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Leveraging Quantum Computing for Accelerated Classical Algorithms in Power Systems Optimization

Rosemary Barrass, Harsha Nagarajan, Carleton Coffrin

TL;DR

The paper tackles the challenge of solving large-scale unit commitment problems on noisy, resource-constrained quantum hardware by proposing QC4UC, a hybrid quantum-classical algorithm. It combines a Benders decomposition framework with a QPU-based binary master problem solving a QUBO, while handling a continuous subproblem on classical hardware; to cope with NISQ limitations, it introduces dynamic precision encoding and rounded optimality cuts, plus a GVNS recovery strategy and a $k$-local neighborhood search. The key contributions are (i) reducing qubit requirements through rounded cuts and adaptive encoding, (ii) maintaining solution quality with near-optimal results on real quantum annealers and high-quality results on simulated annealing, and (iii) demonstrating scalability for larger UC instances via decomposition and recovery techniques. The results on a modified IEEE RTS-96 system show QA can produce solutions within 1% of the Gurobi optimum in a substantial fraction of runs, with significant qubit savings, underscoring a practical pathway for leveraging HQC in power-system optimization on current NISQ hardware.

Abstract

The recent advent of commercially available quantum annealing hardware (QAH) has expanded opportunities for research into quantum annealing-based algorithms. In the domain of power systems, this advancement has driven increased interest in applying such algorithms to mixed-integer problems (MIP) like Unit Commitment (UC). UC focuses on minimizing power generator operating costs while adhering to physical system constraints. Grid operators solve UC instances daily to meet power demand and ensure safe grid operations. This work presents a novel hybrid algorithm that leverages quantum and classical computing to solve UC more efficiently. We introduce a novel Benders-cut generation technique for UC, thereby enhancing cut quality, reducing expensive quantum-classical hardware interactions, and lowering qubit requirements. Additionally, we incorporate a $k$-local neighborhood search technique as a recovery step to ensure a higher quality solution than current QAH alone can achieve. The proposed algorithm, QC4UC, is evaluated on a modified instance of the IEEE RTS-96 test system. Results from both a simulated annealer and real QAH are compared, demonstrating the effectiveness of this algorithm in reducing qubit requirements and producing near-optimal solutions on noisy QAH.

Leveraging Quantum Computing for Accelerated Classical Algorithms in Power Systems Optimization

TL;DR

The paper tackles the challenge of solving large-scale unit commitment problems on noisy, resource-constrained quantum hardware by proposing QC4UC, a hybrid quantum-classical algorithm. It combines a Benders decomposition framework with a QPU-based binary master problem solving a QUBO, while handling a continuous subproblem on classical hardware; to cope with NISQ limitations, it introduces dynamic precision encoding and rounded optimality cuts, plus a GVNS recovery strategy and a -local neighborhood search. The key contributions are (i) reducing qubit requirements through rounded cuts and adaptive encoding, (ii) maintaining solution quality with near-optimal results on real quantum annealers and high-quality results on simulated annealing, and (iii) demonstrating scalability for larger UC instances via decomposition and recovery techniques. The results on a modified IEEE RTS-96 system show QA can produce solutions within 1% of the Gurobi optimum in a substantial fraction of runs, with significant qubit savings, underscoring a practical pathway for leveraging HQC in power-system optimization on current NISQ hardware.

Abstract

The recent advent of commercially available quantum annealing hardware (QAH) has expanded opportunities for research into quantum annealing-based algorithms. In the domain of power systems, this advancement has driven increased interest in applying such algorithms to mixed-integer problems (MIP) like Unit Commitment (UC). UC focuses on minimizing power generator operating costs while adhering to physical system constraints. Grid operators solve UC instances daily to meet power demand and ensure safe grid operations. This work presents a novel hybrid algorithm that leverages quantum and classical computing to solve UC more efficiently. We introduce a novel Benders-cut generation technique for UC, thereby enhancing cut quality, reducing expensive quantum-classical hardware interactions, and lowering qubit requirements. Additionally, we incorporate a -local neighborhood search technique as a recovery step to ensure a higher quality solution than current QAH alone can achieve. The proposed algorithm, QC4UC, is evaluated on a modified instance of the IEEE RTS-96 test system. Results from both a simulated annealer and real QAH are compared, demonstrating the effectiveness of this algorithm in reducing qubit requirements and producing near-optimal solutions on noisy QAH.

Paper Structure

This paper contains 15 sections, 19 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Formulation
  4. Benders' Decomposition Algorithm
  5. Dynamic Precision Encoding
  6. Rounded Optimality Cuts
  7. General Variable Neighborhood Search
  8. $k$-local Neighborhood Search Algorithm
  9. Computational Results
  10. Solution Quality on Quantum Annealing Hardware
  11. Embedding Algorithm Solve Time and Algorithm Run Time
  12. Dynamic Precision Encoding
  13. Conclusion
  14. Acknowledgments.
  15. Disclosure of Interests.

Figures (4)

  • Figure 1: The proposed iterative algorithm with rounded cuts, general variable neighborhood search step, and $k$-local neighborhood search recovery step.
  • Figure 2: (a) Histogram of the 51 out of 100 QC4UC with QA tests achieving within 1% of the Gurobi's optimal objective value. (b) Bar plot of penalty and generation costs of all 100 tests of QC4UC with QA.
  • Figure 3: Embedding algorithm solve time for QC4UC with QA for 100 independent tests.
  • Figure 4: (a) Total QC4UC run time per iteration, including MP solve time, SP solve time, and problem build time for QC4UC with SA and QC4UC with QA, excluding embedding algorithm solve time for QC4UC with QA. (b) Number of binary encoding variables used to approximate $\boldsymbol{\eta}$ at each iteration of QC4UC with QA.