Convex Restriction of Power Flow Feasibility Sets

TL;DR

This paper introduces a convex restriction framework for power flow feasibility sets, providing a guaranteed feasible region for power injections that enhances grid operation under uncertainty.

Contribution

It develops a general method to construct convex restrictions for algebraic sets and applies it to power flow problems, resulting in practical convex quadratic constraints.

Findings

Provides a convex quadratic constraint-based feasible region

Guarantees power flow solution existence within the region

Applicable to uncertain power generation and demand scenarios

Abstract

The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the convex restriction provides a sufficient condition for power flow feasibility and is particularly useful for problems involving uncertainty in the power generation and demand. In this paper, we present a general framework of constructing convex restriction of an algebraic set defined by equality and inequality constraints and apply the framework to power flow feasibility problem. The procedure results in convex quadratic constraints that provide a sufficiently large region for practical operation of the grid.