ( 1 + A - ' A A ) A ( 2.3 ) The terni ( I + A-' A A ) can be shown to have an inverse if To get a better understanding of the use of this voltage stability index, consider a set of non-linear algebraic equations in maîrix format given by Given y and Rx), we want to solve for x This can be done by Newton- Rhapson iterative method, where old values of x are used to generate new values of x i.e. where, J is an invertible rnatrix, called the Jacobian matrix. The Newton-Raphson method c m be applied to solve the load flow problem. The power flow equations in polar coordinates are as follows: P, , Q , : scheduled r d and reactive power supplieci to bus K V, , V, : bus voltages at bus K and n 6 ,, 6 , : phase angles of the bus voltages at bus K and n 8,, :admittance angle Y,, : elements of the bus admittance matrix For the power fiow probiem The Jacobian matrix for the power flow is o f the fonn: The inverse of the matrix J is given by Lf I J I = O, then the Jacobian is non-invertible or singular. The singular value decomposition of the Jacobian matrix gives a measure of the system closeness to voltage collapse. As the power system moves towards voltage collapse, the minimum singular value of the Jacobian matrix approaches zero. 2.5.2 L index In 1986, Kessel and Glavitsch [8] proposed a fast voltage stability indicator. This method provides a means to assess voltage stability without actually computing the operating point. Consider a two bus system as s h o w in Fig.2.4. Y : Series adminance Y : Shunt admittance V , . V, - Nodd v o t t q p Fig.2.4 Line mode1 for two bus system The properties of node 1 can be described in tems of the admittance matru< of the system. s ; Y,, v1 + Y,, v* = 1, = - v; Y,, . Y,, , Y,, . Y, form the admittance matrix [Y] and S, is the complex power. s, = v1 1; Equation 2.13 can be written as s : v,' + vo v; = - v where, It is shown in reference (81 that the solution of equation 2.15 indicates the stability limit of the power system. At t h i s point This relation can be used to define an indicator Lj at each bus for the assessrnent of the voltage stability. It's range is O 5 Lj < 1. The global indicator describing the stability of the complete system is the maximum of al1 Lj values at each and every bus. The indicator L, is a quantitative measure for the estimation of the distance of the actual state of the system to the stability tirnit. The local indicaton Lj can be used to determine the buses fiom which voltage collapse rnay originate. 2.5.3 QV Curves [9] QV curves are presently the workhorse method of voltage stability analysis at many utilities. The QV curves show the sensitivity and variation of bus voltages with respect to reactive power injections. They are used for the assessrnent of the voltage stability of the system. They show the mega volt ampere reactive ( MVAR ) and voltage rnargins to instability and provide information on the effectiveness of reactive power sources in controlling the voltage in different parts of the system. Vo-Vc : Voltage stability mvgin Qc : MVAR stabili~y margin Voltage Instability point Fig.2.5 Sample QV curve For each QV curve, a reactive power source is placed at the selected bus ( QV bus ) to move its voltage in a given range, Vmin to V- by a given step size V*. At each voltage step, the power flow is solved to compute the required MVAR injection Qi, at the QV bus for holding its voltage at Vi. The points of QV curves are computed by starting from the existing voltage, VO and zero MVAR injection and increasing the voltage until V- is reached or the puwer flow fails to solve. Then the system is reset to the initial condition at V. and the QV computation proceeds in the opposite direction by decreasing the voltage until Vmin is reached or the power Bow becornes unsolvable. Fig.2.5 shows a typical QV curve. The voltage difference V A L and the value of Qc provides the voltage and MVAR stability rnargins at the bus and the dope of the cuve provides the sensitivity information. 2.6 Simulation Results and Discussions In this section, a simple 5 bus system is taken as a case study to ver@ the algorithms discussed in the previous sections. The single line diagram is shown in Fig.2.6 [IO]. The line and bus data for the 5 bus system is s h o w in Appendix A. In this system, bus 1 is the reference ( slack ) bus while buses 2 J,4 and 5 are considered load ( PQ ) buses. The test system is studied without considering any limit on the generators. Fig.2.6 Single line diagram of the 5 bus system The system is dnven from an initial operating point ( base case ) up to the collapse ( bifurcation ) point by changmg the loading factor. Loading factor is a scalar parameter used to simuiate the system load changes that drives the systern from base case to the bifurcation point The tem ""bifurcation" [ i l ] in power systems can be explained as follows: For a load condition, in addition to normai load-flow solution, which is typically the actual operating point or stable equilibrium point ( s.e.p ), several solutions may be found for the load-flow equations. The 'closest" one to the s.e.p. is the unstable equilibrium point ( u.e.p ) of interest for voltage collapse studies [12]. These equilibrium points approach each other as the system is loaded, up to the point when only one soiution exists. If the system is loaded m e r , al1 system equilibria disappear. The "lasf7 equilibrium has been identified as the steady-state voltage collapse point This point is known as saddle-node bifurcation point. At this bifurcation point, the real eigenvalue of the load-fiow Jacobian becomes zero, that is., the Jacobian becomes singular. 2.6.1 Singular value decomposition Simulation results of the singular value decornposition method for the 5 bus system is s h o w in Fig.2.7. In this method, the system could not be loaded beyond a loading factor of 3.3 because of the divergence of the load flow solution. Loading factor of 3.3 corresponds «, a total load of 544.5 MW. .................................................................... ( C . . . . . . . . . . . . . . --.' Fig.2.7 Singular value decomposition for 5 bus system From Fig.2.7, it cm be said that as the loading factor is increased From the base case, the minimum singuiar value decreases and finally approaches zero at the collapse point For example, the minimum singular index is 0.8986 at a loading factor of 3.3 ( near the stability limit ), vev close to the collapse point. Hence, the minimum singular value gives a measure of the n e m e s s to instability or in other words 'distance to collapse'. The system is said to have collapsed when the minimum singular value of the Iacobian is zero. It can be seen nom the above figure that at or near the collapse point, the singdar index is very sensitive to load changes and hence there is a sharp drop in its value. Thus, this index fails when the system is operating close to its limits. Another major disadvantage of this method, is the large computation time required to calculate the minimum singular value for larger systems. 2.6.2 L Index Simulation results of the "Lw index method for the 5 bus system is shown in Fig.2.8 and Fig.2.9. Fig.2.8 L index of individual load buses for 5 bus system Fig.2.9 System L index for 5 bus system From Fig.2.8, as the loading factor is increased, the L index of bus 5 approaches more rapidly towards mity than other buses. When the L index is unity, the system collapses. For instance, near the collapse point ( loading factor of 3.3 ), the L index of bus 5 is 0.7165, while for buses 2.3 and 4 the L indices are O.1927,O. 1 90 1,O. 1926 respectively. The maximum of these is 0.7165. This represents the system L index, which gives a quantitative rneasure for the estimation of the distance of the actuai state of the system to the stability b i t Fig.2.9 shows the system L index and the corresponding bus voltage for the 5 bus system The local L index permits the determination of those buses from which collapse May originate. In the above simulation, voltage collapse originates from bus 5. This is considered as the critical bus for this system. Thus, the stability indicator L is able to characterize the load tlow solution and the potential of the system to become unstable. This is bound to the load fiow mode1 and the assumption of a PQ node. The mode1 does not reflect any dynamic behavior. It is based on single node calculations and is therefore easy to calculate. However, it may require substantial engineering judgment in a large system. 2.6.3 QV curves The farnily of QV curves for the three operating cases: basecase ( Load = 165 MW ), near the stability limit ( Load = 565 MW ), at the point of instability ( Load = 584.53 MW ) are s h o w in Fig.2.10, Fig.2.11, Fig.2.12 respectively. Fig.2.10 Farnily of QV curves for the base case of the 5 bus system Fig.2.11 Family of QV curves near the stability limit of the 5 bus system Fig.2.12 Family of QV curves at the collapse point of the 5 bus system The above QV curves are obtained from a commercially available software VSTAB 4.1 [9]. In this program, lists of buses for which QV curves are to be generated and the s p of each Q V curve must be provided. The span of QV curve is specified by providing the maximum and minimum voltage level at a bus. The program is initiated by assigning the parameters QVCRVS = 1 and SELQVC = FALSE in the parameter file of the VSTAB program. For example, consider the base case operating condition of Fig.2.10. The lists of load buses for which QV curves are to be generated are 2 , 3 , 4 and 5 . The span of each QV curve is specified by providing the maximum voltage level V- = 1.1 p . u and minimum voltage level V,, = 0.2 p.& The step voltage is O. 1 p.u. For the bus 2, the base case voltage V, = 1.0475 p.u. For this bus, QV curves are generated by solving the series of power flow equations 2.6 and 2.7 d l V,, is reached Then the system is reset to the initial condition at V, and the QV computation is carried out in the opposite direction by decreasing the voltage. Here, eventhough V,, is assigued at 0.2 p-u, the p w e r fl ow becomes unsolvable at 0.4 p . u itself Hence, compuîations are stoppeci at this value. Thus, the voltage stability margin V, - V,= 1.0475 - 0.6 = 0.4475 p. u. and MVAR stabiIity margin is -497.06 MVAR. From the above results, the following interpretations can be made. At the base case operating point, al1 buses have significant reactive margin, while at the point of instability, the buses have vimially no reactive margin. The reactive margin is the MVAR distance from the operating point tu the bottom of the curve. There is a significant voltage stability margin for the base case operating point compared to the margin at or near the stability limit. For example, corresponding to the most cntical bus i.e. bus 5, the voltage stability margin for the base case and near the stability lirnit is 0.5 18 p.u. and 0.1205 p.u respectively. QV curves cm thus be used in the assessrnent of voltage stability of the system. Another advantage of this rnethod is the characteristics of test bus shunt reactive compensation can be plotted directly on the QV curve. The operating point is the intersection of the QV characteristic and the reactive compensation charactenstic. This is useful since reactive compensation is ofien a solution to voltage stability problem. On the other han& since the method artificially stresses a single bus, conclusions should be confirmed by more reaiistic methods. Also, the c w e s are obtained by a senes of power flow simulations which makes it more time consuming. 