# Modeling and Quantifying the Impact of Wind Power Penetration on Power System Coherency

## TL;DR

This paper analyzes how wind power integration affects power system coherency by altering the spectral properties of the system's Laplacian matrix, with a theoretical framework validated through simulations and measurement analysis.

## Contribution

It introduces a novel theoretical framework to quantify the impact of wind penetration on power system coherency and validates it with numerical and measurement-based methods.

## Key findings

- Wind penetration modifies the Laplacian matrix and affects generator coherency.
- The model predicts changes in coherent areas due to wind farm placement and level.
- Simulation results confirm the theoretical predictions.

## Abstract

This paper presents a mathematical analysis of how wind generation impacts the coherency property of power systems. Coherency arises from time-scale separation in the dynamics of synchronous generators, where generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time-scale due to weaker coupling. This time-scale separation is reflected in the form of a spectral separation in the weighted Laplacian matrix describing the swing dynamics of the generators. However, when wind farms with doubly-fed induction generators (DFIG) are integrated in the system then this Laplacian matrix changes based on both the level of wind penetration and the location of the wind farms. The modified Laplacian changes the effective slow eigenspace of the generators. Depending on penetration level, this change may result in changing the identities of the coherent areas. We develop a theoretical framework to quantify this modification, and validate our results with numerical simulations of the IEEE 68-bus system with one and multiple wind farms. We compare our model based results on clustering with results using measurement-based principal component analysis to substantiate our derivations.