1. PRESENTED BY:-Bhupendra KumarIntegrated M.Tech.

2. Contents Basic concepts and definitions Classification of power system stability Rotor angle stability Transient stability analysis Voltage stability Voltage collapse Factors affecting voltage stability Classification of voltage stability Small signal stability 3. Stability of dynamic systems Dynamic stability analysis Effect of excitation system Power system stabilizers Control of PSS Applications of PSS AESOPS algorithm MAM method Characteristics of small signal stability problem References and bibliography 4. BASIC CONCEPTS AND DEFINITIONS Power system stability may be broadly defined asthat property of a power system that enables it toremain in a state operating equilibirium under normaloperating conditions and to regain an acceptablestate of equilibirium after being subjected to adisturbance. Instability in a power system may be manifested inmany different ways depending on the systemconfiguration and operating mode. Traditionally ,the stability problem has been one ofmaintaining Synchronus operation. 5. BASIC CONCEPTS ANDDEFINITIONS(cont..) Since power system rely on synchronus machines forelectrical power generation, a necessary condition forsatisfactory system is that all syn. machines shouldremain in synchronism. This aspect of stability is influenced by the dynamicsof generators rotor angles and power-anglerelationships. Instability may also encountered without loss ofsynchronism. For example a system consisting of asynchronus generator feeding an induction motorload through a transmission line can becomeunstable because of the collapse of load voltage. 6. BASIC CONCEPTS ANDDEFINITIONS(cont..) In the evaluation of stability the concern is the behavior ofthe power system when subjected to a transientdisturbance. The disturbance may be small or large. Small disturbances in the form of load changes take placecontinually, and the system adjusts itself to the changingconditions. The system must be able to operate under these changesand also be capable of surviving numerous disturbances ofsevere nature, such as short- ckt. on transmission line, lossof a large generator or load , or loss of a tie between twosubsystems. 7. Classification Of PowerSystem Stability 8. ROTOR ANGLE STABILITY Rotor angle stability is the ability of synchronousmachines of a power system to remain insynchronism. In other words, rotor angle or load angle stabilitydenotes the angular displacement between statorand rotor speeds. It is directly proportional to the speed of the m/c i.e.the load connected to the generator. If the Angle is beyond to liable limit, the system willcome out of synchronism. 9. Transient Stability Analysis For transient stability analysis we need to considerthree systems1. Prefault - before the fault occurs the system isassumed to be at an equilibrium point2. Faulted - the fault changes the system equations,moving the system away from its equilibrium point3. Post fault - after fault is cleared the systemhopefully returns to a new operating point 10. VOLTAGE STABILITY & VOLTAGECOLLAPSE Voltage Stability-It refers to the ability of thesystem to maintain a steady frequency, following asystem drastic change resulting in a significantimbalance between generated and demand power Voltage stability margins- 11. Factors affecting voltage stability Voltage stability is a problem in power systems which areheavily loaded, faulted or have a shortage of reactivepower. The nature of voltage stability can be analyzed by examiningthe production, transmission and consumption of reactivepower. The reactive characteristics of AC transmission lines,transformers and loads restrict the maximum of powersystem transfers. The power system lacks the capability to transfer powerover long distances or through high reactance due to therequirement of a large amount of reactive power at somecritical value of power or distance. 12. Scenario of classic voltage collapse The large disturbance causes the network characteristics toshrink dramatically. The characteristics of the network andload do not intersect at the instability point. A load increasebeyond the voltage collapse point results in loss ofequilibrium, and the power system can no longer operate. Thiswill typically lead to cascading outages. The load voltage decreases, which in turn decreases the loaddemand and the loading of EHV transmission lines. Thevoltage control of the system, however, quickly restoresgenerator terminal voltages by increasing excitation. Theadditional reactive power flow at the transformers andtransmission lines causes additional voltage drop at thesecomponents. 13. PV-curve1. Power systems are operated in the upper part of the PV-curve. Thispart of the PV-curve is statically and dynamically stable. The head of the curve is called the maximum loading point. Thecritical point where the solutions unite is the voltage collapse point.The maximum loading point is more interesting from the practicalpoint of view than the true voltage collapse point, because themaximum of power system loading is achieved at this point. Themaximum loading point is the voltage collapse point when constantpower loads are considered, but in general they are different. The voltage dependence of loads affects the point of voltage collapse.The power system becomes voltage unstable at the voltage collapsepoint. Voltages decrease rapidly due to the requirement for an infiniteamount of reactive power. 