2.7 Limitation of Traditionai Methods in Voltage Stabüity Analysis The steady-state techniques described in the previous section have not found widespread practical applications due to the following shortcomings: they do not provide practical rnargins to measure the stability of the system. they provide little or no information regarding the mechanisrn of instability . they focus on the strength of individual buses and not fkom the system wide perspective. they rnake significant modeling assumptions such as constant generator voltages or constant impedance loads and such assumptions may eliminate factors which ifluence system stability. From the analysis of the traditional rnethods, it cm be concluded that the most important aspect of a practical voltage stability index is the computation effort and hence not usefid for rd-time use in energy management system ( EMS ). Moreover, these rnethods depend largely on conventional power fiows to determine the voltage collapse levels of various points in a network. Furthemore, this approach is laborious, t h e consuming and requires analysis of massive amounts of data as the size of the power system increases. When the power system is operating close to its limits, it is essential for the operator to have a clear knowledge of the operating state of the power system. Thus, for on-line applications, there is a need for tools which can quickly detect the potentially dangerous situations of voltage uistability and provide guidance to steer the system away from voltage collapse. Recently, efforts to improve the speed and ability to h a d e stressed power system have led to the development of intelligent systems. N d for Expert Systems in Eleetric Power System In recent years, research in the field of artificiai intelligence ( AI ) has achieved sigmficant success. Arnong the most signifiant of these is the development of "Expert" or "Knowledge-Based" systems and "Artificial Neural Networks ( ANNs )Y Expert systerns and ANNs are subsets of AI. Both these areas have attracted a widespread interest in the field of power system applications. Reference [13] presents a global view of knowledge engineering applications and tools available in the field of power systerns. Expert systems is a branch of AI that makes extensive use of specialized knowledge to solve problerns at the level of a human expert. That is, an expert system is a cornputer system which emuiates the decision-rnaking ability of a human expert. It consists of two main components: knowledge-base and the inference engine. The expert systems will be treated in detail in chapter 4. Expert systems offer a number of advantages [14]: a As& Human Experts An expert system cm reduce tedious and redundant manual tasks and thereby enhance productivity leading to efficient operation. Flexibility Each production d e represeats a piece of knowledge relevant to the task. Hence it is very convenient to add, remove and modiQ a rule in the knowledge base as experience is gained a Rapidity The expert system can provide more rapid reaction to emergency events than human operators. This is very usefbl in power system operation. in the power system area, expert system applications has been m d y devoted to power systern operations [14]. This is because the operation of power systems has become very complex and operaton are unable to deal with the large amount of data associated with the modem energy management systern. Also, power system operation experience is lost when experienced operators retire or change jobs. It is important to preserve this valuable experience as it is not contained in any textbook or manual. Thus, expert systems can assist in decision-making and minimize erron by human operators. 2.9 Summary In this chapter, the basic concepts, d y t i c a l tools and industry experience related to voltage stability analysis of power systems are reviewed. Advantages and disadvantages of the traditional methods are highlighted by simuiating a simple 5 bus system. From the simulation results, it cm be concluded that the existing methods require significantly large cornputations and are not usefid for real-time use in energy management system. Hence, an altemate approach, such as the applications of artificial intelligent techniques to power systems in general is discussed. To enhance the capabilities of the EMS, an integrated approach of knowledge-based systems ( amficial neural networks and expert systems ) and conventional power system solution methodologies has to be adopted. This approach has the potential to achieve secure and economic operation of the p w e r system. Chapter 3 COlYTINUATION POWER FLOW GND MODAL ANALYSE 3.1 Introduction With the growing concem for voltage instability in the power system industry, much attention has been given to investigating this phenornenon. As a result, a number of techniques have been developed to study the problem. However, well accepted cntena and study procedures regarding system voltage stability do not yet exist Many utilities continue to use pst-contingency voltage decline as an indicator of voltage stability, while some others use performance criteria based on either PV or QV curves. Thus, there is a need to develop a practical procedure which utilities can apply as part of their routine studies. Also, results of voltage stability anaiysis using power flow based static techniques need to be validated using detai led time-domain simuiation tools, such as the Transient- Midtem Stability Programs which are similar to EPR17s ETMSP [15]. Static analysis is based on the solution of conventional or modifiai power flow equations. A popular tool for static based voltage stability analysis is EPRI's voltage stability ( VSTAB ) program [9]. The VSTAB, developed by Ontario Hydro, is a voltage stability assessrnent package for large complex power systems. It provides idormation regarding both the proximity to and mechanisms of voltage instability. The main features of the VSTAB package are: Automatic modification of the system state which includes increasing the load in a predefined manner, creating new dispatches, performing sets of contingencies. Comprehensive voltage stability anaiysis like PV curves, QV curves and modal analysis. Determination of Megawatt ( MW ) or Megavar ( MVAR ) distance to voltage instability, which can indicate modes of instabi lity characterized by groups of buses, branches and generators which participate in the imtability. Capability to obtain the nose of the PV c w e s using the continuation power flow. Steady state approximations to tirne fiarnes associated with ULTC action, governor response, Automatic Generator Control ( AGC ) action and economic dispatc b Voltage stability analysis technique based on the eigen-analysis of the reduced steady state Jacobian rnatrix is referred to as modal analysis. It provides masures of proximity to instability and clearly indicates areas ( modes ) which have potential stability problems. The modal analysis dong with continuation power 80w technique [16,17] have been applied to voltage stability analysis of practicd systems. In the following sections, these two techniques are discussed in detail, supplemented by the simulation resuits of typical test systems using VSTAB and EPRi's Interactive Power Flow ( IPFLOW ) [18] tools. 3.2 Continuation Power Flow Technique A parhcular difficulty encountered in indices mentioned in section 2 . 5 , is that the Jacobian of a Newton-Raphson power 80w becomes singuiar at the voltage stability limit. Consequently, conventional power-flow algorithms are prone to convergence problems at operating conditions near the stability Iirnit The continuation power-flow anaiysis overcomes this problem by reformulating the power-flow equations so that they remain well-conditioned at al1 possible loading conditions. 3.2. l Basic principle This technique was proposed by Ajjarapu and Christy in 1992 [19]. The continuation power-fiow analysis uses an iterative process involving a predictor-corrector scherne as shown in Fig.3.1. Fig.3.1 An illustration of the continuation power flow technique From a known initial solution (A), a tangent predictor is used to estimate the solution (B) for a specified pattern of load increase. The corrector step then detemines the exact solution (C) using a conventional power-flow anaiysis with the system load assumed to be fixed. 3.2.2 Mathematical formulation When the objective is to obtain the maximum loadability point of a system, the problem can be fomulated as ~(6, v ) = AK ( 3 . 1 where, S is the vector of bus voltage angles v is the vector of bus voltage magnitude K is the vector representing percent load change at each bus A is the load parameter Equation 3.1 can be re-written as ~ ( 6 , v , R ) = O In the predictor step, a linear approximation is used to predict the next solution for a change in one of the state variables ( i.e. 6, v, A ). Taking the derivatives of both sides of the equation and evaluating the derivatives at the initial solution, will result in the following set of linear equations in To account for one more equation due to the introduction o f an additional variable in the power flow equations ( namely A. ), one of the components of the tangent vector is set to +1 or - 1. This component is referred to as the continuation parameter. Equation 3.2 now becomes L -1 where, e , is a vector where al1 the entries are zero, except for the variable which is chosen as the continuation parameter, where the entry is ' 1 ' . initially, the continuation parameter is chosen as A. ( load parameter ) and the sign of its slope is positive. However, once the tangent vector is found, the continuation parameter is selected as the bus voltage with the iargest entry in the tangent vector and its sign is used during the next predictor step. Once the tangent vector is found, the next solution can be approxùnated as: The step size a should be chosen so that a solution would exist for the specified continuation parameter. I f for a gïven step size, a solution cannot be found in the corrector step, the step size should be reduced d l a successfiil solution is obtained. in the corrector step, the original set of equations F (6, v, A ) = O is augmenteci by one equation that specifies the value of the state variable selected as continuation parameter. The new set of equations can be written as where x, is the state variable that has been selected as the continuation panimeter and 7 is equal to x" . This set of equations is solved using Newton-Raphson power flow method. The introduction of the extra equation rnakes the Jacobian to be non-singular at the maximum Ioadability point and hence a solution can be obtained at that point. 3.3 Modal Analysis [SI The Modal analysis for voltage stability is briefly discussed below. Consider the linearized power flow equation expressed as wtiere, AP is the incrernental change in bus real power. AQ is the incremenuil change in bus reactive power injection. Aû is the inmemental change in bus voltage angle. AV is the incremental change in bus voltage magnitude. J e , , J , ., J Q e , J are the power flow Jacobian elements. System voltage stability is affected by both real and reactive power. However, at each operating point the real power is kept constant and voltage stability is evaluated by considering the incremental relationship between reactive power and voltage. This is analogous to the Q-V cuve approach. Although incrementai changes in real power are negiected in the formulation, the effects of changes in system load or power transfer levels are taken into account by studying the incremental relationship between reactive power and voltage at different operating conditions. To reduce ( 3.6 ), let AP = O , then J , is called the reduced Jacobian mat* of the system. J , is the matrix which direaly relates the bus voltage magnitude and bus reactive power injection. Eliminating the real power and angle part fiom the system steady state equations allows one to focus on the hidy of the reactive demand and supply problem. Voltage stability characteristics of the system can be identified by computing the eigenvalues and eigenvectors of the reduced Jacobian rnatrix J,. Let, J , = t A v where, 5 = right eigenvector matrix of J, . q = left eigenvector matrix of J , . A = diagonal eigenvalue matrix of J , . and J," = 5 A-' 7 From ( 3 . 7 )and ( 3.9 ), we have, A V = 6 A-' q A Q Each eigenvalue A , and the correspondhg right and left eigenvectors and r ) define the i mode of the Q-V response. Since 5 -' = q , equation 3.10 can be written as v A V = A-' q A Q or v = ~ ' q (3.12 ) where, v = 7 A V is the vector of modal voltage variaticm. q = 9 A Q is the vzctor of modal reactive power variation. Thus for the i" mode, i f A , > 0, the i' modal voltage and the i' modal reactive power variation are along the same direction, indicating that the systern is voltage stable. if A , < 0, the i' modal voltage and the i' modal reactive power variation are along opposite direction, indicating that the systern is unstable. In this sense, the magnitude of R detemiines the degree of stability of the i h modai voltage. The smaller the magnitude of positive A , , the closer the i" modal voltage is to k i n g unstable. WhenA , = O, the i' modal voltage collapses because any change in that modal reactive power causes infinite change in the modal voltage. The magnitude of the eigenvalues can provide a relative measure of the proximity to instability. Eigenvalues do not, however, provide an absolute measure because of the non-linearity of the problem. The application of modal analysis helps in identifying the voltage stability critical areas and elements which participate in each mode. The bus participation factors detennine the contribution of A. , to t h e V-Q sensitivity at bus k They cm be expressed in terms of the left and right eigenvectors of J , as P k i = Çti Bü ( 3 . 