Cost-Benefit Analysis for PMU Placement in Power Grids

TL;DR

This paper introduces a cost function balancing PMU installation costs and the costs of unobserved grid parts, analyzing optimal sensor placement strategies in power grids using graph theory.

Contribution

It proposes a novel power domination cost function incorporating installation and observance costs, and develops tools to determine optimal PMU placement based on this model.

Findings

Identifies conditions where observing the entire grid minimizes total cost.

Provides bounds on the number of PMUs needed for cost-effective observability.

Introduces marginal cost and marginal observance concepts for strategic sensor placement.

Abstract

Power domination is a graph-theoretic model for the observance of a power grid using phasor measurement units (PMUs). There are many costs associated with the installation of a PMU, but also costs associated with not observing the entire power grid. In this work, we propose and study a power domination cost function, which balances these two costs. Given a graph $G$, a set of sensor locations $S$, and a parameter $\beta$ (which is the ratio of the cost of a PMU to the cost of non-observance of any given vertex), we define the cost function \[ \mathrm{C}(G;S,\beta)=|S|+\beta\cdot (|V(G)|-|\mathrm{Obs}(G;S)|) \] where $|\mathrm{Obs}(G;S)|$ is the number of vertices observed by sensors placed at $S\subseteq V(G)$ in the power domination process. We explore the values of $k$ for which there is a set $S$ of size $k$ that minimizes this cost function, and explore which values of $\beta$ guarantee that it is optimal to observe the entire power grid to minimize cost. We also introduce notions of marginal cost and marginal observance, providing tools to analyze how many PMUs one should install on a given power grid.