Transient stability analysis of power systems using Liapunov's second method - Lugtu, Renato (1971)
This study is concerned with the application of Liapunov's Theorems to the stability analysis of power systems in the transient state. The method makes use of scalar functions, called Liapunov functions, which are derived from the system equations. A Liapunov function if defined to be one that is positive definite and whose time derivative is negative semi-definite in some region enclosing a critical point of the system. From the properties of such functions , knowledge of the stability characteristics of the system can be obtained. In this study the index of stability used is the critical switching time of faults within the system. The critical switching time is the longest time that a fault can be maintained for the machines in the system not to lose synchronism when the fault is eventually cleared. Through the use of Liapunov's theorems the critical switching time for a particular fault can be automatically determined. This is done by describing a region of stability surrounding a particular equilibrium point by use of a specific Liapunov function. The time it takes for the system trajectory to reach the boundary of such a region from its initial state can therefore be used as an estimate of the critical clearing time of faults. Such an estimate is conservative since the conditions imposed by Liapunov's theorems are sufficient but not necessary for stability. This implies that the region of stability described by using a Liapunov function does not necessarily contain all the system trajectories that are stable. The ability, therefore, of a particular function to define this stability region affects the closeness of the critical clearing time estimate to its actual value. The purpose of this work is to determine new Liapunov functions which include as many stable states as possible for a system with damping and appreciable transfer conductances. The functions and method developed are applied to the actual Philippine electrical system consisting of the combined network of the Manila Electric Company and the National Power Corporation. The results of the study and the computer programs used are given. The results indicate a general validity of the method.
Thesis (Ph.D. Engineering)--Iowa State University.
Keywords: Electric power system stability; Lyapunov stability; Liapunov stability