Equilibria analysis of power systems using a numerical homotopy method

In this paper, we present a homotopy based numerical continuation algorithm to efficiently compute all feasible equilibria of a complex power system model. The dynamic characteristics of conventional power systems are undergoing a sea change due to the impact of large-scale integration of renewables, storage elements, new type of loads etc. Several parameters of these components affect the power system operation leading to multiple feasible equilibria which may be intractable by the traditional load flow techniques. In contrast, our algorithm finds all the feasible solutions over a certain parameter space. We illustrate the results through the simulation of a 5-machine power system model with wind, storage elements, and dynamic loads. We observed that the wind velocity and the reference to the wind bus voltage strongly affect the number and the stability of the system equilibria. Knowledge of these equilibria can benefit small-signal stability assessment and system level planning.