Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems (1902.01697v2)

Abstract: Security-Constrained Unit Commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via Mixed-Integer Linear Programming, sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of ML techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions and affine subspaces where the optimal solution is likely to lie, leading to significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that, using the proposed techniques, SCUC can be solved on average 4.3x faster with optimality guarantees, and 10.2x faster without optimality guarantees, but with no observed reduction in solution quality. Out-of-distribution experiments provides evidence that the method is somewhat robust against dataset shift.

• The paper proposes machine learning models to accelerate the solution of large-scale Security-Constrained Unit Commitment (SCUC) problems in power systems.
• Using ML models to identify redundant constraints and generate good initial solutions achieved speedups of 2.8x and 4.3x, respectively, with minimal accuracy loss.
• Predicting affine subspaces likely containing optimal solutions provided the highest speedup, up to 10.2x, enabling faster resolutions for complex SCUC instances.

Machine Learning for Solving Large-Scale Security-Constrained Unit Commitment Problems

The paper, authored by Alinson S. Xavier, Feng Qiu, and Shabbir Ahmed, presents a machine learning approach to enhance computational performance in solving the Security-Constrained Unit Commitment (SCUC) problem—a critical optimization task in power systems and electricity markets. The SCUC problem requires defining the least-cost production schedule for generating units while adhering to physical, operational, and economic constraints, including maintaining power deliverability without overloading transmission lines, even during contingencies.

Mixed-Integer Linear Programming (MIP) is the conventional tool for SCUC solutions. However, the repetitive nature of SCUC instances in power systems, often with minimal input data alterations, motivates an investigation into pre-learning methodologies to complement existing MIP solvers. This approach is increasingly pertinent given the time constraints in electricity markets, where rapid, multiple daily resolutions of SCUC are necessary.

Three machine learning models were proposed in this paper:

1. Identifying Redundant Constraints: The paper introduces a $k$-Nearest Neighbors (k-NN) based model to predict non-essential constraints, which can be excluded to speed up the solution process. The analysis showed about a 2.8x reduction in computational time when redundant constraints were excluded, aligning with minimal accuracy loss.
2. Generating Good Initial Solutions: Given the importance of high-quality initial feasible solutions, a strategy using historical optimal solutions is deployed to create partial and possibly infeasible warm starts, with subsequent repair by the MIP solver. This method accelerated the solution time by an average factor of 4.3x while maintaining optimality within the accepted threshold.
3. Predicting Affine Subspaces for Optimal Solutions: To exploit solution patterns across similar instances, this paper emphasizes predicting a lower-dimensional affine subspace that is likely to contain the optimal solution, significantly improving computational efficiency. However, while running tests, the approach showed a speedup component of 10.2x, some predictors marginally resulted in sub-optimal yet practically negligible deviations outside the assumed affine subspaces.

The ML methodologies outlined exhibited considerable promise in expediting the resolution of SCUC instances—achieving a performance enhancement of up to 10.2 times faster resolutions in realistic benchmarks. Notably, they showed reasonable resilience even when extrapolated out-of-distribution—suggesting moderate robustness against dataset shifts.

Future directions, as noted in the paper, include refining predictors to maintain efficiency amidst changes in generation fleet characteristics or inputs and leveraging comprehensive historical datasets for model validation and refinement. Additionally, adapting these ML integration techniques could prove beneficial for other challenging large-scale optimization problems beyond the field of power systems scheduling. This paper's approach exemplifies leveraging prior solved instances knowledge to enhance computational efficacy and create systems capable of addressing dynamic and large-scale operations in electricity market applications.