Rate Dependent Transitions in Power Systems

Bifurcations are the sudden qualitative transitions occurring in dynamical systems due to infinitesimal changes in the control parameters. These abrupt qualitative transitions are crucial in deciding the stable operating regime in the case of a power system. However, in the actual power system, the control parameters such as the electrical power demand, the inertia of the system, damping of the system etc. are found to vary with respect to time. In this paper, bifurcations in an electrical power system for the quasi-static and rate dependent variation of the control parameters are investigated. The canonical power system is represented by assuming a single machine connected to an infinite bus (SMIB). The mathematical modeling of the canonical system is carried out by a second order swing equation model of the generator. We observe a delay in the point of transition for rate-dependent variation of the control parameter, mechanical power, P_m. We also investigate the influence of noise and sensitivity to initial conditions in rate-dependent variations of the control parameter. Our study is highly relevant as the stability regimes for the quasi-static and rate dependent variations of control parameters are different.