Stability and convergence of multi-converter systems using projection-free power-limiting droop control

TL;DR

This paper introduces a novel projection-free power-limiting droop control method for grid-connected power electronics, demonstrating its stability, convergence properties, and practical effectiveness through theoretical analysis and EMT simulations.

Contribution

It presents a new projection-free control approach that ensures exponential stability and provides convergence rate bounds, improving upon traditional projection-based methods.

Findings

Networked dynamics are semi-globally exponentially stable.

Convergence rate bounds are established and can be improved via tuning.

Simulation confirms theoretical stability and convergence results.

Abstract

In this paper, we propose a projection-free power-limiting droop control for grid-connected power electronics and an associated constrained flow problem. In contrast to projection-based power-limiting droop control, the novel projection-free power-limiting droop control results in networked dynamics that are semi-globally exponentially stable with respect to the set of optimizers of the constrained flow problem. Under a change to edge coordinates, the overall networked dynamics arising from projection-free power-limiting droop control coincide with the projection-free primal-dual dynamics associated with an augmented Lagrangian of the constrained flow problem. Leveraging this result, we (i) provide a bound on the convergence rate of the projection-free networked dynamics, (ii) propose a tuning method for controller parameters to improve the bound on the convergence rate, and (iii) analyze the relationship of the bound on the convergence rate and connectivity of the network. Finally, the analytical results are illustrated using an Electromagnetic transient (EMT) simulation.