1 4 ) Bus participation facton detennine the areas associated with each mode. The size of bus participation in a given mode indicates the effêctiveness of remedial actions applied at that bus in stabilizing the mode. The branch participation fkctors Pji which give the relative participation of b m c h j in mode i are given by - - A Q loss for b m c h j 'J ' max. A Q loss for al1 branches The A Q loss can be caiculated by calcuiating the A V and A 0 change at both ends of the branch. Branch participation factors indicate for each mode, which branches consume the most reactive power in respome to an incremental change in reactive load Branches with high participations are either weak links or are heavily loaded. Branch participations are usefd for identi f j m g remedial mesures to alleviate voltage stability problems and for contingency selection. The generator participation facton Pm which give the relative participation of machine m in mode i are given by - A Q for machine m P m i - ( 3. 16 ) max. A Q for al1 machines The generator participation factors can be used to determine the generators that supply the most reactive power on demand. Generator participation provide important information regarding proper distribution of reactive reserves among al1 the machines in order to maintain an adequate voltage stability margin. 3.4 Simulation ResuIts and Discussions In this section, two typical test systems: the New England 39 bus system [9] and the IEEE 30 bus system [20], are simulated to illustrate the modal analysis along with continuation power flow technique used for the voltage stability evaluation. 3.4.1 IEEE 30 bus system The single line diagram of the IEEE 30 bus system is shown in Fig.3.2. In this system, the load is increased at buses 3,12,21,26 and 30, while generation at buses 2,5,8,11 and 13 are scaled accordingiy to meet the increased demand. In this system, the base case system load corresponding to the selected buses is 45.2 MW. Fig.3.2 Single line d i a m of the IEEE 30 bus system I f the load in this system i s u n i f o d y increased ( constant power factor ), and the power scaled up accordingiy, the PV curve show in Fig.3.3 is obtained fiom which it is seen that the voltage stability limit is 179.38 MW. r i . .......... > V.V O 20 40 60 80 100 120 140 180 180 200 Total Laad et Sclected 8uws (MW) Fig.3.3 PV curve for bus 30 of the IEEE 30 bus system Here, the PV curve is obtained up to the nose point using the continuation power flow technique. On this PV curve, three operating points are identified: f oint A: base case condition LOAD = 45.2 M W . Point B: near the voltage stability limit LOAD = 170.2 MW. Point C: at the voltage stability limit LOAD = 179.3 MW. Now modal analysis is performed at the three operating points to find five least stable modes for each case. Tabie 3.1 shows the results of the analysis for the three operating cases. Table 3.1 Five smallest eigenvaiues for the three operating cases Eigenvaiues 1 From Table 3.1 ., it is seen that the minimum eigenvdue for operating points A, B, C are 0.5145, 0.1538 and 0.0107 respectively. Table 3.2 shows bus, branch and generator participation factors for the base case ( point A ) and at the voltage stability limit ( point C ) corresponding to the least stable mode ( mode # 1 ). Table 3.2 Participation factors ( P.F ) for base case and critical case Operating Point A B C corresponding to the least stable mode. mode # 1 0.5145 0.1538 0.0107 Total Load ( M W ) 45.2 170.2 179.3 mode # 2 1.0644 0.7068 0.5697 Operating Point Point A Point C mode # 3 1.7985 0.9707 0.8492 Bus Participation Bus No P.F Branch Participation Branch No P.F 30 29 26 30 29 4 - 12 9 - I l 28 - 27 27 - 30 28 - 27 Generator Participation Generator No P.F mode # 4 3.7182 0.2 145 0.1940 0.1740 0.4789 0.2463 1 .O000 0.6622 0.569 1 1 .O000 0.9834 8 13 8 mode # 5 4.2255 L 1 .O000 0.5733 1.0000 2.9505 2.3959 3.2571 2.8459 The above analysis shows that as the system load increases, the magnitude of the eigenvalue decreases and at the point of instability, it becomes essentially zero. Table 3.2 indicates that, at the point of instability, buses 30,29 and branches 27-30,28927 are prone to voltage instability. This cm be justified fkom the fact that, for the least stable mode, buses 30 and 29 participate significantly while the rest of the buses do not contribute to voltage instability. This is evident fiom their participation factors. Table 3.3 gives the voltage stability margin for the three operating cases. Table 3.3 Voltage stability margin for different operating conditions 1 Operathg Point ( Total Load ( MW ) Voltage Stability Margin ( MW ) l Voltage stability rnargin ( VSM ) is a measure of how close the system is to voltage instability. It is defined as the difference between the values of a Key System Parameter ( KSP ) at the current operating condition and the voltage stability critical point [lq. Here, KSP is defined as the total load increase in the selected buses. For example, the voltage stability margin for the base case operating condition is 134.1 MW and near the stability limit ( operating point B ) is 9.1 MW. 3.4.2 New England 39 bus system In this section, modal analysis for the New Englcad 39 bus system [9] is perfomed. This systern is widely w d for voltage stability evaluation. The single iine dia- of the New England 39 bus system is shown in Fig.3.4. Here, the load is increased at buses 3.4, 12, 15 and 2 1. Generation at 3 0 , 3 2 , 3 5 and 37 are scaled accordingly to meet the increased demand. Fig.3.4 Single line diagram of New England 39 bus system The PV curve for bus !2 of the New England 39 bus system is shown in Fig.3.5. Table 3.4 shows five least stable modes for the three operating cases. Operating point A corresponds to 1424.5 MW, operating point B corresponds to 4949.5 MW and operating point C corresponds to 4976.8 M W * 0.4 1 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Total Load at çelected Buses (MW) Fig.3.5 PV curve for bus 12 of the New England 39 bus system Table 3.4 Five smallest eigenvaiues for different loading conditions 1 Point 1 ( M W ) 1 mode 1 mode 2 mode 3 mode 4 mode 5 1 Operating Total Load Point A Eigenvalues Point B 1424.5 10.1145 1 22.5085 1 39.8117 1 45.4208 1 61.3524 4949.5 0.9424 10.5001 16.3547 28.2210 35.0747 Table 3.5 gives bus, branch and generator participation factors for critical case ( at the point of instability ) corresponding to the least stable mode. Table 3.5 Participation factors ( P.F ) for critical case ( point C ) corresponding to the least stable mode ( mode 1 ) From the a b v e results, it c m be concluded that the weakest buses and branch associated with this system are 12, 4, 14 and 10-32 respectively. Table 3.6 shows the voltage stability margin for the three operating cases considered. Table 3.6 Voltage stability margin for the three operating conditions Bus Participation Bus No P.F 1 o p e r a ~ g Point 1 Total Load ( MW ) 1 Voltage Stability Mar@ ( MW ) 1 12 4 14 1 1 t Point A 1 1424.5 I 3552.3 I O. 17 13 O. 1042 0.0949 Branch Participation Branch No P.F 1 1 1 Point B 1 4949.5 1 27.3 1 10 - 32 Generator Participation Generaîor N o P.F I i Point C 4976.8 O 1 1 .O000 32 3 1 3.5 Summary This c hapter has presented a voltage stability assessrnent technique for large power systems using modal analysis in conjunction with continuation power flow technique. The method cornputes a specified number of the smallest eigenvalues of a reduced Jacobian matrix and the associated bus, branch and generator participations. Two typical test systems namely IEEE 30 bus system and New England 39 bus system were used for the purpose of analysis. 1 .O000 0.73 17 The above two examples clearly indicate how the modes represent areas prone to voltage instability. Based on the simulation resuits, the following conclusions can be reached: Each eigenvalue corresponds to a mode of voltage/reactive power variation. - The modes correspondhg to s m a l l eigenvalue represent the modes most proue to loss of stability. - The magnitude of each srnall eigenvalue provides a relative measure of proximity to loss of voltage stability for that mode. Bus, branch and generator participations provide useful information regarding the mechanism of loss of stability. - Bus participations indicate which buses are associated with each mode. - Branch participations show which branches are important in the stability of a given mode. - Generator participations indicate which machines must retaui reactive reserves to ewure the stability of a given mode. The modal analysis along with continuation power flow can be used to determine the voltage stability margin for the base case and a large number of operating cases. Participation factors for the critical case conesponding to the least stable mode is most useful for any remedial actions. It clearly identifies groups of buses and critical bus that participate in the iastability and thereby elirninate the problems associated with traditional methods. Identifjmg the cntical bus will help in taking appropnate control actions. Hence, in the subsequent chapters, this method is used as basis for developing an expert system for voltage stability evaluation. Chapter 4 FUZZY-EXPERT SYSTEMS 4.1 Introduction As rnentioned in chapter two, expert systems are built based on the knowledge acquired nom domain experts. The knowledge of an expert system may be represented in a number of ways. One common method of representing knowledge is in the fonn of IF-THEN type d e s , such as IF the light is red THEN stop If a fact exists that the light is red, this matches the pattern "the light is red". The nile is satisfied and perfonns its action of "stop". Expert systems can be considered declarative programming because the programmer does not specifjr how a program i s to achieve its goal at the level of an algorithm. Expert systems are generally designed very differently fiom conventionai programs because the problems usuaily have no algorithme solution and rely on inferences to achieve a reasonable solution. The strength of an expert system can be exploited fully when it is used in conjuncàon with a database. Changes in the system operating conditions are reflected in the database. The expert system that draws its data fiom the database automatically tracks the system operating conditions. The purpose of this chapter is to introàuce the basic theory of expert systems and funy logic. The concept of membership h c t i o n plays an important role in the design of the proposed fiiW-expert system for voltage stability monitoring and control. Hence, it is relevant to explore these concepts in detail to understand its applicability to power system problems. One of the objective of this thesis is to arrive at a solution that is fasf reliable and usefùi for the power system operators. This chapter will lay a foundation in understanding the proposed fbzzy-expert system in order to achieve the desired objective. in this chapter, the theory of expert system is described in section 4.2. The fundamental concepts of f u n y set theory is explained in section 4.3. Section 4.4 highlights potential applications of fuzzy-set-based approaches and their relevance to power system problems. 4.2 Expert System Structure The structure of an expert system in a general block diagram i s shown in Fig.4.1 [2 11. Expert System Fig.4.1 Expert system structure As shown in Fig-Cl., the expert system consists of two cornponents. The knowledge-base and the inference engine. The kuowledge-base comprises knowledge that is specific to the dornain of application, incluâing simple facts about the domain, d e s that describe relations or phenornena in the domain and hewistics. The inference engine actively uses the knowledge in the kaowIedge-base and draws conclusions. The user interface provides smooth communication between the user and the system. It also provides the user with an insight into the problem-solving process executed by the inference engine. It is convenient to view the inference engine and the interface as one module, usually called an expert system shell. Expert systems are often designeci to deal with uncertainty because reasoning is one of the best tools that have been discovered for dealing with uncertainty. The uncertainty rnay arise in the input data to the expert system and even the knowledge-base itself. At first this rnay seem surprising to people used to conventionai programming. However, much of human knowledge is heuristic, which means that it rnay oniy work correctly pari of the time. In addition, the input data rnay be incorrect, incomplete, inconsistent and have other errors. Algorithmic solutions are not capable of dealing with situations like ths. Depending on the input &ta and the knowledge-base, an expert system rnay corne up with the correct answer, a good answer, a bad answer or no answer at all. While this rnay seem shocking at first, the alternative is no answer al1 the tirne. 