Amirhossein Iraniparast

arXiv2026

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

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.

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arXiv2025

Networked dynamics with application to frequency stability of grid-forming power-limiting droop control

In this paper, we study a constrained network flow problem and associated networked dynamics that resemble but are distinct from the well-known primal-dual dynamics of the constrained flow problem. Crucially, under a change of coordinates, the networked dynamics coincide with primal-dual dynamics associated with the constrained flow problem in edge coordinates. Next, we show that, under mild feasibility assumptions, the networked dynamics are globally asymptotically stable with respect to the set of optimizers of its associated constrained flow problem in nodal coordinates. Subsequently, we apply our stability results to establish frequency stability of power-limiting grid-forming droop control. Compared to conventional grid-forming droop control, power-limiting droop control explicitly accounts for active power limits of the generation (e.g., renewables) interfaced by the converter. While power-limiting droop control has been demonstrated to work well in simulation and experiment, analytical results are not readily available. Moreover, we (i) show that the converter frequencies synchronize to a common synchronous frequency for each grid-forming converter, (ii) characterize the synchronous frequency in the case of converters operating at their power limit, and (iii) establish that power-limiting droop control exhibits power-sharing properties similar to conventional unconstrained droop control. Finally, the analytical results are illustrated using an Electromagnetic transient (EMT) simulation.

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