Impact of wind farm placement on inter-area oscillations in large power systems

This paper presents an analytical method for evaluating how the placement of wind farms in a large, geographically dispersed power system may affect its inter-area oscillation dynamics. We consider a continuum representation of the electro-mechanical swing dynamics for the power system leading to a linear hyperbolic wave equation for the rotor phase angle across the transfer path. The wind power is modeled as the output of a dynamic system entering the wave equation as a point source in space located at a certain electrical distance from one end of the path. We then derive the spectrum of the line power flow for this forced system using a Fourier analysis, and show how its frequency response, especially for the inter-area or low-frequency modes, is parameterized by this distance variable. We finally pose this parametric dependence as a planning problem in light of finding the optimal distance for placing the wind farm such that a specified set of inter-area modes are damped. We illustrate our results using simulations based on a two-area power system model inspired by US west coast transfer paths such as the Pacific AC Inter-tie.