Direct stability analysis of electric power systems using energy functions: Theory, applications, and perspective

Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances. Important conclusions and decisions are made based on the results of stability studies. The conventional method of analyzing stability is to calculate the transient behavior of generators due to a given disturbance. By examining the behavior of generators, one determines whether stability has been maintained or lost. In contrast, direct methods of stability analysis identifi whether or not the system will remain stable once the disturbance is removed by comparing it with a calculated threshold value. Direct methods not only avoid the time-consuming solutions required in the conventional method, but also provide a quantitative measure of the degree of system stability. This additional information makes direct methods very attractive when the relative stability of different plans must be compared or when stability limits must be calculated quickly. This paper presents a theoretical foundation of direct methods for both network-reduction and network-preserving power system models. In addition to an overview, new results are offered. A systematic procedure of constructing energy functions for both network-reduction and network-preserving power system models is proposed. An advanced method, called the BCU method, of computing the controlling unstable equilibrium point is presented along with its theoretical foundation. Numerical solution algo-rithms capable of supporting on-line applications of direct methods are provided. Practical demonstrations of using direct methods and the BCU method for on-line transient stability assessments on two power systems are described. Further possible improvements, en-hancements and other applications of direct methods are outlined. I