43.1 Fnayset theory The theory of uncertainty is based on funy logic. The traditional way of representing which objects are membea of a set is in terms of a characteristic function, sometimes called a discrimination fiuiction If an object is an element of a set, then its characteristic function is 1. If an object is not an element of a set, then its characteristic function is O. This definition is summarized by the following characteristic fûnction: pA(x) = 1 if x is an element of set A O if x is not an element of set A where the objects x are elements of some universe X. In funy sets, an object may belong partially to a set The degree of membenhip in a fwzy set is measured by a generalization of the characteristic fiinciion called the membership function or compatibility function defined as The characteristic function rnaps al1 elements of X into one of exactly two elements: O or 1 . In contrast, the membership function maps X into the codomain of red numbers defined in the interval fiom O to 1 inclusive. That is, the membership fûnction is a reai number 0 1 p , S l where O means no membership and 1 means full rnembership in the set. A particuiar value of the membership hction, such as 0.5, is called a grade of membership. For example, if a person is an adult, then myone about 7 feet and tailer is considered to have a rnembership fhction of 1.0. Anyone Iess than 5 feet is not considered to be in the fuzzy set TALL and so the membenhip function is O. Between 5 and 7 feet, the membenhip h c t i o n is monotonically increasing with height ï h i s paticular rnembership h c t i o n is ody one of many possible functions. The membership h c t i o n for the Fuzzy set TAU is shown in Fig.4.2 Fig.4.2 Membership function for the fuay set TALL The S-function and ri function are two important mathematical hnctions that are often used in fuzLy sets as membership bctions. They are defhed as follows: for x < a 2(%) for a s x l / 3 for x~ y Fig.4.3 The S-f'iinction Fig.4.4 The ïI - h c t i o n The II-bction is shown in Figure 4.4. Notice that the ,8 parameter is now the bandwidth or total width at the crossover points. The Il -function goes to zero at the points x = y t f l while the crossover points are at Funy logic forms the basis of funy-expert systems. In fupy-expert system, the knowledge is captured in natural language which have arnbiguous meanings, such as tall, hot, danprous and so on, which is concerned with the theory of uncertainty based on fuPy logic. The theory is primarily concemed with quantifying the linguistic variable into possible fuzy subsets. A linguistic variable is assigned values which are expressions such as words, phrases or sentences in a naniral or artificial language. For exarnple, the linguistic variable "height" has typical values like "dwarf", "short", "average", "tall", tbgiant". These values are referred to as funy subsets. Every element in these fuPy subsets has its own degree of membership. Besides dealing with uncertainty, furzy-expert systems are also capable of modeling cornmonsense reasoning, which is very dificult for conventional systems. Fuzzy logic is the logic of approximate reasoning. Essentially, approximate or fuzsr reasoning is the inference of a possibly imprecise conclusion fiom a set of possibly imprecise premises. One of the important type of fuzzy logic is based on Zadeh's theory of approximate reasoning 1221, which uses a fuzzy logic whose base is Lukasiewicz L , logic. In this fuzzy logic. truth values are linguistic variables that are ultimately represented by fuey sets. Fuzzy logic operators based on the Lukasiewicz operators are defmed in the Table 4.1. x(A) is a numeric tmth value in the range [ 0,l ] representing the tnith of the proposition " x is A", which c m be interpreted as the membership grade p, (x) . Table 4.1 Fuzzy logic openitors 4.4 Application of Fuzzy-Set Theory to Power Systems One of the fiindamental objectives in the management of power systems is to provide safe and reliable electric power at the lowest possible cost. To achieve this objective, rapid advances in the contml and management technology of power systems has been made. For example, ABB's Energy Management Systems ( EMSYS ) [23] is an innovative, cornputer-based information and control system designed to provide full range of utility solutions, fiom basic SCADA to advanced transmission system network security and distribution automation applications. During this process, power systems have become even more complex in structure and statu. This growing complexity is causing problems to power system operaton. Some of the more evident problems are: rapid increase in the number of real-tirne messages has made operator response more difficult. current numerical processing software m o t meet the operational requirements of power systems in some situations. Typical example is processing difficulty during emergency conditions. moa design, planning and control problems encountered are complex and time consuming because of multiple objective functions, multiple constraints, and complex system interactions. Analytical solution methods exist for many power systems operation, planning and control problems. However, the mathematical formulations of real-world problems are derived under certain restrictive assumptions and even with these assumptions, the solutions of large scale power systems problems is not trivial. On the other han& there are many uncertauities in various power systems problems because power systems are large, complex and infiuenced by unexpected events. These fxts make it difficult to effectively deal with many power systems problems through strict mathematical formulations alone. Therefore, expert systems apjxoaches have emerged in recent yean as a complement to mathematical approaches and have proved to be effective when properly coupled together. Reference [24] gives a bibliographical survey of the research, development and applications of expert systems in electric power systems. As already mentioned, expert systems are built based on the knowledge acquired fiom domain experts. The expert's empirical knowledge is generally expressed by language containing ambiguous or fuzy descriptions. As a resdt, a number of researchers have applied fuay logic concept to power sy stem applications. Some of the applications include fuzzy approach to power system security [25], dynamic generation rescheduling [26], reactive powerhroltage control [27l, short-term load forecasting [28], prioritiüng emergency control [29], contingency consaained optimal power flow [30]. A more comprehensive list of applications of fuPy set theory to power systems is aven in [3 11. When fuzzy set theory is used to solve red problems, the following steps are generally followed [3 1 1: step 1 Description of the ori@ problem. The problem to be solved should first be stated mathernatically/linguistically. step 2 Definition of thresholds for variables. step 3 Furry quantization. Based on the threshold values from step 2, proper foms of membership fwictions are coflstfllcted Many forms of membership fiuictions are available, such as linear, piece-wise linear, trapezoidal and parabolic. The membenhip hctions should refiect the change in degree of satisfaction with the change in variables evaluated by experts. step 4 Selection of the proper fuzzy operations, so that the results obtained is like those obtained by experts. 4.5 Summary This chapter has reviewed some of the hdamental concepts of expert systems and fuPy logic. It introduced the generic expert system çtnicture and the theory of approximate reasoning. The S and n functions were highlighted Funy sets has the potentiai to play an important role in power system operations and control. Some of the drawbacks of conventional expert systems [32] are They process sequential procedures by matching a set of d e s to execute an operation for a given system condition. For firing rules, a complete matching of predetemined conditions for a given input is needed, resulting in limited effective operation when applied to a practical situation. a Lack of practical knowledge and suitable means to represent heurîstics. Funy-expert systems based on approximate reasoning overcomes the above mentioned problems. The following are the advantages of funy-expert systems over conventional expert systems. a It offers flexible processing of lmowledge expressed by d e s . In approximate reasoning, the attributes included in the rules are given by linguistic variables. A linguistic variable measures the proximity of a given value to a fuay set by the grade of membership to the set. Such grading of attributes are known as uncertainty factors. Approximate reasoning pennits mdti-attnhte evaiuation of an input because every condition included in a d e has a numerical value, rather than tnie or false state as in conventional expert system. In the overall context of the research, this chapter introduces the theory behind the proposed fuay-expert system for voltage stability monitoring and control. Chapter 5 FUZZY CONTlROL APPROACH TO VOLTAGE PROFILE ENHANCEMENT FOR PO'WER SYSTEMS 5.1 Introduction The application of funy set theory to power systems is a relatively new area of researck Chapter 4 has highlighted the basic pnnciples involved in this a m However, before attempting to develop a fuay concept for voltage stability evaluation, the f ù z q set theory is first applied to voltage- reactive power control for power systems. As the voltage profile of the electric power system could be constantly affecteci, either by the variations of load or by the changes of network configuration, a real-time control is required to alleviate the problems caused by the perturbations. The problem is how to accurately compose a voltage control stmtegy during emergency conditions when complete system information is not available. To overcome this problern, adjustments to the control devices are needed af€er the perturbations to alleviate voltage limit violations. This can be achieved by determining the sensitivity coefficients of the control devices. Several papers in the literature explore voltage/reactive power control by means of fûzq sets [33], heuristic and algorithmic [34], rule-based systems [35] etc. in this chapter, a voltage-reactive power control model using fuPy sets is described which aims at the enhancement of voltage security. In this model, two linguistic variables are applied to measure the proximity of a given quantity to a certain condition to be satisfied. The two linguistic variables are the bus voltage violation level and the controlling ability of control devices. These are tnuislated to fuay domain to formulate the relation between them. A feasible solution set is first attained using min- operation of fiiw sets, then the optimal solution is determined employing the max- operation. The method was proposed by Ching-Tzong Su and Chien-Tung Lin [36]. 