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Unified Control Scheme for Optimal Allocation of GFM and GFL Inverters in Power Networks

Sushobhan Chatterjee, Sijia Geng

TL;DR

The paper addresses the challenge of coordinating inverter-based resources to ensure stability and favorable transient performance in networks with heterogeneous inverters. It proposes a unified GFM/GFL inverter framework and formulates a non-convex optimization that uses a Lyapunov-based dissipativity objective to determine the optimal P-ω droop gains $\mathbf{K_P}$ for each unified inverter, guaranteeing small-signal stability via $A_{\text{eff}}$ and maximizing energy dissipation during transients. An iterative algorithm decouples equilibrium updates from gain updates, solving a BMI-like Lyapunov constraint and updating the equilibrium until the nonlinear equations are satisfied within a tolerance. Numerical results on a three-bus system show that the optimal $\mathbf{K_P}$ values converge rapidly, and the preferred inverter type (GFM vs GFL) depends on grid strength: GFM is advantageous in weak grids, while GFL is preferable in strong grids. The work provides actionable insight into IBR placement and demonstrates a scalable approach to allocate GFM and GFL resources using a unified control scheme that homogenizes the treatment of diverse inverters.

Abstract

With the rapid adoption of emerging inverter-based resources, it is crucial to understand their dynamic interactions across the network and ensure stability. This paper proposes a systematic and efficient method to determine the optimal allocation of grid-forming and grid-following inverters in power networks. The approach leverages a novel unified grid-forming/following inverter control and formulates an optimization problem to ensure stability and maximal energy dissipation during transient periods. An iterative algorithm is developed to solve the optimization problem. The resulting optimal droop gains for the unified inverters provide insights into the needs for grid-forming and grid-following resources in the network. A three-bus system is used to demonstrate the optimality and dynamic performance of the proposed method.

Unified Control Scheme for Optimal Allocation of GFM and GFL Inverters in Power Networks

TL;DR

The paper addresses the challenge of coordinating inverter-based resources to ensure stability and favorable transient performance in networks with heterogeneous inverters. It proposes a unified GFM/GFL inverter framework and formulates a non-convex optimization that uses a Lyapunov-based dissipativity objective to determine the optimal P-ω droop gains for each unified inverter, guaranteeing small-signal stability via and maximizing energy dissipation during transients. An iterative algorithm decouples equilibrium updates from gain updates, solving a BMI-like Lyapunov constraint and updating the equilibrium until the nonlinear equations are satisfied within a tolerance. Numerical results on a three-bus system show that the optimal values converge rapidly, and the preferred inverter type (GFM vs GFL) depends on grid strength: GFM is advantageous in weak grids, while GFL is preferable in strong grids. The work provides actionable insight into IBR placement and demonstrates a scalable approach to allocate GFM and GFL resources using a unified control scheme that homogenizes the treatment of diverse inverters.

Abstract

With the rapid adoption of emerging inverter-based resources, it is crucial to understand their dynamic interactions across the network and ensure stability. This paper proposes a systematic and efficient method to determine the optimal allocation of grid-forming and grid-following inverters in power networks. The approach leverages a novel unified grid-forming/following inverter control and formulates an optimization problem to ensure stability and maximal energy dissipation during transient periods. An iterative algorithm is developed to solve the optimization problem. The resulting optimal droop gains for the unified inverters provide insights into the needs for grid-forming and grid-following resources in the network. A three-bus system is used to demonstrate the optimality and dynamic performance of the proposed method.

Paper Structure

This paper contains 26 sections, 16 equations, 20 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Network Modeling
  5. Model of the Unified Grid-Forming/Following Inverter
  6. Problem Formulation
  7. Algorithm
  8. Numerical Results
  9. Algorithm Performance
  10. Standard GFM and GFL Models
  11. Grid-Following (GFL) Inverter
  12. Grid-Forming (GFM) Inverter
  13. Evaluation of Dynamic Performance
  14. Case 1: Base impedance network
  15. Case 2: Low-impedance network
  16. ...and 11 more sections

Figures (20)

  • Figure 1: Structure of a network-reduced inverter-based power network.
  • Figure 2: Control blocks of the unified grid-forming/following inverter.
  • Figure 3: Phasor diagram and reference frames of the unified inverter.
  • Figure 4: Schematic of a three-bus power system.
  • Figure 5: Performance of the iterative algorithm (Base impedance).
  • ...and 15 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4