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Distributed Coordination of Grid-Forming and Grid-Following Inverters for Optimal Frequency Control in Power Systems

Xiaoyang Wang, Xin Chen

TL;DR

This work tackles frequency regulation in power systems with high inverter penetration by proposing a fully distributed optimal frequency control framework that coordinates grid-forming and grid-following inverters. The core idea is to cast frequency control as a projected primal-dual gradient problem and to intertwine the algorithm with the physical grid dynamics, enabling distributed implementation with only local measurements and neighbor communication; a fully local variant exists when line-thermal constraints are ignored. Theoretical guarantees are provided via Lyapunov analysis showing global asymptotic convergence to the optimal solution of a modified OFC problem, and high-fidelity EMT simulations on the IEEE 39-bus system validate that nominal frequency is restored while respecting inverter capacities and line limits. The results demonstrate scalable, private, and robust coordination for fast secondary frequency control in inverter-dominated grids, with practical impact for modern power systems and DER integration.

Abstract

The large-scale integration of inverter-interfaced renewable energy sources presents significant challenges to maintaining power balance and nominal frequency in modern power systems. This paper studies grid-level coordinated control of grid-forming (GFM) and grid-following (GFL) inverter-based resources (IBRs) for scalable and optimal frequency control. We propose a fully distributed optimal frequency control algorithm based on the projected primal-dual gradient method and by leveraging the structure of the underlying physical system dynamics. The proposed algorithm i) restores the nominal system frequency while minimizing total control cost and enforcing IBR power capacity limits and line thermal constraints, and ii) operates in a distributed manner that only needs local measurements and neighbor-to-neighbor communication. In particular, when the line thermal constraints are disregarded, the proposed algorithm admits a fully local implementation that requires no communication, while still ensuring optimality and satisfying IBR power capacity limits. We establish the global asymptotic convergence of the algorithm using Lyapunov stability analysis. The effectiveness and optimality of the proposed algorithms are validated through high-fidelity, 100% inverter-based electromagnetic transient (EMT) simulations on the IEEE 39-bus system.

Distributed Coordination of Grid-Forming and Grid-Following Inverters for Optimal Frequency Control in Power Systems

TL;DR

This work tackles frequency regulation in power systems with high inverter penetration by proposing a fully distributed optimal frequency control framework that coordinates grid-forming and grid-following inverters. The core idea is to cast frequency control as a projected primal-dual gradient problem and to intertwine the algorithm with the physical grid dynamics, enabling distributed implementation with only local measurements and neighbor communication; a fully local variant exists when line-thermal constraints are ignored. Theoretical guarantees are provided via Lyapunov analysis showing global asymptotic convergence to the optimal solution of a modified OFC problem, and high-fidelity EMT simulations on the IEEE 39-bus system validate that nominal frequency is restored while respecting inverter capacities and line limits. The results demonstrate scalable, private, and robust coordination for fast secondary frequency control in inverter-dominated grids, with practical impact for modern power systems and DER integration.

Abstract

The large-scale integration of inverter-interfaced renewable energy sources presents significant challenges to maintaining power balance and nominal frequency in modern power systems. This paper studies grid-level coordinated control of grid-forming (GFM) and grid-following (GFL) inverter-based resources (IBRs) for scalable and optimal frequency control. We propose a fully distributed optimal frequency control algorithm based on the projected primal-dual gradient method and by leveraging the structure of the underlying physical system dynamics. The proposed algorithm i) restores the nominal system frequency while minimizing total control cost and enforcing IBR power capacity limits and line thermal constraints, and ii) operates in a distributed manner that only needs local measurements and neighbor-to-neighbor communication. In particular, when the line thermal constraints are disregarded, the proposed algorithm admits a fully local implementation that requires no communication, while still ensuring optimality and satisfying IBR power capacity limits. We establish the global asymptotic convergence of the algorithm using Lyapunov stability analysis. The effectiveness and optimality of the proposed algorithms are validated through high-fidelity, 100% inverter-based electromagnetic transient (EMT) simulations on the IEEE 39-bus system.

Paper Structure

This paper contains 25 sections, 9 theorems, 50 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Dynamic Models and Problem Formulation
  3. Dynamic Models of Inverters and Power Network
  4. Grid-Forming Inverters
  5. Grid-Following Inverters
  6. Optimal Frequency Control (OFC) Problem
  7. Distributed Control Algorithm Design
  8. Modified OFC Problem
  9. Projected Primal-Dual Gradient Dynamics Method
  10. Distributed Optimal IBR Control Algorithm
  11. Fully Local Optimal IBR Control Algorithm
  12. Theoretical Convergence Analysis
  13. General Optimization Problem Formulation
  14. Dynamics Algorithm and Key Stability Result
  15. Proof of Theorem \ref{['theorem:general dynamic']}
  16. ...and 10 more sections

Key Result

Lemma 1

Suppose $(\bm{\omega}^*, {\bm{P}_\mathrm{M}^{\mathrm{r}*}}, {\bm{P}_\mathrm{L}^{\mathrm{r}*}},\bm{P}^*,\bm{\psi}^*)$ is an optimal solution to problem eq:ofc2. Then, $\bm{\omega}^*=\bm{0}$, and $( {\bm{P}_\mathrm{M}^{\mathrm{r}*}}, {\bm{P}_\mathrm{L}^{\mathrm{r}*}},\bm{\theta}^* \!=\! \bm{\psi}^*-

Figures (9)

  • Figure 1: The fully distributed IBR control algorithm (Algorithm \ref{['alg:distributed_optimal_control']}).
  • Figure 2: The fully local IBRs control algorithm.
  • Figure 3: A modified IEEE 39-bus system with 10 IBRs.
  • Figure 4: Frequency dynamics at IBRs terminal buses under step power change.
  • Figure 5: IBRs power setpoint adjustments with OFC.
  • ...and 4 more figures

Theorems & Definitions (12)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Theorem 1
  • Proposition 1
  • Theorem 2
  • Proposition 2
  • Proposition 3
  • Lemma 2
  • ...and 2 more