Invertibility Conditions for the Admittance Matrices of Balanced Power Systems

Abstract

Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or operational objectives are optimized. Due to the non-convexity of the set of feasible OPF operating points, it is non-trivial to transition the power system from its current operating point to the optimal one without violating constraints. On top of that, practical considerations dictate that the transition should be achieved using a small number of small-magnitude control actions. To solve this problem, this paper proposes an algorithm for computing a transition path by framing it as a shortest path problem. This problem is formulated in terms of a discretized piece-wise linear path, where the number of pieces is fixed a priori in order to limit the number of control actions. This formulation yields a nonlinear optimization problem (NLP) with a block tridiagonal structure, which we leverage by utilizing a specialized interior point method. An initial feasible path for our method is generated by solving a sequence of relaxations which are then tightened in a homotopy-like procedure. Numerical experiments illustrate the effectiveness of the algorithm.

Primary Frequency Control Provision by Distributed Energy Resources in Active Distribution Networks

“…Under the adopted assumptions on the real and imaginary parts of the series and shunt admittances, the necessary and sufficient condition for the invertibility of Y is the existence of at least one shunt admittance. The assumptions made are reasonable for distribution networks, and we refer the reader to [21,22] for a broader discussion on the invertibility of Y .…”