Synchronous Machine Transient Stability Ayalysis by an Extension to the Point by Point Method of Solution of the Swing Equation

Abstract

Power System transient stability study is a major component of the Power System course offered in many undergraduate programmes in Electrical Engineering " 'hen the transient stability of a power system is analysed, the transient stability of the rotating synchronous machines connected to the system should be analysed individually or in groups. In transient stability analysis, a synchronous machine is described by a set of differential equations. The type and the number of differential equations needed to represent a single machine depend on the complexity of the model used. But in any model, the swing equation (a second order differential equation) which describes the motion of the rotor under transient conditions, is essentially included. Therefore the simplest representation of a synchronous machine is the swing equation of the machine. The solution of the swing equation of a given machine provides basic information to determine the stability of the machine under transient conditions. The swing equation relating the relative motion of the rotor with time could be solved using any method used for the solution of ordinary differential equations. When the calculations are carried out on a digital computer, modified Euler and fourth-order Runga-Kutta methods are commonly used. But the point by point method developed by Dhal in 1938 is mostly used to solve the swing equation in simple cases where hand calculations are involved. When simple transient stability problems are solved in the classroom to illustrate the behaviour of the machine, the point by point method is preferred because of its simplicity. In this paper an important modification to improve this method is discussed.