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Constraint-Aware Grid-Forming Control for Current Limiting

Dominic Groß

TL;DR

This paper introduces constraint-aware grid-forming control that explicitly accounts for current and modulation limits by projecting unconstrained GFM voltage references onto a feasible voltage set. It constructs the feasible set from modulation and current-limit models, then implements an efficient Cartesian-projection using an ADMM solver to enforce these constraints within the GFM droop framework. The proposed approach yields fast current limiting, improved transient stability, and infinite critical clearing time, demonstrated through simulations and hardware experiments across symmetric faults, phase jumps, and multi-converter interactions. Importantly, it provides a tunable, grid-parameter-agnostic mechanism that preserves GFM features without relying on inner control loops, offering a practical path for grid-code compliance and robust fault ride-through.

Abstract

This work develops a constraint-aware grid-forming (GFM) control that explicitly accounts for current limits and modulation limits within the GFM oscillator dynamics generating the GFM voltage reference (i.e., phase angle and magnitude). Broadly speaking, the voltage reference generated by the constraint-aware GFM control minimizes the deviation from conventional unconstrained GFM droop control, while respecting current and modulation limits. The resulting GFM control achieves fast current limiting while preserving transient stability, e.g., exhibiting infinite critical clearing time. To develop the control, we first characterize and analyze the set of converter voltages that do not result in constraint violations. Next, an efficient algorithm for projecting voltages onto the feasible set is developed. Subsequently, these results are used to restrict the dynamics of GFM droop control to the set of feasible voltages. Finally, detailed simulation studies and hardware experiments are used to illustrate and validate the response to short-circuit faults and phase jumps.

Constraint-Aware Grid-Forming Control for Current Limiting

TL;DR

This paper introduces constraint-aware grid-forming control that explicitly accounts for current and modulation limits by projecting unconstrained GFM voltage references onto a feasible voltage set. It constructs the feasible set from modulation and current-limit models, then implements an efficient Cartesian-projection using an ADMM solver to enforce these constraints within the GFM droop framework. The proposed approach yields fast current limiting, improved transient stability, and infinite critical clearing time, demonstrated through simulations and hardware experiments across symmetric faults, phase jumps, and multi-converter interactions. Importantly, it provides a tunable, grid-parameter-agnostic mechanism that preserves GFM features without relying on inner control loops, offering a practical path for grid-code compliance and robust fault ride-through.

Abstract

This work develops a constraint-aware grid-forming (GFM) control that explicitly accounts for current limits and modulation limits within the GFM oscillator dynamics generating the GFM voltage reference (i.e., phase angle and magnitude). Broadly speaking, the voltage reference generated by the constraint-aware GFM control minimizes the deviation from conventional unconstrained GFM droop control, while respecting current and modulation limits. The resulting GFM control achieves fast current limiting while preserving transient stability, e.g., exhibiting infinite critical clearing time. To develop the control, we first characterize and analyze the set of converter voltages that do not result in constraint violations. Next, an efficient algorithm for projecting voltages onto the feasible set is developed. Subsequently, these results are used to restrict the dynamics of GFM droop control to the set of feasible voltages. Finally, detailed simulation studies and hardware experiments are used to illustrate and validate the response to short-circuit faults and phase jumps.

Paper Structure

This paper contains 36 sections, 1 theorem, 24 equations, 24 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Converter Model and Control Objectives
  3. Voltage Source Converter Model
  4. Voltage Source Converter Constraints
  5. Control Objectives and Architecture
  6. Review of optimal virtual impedance current limiting
  7. The Set of Feasible Converter Voltages
  8. Modulation Limits
  9. Current Limits
  10. Constraints Beyond Modulation and Current Limits
  11. The Set of Feasible GFM Voltages
  12. Projection onto the Feasible Set
  13. Polar Coordinates
  14. Cartesian Coordinates
  15. Efficient Projection in Cartesian Coordinates
  16. ...and 21 more sections

Key Result

Proposition 1

Assume that $\| i^{\alpha\beta}_\textup{f}(t_k) \| \leq i_{\max}$ and $v^{\alpha\beta}_\textup{f}(t_k) + v^{\alpha\beta}_\textup{ad}(t_k) \in \mathcal{C}^{\alpha\beta}_\textup{mod}(t_k)$. Then, $\mathcal{C}^{\alpha\beta}(t_k)$ is non-empty.

Figures (24)

  • Figure 1: Voltage source converter model and broad categorization of current limiting controls for GFM converters.
  • Figure 2: Constraint-aware GFM control.
  • Figure 3: The set of feasible voltages during a symmetric short-circuit fault.
  • Figure 4: Set of feasible voltages during a short-circuit fault: reference voltage provided by GFM droop control ($\mathord{\text{✚}}$) and its projection onto the set of feasible voltages ($\mathord{\text{✖}}$).
  • Figure 5: Set of feasible voltages during a short-circuit fault: reference voltage $\hat{v}$ provided by GFM droop control ($\mathord{\text{✚}}$) in dq-frame with angle $\hat{\theta}$ and its projection onto the set of feasible voltages ($\mathord{\text{✖}}$).
  • ...and 19 more figures

Theorems & Definitions (4)

  • Remark 1: Robustness and inductor nonlinearities
  • Proposition 1: Non-empty feasible set
  • proof
  • Remark 2: Low switching and sampling frequencies