Static Voltage Stability Analysis In Power Systems Engineering Essay

Static potential perceptual constancy analytic thinking In role constitutions Engineering Essay electromotive force perceptual constancy, one of the principal aspects of office staff arrangement s evadeness, has been the main reason for many of major hatfuliness office carcass of rules memory loss incidents everywhere the last few decades. It is acknowledged universally that potential perceptual constancy is and leave alone remain a challenge in the 21st century, even likely to increase in importance. Therefore a ruin understanding of electric potential stableness in mogul ashess is necessary for power engineers, who might crackicipate in the planning, designing, and operation of modern power systems. This encompass talks ab out(p) a relevant engineering thesis encounter Static emf constancy Analysis in Power clays, which is carried out for 2 semesters from July two hundred9 to June 2010.The aim of this thesis project is to submit a more comprehensive te ach into the theory of quiet emf st world power, and investigate a new approach for power blend analysis 3-dimension P-Q-V curve. kickoff of all, the basic knowledge of static potential drop stability is reviewed, and analysis on an elementary power system, radial system, is carried out including power be given study, P-V and Q-V curve analysis. establish on the 2- dimension P-V and Q-V plotting, the transactionhip of P, Q, and V is force outvas and a new method for static voltage stability analysis is tried P-Q-V curve.The second part of this project focuses on the analysis of WSCC three- source-nine-bus system. Simulation of the system is carried through by path of UWPFLOW and causationWORLD. Direct power flow method and continuation power flow method argon applied and the weakest bus is studied. Last but not least, curves be obtained and results are discussed.Keywords Static Voltage stableness Radial System Power Flow Method Continuation Power Flow Method P-V Curve Q-V Curve P-Q-V Curve.CONTENTS iABSTRACT iiCONTENTS ivCHAPTER 1 INTRODUCTION 1CHAPTER 2 POWER SYSTEM potency STABILITY 8CHAPTER 3 STATIC potential STABILITY ANALYSIS OF ELEMENTARY POWER SYSTEM 11CHAPTER 4 STATIC VOLTAGE STABILITY ANALYSIS OF WSCC NINE-BUS SYSTEM 26CHAPTER 5 CONCLUSION 39REFERENCES 41ACKNOWLEDGEMENTS 43 supplement A MATLAB CODES FOR FIGURE 3.8 44APPENDIX B MATLAB CODES FOR FIGURE 4.2 46APPENDIX C MATLAB CODES FOR FIGURE 4.3 47APPENDIX D MATLAB CODES FOR FIGURE 4.4 48APPENDIX E MATLAB CODES FOR FIGURE 4.5 49APPENDIX F MATLAB CODES FOR FIGURE 4.6 50APPENDIX G MATLAB CODES FOR FIGURE 4.7 51APPENDIX H info OF WSCC NINE-BUS SYSTEM 52CHAPTER 1 INTRODUCTIONAn Overview of Modern Power SystemA power system is a earnings of conductors and devices which allows electrical energy to be transferred from the generating power stations to make full centers through transmission network. Since the first electric network in the United States was established at the Pearl Street ran ge in New York City by Thomas Edison in 1882 1, power systems have been experiencing more than light speed years development and improvement. Nowadays, modern power system has developed to be a complex interconnected network, which shtup be sub dissever into four partsGenerationPrivate and publicly owned generators produce the electricity that feeds into naughty voltage grids.TransmissionHigh voltage transmission grids transport power from generating units at various locations to distribution systems which ultimately supply the load. distributionDistribution systems deliver the power from local bulk supply points to the consumers service-entrance equipments.LoadsLoads of power systems are composed of industrial, commercial, and residential load. assure 1.1 Modern Power System 2Power System StabilityA power system is said to be stable if it has the property that it retains a state of equilibrium under typical operating conditions and regains an acceptable state of equilibrium af ter being subjected to a disturbance. Of all the complex phenomena on power system, power system stability is the approximately intricate to understand and challenging to analyze 3. Damage to power system stability may cause the system to blackout or pass as well as other catastrophic incidents, leading to enormous social and economic losses. potpourri of Power System StabilityBased on the systems distinguishable properties, network structures and operation modes, the system unbalance post behave in many incompatible ways. Accordingly power system stability study is divided mainly into three fields tend stability, frequency stability and voltage stability. The diagram below shows visually