Convexity and Optimal Online Control of Grid-Interfacing Converters with Current Limits

TL;DR

This paper introduces a convex optimal control framework for grid-interfacing converters with current limits, ensuring stability and optimality in real-time without complex tuning.

Contribution

It proves the convexity of the feasible output region and develops a projected gradient descent controller with convergence guarantees for converters.

Findings

Controller ensures stable operation under current limits.

Simulation confirms real-time optimality and stability.

Applicable to single and multi-converter systems.

Abstract

Converter-based generators and loads are growing in prevalence on power grids across the globe. The rise of these resources necessitates controllers that handle the power electronic devices' strict current limits without jeopardizing stability or overly constraining behavior. Existing controllers often employ complex, cascaded control loop architecture to saturate currents, but these controllers are challenging to tune properly and can destabilize following large disturbances. In this paper, we extend previous analysis to prove the feasible output region of a grid-connected converter is convex regardless of filter topology. We then formulate a convex optimal control problem from which we derive a projected gradient descent-based controller with convergence guarantees. This approach drives the converter toward optimality in real-time and differs from conventional control strategies that regulate converter outputs around predefined references regardless of surrounding grid conditions. Simulation results demonstrate safe and stabilizing behavior of the proposed controller, in both the single-converter-infinite-bus systems and multi-converter networks.