发表机构
Cheikh Anta Diop University of Dakar; University of Nairobi; Laboratoire Eau, Energie, Environnement et procédés Industriels (LE3PI); Centre de Tests des Systèmes Solaires (CT2S)（达喀尔谢赫安塔·迪奥普大学; 内罗毕大学; 水、能源、环境与工业过程实验室; 太阳能系统测试中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
InFlow提出结合熵鲁棒SDDP与HJB交叉验证的框架，用于季节性水库调度，通过严格验证和鲁棒性分析，显著降低风险并保持成本稳定。
AI 中文摘要
季节性水库调度需要能够在强周期性和不确定的入流动态下保持可靠的优化方法。我们提出InFlow，一个面向验证的框架，结合了周期性随机对偶动态规划（SDDP）、熵鲁棒性、控制空间Bellman退火，以及独立离散化的Hamilton-Jacobi-Bellman（HJB）基准。熵转移算子被解释为KL惩罚的最坏情况期望，并通过Lagrange对偶与固定半径KL模糊集相联系。我们建立了均匀软Bellman逼近界，并证明了Gibbs倾斜SDDP割的有效性。基准依赖于归一化的季节性Cox-Ingersoll-Ross入流过程，其正性条件在最干旱的几周内失效，需要对退化边界进行显式处理。独立验证显示，HJB储水梯度与HiGHS储水平衡对偶之间高度一致，标准实现和仅精确割实现的水价值相关性分别为0.995和0.996。将HJB网格从61^2细化到81^2个状态，年平均值水价值仅变化0.6%，峰值变化小于0.1%。基于3,000条独立轨迹的样本外模拟表明，鲁棒性水平gamma=5使名义平均成本增加4.6%，同时将CVaR90降低11.2%。在入流减少40%的旱季压力情景下，平均成本差异变得统计上不显著，而CVaR90改善11.5%。鲁棒性扫描确认了风险调整价值的单调性。最后，一个两水库级联以0.999的相关性重现了电网Oracle边际水价值，并恢复了预测的上游到下游价值比为2。InFlow旨在作为一个透明的方法论基准，而非校准后的运行水库模型。
英文摘要
Seasonal reservoir operation requires optimization methods that remain reliable under strongly periodic and uncertain inflow dynamics. We present InFlow, a verification-oriented framework combining periodic stochastic dual dynamic programming (SDDP), entropic robustness, control-space Bellman annealing, and an independently discretized Hamilton-Jacobi-Bellman (HJB) benchmark. The entropic transition operator is interpreted as a KL-penalized worst-case expectation and linked to fixed-radius KL ambiguity sets through Lagrange duality. We establish a uniform soft-Bellman approximation bound and prove the validity of Gibbs-tilted SDDP cuts. The benchmark relies on a normalized seasonal Cox-Ingersoll-Ross inflow process whose positivity condition fails during the driest weeks, requiring explicit treatment of the degenerate boundary. Independent verification shows strong agreement between HJB storage gradients and HiGHS storage-balance duals, with water-value correlations of 0.995 and 0.996 for the standard and exact-cut-only implementations. Refining the HJB grid from 61^2 to 81^2 states changes the annual mean water value by only 0.6% and the peak value by less than 0.1%. Out-of-sample simulations based on 3,000 independent trajectories show that a robustness level of gamma=5 increases nominal mean cost by 4.6% while reducing CVaR90 by 11.2%. Under a dry-season stress scenario with inflows reduced by 40%, the mean-cost difference becomes statistically insignificant whereas CVaR90 improves by 11.5%. A robustness sweep confirms monotonicity of the risk-adjusted value. Finally, a two-reservoir cascade reproduces grid-oracle marginal water values with correlation 0.999 and recovers the predicted upstream-to-downstream value ratio of two. InFlow is intended as a transparent methodological benchmark rather than a calibrated operational reservoir model.
