Paper
Progressive Integrality Outer-Inner Approximation for AC Unit Commitment with Conic Formulation
Authors
Yongzheng Dai
Abstract
The alternating-current unit commitment (AC-UC) problem provides a realistic representation of power system operations, which is a nonconvex mixed-integer nonlinear programming problem and hence is computationally intractable. A common relaxation to the AC-UC is based on the second-order cone (SOC), which results in a mixed-integer second-order cone program and remains computationally challenging. In this paper, we propose an outer-inner approximation framework that alternatively solves a mixed-integer linear programming (MILP) as an outer approximation and a convex second-order cone programming as an inner approximation to find a (near-)optimal solution to the SOC-based AC-UC. To improve computational efficiency, we introduce a progressive integrality strategy that gradually enforces integrality, reducing the reliance on expensive MILP solutions in early iterations. In addition, time-block Benders cuts are incorporated to strengthen the outer approximation and accelerate convergence. Computational experiments on large-scale test systems, including 200-bus and 500-bus networks, demonstrate that the proposed framework significantly improves both efficiency and robustness compared to state-of-the-art commercial solvers. The results show faster convergence, higher-quality solutions, and improved scalability under different formulations and perturbed load scenarios.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.19012v1</id>\n <title>Progressive Integrality Outer-Inner Approximation for AC Unit Commitment with Conic Formulation</title>\n <updated>2026-03-19T15:19:12Z</updated>\n <link href='https://arxiv.org/abs/2603.19012v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.19012v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>The alternating-current unit commitment (AC-UC) problem provides a realistic representation of power system operations, which is a nonconvex mixed-integer nonlinear programming problem and hence is computationally intractable. A common relaxation to the AC-UC is based on the second-order cone (SOC), which results in a mixed-integer second-order cone program and remains computationally challenging. In this paper, we propose an outer-inner approximation framework that alternatively solves a mixed-integer linear programming (MILP) as an outer approximation and a convex second-order cone programming as an inner approximation to find a (near-)optimal solution to the SOC-based AC-UC. To improve computational efficiency, we introduce a progressive integrality strategy that gradually enforces integrality, reducing the reliance on expensive MILP solutions in early iterations. In addition, time-block Benders cuts are incorporated to strengthen the outer approximation and accelerate convergence. Computational experiments on large-scale test systems, including 200-bus and 500-bus networks, demonstrate that the proposed framework significantly improves both efficiency and robustness compared to state-of-the-art commercial solvers. The results show faster convergence, higher-quality solutions, and improved scalability under different formulations and perturbed load scenarios.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.OC'/>\n <published>2026-03-19T15:19:12Z</published>\n <arxiv:primary_category term='math.OC'/>\n <author>\n <name>Yongzheng Dai</name>\n </author>\n </entry>"
}