the classification of power system stability.Figure 1.2 Classification of Power System StabilityHistory of Study on Power System StabilityInitially, angular stability was firstly paid attention to and studied since power transmission capability had traditionally been limited by either rotor a ngle (synchronous) stability or by thermal loading capability. And the blackout problems had been associated with transient stability, which were diminished by fast short circuit clearing, powerful excitation systems and varies special stability fits 3. In other words, nowadays the theory and methods on angular stability are relatively more complete.Meanwhile, study on voltage stability had been quite slow, which mainly attributed to two reasonsIncidents ca utilise by voltage mental unsoundness or voltage dissect occurred relatively late, not until which did people paid attention to voltage instability problems.Understanding of voltage instability was not so profound as other kinds of instability problems in the early days. Varies of issues arose during the study on voltage stability such(prenominal) as load-based modeling, dynamic behaviors of different components as well as their interaction, and so on.Overview of Power System Voltage StabilityVoltage Instability Incidents in t he WorldPower system voltage stability was firstly introduced in 1940s, but failed to draw peoples attention until 1970s, since which voltage instability and collapse had resulted in several major system failures or blackouts throughout the world, as propensityed below 4, 5, 22 howling(a) 22, 1970, Japan, 30 minutesSeptember 22, 1970, New York, several hoursSeptember 22, 1977, Jacksonville, Florida, few minutesDecember 19, 1978, France, 26 minutesAugust 4, 1982, Union Belgium, 4.5 minutesSeptember 2, November 26, December 28 30, 1982, Florida, 1-3 minutesMay 21, 1983, Northern California, 2 minutesDecember 27, 1983, Sweden, 55 secondsJune 11, 1984, Northeastern USA, several hoursMay 17, 1985, southwestward Florida, 4 secondsApril 1986, Winnipeg, Canada Nelson River HVDC links, 1 secondMay 20, 1986, England, 5 minutesNovember 1986, SE Brazil, Paraguay, 2 secondsJanuary 12, 1987, Western France, 6-7 minutesJuly 20, 1987, Illinoisand India, several hoursJuly 23, 1987, Tokyo Japan, 20 minutesAugust 22, 1987, Western Tennessee, 10 secondsJuly 2, 1996, Western System Coordination Council (WSCC), Northern USAAugust 1996, MalaysiaAugust 14, 2003, USA CanadaSeptember 28, 2003, Italy.Progress of Study on Voltage StabilityThe large numbers of worldwide voltage collapse incidents made it become the focus of worlds attention to study voltage stability of power system. In the 1982s researching list of Electric Power Research Institute (EPRI) in USA, voltage stability was considered as the most significant issue. Over the last thirty years, and especially over about the last twenty years, utility engineers, consultants, and university researchers have intensely studied voltage stability. Hundreds of technical papers have resulted, along with conferences, symposiums, and seminars. Utilities have developed practical analysis techniques, and are now planning and operating power systems to prevent voltage instability for credible disturbances 6.Importance of Voltage Stabil ity in future(a)In a foreseeable future, the global fast-growing power consumption forget require more intensive use of available transmission facilities, which means an operation of power systems closer to their voltage stability limits. The increased use of existing transmission is made possible, in part, by labile power hire 6. Undoubtedly, voltage stability is and will remain a challenge in the 21st century, even likely to increase in importance. Therefore a better understanding of voltage stability in power systems is necessary for power engineers, who might participate in the planning, designing, and operation of modern power systems.Topic explanation and ScopeThe topic of this project is Static Voltage Stability Analysis in Power Systems, which mainly focuses on the followingOverview of the phenomena of static voltage stabilityAnalysis associated with the phenomenaReasons why voltage collapse happensMeasures to improve static voltage stability.In consideration of restric tions on the simulation, a three-generator-nine-bus case is used throughout the self-coloured project while a typical two-bus (one-generator-one-load) case is used for the P-Q-V curve analysis.Aims and ObjectivesThe main objective of this project is to get a wider and deeper understanding of static voltage stability in power systems, which can be reduced into sub-objectivesTo conduct a more comprehensive study into the theory of