Slow flow solutions and stability analysis of single machine to infinite bus power systems

Nonlinearity is a major constraint in analysing and controlling power systems. The behaviour of the nonlinear systems will vary drastically with changing operating conditions. Hence a detailed study of the response of the power system with nonlinearities is necessary especially at frequencies closer to natural resonant frequencies of machines where the system may jump into the chaos. This paper attempt such a study of a single machine to infinite bus power system by modelling it as a Duffing equation with softening spring. Using the method of multiple scales, an approximate analytical expression which describes the variation of load angle is derived. The phase portraits generated from the slow flow equations, closer to the jump, display two stable equilibria (centers) and an unstable fixed point (saddle). From the analysis, it is observed that even for a combination of parameters for which the system exhibits jump resonance, the system will remain stable if the variation of load angle is within a bounded region.