Optimal Power Flow with Inelastic Demands for Demand Response in Radial Distribution Networks

TL;DR

This paper addresses the complex problem of optimal power flow with inelastic demands in radial distribution networks, highlighting its computational hardness and proposing an efficient approximation algorithm with practical effectiveness.

Contribution

It demonstrates the inapproximability of the problem in general networks and introduces a novel approximation algorithm for radial networks with proven performance bounds.

Findings

The problem is inapproximable in general networks with voltage bounds.

An efficient approximation algorithm is proposed for radial networks.

Simulations show the algorithm yields near-optimal solutions.

Abstract

The classical optimal power flow problem optimizes the power flow in a power network considering the associated flow and operating constraints. In this paper, we investigate optimal power flow in the context of utility-maximizing demand response management in distribution networks, in which customers' demands are satisfied subject to the operating constraints of voltage and transmission power capacity. The prior results concern only elastic demands that can be partially satisfied, whereas power demands in practice can be inelastic with binary control decisions, which gives rise to a mixed integer programming problem. We shed light on the hardness and approximability by polynomial-time algorithms for optimal power flow problem with inelastic demands. We show that this problem is inapproximable for general power network topology with upper and lower bounds of nodal voltage. Then, we propose an efficient algorithm for a relaxed problem in radial networks with bounded transmission power loss and upper bound of nodal voltage. We derive an approximation ratio between the proposed algorithm and the exact optimal solution. Simulations show that the proposed algorithm can produce close-to-optimal solutions in practice.