static voltage stabilityTo look for reasons why voltage collapse happensTo investigate a new approach for power flow analysis 3-dimension P-Q-V plottingTo propose proper measures of improving static voltage stability in power systemsTo conclude generation direction and load direction for the analyzed power system.CHAPTER 2 POWER SYSTEM VOLTAGE STABILITYBasic Concepts of Voltage StabilityIEEE DefinitionsIEEE 7 provided a formal definition of voltage stability and relative concepts as given belowVoltage Stability Voltage stability is the ability of a system t o maintain voltage so that when load admittance is increased, load power will increase and so that both power and voltage are controllable.Voltage Collapse Voltage collapse is the process by which voltage instability leads to very low voltage profile in a significant part of the system.Voltage Security Voltage security is the ability of a system not only to operate stably, but as well to remain stable (as for as the maintenance of system voltage is concerned) following any reasonable credible contingency or ill system vary.CIGRE DefinitionsNevertheless, the to a higher place definitions of voltage stability conditions were not directly compatible with the general IEEE definition for stability concept. Hence new definitions were given in CIGRE report 8, which are as followingVoltage Stability A power system, at a given operating state and subjected to a given disturbance, is voltage stable if voltages near loads approach post-disturbance equilibrium values. The disturbed state is within the region of the stable post-disturbance equilibrium.Voltage Instability Voltage instability is the absence of voltage stability, and results in progressive voltage decrease (or increase). Destabilizing control reaching limits, or other control actions (e.g. load connection), however, may establish global stability.Voltage Collapse Following voltage instability, a power system undergoes voltage collapse if the post-disturbance equilibrium voltages near loads are below acceptable limits. Voltage collapse in the system may be either total (blackout) or partial. Voltage collapse is more complex than simple voltage instability leading to a low-voltage profile in a significant part of the power system.Other Relative ConceptsLarge-disturbance Voltage Stability Large-disturbance voltage stability is concerned with a systems ability to control voltages following large disturbances such as system faults, loss of generation, or circuit contingencies. The study period of invade may extend from a few seconds to tens of minutes. Therefore, long-term dynamic simulations are required for analysis.Small-disturbance Voltage Stability Small-disturbance voltage stability is concerned with a systems ability to control voltages following small perturbations such as incremental changes in system load. For such case, static analysis is effectively used.Relation of Voltage Stability to Rotor Angle StabilityVoltage stability and rotor angle (or synchronous) stability are more or less interlinked. Transient voltage stability is often interlinked with transient rotor angle stability, and slower forms of voltage stability are interconnected with small-disturbance rotor angle stability.Voltage Stability is concerned with load areas and load characteristics. For rotor stability, we are often concerned with integrating remote power plants to a large system over long transmission lines. Voltage stability is basically load stability, and rotor angle stability is basically generator stability 6.In a large interconnected system, voltage collapse of a load is possible without loss of synchronism of any generators. Transient voltage stability is usually closely associated with transient rotor angle stability. long-term voltage stability is less interlinked with rotor angle stability. We can consider that if voltage collapses at a point in a transmission system remote from loads, it is an angle instability problem. If voltage collapses in a load area, it is possibly mainly a voltage instability problem.CHAPTER 3 STATIC VOLTAGE STABILITY ANALYSIS OF ELEMENTARY POWER SYSTEM debut of an Elementary toughie Radial SystemSimple radial system network is used to develop most of the concepts of the static voltage stability. Once basic concepts are understood, we can re front as much as appropriate in calculating machine simulation, which will be carried out in Chapter 4. Figure 3.1 shows an equivalent circuit of the power system, and a model called radial system is form ed to represent such power system, as shown in Figure 3.2.Figure 3.1 Equivalent Circuit of Power SystemFigure 3.2 Radial System ModelThe sending-end and receiving-end