14. PV-curve The lower part of the PV-curve (to the left of the voltage collapse point) isstatically stable, but dynamically unstable. The power system can onlyoperate in stable equilibrium so that the system dynamics act to restorethe state to equilibrium when it is perturbed.V1=400 kV and X=100 Ohm 15. Classification of Voltage stabilitySmall-disturbance Voltage Stability- this categoryconsiders small perturbations such as an incrementalchange in system load. It is the load characteristics and voltage controldevices that determine the system capability tomaintain its steady-state bus voltages. This problem is usually studied using power-flow-basedtools (steady state analysis). In that case the power system can be linearisedaround an operating point and the analysis is typicallybased on eigenvalue and eigenvector techniques 16. Large-disturbance Voltage Stability Here, the concern is to maintain a steady bus voltagesfollowing a large disturbance such as system faults,switching or loss of load, or loss of generation. This ability is determined by the system and loadcharacteristics, and the interactions between the differentvoltage control devices in the system. Large disturbance voltage stability can be studied by usingnon-linear time domain simulations in the short-term timeframe and load-flow analysis in the long-term time frame(steady-state dynamic analysis) The voltage stability is. however, a single problem on whicha combination of both linear and non-linear tools can beused. 17. Short-term voltage stability Short-term voltage stability is characterized bycomponents such as induction motors, excitation ofsynchronous generators, and electronically controlleddevices such as HVDC and static var compensator.The time scale of short-term 18. Long-term voltage stability The analysis of long-term voltage stability requiresdetailed modeling of long-term dynamics Two types of stability problems emerge in the long-termtime scale:1. Frequency problems may appear after a majordisturbance resulting in power system islanding.Frequency instability is related to the active powerimbalance between generators and loads. An islandmay be either under or over-generated when thesystem frequency either declines or rises.2. Voltage problems 19. Small Signal Stability Small signal stability refers to the systems ability tomaintain steady voltages when subjected to smallperturbations such as incremental changes in system load. This form of stability is influenced by the characteristics ofloads, continuous controls, and discrete controls at a giveninstant of time. This concept is useful in determining, at any instant,how the system voltages will respond to small systemchanges. 20. Forms of InstabilityTwo forms of Instabilityoccur under theseconditions: Steady Increase in RotorAngle due to lack ofsufficient SynchronisingTorque Rotor oscillations ofincreasing amplitude dueto lack of sufficientdamping torque 21. Small-Signal Stability of Multi-machineSystems Analysis of practical power systems involves thesimultaneous solution of equations representing thefollowing: Synchronous machines, and the associated excitationsystems and prime movers. Interconnecting transmission network. Static and dynamic (motor) loads Other devices such as HVDC converters, static varcompensators 22. For system stability studies it is appropriate toneglect the transmission network and machine statortransients. The dynamics of machine rotor circuits, excitationsystems, prime mover and other devices arerepresented by differential equations. The result is that the complete system modelconsists of a large number of ordinary differentialand algebraic equations. 23. Stability of a Dynamic System The stability of a linear system is entirely independentof the input, and the state of the stable system withzero input will always will return to the origin of thestate space, independent of the finite initial state. In contrast stability of the non linear system dependson the type and magnitude of input, and the initialstate. 24. In control system theory, it is common to classifynonlinear stability into following categories:- Local Stability Finite Stability Global Stability 25. Local problems Associated with rotor angle oscillations of a singlegenerator or a single plant against the rest of the powersystem. Such oscillations are called local plant modeoscillations. Most commonly encountered small-signal stabilityproblems are of this category. Local problems may also be associated with oscillationsbetween the rotors of a few generators close to eachother. 26. Such oscillations are called inter-machine or inter-plantmode oscillations. The local plant mode and interplant mode oscillationshave frequencies in the range of 0.7 to 2.0 Hz. Analysis of local small-signal stability problems requiresa detailed representation of a small portion of thecomplete interconnected power system. 27. Finite Stability If state of a system remains within a finite region R, itis said to be stable within R. if further, the state of thesystem returns to the equilibrium point from anypoint within R, it is asymptotically stable within finiteregion R. 28. Global Stability Problems Global small-signal stability problems are caused byinteractions among large groups of generators andhave widespread effects. They involve oscillations of a group of generators inone area swinging against a group of generators inanother area. Such oscillations are called inter-areamode oscillations. 29. Eigen value And Stability Stability of the linearized system is described by theeigenvalues of the state matrix A real eigen value, or a pair of complex eigenvalues, isusually referred to as a mode 30. For a complex mode =j, two quantities are of maininterest: Frequency (in Hz) :f=/2 Damping ratio (in %):=100/(^2+^2) The system is unstable if is negative To ensure the acceptable performance, a damping marginin the range of 3%-5% is normally required 31. Model Characteristics While an eigenvalue indicates the stability, its rightand left eigenvectors give much more information onthe characteristics of the mode The right eigenvector shows the mode shape, i.e., theobservability of the mode A mode should be observable from generatorrotor oscillations if the generator is high in itsmode shape 32. A weighted left eigenvector shows the participationfactors, i.e., the controllability of the mode A mode should be controllable from generator if thegenerator is high in its participation factors A generator which is high in the mode shape of amode is not necessarily high in the participationfactor of the same mode 33. DYNAMIC STABILITY ANALYSIS The analysis of dynamic stability can be performed byderiving a linearized state space model of the systemin the following formp X = A X + B u Where the matrices A and B depend on the systemparameters and the operating conditions. The Eigen values of the system matrix A determinethe stability of the operating point. 