An Approximate Analysis of the Transient Stability of One- or Two-Machine Systems

Abstract

In this paper, first, we correct Hano's approximate analysis of power system stability in which he has neglected to consider the initial angular displacement and velocity of machines when he solved his approximate differential equation of angular motion of one or two machines in power systems. Next we propose better procedures, based on approximating the trigonometric function in the original nonlinear differential equation of angular motion of the machines by more appropriate triangles than Hano's, or by trapezoids. Then developing these approximate procedure, we derive a sort of stability criterion of one- or two- machine systems, the simple formulae for the critical switching time and so on, when the circuit breakers are reclosed or not reclosed after the fault has been cleared. At last, comparing the calculated results of some transient stability problems by the approximate procedures with those by the conventional step-by-step method, we ascertain that the approximate analysis of system stability, especially the trapzoid-approximation is a good approximate analysis of system stability.