水库防洪补偿调节线性规划模型及应用

防洪补偿调节是水库防洪规划和实时调度的基本原理，构模方法及后效性是制约水库洪水优化补偿调节数学模型求解的关键问题。对于一个水库和一个防洪控制点所组成的基本防洪系统，基于水库调度阶段划分及出流上界分析引入水库出流上下界约束，将水库防洪库容最小目标转换为累计蓄水量最小的等价目标，建立了水库防洪补偿调节线性规划模型（RFCR-LP），实现了水库调度决策和下游河道水流演进的完全耦合，避免了常规多阶段决策优化方法的后效性。该模型不仅具有结构简单、易于求解等显著特点，而且实现了水库防洪规划与实时调度优化数学模型的统一，基本形成了覆盖水库全周期的多功能洪水优化补偿调节模型，为构建水库群防洪优化补偿调节模型提供了一种解决方案。实例验证了RFCR-LP的适用性、灵活性及稳定性。

Development and application of a compensative regulation linear programming model for reservoir flood-control

Flood compensative regulation is the fundamental principle of reservoir flood-control planning and real-time operation, while the solution to the flood compensative regulation mathematical model is heavily restricted by the modeling methods and the aftereffect. In a basic flood control system consisting of a reservoir and a flood control station, the objective function transforms from minimizing the flood control volume to minimizing the cumulative water storage. The transformation is based on the stage division of operation and the analysis of outflow limits upon which a linear programming model of Reservoir Flood Compensative Regulation (RFCR-LP) has been established. This model couples the operational decisions and downstream routing methods, which avoids the aftereffect accompanying conventional methods for a multi-stage decision. The RFCR-LP is a simple structure that is easy to solve, and it unifies the optimal mathematical model between flood-control planning and real-time operation, which forms a multi-function and full-cycle model for reservoir flood-control compensative regulation. The proposed model promotes an efficient solution for complex system modeling. The feasibility, flexibility and stability of the RFCR-LP has been verified by the case study.