Optimal Control of Grid-Interfacing Inverters With Current Magnitude Limits

TL;DR

The paper tackles current-magnitude saturation in grid-interfacing inverters by deriving a Lyapunov-based SDP (LMI) stability condition for saturated linear controllers. It then leverages offline model predictive control to generate data and fit a static gain $K$ that preserves stability while achieving performance close to MPC. Simulation results show the MPC-derived $K$ can outperform a baseline LQR on average and avoid saturation-induced stagnation, offering a practical, robust route to exploit fast inverter dynamics under current limits. The approach is validated on both simplified and full-order inverter–LCL models, with robust design insights for uncertain grid parameters and clear directions for future work on disturbances and objective variation.

Abstract

Grid-interfacing inverters act as the interface between renewable resources and the electric grid, and have the potential to offer fast and programmable controls compared to synchronous generators. With this flexibility there has been significant research efforts into determining the best way to control these inverters. Inverters are limited in their maximum current output in order to protect semiconductor devices, presenting a nonlinear constraint that needs to be accounted for in their control algorithms. Existing approaches either simply saturate a controller that is designed for unconstrained systems, or assume small perturbations and linearize a saturated system. These approaches can lead to stability issues or limiting the control actions to be too conservative. In this paper, we directly focus on a nonlinear system that explicitly accounts for the saturation of the current magnitude. We use a Lyapunov stability approach to determine a stability condition for the system, guaranteeing that a class of controllers would be stabilizing if they satisfy a simple SDP condition. With this condition we fit a linear-feedback controller by sampling the output (offline) model predictive control problems. This learned controller has improved performances with existing designs.

Figures (6)

• Figure 1: Simplified inverter system model under study.
• Figure 2: Illustrative figures showing the impact the shape of the Lyapunov level sets has on asymptotic stability. The saturation function boundary and the Lyapunov level sets are represented as ellipses with solid and dashed lines, respectively.
• Figure 3: $| \Delta I_\mathrm{dq} |$ trajectories for $K, K_\mathrm{fit}$, and MPC controllers with $x_0 = (0.00~\unit{\ampere}, 0.00~\unit{\ampere})$, $x^* = (2.95~\unit{\ampere}, 2.95~\unit{\ampere})$
• Figure 4: $\Delta V, \Delta \delta$ inputs for $K, K_\mathrm{fit}$, and MPC controllers with $x_0 = (0.00~\unit{\ampere}, 0.00~\unit{\ampere})$, $x^* = (2.95~\unit{\ampere}, 2.95~\unit{\ampere})$
• Figure 5: dq currents of the simplified and full-order systems for a step in $(P^*, Q^*)$ from $(0~\unit{\watt}, 0~\unit{\var})$ to $(775~\unit{\watt}, -775~\unit{\var})$

Theorems & Definitions (2)

• Theorem 1
• Theorem 2