Convex Restriction of Power Flow Feasibility Sets

The convex restriction of power flow feasibility sets identifies the convex subset of power injections where a solution for power flow equations 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 under variations in power generation and demand. In this article, we present a general framework to construct convex restrictions of an algebraic set defined by equality and inequality constraints and apply this framework to the power flow feasibility problem. The procedure results in convex quadratic constraints that provide a sufficiently large region for practical operation of the grid.