5.2 Problem Statement In power system operation, any changes to system topology and power demand can cause a voltage violation. When a voltage emergency has been identifie4 control actions mut be initiated, either automatically or manually, to alleviate the abnomai condition. The reaction time is critical. For example, when a destructive storm passes through an area, communication systems can be disrupted, reducing the information received at the system control center. If bus voltages are beyond desirable limits during such an emergency, the voltage control problem cannot be solved by conventional methods i.e., using load flow solution techniques. This is due to incomplete information needed to construct the system network modeI. Optimal control of voltage and reactive power is a significant technique for improvements in voltage profiles of power system. The objective is to improve the system voltage profile, such that it will lead as closely as possible to the desired system condition. The network constraints include the upper and lower bounds of bus voltage magnitudes as well as the adjustable minimum and maximum quantities of controlling devices. When a load bus voltage violates the operational limits, control actions m u t be taken to alleviate the abnormal condition. Consider an N-bus system, with buses 1 to L as load buses, buses L+ 1 to N-1 as generator buses. By adjusting the controlling device on bus j, the voltage improvement of bus i is given by AVi = S i j A U j ( 5 - 1 ) 1 2 . L ; j = 1 2 ,......, N-1 where, AV, isthevoltagechangeofbus i. S i is the sensitivity coefficient of bus j on bus i. A U is the adj ustment of controlling device at bus j . Sensitivity coefficient in general gives an indication of the change in one system quantity ( eg: bus voltage, MW flow etc. ) as another quantity is varied ( VAR injection, generator voltage magnitude. transfomer tap position etc. ). Here, the assumption is that as the adjustable variable is changecl, the power system reacts so as to keep al1 of the power flow equations solved As such, sensitivity coefficients are linear and are expressed as partial derivatives. For exarnple, expression 5.2 represents the sensitivity of voltage at bus i for reactive power injected at bus j. Adjustment of the controlling device is constrained as m i n < AU, - A U j I A UJ'" ( 5.3 ) where, A Ur " and A Ur ' " represent the adjustable minimum and maximum reactive power. The Ioad bus voltage deviation should be conûolled within I 5% of the nominal voltage Vn O . which can be expressed as yin 5 vi vpiax where, ymi" ( = 0.95 V n o m )and Tax ( = 1.05 VnO" ) are the lower and upper voltage limits of bus i respectively and Vi is the input of the system. 5.3 Fnzzy Modeling Two linguistic variables namely, the bus voltage violation level and the controlling ability of controlling devices are modeled in the fuzzy domain as folIows 53.1 Bus voltage violation level The membership function of the bus voltage violations is shown in F i g 5 1 . The maximum deviation of the bus voltage is A V," ' " = Vy ' " - VO " " , the minimum deviation of bus voltage is A v,"' " = V," ' " - VoO " . V i m a x , V , m i n and v n o m take the values 1.05, 0.95 and 1.0 p.u. Here, it is desirable to control the bus voltage deviation within f 5% of the nominal voltage. 0 i 408 4 0 6 O M 4 0 2 0 0 0 2 0 0 . 0.06 0 0 6 0 1 Daviatioo of Bua Voltage AV @.a) F i g 5 1 Fuzzy model for bus voltage violation level 5.3.2 Controüisg ability of controllhg devices The funy representation of the controlling ability of the controlling device is show in Fig.5.2. The controlling ability is Cij = Si, M, ( 5.5 where, M , is the controlling margin of the controlling device ai bus j . Si is the sensitivity coefficient of bus j on bus i. Ci is the controlling ability for controlling device of bus j on bus i. Fig-5.2 F u ~ y mode1 of controlling ability of controlling device 5.33 Control Strategy The violation of bus voltages and the controlling ability of the controlling devices are first fupified with the fuPy models defined in Fig.5.1 and Fig.5.2. To alleviate the bus voltage violatioc a suitable control strategy is adopted The strategy coosists of selecting an optimal controlling device and the adjustment of that device. The two most effective watrol devices are Static Var Compensators ( SVC ) and generator controls. Since, voltage violation is a local phenornena, SVC's are given a greater priority compared to generator controls [37l. ïhe control strategy coosists of three steps as descnbed below Let p and p be the membership value of voltage violation and controlling ability of the controlling device respectively for a pam'cular controlled bus i. Select a controlling device j with conesponding membership value p of controlling ability, take the min- operation R i j = m h ( ~ J * , / f c ) ( 5.6 Repeat the above min- operation for ail controlling devices. Take the max- operation to the j terms of R,, obtained above. K,, = m a x ( R i i , R ,,...., RÏ) ( 5-7 ) where, j represents the total number of controlling devices. O For each of the L controlled buses, repeat the min-max operations L terms of K i , are obtained Take the max- operation totheLtermsof K i , . Pi, = rnax(K,,, K,, . . . ., K, ) ( 5 - 8 where, Pi, represents the membenhip value of controlling ability for controlling device at controlling bus j on controlled bus i. Note that the above three operations are to be done independently for SVC and generator controllers. 5.4 Methodology The following are the computational steps involved in the film control approach for the voltage profile enhancement. For the given system and loading conditions, perfom the base case load flow using a comrnercially available software package, for example, the Interactive Power Flow ( I P E O W ) version 4.1. IdentiQ those affected load bus voltages that violate either the upper or lower bound voltage limits. For the available controllers, find their sensitivity coefficients. Calculate the available control margin which is the difference between the present setting and the maximum possible setang of a parhcuiar controller. Find the mernbership value of bus voltage violation level and coatrolling ability. Evaluate the optimal control solution as described under control strategy in section 5.3. ModiQ the value of the control variables. Perform the load flow study and output the resdts. 5.5 Simulation Results and Discussions To verie the above method, a modified IEEE 30 bus test system is taken as a numerical example. Modifications are made to the original IEEE 30 bus system at bus 13 and bus 1 1. Their pre-modified initial terminal voltages are 1.071 and 1.082 p.u respectively. Base case voltage profiles of the modified IEEE 30 bus system are shown in Table 5.1. In this system, the reactive power sources are assumed to be at buses 10, 19, 24, 29 and generator voltage regulators at buses 2, 5, 8. The following three cases are investigated case 1: Load is increased at bus 26, causing bus 26 to violate the voltage constraint, but the violation is not serious. case 2: Load is increased at buses 7 and 15 causing voltage violation at buses 15, 18 and 23. case 3 : For load increase at bus 15 and outage of line 12- 15, buses 15 and 23 violate the voltage constraint. Table 5.1 Base case voltage profiles of the modified IEEE 30 bus systern Table 5.2 shows the lower and upper limits of the available controllers. control action is initiated are 0,0,0,0, 1 - 0 6 , 1 .O 1, 1 .O 1 respectively. Table 5.2 Lower and upper limits of the controllers Controller Type Q 10 Q 19 Q 24 Q 29 V2 V5 V8 Lower Limit ( p.u ) -1.0 - 1 .O -1.0 -1.0 0.95 0.95 0.95 Upper Limit ( p.u ) 1 .O 1 .O 1 .O 1 -0 1 .O5 1 .O5 1 -05 Table 5.3 compares the load bus voltage profiles before and after the control actions for the three cases considered and Table 5.4 shows the optimal fuPy control solution. Table 5.3 Load bus voltage profiles before and after control actions Load Bus No Case 3 VoItages ( p.u ) initial F i 1 Case 1 Voltages ( p.u ) initial Final Case 2 Voltages ( p.u ) Initial Final Table 5.4 Optimal fuay control solution Finai Value of the The results for case I in Table 5.3 show that the load increase at bus 26 causing bus 26 to violate the voltage limits. The lower and upper voltage limits are 0.95 and 1.05 p.u respectively. The voltage violation at bus 26 is 0.007 1. From Fig. 5.1 ., the membership value corresponding to the voltage violation, which in this case is 0.142, is obtained. Then, for al1 the available controllen, from the sensitivity anal ysis and fiom controlling margin of the controlling devices, the controlling ability of the controlling devices ( Ci ) is detertnined. From Fig 5.2, the membership values for these controlling abilities are obtained. Findly, by applying min-max operations, controllers 429 and V8 are obtained as indicated in Table 5.4. To obtain the final value of the controller 429, sensitivity analysis is perfomed. The sensitivity coefficient of the controller 429 with respect to bus 26 is 0.0024. Hence, the final value of Q29 is 0.0295 p-u. If there is a voltage violation at more than one bus as in case 2, then the above procedure has to be repeated for each violated bus independently. This is referred to as layer-1 operation. Then fiom the selected controllen of layer-1, max operation is perfomed to anive at the proper solution This is known as layer-2 operation. 5.6 Summary In this chapter, a simple method using fuPy sets for the voltage-reactive power control to improve the system voltage level is presented. The control strategy is obtained by employing max-min operatiom. A modified EEE 30 bus system is used as an example to illustrate this m e t h d From the simulation results, it can be iderred that fuPy models are indeed effective in power system control applications. One of the desirable feature of this fuzzy mode1 is that if the operator is not satisfied with the grading of the fuzzy model, the operator can adjust the parameters associated in the definition of the membership function to suite the needs of the desired system operation. Chapter 6 F'UZZY-EXPERT SYSTEM FOR VOLTAGE STABlLITY MONITORING AND CONTROL 6.1. Introduction In the preceding chapters, considerable attention bas been aven to the concepts of voltage stability, modal analysis technique, fuzzy-expert systems and their application to typical test systems. Simulation results of these test systems are encouraging and have ken a motivation to investigate this concept for the voltage stability problem. In this chapter, a new fuPy-expert system is proposed for voltage stability monitoring and control. The phenornena o f voltage sîability can be attributed to slow variation in system load or large disturbances such as loss of generators, transmission lines or transformers. The impact of these changes leads to progressive voltage degradation in a significant part of the power system causing instability . In the context of real-time operation, voltage stability analysis should be perfomed on-line. A nurnber of special algorithms and rnethods have been discussed in chapter 2. However, these methods require significant computation time. When the power system is operating close to its limits, it is essential for the operator to have a clear knowledge of the operating state of the power system. For on-line applications, there is a need for tools that can quickly detect the potentially dangerous situations of voltage instability and provide guidance to stem the system away from voltage coilapse. In an effort to improve the speed and ability to handle stressed power systems, a funy-expert system approach is proposed A number of researchers have made an attempt in this direction. An expert system prototype was developed to correct for voltage steady state stability [38]. In this approach, an expert system arrives at a fast solution by considering an overall system threshold indicator to decide on the degree of VAR shortage and the vulnerability of the system to voltage instability. Yuan- Yih Hsu and ChungChing Su [39] proposed a de-based expert system for srnall-signal stability analysis. They developed an efficient on-line operational aid, wherein the expert system perfoms deductive reasoning to arrive at the degree of stability without the need to calculate the eigenvalues. In this chapter, a fiiny-expert system approach to steady- state voltage stability monitoring and control is proposed. The results of chapter five have been a usefbi starhg point for this new approach- The proposed expert system evaluates system state through deductive reasoning by operating on a set of fÙzzy rulebase. The funy d e b a s e is system dependent, but once fomed, it cm handle any operating condition. An integrated approach of expert systems and conventional power system solution rnethodologies has the potential to provide real-time monitoring and control. The chapter is organized as follows. Section 6.2 highlights the concepts of fuzy-expert system, design of database and debase specifically for the New Englaad 39 bus system. Sections 6.3 and 6.4 present the inference engine and simulation results of the New England 39 bus system respectively. Section 6.5 provides a summary of this new approach. 