34. The Eigen value analysis can be used not only for thedetermination of the stability regions, but also for thedesign of the controllers in the system. 35. Small Signal Stability of Single M/CInfinite Bus System In this section we study the small signal performance of asingle machine connected to a large system throughtransmission lines. A general system configuration is shown as- Fig. a reduced as fig. b using Thevenins Equivalent suchas virtually there is no change in voltage & frequency ofThevenins voltage E. Such a voltage source of constt. Voltage & frequency isreferred as Infinite Bus. 36. For any given system condition, the magnitude of theinfinite bus voltage E remains constt. when themachine is perturbed. However as the steady statesystem conditions change, magnitude of E maychange, representing a changed operating condition ofexternal network. 37. Effects of Excitation System In this section we extend the state space model & blockdiagram to include the excitation system. Fast excitation-systems are usually acknowledged to bebeneficial to transient stability. These fast excitation changes are not necessarilybeneficial in damping the oscillations that follow the firstswing. 38. They sometimes contribute growing oscillations severalseconds after the occurrence of a large disturbance. With proper design and compensation, a fast exciter canbe an effective means of enhancing stability in thedynamic range as well as in the first few cycles after adisturbance. 39. Some General Comments on theEffect of Excitation on Stability For less severe transients, the effect of modern fastexcitation systems on first swing transients is marginal. For more severe transients or for transients initiated byfaults of longer duration, these modern exciters can havea more pronounced effect. 40. Their effects on damping torques are small; but in thecases where the system exhibits negative dampingcharacteristics, the voltage regulator usuallyaggravates the situation by increasing the negativedamping. Supplementary signals to introduce artificialdamping torques and to reduce inter machine andintersystem oscillations have been used with greatsuccess. 41. Large interconnected power systems experiencenegative damping at very low frequencies ofoscillations. The parameters of the PSS for aparticular generator must be adjusted after carefulstudy of the power system dynamic performance. 42. POWER SYSTEM STABILIZERS The dynamic stability of a system can be improved byproviding suitably tuned power system stabilizers onselected generators. to provide damping to criticaloscillatory modes. Suitably tuned Power System Stabilizers (PSS), willintroduce a component of electrical torque in phasewith generator rotor speed deviations resulting indamping of low frequency power oscillations in whichthe generators are participating. 43. The input to stabilizer signal may be one of the locallyavailable signal such as changes in rotor speed, rotorfrequency, accelerating power or any other suitablesignal. 44. CONTROL OF PSSA Typical Control Schematic Diagram ofPower System Stabilizer 45. APPLICATIONS OF PSS 46. STRUCTURE OF COMPLETE POWERSYSTEM MODEL For system stability it is appropriate to neglect thetransmission network and machine stator transients. The dynamics of machine rotor ckts., excitationsystems, prime movers and other devicesrepresented by differential equations. Result in that the complete system model consists ofa large no. of ordinary differential and algebricequation. 47. SPECIAL TECNIQUES FOR ANALYSISOF VERY LARGE SYSTEMS Two methods have been found to be efficient, and,they complement each other in meeting therequirements of small-signal stability- 1. the AESOPS algorithm 2. the Modified Arnoldi Method(MAM) 48. THE AESOPS ALGORITHM The AESOPS algorithm is a type of selective eigenvalue analysis method and it is found very effective incomputing modes. This allows the efficient studies of local modes withoutthe need to reduce the system model 49. . THE MODIFIED ARNOLDI METHOD 50. CHARACTERISTICS OF SMALLSIGNAL STABILITY PROBLEMIn large power systems, small signalstability problem may be either local orglobal in nature. 51. LOCAL PROBLEMS Local problems involve a small party of the system. They may be associated with rotor angle oscillationsof a single generator or a single plant against the restof power system. Such oscillations are called local plant modeoscillations. the stability problems related to such oscillationsare similar to infinite bus system. 52. Local problems may also associated with oscillationsbetween the rotors of a few generators close to eachother. Such oscillation are called inter-machine or interplantmode oscillations. Other possible local; problems include instability ofmodes associated with controls of equipments such asgenerator excitation system, HVDC converters, andstatic var compensators. 53. GLOBAL PROBLEMS 54. is in order of 0.1 to 0.3 Hz.Higher frequency modes involving subgroups ofgenerators swinging against each other.The frequency of these oscillations is typically in therange of 0.4 to 0.7 Hz. 55. References and Bibliography Prabha Kundur , Power System Stability and Control , TMHPublication,2008. Kimbark E W, Power System Stability, Volume I, III, Wileypublication. C. Radhakrishna : Stability Studies of AC/DC Power Systems ,Ph. D. Thesis , submitted to Indian Institute of TechnologyKanpur, India, 1980. Presentation on Voltage collapse- M.H.Sadegi Small Signal Stability Analysis Study:study prepared by Powertech Labs Inc. for ERCOT www.Google.com