Warm-Startable Progressive Integrality Outer-Inner Approximation for AC Unit Commitment with Conic Formulation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914447390408704 |
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| author | Dai, Yongzheng |
| author_facet | Dai, Yongzheng |
| contents | The alternating-current unit commitment 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 alternating-current unit commitment problem is based on the second-order cone, which results in a mixed-integer second-order cone program and remains computationally challenging. In this paper, we propose a warm-startable 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 second-order cone-based alternating-current unit commitment problem. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19012 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Warm-Startable Progressive Integrality Outer-Inner Approximation for AC Unit Commitment with Conic Formulation Dai, Yongzheng Optimization and Control The alternating-current unit commitment 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 alternating-current unit commitment problem is based on the second-order cone, which results in a mixed-integer second-order cone program and remains computationally challenging. In this paper, we propose a warm-startable 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 second-order cone-based alternating-current unit commitment problem. 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. |
| title | Warm-Startable Progressive Integrality Outer-Inner Approximation for AC Unit Commitment with Conic Formulation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.19012 |