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North American Power Symposium (NAPS)

Evaluate Quantum Combinatorial Optimization for Distribution Network Reconfiguration

Anh Phuong Ngo, Christan Thomas, Hieu Trung Nguyen, Abdullah Eroglu, Konstantinos Oikonomou

Published Oct 9, 2022• 2 citations
Publisher

Abstract

This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming formulation for the reconfiguration of radial distribution network in response to faults in distribution lines. Comparing to existing bus injection model in the literature, our formulation based the branch flows model is theoretically equivalent without needing non-explainable variables, thus being more numerically stable. The network reconfiguration model is then used as a benchmark to evaluate the performance of quantum computing algorithms in real quantum computers. It shows that while current quantum computing algorithms with fast execution time in quantum computers can be a promising solution candidate, its heuristic nature stem from its theoretical foundation should be considered carefully when applying into power grid optimization problems.

DOI
10.1109/naps56150.2022.10012259

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This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming formulation for the reconfiguration of radial distribution network in response to faults in distribution lines. Comparing to existing bus injection model in the literature, our formulation based the branch flows model is theoretically equivalent without needing non-explainable variables, thus being more numerically stable. The network reconfiguration model is then used as a benchmark to evaluate the performance of quantum computing algorithms in real quantum computers. It shows that while current quantum computing algorithms with fast execution time in quantum computers can be a promising solution candidate, its heuristic nature stem from its theoretical foundation should be considered carefully when applying into power grid optimization problems.
This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming formulation for the reconfiguration of radial distribution network in response to faults in distribution lines. Comparing to existing bus injection model in the literature, our formulation based the branch flows model is theoretically equivalent without needing non-explainable variables, thus being more numerically stable. The network reconfiguration model is then used as a benchmark to evaluate the performance of quantum computing algorithms in real quantum computers. It shows that while current quantum computing algorithms with fast execution time in quantum computers can be a promising solution candidate, its heuristic nature stem from its theoretical foundation should be considered carefully when applying into power grid optimization problems.
This paper reviews a hybrid quantum-classical distributed algorithm for NP-hard combinatorial optimization problems, which is embedded in IBM Qiskit's Alternating Direction Method of Multipliers (ADMM) optimizer. We demonstrate a proof of concept for solving Mixed-Integer Convex Programs (MICP) in power system applications using a use case on power distribution network reconfiguration in IBM quantum computers. Using the Qiskit ADMM optimizer, the MICP is decomposed into two subproblems: a quadratic unconstrained binary optimization (QUBO) solved by quantum algorithms and a convex one solved by classical solvers. Our essential contribution is integrating the Quantum Random Access Optimization (QRAO) into the quantum-classical distributed framework and the existing Quantum Approximate Optimization Algorithm (QAOA) implemented in the Qiskit ADMM Optimizer. QRAO utilizes Quantum Random Access Codes (QRACs) to minimize qubit requirements and utilizes quantum state rounding for solution extraction. We examine the impact of noise on solutions derived from QRAO and compare them with results from QAOA using a use case on network reconfiguration in response to faults in the power distribution system.
Optimization models for large smart grids need to consider network constraints, renewable energy uncertainty, storage dynamics and flexible demand simultaneously. The mixed discrete-continuous nature of these problems is not suitable for the operational time constraints, and a single quantum processor cannot yet handle real grid instances. A distributed quantum computing framework for an electrical network is proposed in this paper, which divides the network into coupled regions, assigns compact quadratic unconstrained binary optimisation subproblems to heterogeneous quantum workers, and employs an asynchronous classical coordinator to enforce boundary consensus. The four components of the framework are adaptive penalty encoding, warm-started variational circuits, confidence-aware result aggregation and projection-based feasibility repair. A reproducible simulation study is constructed for modified 33-bus, 118-bus, 300-bus and 1354-bus systems with renewable generation, batteries and responsive loads. In all the test cases, the proposed method reduced the operating cost and constraint violation compared with centralised QAOA, quantum annealing, ADMM, and mixed-integer programming under the same time budget. It still performs reasonably well under high worker latency and depolarising noise. Based on the above results, near-term quantum resources will be more credible as coordinated regional accelerators than as a single grid optimizer. Therefore, it will be presented as an engineering architecture, an explicit optimisation map and a multi-metric evaluation system for scalable quantum-assisted smart grid operation.
We present a hybrid quantum-classical algorithm for distribution network reconfiguration, a combinatorial optimization problem on power distribution networks, that combines a radiality preserving branch-exchange encoding with iterative warm-start quantum imaginary-time evolution to minimize active line losses. The encoding uses a fixed-width binary representation of sequential branch-exchange actions, ensuring that every register outcome decodes to a radial configuration. The quantum subroutine is informed by a surrogate model fit to classically-solved alternating current power flow (ACPF) labels. After a set budget of ACPF solves and circuit samples is exhausted, the algorithm returns the lowest-loss configuration seen. We employ our algorithm on ten test cases, including seven commonly-used benchmark cases and three cases we modified from these and similar standard systems. We include two methods to reduce problem size, which enable extensions of the algorithm to larger networks. We successfully reach minimal-loss configurations for six cases and find configurations with losses from 0.2 percent to 2.18 percent above the reported reference minimal loss for the other four.
Optimizing the topology of networks is an important challenge across engineering disciplines. In energy systems, network reconfiguration can substantially reduce losses and costs and thus support the energy transition. Unfortunately, many related optimization problems are NP hard, restricting practical applications. In this article, we address the problem of minimizing losses in radial networks, a problem that routinely arises in distribution grid operation. We show that even the computation of approximate solutions is computationally hard and propose quantum optimization as a promising alternative. We derive two quantum algorithmic primitives based on the Quantum Alternating Operator Ansatz (QAOA) that differ in the sampling of network topologies: a tailored sampling of radial topologies and simple sampling with penalty terms to suppress non-radial topologies. We show how to apply these algorithmic primitives to distribution grid reconfiguration and quantify the necessary quantum resources.
Modern smart grids generate increasingly rich operational data and deploy greater numbers of remotely controlled switching assets than ever before, creating new opportunities for data-driven distribution network reconfiguration (DNR). DNR optimizes grid topology to improve efficiency, reduce power losses, and maintain operational constraints, but finding optimal switch configurations remains a computationally demanding combinatorial problem. In this paper, we propose a deep reinforcement learning (DRL) framework for static DNR to systematically investigate how the Q-network architecture affects both solution quality and learning performance. We evaluate multiple architectures within a controlled DRL framework, varying only the Q-network to isolate the contribution of each architectural choice. Our results show that quantum-enhanced Q-networks can achieve higher rewards with fewer parameters than their classical counterpart, suggesting that such architectures are a promising direction for combinatorial power systems optimization.