6.2 Expert System and Design Expert system consists of two main components. The knowledge-base and the inference engine. A knowledge-base is a collection of facts and d e s describing how the facts are linked Based on the facts, the expert system draws conclusions by the inference engine. rii fiizzy-expert system, the knowledge is captured in nahnal language which have arnbiguous meaoings, such as tall, hot and dangerous, and is concerned with the theory of uncertainty based on fwry logic. The theory is primarily concemed with quantimg the linguistic variable say % i l " into possible fuzzy subsets like "low", "high", "medium". Every element in these fûzzy subsets has its own degree of rnembership. The main reasons for the use of funy logic to voltage stability m o n i t o ~ g and control are The approach is simple, straightfoward and fast, where it only needs key system variables to arrive at the solution state. Due to the veiy nature of the problem, the imprecision of the linguistic variables can easily be transferred into funy domain, which would otherwise be difficult to manage. Fuzzy logic can hancile non-linearity of power system problem and does not require complex cornputations as in traditional methods. Thus, it is more efficient than conventionai methods for voltage stability anaiysis. In the proposed fkq-expert system, the key system variables like load bus voltage, generator MVAR reserve and generator terminal voltage which are used to monitor the voltage stability are stored in the database. Changes in the system operating conditions are reflected in the database. The above key variables are funified using the theory of uncertainty. The debase comprises a set of production rules which form the basis for logicai reasoning conducted by the inference engine. The production d e s are expressed in the form of IF-THEN type, that relates key system variables to stability. The strength of the above fùzzy-expert system can be exploited Mly when the rulebase is used in conjunction with the database. The modal analysis technique dong with continuation power flow discussed in chapter two, play an important d e in the development of the proposed fuzzy-expert system. It is not a part of the fuzzy-expert system. It is used as an aid in the formulation of database and as a benchmark tool for validating the accuracy of the proposed approach. 6.2.1 The Database The key variables identified are load bus voltage, generator MVAR reserve and generator temiinal voltage. The three key variables are selected based on the solution obtained by repeated load flow and modal analysis performed for various operating conditions. Based on the simulations carried out for different loading factors, it is found that load bus voltage and reactive generation reserve are significantly affected as the system approaches collapse point for a specific loading pattern. Aiso, the terminal voltage of the generaton has an effect on voltage stability margin. Hence, the above three variables are used to monitor the voltage stability of the system. Each of these variables is M e r divided into four linguistic variables and then transfonned into fuzzy domain: Low, Tolerable, Moderate and Safe. The membership f'unctions for these linguistic variables are of the general form given by where, K may be any one of the key variables. A and a are constants. The membenhip fiuictions of the key variables are s h o w in Fig.6.1, Fig.6.2 and Fig.6.3. Fig.6.l Membenhip fiuiction for the worst load bus voltage. Lem 0.8 ......--...... Fig.6.2 Membenhip h c t i o n for the worst MVAR reserve. Ganeretor Terminal Voltage (p-u) Fig.6.3 Membership function of the generator terminal voltage corresponding to the worst MVAR reserve. For example, in Fig.6.1 corresponding to the load bus voltage of 0.6 p.u, the fuay sets Low, Tolerable, Moderate and Safe have membership grades 1.0, 0.2, 0.1 and 0.02 respectively. The union of the above hiay sets represents the total uncertainty in the stability of the system. The membeahip functiom of the key variables can take the form monotonie, bell-shaped, trapezoidal or even tnangular. The selection of the type, depends on the application and how ciosely it c m descnbe the system behavior. In the following studies that involve non-linear equations, bell-shaped coupled with S-shape is the closest that describes the behavior of power system in general. The constants 'a" and "A" are selected such that the membership fiinction covers the entire range of the key variables. For example in Fig.6. l., the rnembeahip h c t i o n of the four linguistic variables should cover lower limit ( 0.6 p.u ) and upper limit ( 1 .O p. u ). Panuneten "a" and "A" are selected such that the desired stability condition is çatisfied for the test cases. In this way, proper membership grades are obtained. In an utility environment, the peak values of these linguistic variables of the key variable is obtained from the operator's experience [39]. In the studies supported here, peak values have been found by trial and error. Extensive simdations are performed to identiQ the range of key variables. The constants "ay7 and "A" in equation 6.1 are selected appropnately to give proper membership grades. For instance, the parameters "a" and "A" for the rnembenhip h c t i o n of the worst load bus voltage, worst MVAR reserve, generator terminal voltage corresponding to the worst MVAR reserve are shown in Table 6.1. Table 6.1 Parameters a and A for the mernbenhip function of the key variables. Linguistic Variables 1 1 For membership hction of the worst load bus voltage 1 L a ( MVAR) [ 8000 1 8500 1 9250 1 9500 Low L 1 1 For rnembership bction of the generator terminal voltage a ( P-u 1 A ( Phu Having represented the inputs to the expert system as linguistic variables, the output of the expert system is the degree of voltage stability represented by four linguistic variables: Very stable ( VS ), stable ( S ), critically stable ( CS ) and unstable ( US ). The four linguistic variables correspond to the following situations. VS: Â. > 10.0 S : 10.0 2 A > 6.5 CS: 6.5 >, A. > 2.0 us: A 5 2.0 where,A is the minimum of the absolute real part of the eigenvalues of the reduced Jacobian matrix J , of equation 3.7. Toierable For membership fiuiction of the w o m MVAR reserve 0.7 0.06 Moderate Safe 0.8 O. i 0.9 0.1 0.95 O. 06 6.2.2 The Rulebase Two separate sets of rulebase are formed, one for monitoring and other for control stage. In t h s stage, the rule base is divided into four groups. group 1:ruies that relate worst load bus voltage to stability measure. group 2:rules that relate key generator MVAR reserve to stability measure. group 3:niles that relate key generator terminal voltage to stability measure. group 4:rules that combine stability masures of the above three parameters. Typicai d e for groups 1 J and 3 is of the fom: IF K is X1 THEN S is X2, with rnembership value p (XI, X2)., where K is any one of the key variables. X1 is any one of the four possible fuey subset ( low, tolerable, moderate, safe ) characte~ng the key variables. S is membership grade. X2 is any one of the four possible fuay subset (VS, S, CS, US) characterizing stability measure. There are 48 d e s relating key variables to stability measure, 16 d e s for each variable. Among the 16 rules, there are 4 rules which will yield g ( VS ). The resdtant p ( VS ) is obtained by max-min compositional rule of inference as follows The membership values for p ( S ), p ( CS ) and p ( US ) c m be derived similarly. For group 4, the stability measures derived for wont load bus voltage ( psb (VS),psb (S),jsb (CS) and psb (US) ), worst generator MVAR reserve ( psm (VS), psm (S), psm (CS) and pm (US) ), corresponding generator terminal voltage of wont MVAR reserve ( psg (VS), psg ( S ) , psg (CS) and psg (US) ), are combined together using max-min composition to yeild the overall stability of the power system. Thus, in this group, there are 256 d e s . The stability rneasure with the greatest membership value gives the state of the systern. The procedure is exactly the same as mentioned in the monitoring stage, but the only difference is that the number of inputs to the expert system is two instead of three. Here, the generator terminal voltage is not taken as one of the key input variable because of its value k i n g fïxed throughout the control phase. This stage has 96 rules. The reasoning process of the inference engine that involves both monitoring and control is implemented in MATLAB [40]. Appendix B shows the rules relating key variables to stability rneasure. Appendix C shows the data used for the formulation of the nilebase with reference to the monitoring stage. 6.3 Inference Engine The inference engine takes the key variables such as load bus voltage, reactive generation reserve and terminal voltage of the generator as its inputs and uses the production d e s to perfom deductive reasoning. nie steps involved in the reasoning process are s h o w below Monitoring stage: (1) Read in load bus voltage, reactive generation reserve and terminal voltage of the generator. (2) F d f y each of these key elements into four linguistic variables using equation 6.1 to obtain their membership grades. (3) input the membership grades into the fuzzy debase. (4) From the niles formed under group 1, obtain the stability measures corresponding to the worst load bus voltage. ( 5 ) From the d e s formed under group 2, obtain the stability measures corresponding to generator MVAR reserve. ( 6 ) From the rules formed under group 3, obtain the stability measures corresponding to key generator terminal voltage. (7) From the niles formed under group 4, evaluate the global stability membership grade of the system. lf the system state is either critically stable or unstable, then perform the control action. Control stage: (8) To improve the voltage profile of the worst load bus, VAR compensation andor raise in generator terminai voltage is performed at the exisring wntrollers. ( 9 ) Fuzzie these new improved values and combine with stability d e s to obtain the new global stability state. 6.4 Simulation Reaolts and Discussions To show the effectiveness of the proposed fuay-expert syçtern, the New England 39 bus system is taken as an example. The single line diagram of the system is shown in Fig.3.4. Here, the load is increased at buses 3, 4, 12, 15, 21 and generation at buses 30, 32, 35 and 37 are scaled accordingly to meet the increased demand. The simulation is camed out under six different operating conditions. condition 1 : No contingency and generator 32 terminal voltage is maintaineci at 0.983 1 p.u. condition 2 : No contingency and generator 32 terminal voltage is maintained at 0.95 p.u. condition 3 : No contingency and generator 32 terminal voltage is maintained at 1-05 p.u. condition 4 : line 6-1 1 outage. condition 5 : generator 36 outage. condition 6 : line 6-1 1 and generator 36 outage. To simplify the analysis, only six conditions are considered. In reality, for the proposed fuay-expert systern to be valid, al1 possible conditions have to be taken into accowzt. Note tiiat some of the worst cases have been considered to validate the correctness of the proposed system. Extensive number of operating conditions are tested to verifL the correctness of the expert system output during the monitoring stage. A cornplete list of expert system output for al1 cases is show in Appendk D. Table 6.2 below shows the comesponding operating condition for the 32 cases listed in Appendix D. Each case is for a specific Ioading condition. Table 6.2 Operating conditions for the 32 cases listed in Appendix D Table 6.3 Expert system output - Monitoring Index No 1-7 Operathg Condition 1 I CONTINGENCY Index No NO CONTINGENCY Gen.32 Volt (p.u) Bus 12 Load Volt b u ) Gen32 M'VAR Global state VSTAB output Eigen System vaiue state For the purpose of analysis, consider the eleven cases s h o w in Table 6.3. The expert system output for these eleven operating cases correspond to the monitoring stage. Here, the fuzzy-expert system output ( Global state ) is compared with the simulation results given by VSTAB 4.1 output through modal anaiysis. In Table 6.3, index Nos.1 and 2 correspond to operating condition 1, index No.3 refers to operating condition 2, index Nos.4 and 5 correspond to operating condition 3, index Nos.6 and 7 correspond to operating condition 4, index Nos.8 and 9 correspond to operating condition 5 and finally index Nos.10 and 11 correspond to operating condition 6. As shown in Table 6.3, the input variables to the expert system are bus 12 load voltage, generator 32 MVAR reserve and generator bus 32 terminal voltage. The basis for their selection is from îheir m c i p a t i o n factors described in chapter 3. Appendix E shows the participation factors for the critical case ( at the voltage stability limit ) for each of those six conditions. As seen in Table 6.3, there are some operating cases that are either unstable or cntically stable. These are the cases that need control. To show the difference between conventional methods and the proposed approach, consider the index No.7 of Table 6.3. The input variables to the fupy-expert system are bus 12 load voltage = 0.6059 peu, generator 32 terminal voltage = 0.983 1 p.