Transient Stability of Power Systems A Unified Approach to Assessment and Control By Rishika Chavala
IntroducAon What is transient stability? Numerical integra4on methods are used to assess it accurately such as 4me- domain methods- (calcula4ons of the system s dynamic equa4ons were carried out manually to compute the machine s swing curve). Another way of tackling is a graphical method called equal- area criterion (EAC)- (It is used to assess the system s stability margins and limits, for evalua4ng the influence of various system parameters). The EAC energy concept is a par4cular case of the Lyapunov s general theory. Lyapunov s method is promising as it covered prac4cal stringent needs that T- D approaches cannot meet sa4sfactorily.
Security: DefiniAon and Study Context What is power system security? Power system security is usually sub divided into sta4c and dynamic phenomena. Power system stability currently refers to the dynamic part of stability. It is a mul4faceted problem depending on many factors : ü The 4me span(short term or long term) ü The size of disturbance considered(large or small) ü Physical nature of resul4ng instability
Types of power system stability phenomena
Dy Liacco s diagram- defines different operaang modes
OperaAng Modes PrevenAve security assessment is concerned with a ques4on whether a system in its normal state is able to withstand every plausible con4ngency. Emergency state detecaon aims at assessing whether the system is in the process of losing integrity following a disturbance- (response 4me cri4cal, economic considera4ons secondary). In the restoraave mode, the task of the operator is to minimize the amount of undelivered energy by re- synchronizing lost genera4on ASAP and picking up the disconnected load.
Common needs of Power System relaave to the paracular field of applicaaon
Models 1. General Modeling Dynamic 4me constants in power systems range from frac4on of microseconds to hours. The dynamic behavior is governed by two sets of non- linear equa4ons: x. = f(x, y, p) o = g(x, y, p) The dimension of vector x is lower bounded by twice the number of system machines(typically>=50). The dimension of vector y is lower bounded by twice the number of nodes of the power system model. Vector p represents parameters whose influence on dynamic security may be studied.
StaAc and Dynamic Models Suppose that the system is in an acceptable steady- state pre- fault opera4ng regime, ü The sta4c part of security assessment consists in evalua4ng the proper4es of post- fault equilibrium state, by checking that it leads to viable opera4ng condi4ons. ü The dynamic part of the security assessment considers whether the system would be able to reach its post fault opera4ng condi4ons. Transient Stability Models ü Machine state variables ü Load state variables ü Special devices
Transient Stability- Time Domain Approach What is a disturbance? So, to assess the system robustness with a given disturbance, the T- D approach simulates the system dynamics in the during- fault and post- fault configura4ons either by ü Fixing a clearing 4me, t e, and assess whether the system loses synchronism ü Or by assessing stability limits: CCT for a given pre- fault opera4ng condi4on. Strength and Weaknesses of T- D methods T- D methods cannot meet the major needs iden4fied rela4ng to control(preven4ve or emergency type).
Direct Approaches and ApplicaAons The deficiencies of T- D methods gave an impetus to the development of direct methods like Lyapunov(started in 60 s) and automa4c learning ones. A]rac4ons were : ü Capability of restric4ng T- D simula4ons solely to the during- fault period and providing sound stability margins. The basic procedure of Lyapunov s direct method is to generate a scalar energy- like func4on(v- func4on) for the dynamic system and examine its 4me varia4on. Principle under preassigned stability condi4ons(i.e., a preassigned disturbance and its clearing scenario) assess whether the system entering its post- fault configura4on is stable. Upon construc4ng a Lyapunov func4on for a post- fault system, the value of V(x(t e )) is computed where x is computed for during- fault trajectory and the system is stable if it is smaller than V L =V(x u ); unstable otherwise. x(t e )- values taken by the components of system state vector at t e x u - the value that the components of the system state vector take at a point located on the boundary of stability domain
ObjecAves: Transient stability problem in the realm of power system security, its opera4ng modes, applica4on context and corresponding needs is defined. Transient stability phenomena and modeling is elaborated. Strengths and weaknesses of the conven4onal 4me- domain approach is discussed. conven4onal direct approaches and their applica4ons are reviewed.
Chapter 2: IntroducAon to SIME Single Machine Equivalent first aimed to combine the advantage of T- D and direct methods. It belongs to the general class of transient stability methods which rely on a one- machine infinite(omib) bus equivalent. OMIB may be viewed as a transforma4on of the mul4dimensional mul4- machine dynamic equa4ons into a single dynamic equa4on. SIME is a transient stability method based on a generalized OMIB. The SIME coupled with T- D approach is named as Preven4ve SIME, which operates in preven4ve mode(prior to disturbance) while the emergency SIME aims at controlling the power system acer a disturbance.
Principle of SIME SIME relies on two Proposi4ons. ProposiAon 1: the mechanism of loss of synchronism in a power system originates from the irrevocable separa4on of its machines into two groups: one composed of the cri4cal machines (CMs), which are responsible of the loss of synchronism, the other of the noncri4cal machines (NMs). ProposiAon 2:SIME may be viewed as a means of compressing mul4- machine data to extract informa4on about transient stability margins and cri0cal machines.