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arXiv:2307.12678 · International Conference on Electrical, Computer and Energy Technologies (ICECET)

Application of Power Flow Problem to an Open Quantum Neural Hardware

Ekin Erdem Aygül, Melih Can Topal, Ufuk Korkmaz, Deniz Türknençe

Published Nov 16, 2023• 0 citations
arXivHTMLPDF

Abstract

Significant progress in the construction of physical hardware for quantum computers has necessitated the development of new algorithms or protocols for the application of real-world problems on quantum computers. One of these problems is the power flow problem, which helps us understand the generation, distribution, and consumption of electricity in a system. In this study, the solution of a balanced 4-bus power system supported by the Newton-Raphson method is investigated using a newly developed dissipative quantum neural network hardware. This study presents the findings on how the proposed quantum network can be applied to the relevant problem and how the solution performance varies depending on the network parameters.

DOI
10.1109/icecet58911.2023.10389382

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Significant progress in the construction of physical hardware for quantum computers has necessitated the development of new algorithms or protocols for the application of real-world problems on quantum computers. One of these problems is the power flow problem, which helps us understand the generation, distribution, and consumption of electricity in a system. In this study, the solution of a balanced 4-bus power system supported by the Newton-Raphson method is investigated using a newly developed dissipative quantum neural network hardware. This study presents the findings on how the proposed quantum network can be applied to the relevant problem and how the solution performance varies depending on the network parameters.
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Quantum computing has the potential to solve many computational problems exponentially faster than classical computers. The high shares of renewables and the wide deployment of converter-interfaced resources require new tools that shall drastically accelerate power system computations, including optimization and security assessment, which can benefit from quantum computing. To the best of our knowledge, this is the first paper that goes beyond quantum computing simulations and performs an experimental application of Quantum Computing for power systems on a real quantum computer. We use five different quantum computers, apply the HHL quantum algorithm, and examine the impact of current noisy quantum hardware on the accuracy and speed of an AC power flow algorithm. We perform the same studies on a 3-bus and a 5-bus system with real quantum computers to identify challenges and open research questions related with the scalability of these algorithms.
This paper presents Newton-Raphson method using HHL algorithm for power flow quantum computation. The proposed Newton-Raphson HHL Quantum method converges to the solution within four iterations compared to the Newton-Raphson classical solution which converged in five iterations. The Newton-Raphson classical solution voltageV2=0.96674\mathrm{V}_{2}=0.96674V2​=0.96674pu, angleδ2=−0.04816\delta_{2}=-0.04816δ2​=−0.04816rads, angleδ3=0.04096\delta_{3}=0.04096δ3​=0.04096rads. The Newton-Raphson-HHL Quantum method voltageV2=0.98173\mathrm{V}_{2}= 0.98173V2​=0.98173pu, angleδ2=−0.05018\delta_{2}=-0.05018δ2​=−0.05018rads, angleδ3=0.04021\delta_{3}=0.04021δ3​=0.04021rads. This work Newton-Raphson HHL Quantum method for 3-bus time to converge is O.228s228\mathrm{s}228s. The fidelity is calculated to be 0.981436 with circuit width of 4 which is the number of qubits used in the circuit and the circuit depth gate layers is 126.
In this paper, we model and solve a fundamental power system problem, i.e., DC power flow, using a practical quantum computer. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm is used to solve the DC power flow problem. The HHL algorithm for the solution of a system of linear equations (SLE) offers an exponential speedup over the classical computers. The speedup advantage is more significant when the size and the frequency of solving the power flow problem become more substantial. Verified quantum computing applications to power systems are merely nonexistent at this point. Through this paper, we plan to (1) provide a proof-of-concept that practical power system problems can be solved using quantum technology, (2) build a quantum-grid foundation by solving a fundamental power system problem with applications in many other critical grid problems, and (3) apply HHL to solve an SLE which has broad applications in many power system problems. A small 3-bus system is used for testing and demonstration purposes, considering the limitations of the available quantum computing hardware and software. The proposed method's merits and effectiveness are demonstrated using IBM open-source quantum computer and reported through proof-of-concept experimental demonstration using a 4-qubit quantum information processor.
Practical quantum computing applications to power grids are nonexistent at the moment. This paper investigates how a fundamental grid problem, namely DC power flow, can be solved using quantum computing. Power flow is the most widely used power system analysis technique, either as a stand-alone application or embedded in other applications; therefore, its fast and accurate solution is of utmost significance for grid operators. We base our studies on the Harrow-Hassidim-Lloyd (HHL) quantum algorithm, which has a proven theoretical speedup over classical algorithms in solving a system of linear equations. Practical studies on a quantum computer are conducted using the WSCC 9-bus system.
This study further explores reformulating power flow (PF) analysis as a discrete combinatorial optimization problem, proposed in our earlier study using the Adiabatic Quantum Power Flow (AQPF) algorithm, which can be executed on Ising machines, including quantum and quantum-inspired hardware. This approach provides a new representation of the underlying equations, analogous to how neural networks approximate complex functions using simple operations. While the resulting combinatorial optimization problem is NP-hard, it is compatible with emerging quantum hardware designed to address such complexity. We introduce the Adiabatic Quantum Optimal Power Flow (AQOPF) algorithm, which transforms the classical optimal power flow (OPF) equations into quadratic unconstrained binary optimization (QUBO) models. Furthermore, the AQPF and AQOPF algorithms are evaluated on standard test cases ranging from 4- to 1354-bus systems using D-Wave's Advantage\texttrademark\ system (QA), its hybrid quantum-classical solver (HA), and Fujitsu's third-generation Digital Annealer (DAv3) and Quantum-Inspired Integrated Optimization (QIIO) platform. Both full and partitioned formulations are investigated, with particular attention to scalability and robustness in ill-conditioned scenarios. The results demonstrate that the algorithms can reproduce feasible PF and OPF solutions and exhibit promising computational scalability when supported by scalable hardware.