Evaluating Quantum Optimization for Dynamic Self-Reliant Community Detection

TL;DR

This paper explores quantum optimization methods for dynamic community detection in power grids, aiming to improve resilience by identifying self-reliant grid subsets more efficiently than classical approaches.

Contribution

It formulates the community detection problem as a QUBO for quantum solving and benchmarks quantum hybrid, classical heuristics, and exact solvers on power grid cases.

Findings

Hybrid quantum-classical solvers show promising solution quality within time limits.

Quantum annealing hardware underperforms compared to hybrid and classical methods.

The problem exhibits exponential runtime scaling on classical algorithms.

Abstract

Power grid partitioning is an important requirement for resilient distribution grids. Since electricity production is progressively shifted to the distribution side, dynamic identification of self-reliant grid subsets becomes crucial for operation. This problem can be represented as a modification to the well-known NP-hard Community Detection (CD) problem. We formulate it as a Quadratic Unconstrained Binary Optimization (QUBO) problem suitable for solving using quantum computation{\color{blue}, which is expected to find better-quality partitions faster. The formulation aims to find communities with maximal self-sufficiency and minimal power flowing between them}. To assess quantum optimization for sizeable problems, we apply a hierarchical divisive method that solves sub-problem QUBOs to perform grid bisections. Furthermore, we propose a customization of the Louvain heuristic that includes self-reliance. In the evaluation, we first demonstrate that this problem examines exponential runtime scaling classically. Then, using different IEEE power system test cases, we benchmark the solution quality for multiple approaches: D-Wave's hybrid quantum-classical solvers, classical heuristics, and a branch-and-bound solver. As a result, we observe that the hybrid solvers provide very promising results, both with and without the divisive algorithm, regarding solution quality achieved within a given time frame. Directly utilizing D-Wave's Quantum Annealing (QA) hardware shows inferior partitioning.