% generator 32 MVAR reserve = 8 102.4 MVAR* From Fig.6. l., the membership function of the linguistic variables - low, tolerable, moderate, safe for the worst load bus voltage are mu-Io = 1.0 mub_tol= 0.2098 mub-mod = 0.1036 mub - saf= 0.0295 From Fig.6.2., the membenhip fiuiction of the linguistic variables for the worst MVAR reserve are muv 10 = 0.8657 - muv-tol = 0.2995 muv-mod = 0.0295 muv-saf = 0.020 1 From Fig.6.3., the membership function of the linguistic variables for the generator terminai voltage are m e m g l o = 0.0836 merngtoI= 0.5497 ( 6.6 m e m g m o d = 0.8936 merngsaf = 0.0684. Once the membership fùnction of the linguistic variables are determined, the next step is to relate these variables to the stability measure. From the d e s formed under group 1, the stability measure for the very stable (VS) case is obtained as follows vsb 1 = min ( mub-10, murb (4,l ) ) vsb2 = min ( mub-tol, murb (3,l ) ) vsb3 = min ( mub-mod, murb (2,1 ) ) vsM= min ( m u b - d , murb (1,l ) ) where, murb matrix gives the required d e s relating the load bus voltage to the stability measure of group 1 as shown in Appendix B. Thus, the overall stability measure for 'tery stable" is given by mb - vs = max ( vsbl, vsb2, vsb3, vsb4 ) = 0.1036 ( 6-8 SimiIarly, the stability measures for stable, critically stable and unstable cases are obtained as mb-s = 0.2098 mb-CS = 0.5 ( 6-9 mb-us = 1 .O Following the same procedure as mentioned above, the d e s for group 2 can be derived. The çtability measures corresponding to key generator MVAR are rnr-vs = 0.0295 mr-s = 0.2995 mecs = 0.5 - u s = 0.8657 From d e s forrned under group 3, the stability measures corresponding to generator terminai voltage are m g v s = 0.6 mg-s = 0.8936 mg-CS = 0.8936 mg-us = 0.4 Finally, fiom the niles formed under group 4, the stability measures o f the system are s- = 0.2098 ss-s = 0.4 ss-CS = 0.8 ss-us = 0.8657 The overall system stability is given by gl-sta = max ( ss vs, ss-s, ss-CS, ss-us ) = 0.8657 - Hence, the system staôility is unstable. From the above analysis, it is seen that the solution is obtained by simple max-min d e s of fuey logic and thereby avoiding detailed computatiom of conventionaf methods. For the purpose of control, consider the following three cases. Case A: In this case, it is assumed thai Stafic Var Compensators (SVC) are available at buses 6,8,13 with maximum capacity of 100 MVAR each, while the voltage of generaton at buses 32 and 37 c m be adjusted up to a maximum of 1.05 p.& Case B: Here, assume improved lirnits on controllers in the same buses as in case A. SVC controllers at buses 6, 8, 13 operate with a maximum capacity of 400 MVAR each, while the upper limit of generator voltage at buses 32 and 37 is 1.06 p.u. Case C: In h s case, SVC controllers are available at buses 6, 8, 13, 21 with a maximum capacity of 400 MVAR each, the upper limit of generator voltage at buses 30,32,35,37 is 1 .O6 p u and the upper limit of the taps of tap changing transformer in branches 12- 1 1 and 19-20 is 1.07 p.u. Thus, ten controllers are considered for this case. Table 6.4, Table 6.5 and Table 6.6 show the expert system output after the control action for those cases needing control. Table 6.4 Expert system output - control stage ( case A ) Table 6.5 Expert system output - control stage ( case B ) index No 2 3 ' 5 7 8 9 *11 * misclassification * misclassification Bus 12 Load Volt (P.@ O. 7944 0.8192 0.8673 0.8229 0.9349 0.8307 0.8362 Index No '2 3 5 7 8 9 11 Gen 32 W A R 8490.7 86 1 O. 5 8843.5 8656.3 9176.7 8682.6 8720.4 Bus 12 Load Volt (P-u) 0.9 179 0.9336 0.967 1 0.9325 0.9349 O. 9475 0.9443 Global state CS CS - CS S CS - Gen. 32 M V A R 8988.1 9067.5 9234.5 9087.8 91 76.7 9147.7 9145.5 Gfobal state - VS/S S S S S S VSTAB output Eigen System value state VSTAB output Eigen System d u e state 4-12 4.76 6.03 4.63 7.1 1 4.44 4.48 6.74 7.2 8.19 7.2 7.1 1 6.79 6.83 CS CS CS CS S CS CS S S S S S S S A Table 6.6 Expert system output - control stage ( case C ) It can be seen from Tables 6.4 to 6.6 that the global state of the system has Index No 2 3 5 7 * 8 9 11 changed after the control action. For example, in case C, the operating condition corresponding to index number 9 is unstable (US) before the * misclassification Bus 12 Load Volt (PJ) 0.9620 0.9768 1 .O092 0.9744 1.0656 0.992 1 0.9879 control action and stable after the control action. Note that the output of the expert system is either very stable or stable for the operating condition G e n 32 MVAR 9060.8 9133.7 9292.0 9148.4 9566.3 92 17.9 921 1.7 corresponding to the index 2. This is a typical case where, the expert system is able to corne out with an approximate solution only, considenng Global state VS/S S S S VS S S the fact that no solution may be possible by other conventional methods Note: The tenn "misclassification" refers to the error in the chsification state by the fitay-expert system output. The four classification states are Very Stable, Stable, Critically Stable and Unstable. If there is a discrepancy between the fûzzy-expert system output ( GIobai state ) and the system state of the VSTAB outpu& then a "misclassification" is said to OCCUT. VSTAB output Eigen System value state 7.44 7.86 8.78 7.77 9.47 7.52 7.5 S S S S S S S From the above Tables, it is seen that there is a considerable improvement in the voltage stability rnargïn of the system, limited oniy by the number of controllen available and their operational lirnits. Voltage stabiliîy m a r e ( VSM ) is a measure of how close the system is to voltage instability. It is defineci as the difference between the values of a Key System Parameter ( KSP ) at the current operating condition and the voltage stability critical point [IV. Here, KSP is defined as the total load increase in the selected buses. Fig. 6.4 shows the voltage stability margin improvement afler the control action for the cases A, B and C. TabIe 6.7 shows the voltage stability margin corresponding to Fig. 6.4. Fig. 6.4 Voltage stability margin (VSM) for pre and p s t control cases Table 6.7 Voltage Stability Margin ( VSM ) for pre and post control cases 1 No 1 Sdected Buses 1 VSM 1 I Total Laad at From the above simulation results, it is seen that given the key variables ( load bus voltage, generator MVAR reserve and generator terminal voltage ), the expert system arrives at the global state without the need for complex computations. With reference to the selection of the number of input variables on the size and complexity of fupy-expert system, consider the monitoring stage of the proposed expert system. Here, three input variables are selected. The total nurnber of d e s under the four groups is 304. if only two input variables are selected, the number of d e s is reduced to 96. Thus, the size of the d e s will have an effect on the computational complexity of the fÙzzy-expert system. Pn-Coatrol The designed expert system is tested for a total of 68 cases covering a wide range of operating conditions. 32 cases are listed under Appendix D, 21 cases listed in the control stages - Case A, Case B and Case C, 15 cases Post-Contml VSM ( MW ) i listed under Appendur C, totalling 68 cases. Out of these 68 cases, 4 cases are misclassifieci. The source of error for the misclassified cases is probabiy due to the inadequate tky-expert system framework. Within this framework, two key factors are the membership function of the key variables and inappropnate mernbership value assigned to the linguistic variables descniing the imprecision of the d e . Since the membership function of the key variables described by the equation 6.1 is fonned based on the extensive simulations, the only other parameter responsible for the misclassification is the latter. For example, consider the operating case conesponding to the index No. 5 of Table 6.4. The input variables to the furzy-expert system are bus 12 load voltage = 0.8673 p u and generator 32 MVAR reserve = 8843.5 MVAR. From Fig.6.l. and applying ma-min compositional nile of inference. the membership fiinction of the stability measures VS, S, CS and US for the load bus voltage are ml-vs = 0.6 ml-s = 0.9034 (6.14 ) ml-CS = 0.6882 ml-us = 0.4 Similady, fiom Fig.6.2 and applying max-min compositional mie of inference, the membership function of the stability measures VS, S, CS and US for the genemtor MVAR reserve are mg-vs = 0.1948 mg-s = 0.3642 mg-cs = 0.3642 mg-us = 0.3642 The rules nlating load bus voltage. generator MVAR reserve and stability measure is given by the "mugi" ma& as s h o w below From the above matrix, the stability mesures for the entire system are SS-vs = 0.3642 SS-s = 0.3642 ( 6.17) ss-CS = 0.3642 ss-us = 0.3642 From the above solution, one cannot infer whether the system is very stable, stable, critically stable or unstable. For the above operating condition, the fimy-expert system did not arrive at the proper solution. The fuPy-expert system output is significantly kdïuenced by the "mugl" matrix. The membership values in the "mugl" matrix describes the imprecision of the d e s and is obtained by trial and error method. In achlal field situation, the "mugl" matrix is fonned tlirough operator experience. Hence, the projected 10% classification error may not be taken as a sole criteria for the proposed fuay-expert system to be acceptable in a field situation. The limitations of the proposed funy-expert system in accurately classifjmg the voltage stability condition are The sire of the debase is large due to the selection of thtee input variables for the monitoring stage and two input variables for the control stage. The total number of mies for the above two stages is 400. The viability of the proposed fupy-expert system in an actual field situation is questionable due to the projected 10% classification error and non-availability of irnprovement in the computational speed compared to the conventional voltage stability methods. The proposed funy-expert system assumes a constant power load mode1 and test results limited to sixty four operating conditions. To make a proper voltage stability assessrnent for a practical power system, suitable load models have to be incorporated. Initially, the knowledge-base of fuzzy-expert system starts with 15 operating cases as indicated in Appendix C. Once the data used for the formation of the rulebase is established, the 32 cases listed in Appendix D are tested. The füzzy-expert system updates its knowledge-base to 47 cases and so on. Each tirne a new operating case is tested and verified, it is stored in the knowledge-base and thereby its performance c m be improved. In a utility operation, the tnie potential of the proposed fuzzy- expert system with its vast knowledge-base can be realized Mly only after a considerable period of time and experience. It is possible to investigate the optimum selection of the number of key variables for evaluating the voltage stability of any complex power system under "any operating condition", if sufficient resources and system &ta are available. in order to establish firm conclusions based on the concepts developed in the preceding chapten, extensive simulations on various power utility systems need to be perfonned, and factors that affect the performance of funy-expert system identified In the studies reported in this thesis, only limited number of cases were tested on the sample New England 39 bus system because of non-availability of resources and real utility system data. 6.5 Integration of f u z y s r p e r t system into an Energy Management S y stem The main challenge for the implementation of an on-line voitage stability evaluation in Energy Management System ( EMS ) is the cornputational burden and the ability to arrive at the operating state of the system. Also, it is essentiai for the operator to bave a clear Imowledge of the o p e r a ~ g state when the power system is operating close to its limits. This is where the fuzzy-expert system plays an important role. Since, the proposeci fuay- expert system uses input pammeten already monitored by the EMS, additional data acquisition equi pment and other associated communication systems become unnecessary. Hence, speed c m be improved w osiderab1 y. Man Machine Intcrfücc To design an efficient fuzzy-expert system, key variables that affect the system voltage stability have to be identified first either by off-Iine simulations