Exploring the Impact of Wind Penetration on Power System Equilibrium Using a Numerical Continuation Approach

TL;DR

This paper uses a numerical continuation method to analyze how increasing wind power affects power system equilibrium, revealing potential unstable states and aiding stability assessment.

Contribution

It introduces a parameter-homotopy based numerical continuation approach to efficiently compute all power flow solutions across varying wind penetration levels.

Findings

Multiple equilibria can occur at high wind penetration levels.

Unstable equilibria may emerge depending on wind setpoints.

The method improves computational efficiency over traditional iterative solutions.

Abstract

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 differential-algebraic model of a power system network consisting of synchronous generators, loads and a wind power plant modeled by a wind turbine and a doubly-fed induction generator (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 only local solutions, we apply a recently developed parameter-homotopy based numerical continuation algorithm to compute all possible solutions. The method solves the power flow equations over multiple values of the wind penetration level with far less computational effort instead of solving them at each value individually. 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.