Admissible Control Laws for Constrained Linear Power Flow: The General Case

Abstract

Linearized power flow with line flow and voltage constraints can be modeled as a system of linear inequalities depending on the power injections. When some injections are controlled by the grid operator while others are determined exogenously, robust control aims at determining grid operator's actions under imperfect system observability such that the grid state is feasible for all possible realizations of the exogenous actions. It was shown how to design and analyze such admissible control policies efficiently for the subclass of affine control laws, but this paper shows that there are important cases that require more general control policies. We show that, for the constrained linear power flow setting, general admissible control policies can always be chosen as piecewise affine (PWA) mappings. The PWA mapping can be explicitly characterized offline or control actions can be computed online by solving an optimization problem given a current observation. For the latter setup, we provide an algorithm that verifies offline that the online control scheme is admissible. This verification step is a crucial precondition to apply the online control scheme in real, safety-critical power grids. The proposed framework is demonstrated with applications to voltage regulation in active distribution grids subject to uncertain prosumers and low observability.