voltages are off-key to be fixed and can be interpreted as points in large systems where voltages are stiff or secure. The sending end and receiving end are connected by an equivalent reactance.Basic Analysis of Radial SystemActive Power TransmissionApplying the radial system in Figure 3.2, the relations can be easily calculatedSimilarly, for the sending endThe familiar equations for and are equal since we assume a lossless system, and maximum power transferred is at a power load angle equal to 90 degree. Note that the 90-degree maximum power angle is nominal, in other words, maximum power occurs at a different angle if we apply transmission losses or resistive transfer loads. And the case with impedance load at the receiving end will be discussed in section 3.2.2.responsive Power TransmissionIn the study of the stati c voltage stability in power system, the transmission of antiphonal power is especially of interest. Usually we are interested in variable voltage order of magnitudes. Particularly, we are interested in the oxidizable power that can be transmitted crosswise a transmission line, or a transformer as the receiving-end voltage sags during a voltage emergency or collapse. Considering the reactive power flow over the transmission line alone, we can write approximate formulas for Equations (3.3) and (3.5) in terms of small angles by using From Equations (3.6) and (3.7), it can be observed that reactive power transmission depends mainly on voltage magnitudes and flows from the spunkyer voltage to the lower voltage. Such observation, however, cannot be applied in the case of high stress, i.e. high power transfers and angles, where the angle is large enough and no longer approaches 1. This is important as voltage stability problems normally happen during highly stressed conditions.Difficul ties with Reactive Power TransmissionReactive Power Transmission Behavior in Different CasesFirst of all, take an example of the radial system in Figure 3.2, assuming X=0.2 p.u. with alter values of voltage magnitude and angles, i.e. varied loading conditions. Applying Equations (3.3) and (3.5), and can be calculated as listed in the following tableConditions(p.u.)(p.u.)(degree)(p.u.)(p.u.)Lightly loaded1.101.00100.6340.416Moderately loaded1.050.90201.0720.390Heavily loaded1.000.80502.429-0.629Table 3.1 Reactive Power Transmission in varied conditionsFrom the table, it is clear that at higher loading, transmission lines are more difficult to transfer reactive power and reactive power cannot be transmitted crossways large power angles (the value of becomes negative in the case with a power angle of 50 degree).Minimizing Transfer of Reactive PowerHigh angles are collect to long lines and high real power transfers. It is therefore required to maintain voltage magnitude profiles with voltages of approximately 1 p.u.. Compared with real power transfers, reactive power cannot be transmitted across long distances. It has been observed that the greater distance of the reactive power sources from the reactive demand will lead to 9greater voltage gradient on the lines supplying the reactive powergreater amount of required reactive power compensationmore difficult to control the voltage levelAnother reason to minimize the transfer of reactive power is minimizing the real and reactive losses. The purpose to reduce real losses is due to economic reasons while minimizing the reactive losses can reduce investment in reactive devices such as shunt capacitors.As we know, the losses across the series impedance of a transmission line are and . For , we haveandObviously, to minimize losses, we should minimize reactive power transfer and keep voltage high at the uniform time. Keeping voltage high to minimize reactive losses helps maintain voltage stability. In other words, rea ctive power should be generated close to the receiving end.Power Flow AnalysisIn a power system, powers are known rather than currents. Thus power flow analysis is acantha of static voltage stability studies. Power flow analysis, also known as load flow analysis, involves the calculation of power flows and voltages of a transmission network for specified terminals or bus conditions.Bus ClassificationIn solving a power flow problem, a power system is supposed to be operating under balanced conditions and a single-phase model is used. Associated with each bus are four quantities active power P, reactive power Q, voltage magnitude , and voltage angle.The following types of buses (nodes) are represented, and at each bus two of the above four quantities are specifiedVoltage-controlled (P-V) buses These buses are the generator buses. They are also known as regulated buses or P-V