AI 中文总结
针对多阶段随机清洁能源转型规划问题，本文提出带部分非预见性松弛的Benders分解算法，通过鲁棒重构等提升计算性能，成功求解校园案例并验证其可提升运营可靠性。
AI 中文摘要
本文研究在战略层面和运营层面不确定性下的校园级综合电-热系统清洁能源转型规划问题。我们构建了一个多阶段随机混合整数规划模型，联合优化可再生能源发电、储能和传热技术的投资与运营决策，这些技术的成本和效率随阶段随机变化。为考虑短期运营不确定性，我们进一步基于需求、可再生能源发电和传热性能的盒式不确定性集推导了鲁棒重构模型。为求解该大规模模型，我们开发了一种带有部分非预见性松弛的Benders分解算法：主问题保留投资变量及其非预见性约束，而运营变量被分配到各场景子问题中，其非预见性约束被松弛；仅在算法终止时，通过一个小型线性规划恢复运营变量的非预见性。我们证明该校正步骤仅会使目标函数值增加有限的边界。我们通过有效不等式和两阶段割添加策略提升了所开发算法的计算性能。使用所提方法，我们在合理计算预算内以高时间分辨率求解了中东技术大学校园案例研究，这是扩展形式或经典Benders分解无法实现的。我们通过滚动时域蒙特卡洛模拟结合样本外分析评估了所得投资计划，证明增加的鲁棒性可在总成本适度增加的情况下显著提升转型计划的运营可靠性。
英文摘要
We study clean energy transition planning for campus-scale integrated electricity-heat systems under both strategic level and operational level uncertainties. We formulate a multi-stage stochastic mixed-integer program that jointly optimizes investment and operational decisions for renewable generation, storage, and heat-transfer technologies whose costs and efficiencies evolve stochastically across stages. To account for short-term operational uncertainty, we further derive a robust reformulation based on box uncertainty sets for demand, renewable generation, and heat-transfer performance. To solve the resulting large-scale model, we develop a Benders decomposition algorithm with partial non-anticipativity relaxation. Investment variables and their non-anticipativity constraints are retained in the master problem while operational variables are assigned to scenario-wise subproblems where their non-anticipativity constraints are relaxed. Non-anticipativity of operational variables is restored only at termination through a smaller linear program. We prove that this correction step can only increase the objective function value by a finite bound. We improve the computational performance of the algorithm developed with valid inequalities and a two-phase cut-addition strategy. Using the proposed approach, we solve the Middle East Technical University campus case study at high temporal resolution within a reasonable computational budget, which is not otherwise possible with the extensive form or the classical Benders decomposition. We evaluate the resulting investment plans through rolling-horizon Monte Carlo simulations with an out-of-sample analysis and demonstrate that the added robustness can significantly improve the operational reliability of the transition plans with a moderate increase in total cost.
Comments30 pages, 3 figures
