Complexity and inapproximability results for the Power Edge Set problem

Abstract

We consider the single channel PMU placement problem called the Power Edge Set (PES) problem. In this variant of the PMU placement problem, (single channel) PMUs are placed on the edges of an electrical network. Such a PMU measures the current along the edge on which it is placed and the voltage at its two endpoints. The objective is to nd the minimum placement of PMUs in the network that ensures its full observability, namely measurement of all the voltages and currents. We prove that PES is NP-hard to approximate within a factor (1.12)-, for any > 0. On the positive side we prove that PES problem is solvable in polynomial time for trees and grids.Keywords PMU placement problem · Power Edge Set · NP-hardness · inapproximability This work was carried out as part of the SOGRID project (www.so-grid.com), co-funded by the French agency for Environment and Energy Management (ADEME) and developed in collaboration between participating academic and industrial partners.