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

Abstract

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.