or through operator's experience. in order to establish database that reflects al1 possible operating conditions of the system, numerous simulations are to be performed and verified by a standard bench mark tool. A set of decision rules relating key system variables to stability are formed. This is a continuous process wherein the funy-expert system updates its knowledge-base and thereby improve its performance. Fig 6.5 shows a block diagram of the proposed scheme integrating fuzy- expert system for voltage stability evaluation as part of an Energy Management System. Power System A r Fig 6.5 Fuzzy-expert system as a part of new EMS R T U R m RW A v e SCADA r Fu ny - Expert S ystcm The Remote Terminal Units (RTUs) collect data fiom various locations in the power system and reiay them to the S u p e ~ s o r y Control and Data Acquisition (SCADA). The SCADA is comected to the Man Machine Interface (MMI), which allows the operator to interact with the EMS. The funy-expert system gets its inputs Erom the SCADA. The main fùnction of the SCADA is to perform various control actions like switching on and off of circuit breaker, transformer taps, capacitor banks etc. Based on the production d e s developed which form the basis for logical reasoning conducted by the inference engine, the expert system arrives at the system state and alerts the system operator to any potentidly dangerous situations. Before taking the control action, the operator performs the load flow solution by incorpo rating appropriate VAR compensation or other available control devices in the secondary analysis to obtain improved load bus voltage and reactive generation reserve. The secondary andysis contains application fùnctions like contingency analysis, load flow, short- circuit analysis, stability analysis and optimal power flow. When the operator is satisfied with the seconàary analysis output, the improved load bus voltage and reactive generation reserve serve as input to the SCADA after verifjmg the system state fiom the fuay-expert system output. The SCADA takes the necessary control action to alleviate the voltage stability problem. The proposeci fiizzy-expert system does not replace any of the well developed algonthmic solutions of the secondary aoalysis. However, it offen a powemil and effective tool for the use of these programs. 6.6 Summary This chapter addresses the issues conceming the selection of the number of input variables and its impact on the size and cornplexity of the furzy-expert system. It also includes factors to be taken into account for proper selection of parameters "a" and "A7' of the generk equation describing the membership b c t i o n s of the key variables. Issues like accuracy of the method and erroa are also addresseci It also substantiates the claims for the use of fuzzy logic approach by showing a reliable assessrnent of stability for the monitoring stage without perforrning the detailed voltage stability calculations for a given operating point. In the proposed funy-expert system, the key variables like load bus voltage, generator MVAR reserve and generator terminal voltage w hich are used to rnonitor the voltage stability are stored in the database. Changes in the system operating conditions are reflected in the database. The rulebase comprises a set of production rules which form the basis for logical reasoning conducted by the inference engine. The reasoning process of the inference engine is implemented in MA=. Given the key variables, the expert system arrives at the global state without the need for complex computations. The New England 39 bus system is taken as a case study to illustrate the proposed procedure. Extensive operating conditions have been tested to validate the proposed system. The results that are k i n g compared are the fuzzy-expert system output ( global state ) and the system state of the VSTAB output for the 68 operating cases. The misclassification is f d to be less than 10%. Hence, it has the potential to be integrated for on-line implementation in Energy Management System. In this new system. the rnembership fiinctions of the key variables and the debase may be defined based on system requirements and operator's experience. Thus, it offers flexibility and satisfactory results in a very efficient way. Chapter 7 CONCLUSIONS 7.1 Contribution of the Research The concept of voltage stability phenornena in power systems has been thoroughly reviewed As power systems continue to be loaded closer to their stability limit, there is a need for suitable voltage stability indices. Three simple stability indices were investigated with the help of a sample 5 bus power system. They are singular value decomposition, "L" Index and QV curves. The simulation resdts showed that singular value decomposition and "L" Index indicate proximity or neamess to the voltage collapse point. But the cooslraint in these indices is that the load flow solution does not converge at the bifurcation point. Regarding QV cuves, the rnethod artificially stresses a single bus, hence conclusions should be confirmed by more realistic methods. Also, the curves are obtained by a series of power 80w simulations that make it more time consuming. Modal analysis technique in conjunction with continuation power flow, which is a better performance criteria for the assessrnent of voltage stability was investigated. Simulations were carried out for the IEEE 30 bus system and the New England 39 bus system. The above two examples indicate how modes represent areas prone to voltage instability. Thus, modal analysis clearly identifies groups of buses and critical bus that participate in the instability and thereby eliminate the problems associated with traditional rnethods. Though time consuming, this method is used as a benchmark for developing an expert system for voltage stability evaluation. Expert sysiems, a subset of artificiai intelligent system, have attracted wide spread interest to power system applications. This is due to their ability to bandle stressed power system and improve speed. in this regard, the concept of fuzzy-expert systems has k e n described in detail. A modified IEEE 30 bus system applied to voltage control was simulated to emphasize the concepts developed in the fuzzy-expert systems. To M e r explore its suitability to voltage stability monitoring and control, the New England 39 bus system was taken as case study. Extensive operating conditions were tested to validate the proposed scheme. The percentage error was found to be less than 10%. Based on the simulation results, this new approach was found to be simple and straight fonivard, where it ody needs key system variables to mive at the solution state. In general, the method is able to handle non-linearity of power systern problem and does not require complex computations as in traditional methods. Thus, it is more efficient than conventional methods for voltage stability analysis. The proposed hiny-expert system was tested for 68 different operating conditions. Four cases were misclassified totally and three cases partially misclassified. The source of error for these misclassified cases was probably due to the inappropriate values assigned to the linguistic variables of the key variables in the nilebase of group 4. To give a guarantee or bound on the error with this method, d l possible operating cases are to be tested and verified with standard bench mark tool. With the three input variables, the total number of d e s for the monitoring stage was determined to be 304. The size of the rulebase can be reduced to 96 if two input variables are selected judicially. Thus, the sue of the rulebase will have an effect on the computational compiexity of the futzy-expert system. There is considerable interest among utilities in developing on-line voltage stability twls that will enable the power systerns to be operated at higher loads without risking voltage collapse. The fbq-expert system proposed in this thesis has the potential to be integrated for on-line implementation in Energy Management System to achieve the goals of secure power system operation. This will allow power system operators to continuously monitor the system state and thereby obviate any impending dangers of voltage collapse. However, to realize this challenge, an efficient database that reflects al1 possible system operating conditions should be formed. 7.2 Recommendations for Future Work The voltage stability analysis considered in this thesis assume a constant power load model, which is not the case with a practical power system. Suitable load models can be incorporateci in the stability assessment. The present study is lirnited to around si* four operating conditions. To assess the viability of fuzzy-expert systems to a larger realistic power systems, al1 possible operating conditions should be considered. In order to enhance the efficiency of the present fiipv-expert system, better funy models and rulebase that descnbe both monitoring and control under one urnbrella is recommended. REFERENCES IEEE Speciai Publication 90TH0358-2-PWR, Voltage Stability of Power Systeis: Concepts, Analfical Tools and Industry Experience, 1990. B. 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Lefebvre and Xuan-Dai Do, "An Expert System for S teady-State Voltage Stability ", Canadian Conference for Electrical and Cornputer Engineering, Hafi fax, September 1994, pp. 696- [39] Yuan-Yih Hsu and ChungChing Su, "A RulaBaseci Expert System for Steady-State Stability Analysisw, IEEE T m . Power Systems, Vol. 6 , No. 2, May 199 1, pp. 77 1-777. 1401 M T . Version 4.1, The MathWorks Inc., Natick, Massachusetts 01760, August 1992. APPENDIX - A Line and Bus data for the S bus system Table. A l Line data for the 5 bus system Table. A2 Bus &ta for the 5 bus systern Bus I Code 1 2 Assumed Bus V o h p ( p.u ) 1 .O6 1 .O Load MW MVAR O 1 O 20 1 1 0 Gentration MW MVAR O 40 O 30 APPENDIX - B Rules relating key variables to stabüity meesure of the New England 39 bus system Table. B 1 Rdes relacing worst load bus voltage to stability measure under group 1 0 Moderate 1 0.6 1 1.0 1 0.4 1 0.0 Table. B2 Rdes relating key generator MVAR reserve to stability Tolerable rneasure under group 2 Safc 1 .O O. 8 0.3 0.0 0.0 1 1 1 1 Moderate 1 0.6 1 1.0 1 0.4 1 0.0 Tolerable 0.0 O. 7 1 .O 0.4 0.7 I Low 0.0 0.2 0.5 1 .O Table. B3 Rules relating key generator terminal voltage to stability 1 .O measure under group 3 0.4 1 Safe 1 .O 0.8 0.3 0.0 Tolerable I l l Low 0.0 0.0 0.7 1 1.0 1 0.4 0.2 o. 5 1 .O Table. 84 Rules relating combined key variables to stability measure under group 4 Data used for the rulebase formation for the monitoring stage of the New Eogland 39 bus system Table. C 1 Data used for the miebase formation Case No 1 Totai Load at Selected Buses ( MW ) Gen 32 Volt ( p.u ) Bus 12 Load Voit ( P - U Gen 32 MVAR Complete list of expert system output for the monitoring stage of the New Engiand 39 bus system Table. Dl Expert system output for various neighborhood points - Monitoring stage h d a No Gen 32 Volt (PJ) Total Load at Selected B u s ~ s ( M W ) NO CONTINGENCY Bus 12 Load Voit (PW 1 2 3 4 5 6 7 8 9 1 O 11 12 13 14 15 16 17 Gen 32 W A R 1424.5 1824.5 2624. 5 4624. 5 4958.8 4968.2 497 1.4 3824.5 4774.5 48 12.0 1424.5 1824.5 4424.5 4824.5 5 124.5 5174.5 5183.8 0.983 1 0.983 1 0.983 1 0.9831 0.983 1 0.9831 0.9831 0.95 0.95 0.95 1.05 1 .O5 1 .O5 1 .O5 1-05 1 .O5 1 .O5 18 1424.5 S GIobal State 9823.0 1.0072 0.9879 0.9428 0.7399 0.6250 0.6141 0.6093 0.8276 0.6580 0.6399 1.0374 1.0190 0.8263 0.7644 0.6801 0.6482 0.6378 CONTINGENCY VSTAB output Eigen System vaiue State A 9.89 VS S 10.1 1 9746.5 9556.6 8628.3 81 19.3 8073.1 8052.4 9199.7 8439.0 8361.4 9630.3 9554.9 8663.0 8367.8 7976.0 7832.3 7786.4 VS 9.63 8.50 3.40 0.76 0.52 0.39 5.77 1.71 1.30 10.55 10.09 5.10 3.55 1.53 0.79 0.56 S S CS US U S US CS US US VS VS CS CS US US US S S CS US US US CS US US VS VS CS CS US US US Participation factors for the criticai case 1 Case 1 ( at the voltage stability Iimit ) of the New England 39 bus system Table. E 1 Bus and Generator participation factors for criticai case Bus Participation Factors Bus N o Participation Factors Genefator Participation Factors Gen No Participation Factors 12 4 14 Case 5 Case 2 O. 1713 O. 1042 0.0949 3 2 3 1 12 4 14 Case 6 1.0000 0.73 17 Case 3 0.1788 0.1015 0.094 1 32 31 12 4 14 13 1 .O000 0.7390 Case 4 O. 1562 O. 1093 0.0965 0.0795 32 3 1 1 -0000 0.7150 l MAGE NALUATION TEST TARGET (QA-3) APPLIED - lN1AGE. lnc = 1653 East Main Street - -. , , Rochester, NY t 4604 USA ,=-* Phone: i l 6 / ~ 8 ~ ~ -- -- - - Fax: 71 a12û8-5989