A Branch-Decomposition Approach to Power Network Design

TL;DR

This paper introduces an exact, polynomial-time method for power network design problems using branch-decomposition and dynamic programming, effective especially for planar graphs with small branch-width.

Contribution

It presents a novel approach combining branch-decomposition and dynamic programming to solve power network design problems efficiently and exactly for certain graph classes.

Findings

Method is exact and polynomial for planar graphs with small branch-width.

Planarity and small branch-width are common in practical power networks.

Proposed approach outperforms standard integer programming and heuristics in efficiency.

Abstract

This paper proposes a procedure to solve combinatorial power network design problems such as phasor measurement unit (PMU) placement and protection assignment against cyber-physical attacks. The proposed approach tackles the design problems through solving a dominating set problem on the power network graph. A combined branch-decomposition and dynamic programming procedure is applied to solve the dominating set problem. Contrary to standard integer programming and heuristic/evolutionary approaches for power network design, the proposed approach is exact and requires only polynomial computation time if the graph is planar and has small branch-width. A planarization technique is explored for problem instances with nonplanar graphs. A case study in this paper with benchmark power networks verifies that planarity and small branch-width are not uncommon in practice. The case study also indicates that the proposed method shows promise in computation efficiency.