Catastrophe theory model of multimachine power systems for transient stability studies

A catastrophe theory model of interconnected multimachine power systems is proposed for the study of transient stability problems. The swing equations are put in the form of one of the elementary catastrophes-the swallowtail catastrophe. The manifold of the catastrophe defines the boundary between transient stability and instability in terms of three control variables, which are functions of the parameters and operating conditions of the power system. Thus stability is easily assessed from the system parameters and operating conditions; no solution of the swing equations is required. The catastrophe model is used to check the transient stability of the system by considering that one or more generators are critical. Results are given for the simplified WSCC system of three generators and for the seven-machine CIGRE system. The catastrophe theory results compare favourably with the time-solution results for the systems for the same three-phase short-circuit disturbances.<>