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Structural Impact of Grid-Forming Inverters on Power System Coherency

Sayak Mukherjee, Ramij Raja Hossain, Kaustav Chatterjee, Soumya Kundu, Kyung-Bin Kwon, Sameer Nekkalapu, Marcelo Elizondo

TL;DR

This work addresses how grid-forming inverters (GFMs) replacing traditional synchronous generators affect slow coherency and inter-area oscillations in future power systems. It develops a structure-preserving small-signal model that combines SG swing dynamics with GFM P–ω and Q–V droop control, yielding a Kron-reduced, inertia-weighted Laplacian representation for mixed inverter–generator grids. The key contributions include proving that the Laplacian structure is preserved (the all-ones vector lies in the nullspace of the Laplacian), showing that substantial GFM replacement perturbs the slow eigenspace and can shift coherent boundaries, and validating these insights on the IEEE 68-bus test system with scenarios that demonstrate changes in inter-area modes. The findings provide a theoretical and numerical framework for dynamic equivalencing, damping control design, and planning in inverter-dominated grids, informing how to anticipate and mitigate low-frequency oscillations in future power networks.

Abstract

This paper addresses the following fundamental research question: how does the integration of grid-forming inverters (GFMs) replacing conventional synchronous generators (SGs) impact the slow coherent eigen-structure and the low-frequency oscillatory behavior of future power systems? Due to time-scale separated dynamics, 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. Our mathematical analysis shows that due to the large-scale integration of GFMs, the weighted Laplacian structure of the frequency dynamics is preserved, however, the entries of the Laplacian may be significantly modified based on the location and penetration levels of the GFMs. This can impact and potentially significantly alter the coherency structure of the system. We have validated our findings with numerical results using the IEEE 68-bus test system.

Structural Impact of Grid-Forming Inverters on Power System Coherency

TL;DR

This work addresses how grid-forming inverters (GFMs) replacing traditional synchronous generators affect slow coherency and inter-area oscillations in future power systems. It develops a structure-preserving small-signal model that combines SG swing dynamics with GFM P–ω and Q–V droop control, yielding a Kron-reduced, inertia-weighted Laplacian representation for mixed inverter–generator grids. The key contributions include proving that the Laplacian structure is preserved (the all-ones vector lies in the nullspace of the Laplacian), showing that substantial GFM replacement perturbs the slow eigenspace and can shift coherent boundaries, and validating these insights on the IEEE 68-bus test system with scenarios that demonstrate changes in inter-area modes. The findings provide a theoretical and numerical framework for dynamic equivalencing, damping control design, and planning in inverter-dominated grids, informing how to anticipate and mitigate low-frequency oscillations in future power networks.

Abstract

This paper addresses the following fundamental research question: how does the integration of grid-forming inverters (GFMs) replacing conventional synchronous generators (SGs) impact the slow coherent eigen-structure and the low-frequency oscillatory behavior of future power systems? Due to time-scale separated dynamics, 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. Our mathematical analysis shows that due to the large-scale integration of GFMs, the weighted Laplacian structure of the frequency dynamics is preserved, however, the entries of the Laplacian may be significantly modified based on the location and penetration levels of the GFMs. This can impact and potentially significantly alter the coherency structure of the system. We have validated our findings with numerical results using the IEEE 68-bus test system.
Paper Structure (7 sections, 17 equations, 4 figures, 5 tables)

This paper contains 7 sections, 17 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. System Model: GFM Integration Replacing Synchronous Resources
  3. Main Results: Impacts of GFMs on System Laplacian and Slow Coherency
  4. Structure-preserving Laplacian Sub-Matrix
  5. Perturbation in Coherent Boundaries
  6. Case Studies and Numerical Validations
  7. Conclusions

Figures (4)

  • Figure 1: GFM dynamics based on droop controls.
  • Figure 3: Coherent inter-area boundary between areas 1 and 2 for the base case.
  • Figure 4: Generator modeshapes of the dominant inter-area mode for different test scenarios: $(a)$ Base case, $(b)$ Scenario 1, and $(c)$ Scenario 2.
  • Figure 5: Coherent inter-area boundary between Areas 1 and 2 for Scenarios 1 and 2.