Exploring the impact of wind penetration on power system equilibrium using a numerical continuation approach

In this paper we investigate how the equilibrium characteristics of conventional power systems may change with an increase in wind penetration. We first derive a differentialalgebraic model of a power system network consisting of synchronous generators, loads and a wind power plant modeled by wind turbines and doubly-fed induction generators (DFIG). The models of these three components are coupled via nonlinear power flow equations. In contrast to the traditional approach for solving the power flows via iterative methods that often lead to a local solution, we apply a recently developed parameterhomotopy based numerical continuation algorithm to compute all possible solutions. The method obtains all the solutions of the power flow equations over multiple values of the wind penetration. We observe that depending on the penetration limit and the setpoint value for the magnitude of the wind bus voltage, the system may exhibit several undesired or even unstable equilibria. We illustrate these results through a detailed simulation of a 5-machine power system model with wind injection, and highlight how the solutions may be helpful for small-signal stability assessment.