A Path Towards Quantum Advantage for theUnit Commitment Problem

A Path Towards Quantum Advantage for the Unit Commitment Problem

Abstract:

This work presents a solution to the unit commitment problem (UCP) in energy grid management, an optimization problem that involves solving a system of equations to calculate costs for a given solution. We characterize the UCP as a Mixed-Integer Nonlinear Programming (MINLP) problem and solve it using a quantum simulation-based optimization (QuSO) approach, defining a class of equivalent problems solvable with the proposed algorithm. By modeling the energy grid as a specific graph, we gain valuable insights into the structure and characteristics of the susceptance matrix. We also incorporate approximate Direct Current (DC) power flow constraints into the model. The proposed quantum routine begins by inverting the reduced susceptance matrix via Quantum Singular Value Transformation (QSVT) using a specific matrix inversion polynomial. A quantum phase estimation routine, along with an additional QSVT procedure, is used to construct the cost function, which is then optimized using the Quantum Approximate Optimization Algorithm (QAOA). This hybrid quantum-classical approach leverages the computational power of quantum algorithms to enhance efficiency in solving such optimization problems. Our results evaluate the algorithm’s complexity and demonstrate its significant potential for QuSO problems. Specifically, the QSVT matrix inversion can reduce time complexity exponentially in scenarios where classical methods scale poorly with problem size. This reduction in complexity could enable real-time optimization of large-scale energy grids, thereby improving operational efficiency and reliability.

Author:

David Fischer

Advisors:

Claudia Linnhoff-Popien, Dirk André Deckert, Jonas Stein, Jago Silberbauer, Philipp Altmann

Student Thesis | Published September 2024 | Copyright © QAR-Lab
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