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

Sayak Mukherjee, Aranya Chakrabortty, Saman Babaei

TL;DR

The paper develops a singular-perturbation framework to quantify how wind penetration and placement—via DFIG-based wind farms—perturbs power-system coherency. By deriving an equivalent Laplacian $\mathcal{L}_{eq}$ from the wind-integrated linearized model, it captures changes to the slow eigenspace that define inter-area coherency, and shows wind can reconfigure coherent groups depending on location and magnitude. The authors validate the theory on the IEEE 68-bus benchmark using both model-based clustering (via $M^{-1}\mathcal{L}_{eq}$) and data-driven PCA, demonstrating alignment and also highlighting cases where coherency is reorganized. These results offer practical guidance for wind-plant siting and for retuning wide-area control gains to maintain stable inter-area oscillations under high renewable penetration.

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.

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

TL;DR

The paper develops a singular-perturbation framework to quantify how wind penetration and placement—via DFIG-based wind farms—perturbs power-system coherency. By deriving an equivalent Laplacian from the wind-integrated linearized model, it captures changes to the slow eigenspace that define inter-area coherency, and shows wind can reconfigure coherent groups depending on location and magnitude. The authors validate the theory on the IEEE 68-bus benchmark using both model-based clustering (via ) and data-driven PCA, demonstrating alignment and also highlighting cases where coherency is reorganized. These results offer practical guidance for wind-plant siting and for retuning wide-area control gains to maintain stable inter-area oscillations under high renewable penetration.

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.

Paper Structure

This paper contains 16 sections, 35 equations, 10 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Recapitulation of Coherency
  3. Motivating Example
  4. Quantification of perturbation
  5. Wind farm (WF) model
  6. Linearized wind-integrated model
  7. Quantification of perturbation in $\mathcal{L}$
  8. Extension to multiple wind farms
  9. Perturbation analysis for two time-scale property
  10. Perturbation in $\mathcal{L}_0^I$ and $\mathcal{L}_0^E$
  11. Extraction of the equivalent Laplacian
  12. Simulation Results
  13. Nominal system without wind plant
  14. Single wind plant connected to the grid
  15. Wind plants at buses $32,66$ and $57$
  16. ...and 1 more sections

Figures (10)

  • Figure 1: PCA weightings for scenario A
  • Figure 2: PCA weightings for scenario B
  • Figure 3: Intuition behind change in grouping
  • Figure 4: Row vectors of slow subspace of the nominal system
  • Figure 5: Change in the entries of $\mathcal{L}_{eq}$ vs. $\mathcal{L}_0$ for machine $1$ with wind injection at bus $66$
  • ...and 5 more figures