buses. For such kind of buses, the real power P and voltage magnitude are specified, while the reactive power Q and the voltage angle are unknown.Load (P-Q) buses Load buses are also called P-Q buses as their real power P and reactive power Q are specified. The voltage magnitude and angle are to be determined.Slack (Swing) bus Such bus is taken as reference of the whole power system. For a open bus, the voltage magnitude and voltage angle are specified. As the power losses in the system are not known a priori, at least one bus must have unspecified P and Q. Thus the depression bus is the only bus with known voltage. This bus makes up the difference between the scheduled loads and generated power that are caused by the losses in the network 1. Traditionally while analyzing, the voltage magnitude of slack bus is assumed to be 1 p.u. and the voltage angle is assumed to be 0 degree.Transmission Line ModelingThe transmission line is traditionally represented with two types of models nominal model and nominal T model, as shown in Figure 3.3 and Figure 3.4 where Z is the series impedance and Y i s the shunt admittance due to the line charging capacitance. Neither nominal T or nominal exactly represent the actual line, however, they brings great convenience in the power flow analysis, especially in the application of NEWTON-RAPHSON method, which will be discussed in the coming section.Figure 3.3 Nominal ModelFigure 3.4 Nominal T ModelNEWTON-RAPHSON Power Flow MethodIn order to include all the three types of buses (P-V bus, P-Q bus and slack bus as introduced in 3.3.1) at the same case, a 3-bus power system is considered as shown in Figure 3.5, whereBus 1 is the slack bus, i.e. and are specified as .Bus 2 is a voltage-controlled bus, i.e. and are known while and are unknown.Bus 3 is a load bus, i.e. and are known while and are unknown.Figure 3.5 3-bus Power SystemThe network performance equation of such a sample iswhereApplying the bus-loading equationsNow NEWTON-RAPHSON Power Flow Method can be approached asP-V Curve AnalysisP-V curve is useful for conceptual analysis of st atic voltage stability and for study of radial system, where P is the load in an area and V is the voltage at a critical or representative bus. Besides, P can also be the power transferred across a transmission interface or interconnection. Voltage at several busses can be plotted.Consider the radial system as shown in Figure 3.2. The receiving-end active power can be expressed as in the Equation 3.2. Then a P-V cueve can be plotted as in Figure 3.6, which shows alliance between P and V at the receving end for different values of load power factor and the locus of the critical operting point is shown by the dotted line. Nornally, only the operting points above the locus of the critical points represent satisfying operating condition. A sudden reduction in power factor or increase in Q can thus cause the system to change from a stable operating condition to an unsatisfactory and possibly unstable 10.Figure 3.6 V versus P for different power factors 10Q-V Curve AnalysisQ-V curve is p resently the workhorse method of voltage stability analysis at many utilities 6. Considering the system in Figure 3.2, we can obtain reactive power both at sending end and receiving end, or and by means of Equation (3.5) and Equation (3.3). Then a Q-V cueve can be plotted as in Figure 3.7, which shows relationship between Q and V. The reactive power margin is the MVAr distance from the operating point to either the butt joint of the curve, or to a point thaere the voltage squared characteristic if an applied capacitor is tanfent to the V-Q curve 6. Additionally, the slope of the V-Q curve indicates the stiffness of the bus.Figure 3.7 Typical Q V CurveA New Method for Static Voltage Stability Analysis P-Q-V Curve AnalysisIntroduction of MATLAB SoftwareMATLAB is a numerical cipher environment and fourth generation programming language. Developed by The MathWorks, MATLAB allows matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interf aces, and interfacing with programs in other languages 18. An additional package, Simulink, adds graphical multi-domain simulation. This project greatly benefits from MATLAB to handle 3-dimension curve drawing for P-Q-V curve study, as well as the matrix manipulation associated with power flow analysis, 2-dimension curve plotting for P-V/Q-V curve study in the analysis of WSCC nine-bus system, which will be described in detail in CHAPTER 4.P-Q-V CurveIn this section, for convenience of forming an ideal voltage source, we assume the angle of the to be zero while the angle of to be degree. Then Equation 3.2 and 3.3 becomeNoting thatWe can eliminate