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arXiv:2305.07899

A study of the optimization problem on the combination of sectionalizing switches in power grid with quantum annealing

Masaya Takahashi, Nishioka, Hiroaki, Masahiro Hirai, Hidetaka Takano

Published May 13, 2023• 2 citations
arXivHTMLPDF

Abstract

From the perspective of global warming, efficiency improvement of power grids is a pressing issue. Power grids have many switching devices to control the flow of electricity. Since there is a slight resistance in the wires and power consumption is proportional to the square of the current, the value of power loss on the wires changes depending on the combination of switch values that change the supply path of the current. The total number of switch combinations increases exponentially with the number of switches, and various algorithms have been studied to find the optimal combination of switch values. We propose a method to capture the switch combination problem in power grids as quadratic unconstrained binary optimization (QUBO) and derive an evaluation function to solve it using quantum annealing. The result is registered as a patent P6736787 at Japanese patent office.

DOI
10.48550/arxiv.2305.07899

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The quantum annealing devices, which encode the solution to a computational problem in the ground state of a quantum Hamiltonian, are implemented in D-Wave systems with more than 2,000 qubits. However, quantum annealing can solve only a classical combinatorial optimization problem such as an Ising model, or equivalently, a quadratic unconstrained binary optimization (QUBO) problem. In this paper, we formulate the QUBO model to solve elliptic problems with Dirichlet and Neumann boundary conditions using the finite element method. In this formulation, we develop the objective function of quadratic binary variables represented by qubits and the system finds the binary string combination minimizing the objective function globally. Based on the QUBO formulation, we introduce an iterative algorithm to solve the elliptic problems. We discuss the validation of the modeling on the D-Wave quantum annealing system.
Optimization of electricity surplus is a crucial element for transmission power networks since it leads to reducing costs as well as increasing efficiency across the network as a whole. In this paper, we show how to optimize such network costs using a quantum annealing approach. First, we define the Quadratic Unconstrained Binary Optimization (QUBO) problem for network partitioning. To achieve this, we introduce a method to translate inequality constraints with real-valued coefficients into approximate penalty functions. Next, we test the implementation on purely quantum and quantum-classical hybrid architectures. We then solve the problem using the D-Wave hybrid Constrained Quadratic Model (CQM) solver, the D-Wave hybrid Binary Quadratic Model (BQM) solver, as well as classical solvers available on Azure Quantum Cloud. Finally, we find that the value of the objective function obtained with the quantum-classical hybrid solvers is always lower compared to the classical approaches across a range of different problem sizes. This demonstrates that the quantum-classical hybrid methods outperform the classical methods in terms of solution quality.
Graph partitioning has many applications in powersystems from decentralized state estimation to parallel simulation. Focusing on parallel simulation, optimal grid partitioning minimizes the idle time caused by different simulation times for the sub-networks and their components and reduces the overhead required to simulate the cuts. Partitioning a graph into two parts such that, for example, the cut is minimal and the subgraphs have equal size is an NP-hard problem. In this paper we show how optimal partitioning of a graph can be obtained using quantum annealing (QA). We show how to map the requirements for optimal splitting to a quadratic unconstrained binary optimization (QUBO) formulation and test the proposed formulation using a current D-Wave QPU. We show that the necessity to find an embedding of the QUBO on current D-Wave QPUs limits the problem size to under 200 buses and notably affects the time-to-solution. We finally discuss the implications on near-term implementation of QA in combination to traditional CPU or GPU based simulation.
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