Discrete Shortest Paths in Optimal Power Flow Feasible Regions

TL;DR

This paper introduces a novel algorithm that computes minimal-control transition paths in the feasible regions of optimal power flow problems by framing it as a shortest path problem in a discretized space, leveraging a specialized interior point method.

Contribution

It formulates the transition path problem as a shortest path in a discretized space and develops an efficient NLP solver tailored for this structure, enabling practical control actions.

Findings

The algorithm effectively computes transition paths in OPF feasible regions.

Numerical experiments demonstrate the method's efficiency and effectiveness.

The approach reduces the number of control actions needed for system transitions.

Abstract

Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or other 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 sparse 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.