in Equations 3.16 and 3.17, which obtainsorObviously, with specified , and , Equation 3.19 shows relationship of , and . To work out such relationship visually, MATLAB is applied and a P-Q-V curve is obtained as below, where P stands for , Q stands for V stands for and E stands for . Refer to Appendix A for details on MATLAB codes, with th e assumsion that E = 1 , X= 0.2 and the values of tan are chosen randomly as -0.41, -0.2, 0, 0.2, 0.41, 1, 10, 100, 1000.Figure 3.8 P Q V CurveCHAPTER 4 STATIC VOLTAGE STABILITY ANALYSIS OF WSCC NINE-BUS SYSTEMIntroduction of WSCC Nine-bus SystemWSCC nine-bus system is a typical testing system develped by Western Systems set up Council. It is commonly uesd in jornals and papers for power system studying. Figure 4.1 shows an overview of the WSCC nine-bus system. Refer to Appendix H for parameters of this system.Figure 4.1 Single Line Diagram of WSCC Nine-bus SystemIntroduction of UWPFLOW SoftwareFor determining the static voltage stability of the WSCC nine-bus system, UWPFLOW software is used. This software has been developed by University of Waterloo, Canada, and distributed free on the Power Globe. It was written in C and runs under DOS and UNIX enviroments. It has no limitation on the system size other than those imposed by memory limitation in the corresponding enviroment, i.e . thump and swap space in the UNIX and exrended memory in DOS 16, 20.UWPFLOW is a research tool that has been designed to calculate local bifurcation characterized by a property in the power system Jacobian. This was developed based on power flow method. This software also generates a series of output files that allow pass on analysis. UWPFLOW reads AC power flow data in WSCC format 11 or IEEE common format 12, DC data in ETMSP format 13, FACTS devices data in s special format described in 14, and steady state load model data in OH format 15. However in the present study IEEE common format data is used. Additional UN format data is required for bifurcation analysis, such as direction of generation change, direction of load change and maximum genertion limit 10. The software assumes that one parameter the loading factor, is allowed to change. All steady state system controls remain operational unless otherwise specified by means of the software option.Introduction of POWERWORLD So ftwarePOWERWORLD Simulator is an interactive power system simulation package designed to simulate high voltage power system operation on a time frame ranging from several minutes to several days 17. POWERWORLD provides a linear programming based optimal power flow package Simulator OPF, which ideally suits to do power flow analysis. Whats more, the planning-mode tool Simulator PVQV fulfills the need of Q-V curve drawing. Throughout the project, PowerWorld Simulator will be used to carry out power flow analysis and Q-V curve study of the twelve-bus case.Analysis of WSCC Nine-bus SystemDirect Method Repeated Power FlowFirst of all, the WSCC nine-bus system in Figure 4.1 is built in UWPFLOW software. By running the system and increasing the loading level of step by step, attention will be focussed on getting convergence and the maximum loading level. For loading direction, assume all the loads are increased by the same ratio, and only generator at Bus-1 is allowed to dispatch required additional real power.With the load P and Q increased simultaneously with the ratio of 10%, in the same loading direction, the bus voltages in per unit measurement are tabulated in Table 4.1. Couples of data points are collected near the system divergence point. Table 4.1 has shown that the system started to collapse (or diverge) at the point where all loads at the 3 load buses are increased in the same direction till 116%. Note that in Table 4.1, the starting point is denoted as 0% as there is no additional loads added, which is named as basic load. Then we can conclude from Table 4.1 that the maximum loading level for the WSCC nine-bus system is at additional of 116% loading direction on all 3 load buses.Load maturation (%)Bus5Bus7Bus9P (MW)Q (Mvar)V (p.u.)P (MW)Q (Mvar)V (p.u.)P (MW)Q (Mvar)V (p.u.)090301.0129100351.0162125501.02611099331.006911038.51.0105137.5550.988620108361.004120421.0053150600.98130117390.992813045.50.999162.5650.97240126420.9846140490.993175700.962550135450 .975315052.50.9862187.5750.951660144480.9648160560.979200800.939470153510.95317059.50.9711212.5850.925780162540.9396180630.9626225900.910290171570.924219066.50.9532237.5950.8923100180600.9061200700.94282501000.8714110189630.88121073.50.9239262.51050.84112190.863.60.873721274.20.91672651060.83114192.664.20.865721474.90.9087267.51070.8191115193.564.50.8621575.250.9024268.75107.5