Computing Critical $k$-tuples in Power Networks

TL;DR

This paper addresses finding the sparsest critical measurement sets in power networks, proposing an efficient approximate method using Min-Cut and an exact formulation via MILP, to identify weak points and optimize meter placement.

Contribution

It introduces a novel approach combining Min-Cut approximation and MILP formulation for the critical k-tuple problem in power networks, improving efficiency and accuracy.

Findings

The Min-Cut method provides a fast approximation with high accuracy.

The MILP formulation yields exact solutions using standard solvers.

Numerical results demonstrate the effectiveness of the proposed methods.

Abstract

In this paper the problem of finding the sparsest (i.e., minimum cardinality) critical $k$-tuple including one arbitrarily specified measurement is considered. The solution to this problem can be used to identify weak points in the measurement set, or aid the placement of new meters. The critical $k$-tuple problem is a combinatorial generalization of the critical measurement calculation problem. Using topological network observability results, this paper proposes an efficient and accurate approximate solution procedure for the considered problem based on solving a minimum-cut (Min-Cut) problem and enumerating all its optimal solutions. It is also shown that the sparsest critical $k$-tuple problem can be formulated as a mixed integer linear programming (MILP) problem. This MILP problem can be solved exactly using available solvers such as CPLEX and Gurobi. A detailed numerical study is presented to evaluate the efficiency and the accuracy of the proposed Min-Cut and MILP calculations.