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Safe Control of Grid-Interfacing Inverters with Current Magnitude Limits

Trager Joswig-Jones, Baosen Zhang

TL;DR

This work addresses enforcing current magnitude limits on grid-interfacing inverters while preserving nominal voltage-source control. It introduces a safety-filter framework built on a control barrier function to bound current, and provides a closed-form solution for the scalar control input, enabling real-time implementation. The authors prove the existence of a safe linear controller under the inverter-RL model and demonstrate that the safety filter can maintain safety without substantially sacrificing performance, as shown by simulations across boundary and randomized scenarios. The approach offers a practically implementable, safety-critical method for improving grid stability with inverter-based resources.

Abstract

Grid-interfacing inverters allow renewable resources to be connected to the electric grid and offer fast and programmable control responses. However, inverters are subject to significant physical constraints. One such constraint is a current magnitude limit required to protect semiconductor devices. While many current limiting methods are available, they can often unpredictably alter the behavior of the inverter control during overcurrent events leading to instability or poor performance. In this paper, we present a safety filter approach to limit the current magnitude of inverters controlled as voltage sources. The safety filter problem is formulated with a control barrier function constraint that encodes the current magnitude limit. To ensure feasibility of the problem, we prove the existence of a safe linear controller for a specified reference. This approach allows for the desired voltage source behavior to be minimally altered while safely limiting the current output.

Safe Control of Grid-Interfacing Inverters with Current Magnitude Limits

TL;DR

This work addresses enforcing current magnitude limits on grid-interfacing inverters while preserving nominal voltage-source control. It introduces a safety-filter framework built on a control barrier function to bound current, and provides a closed-form solution for the scalar control input, enabling real-time implementation. The authors prove the existence of a safe linear controller under the inverter-RL model and demonstrate that the safety filter can maintain safety without substantially sacrificing performance, as shown by simulations across boundary and randomized scenarios. The approach offers a practically implementable, safety-critical method for improving grid stability with inverter-based resources.

Abstract

Grid-interfacing inverters allow renewable resources to be connected to the electric grid and offer fast and programmable control responses. However, inverters are subject to significant physical constraints. One such constraint is a current magnitude limit required to protect semiconductor devices. While many current limiting methods are available, they can often unpredictably alter the behavior of the inverter control during overcurrent events leading to instability or poor performance. In this paper, we present a safety filter approach to limit the current magnitude of inverters controlled as voltage sources. The safety filter problem is formulated with a control barrier function constraint that encodes the current magnitude limit. To ensure feasibility of the problem, we prove the existence of a safe linear controller for a specified reference. This approach allows for the desired voltage source behavior to be minimally altered while safely limiting the current output.
Paper Structure (15 sections, 4 theorems, 29 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 15 sections, 4 theorems, 29 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Control Objective
  3. Inverter Model
  4. Safety and Stability
  5. Current Limiting Safety Filter
  6. Safety Filter Formulation
  7. Safety Filter Feasibility
  8. Proof of Theorem \ref{['thm:main']}
  9. Proof of Lemma 1
  10. Proof of Lemma 2
  11. Simulation Results
  12. Initial conditions at boundary tests
  13. Sampled initial conditions and reference tests
  14. Small-angle assumption
  15. Conclusions

Key Result

Theorem 1

Given the linear system in eqn:linear-system and assume that the setpoints $x^*$ and $u^*$ are feasible. Consider the magnitude barrier function $h(x) = \left| I \right|_\mathrm{max}^2 - \|x\|_2^2$. If $A + A^\top \prec 0$, and $A^{-1} B \ne 0$, then a safe and stable control actions always exists s

Figures (6)

  • Figure 1: Simplified inverter system model under study.
  • Figure 2: $I_\mathrm{dq}$ trajectories for CBF, LQR, and $K_\mathrm{safe}$ controllers with $x_0 = (-1.55~\unit{\ampere}, -4.76~\unit{\ampere}), x^* = (3.56~\unit{\ampere},3.51~\unit{\ampere})$. The LQR control is seen to exceed the safety bound, the safe $K$ control has costly performance, and the CBF control performs well and remains safe.
  • Figure 3: $\delta$ input values for CBF, LQR, and $K_\mathrm{safe}$ controllers with $x_0 = (-1.55~\unit{\ampere}, -4.76~\unit{\ampere}), x^* = (3.56~\unit{\ampere},3.51~\unit{\ampere})$.
  • Figure 4: Costs of CBF, LQR, and $K_\mathrm{safe}$ controllers for 1,000 randomly sampled $x_0$ and $x^*$ values.
  • Figure 5: $I_\mathrm{dq}$ trajectories for for the linear and nonlinear systems with CBF control and $x_0 = (-1.55~\unit{\ampere}, -4.76~\unit{\ampere}), x^* = (3.42~\unit{\ampere},3.64~\unit{\ampere})$. The linear and nonlinear systems have a similar trajectories.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Theorem 1
  • Lemma 1: Conditions for a safe & stable system
  • Lemma 2: Existence of a safe & stable $K$
  • proof : Proof of Lemma \ref{['lemma:safety']}
  • Lemma 3
  • proof
  • proof : Proof of Lemma \ref{['lemma:existance']}