The mathematical theory for optimal switching is by now relatively well developed, but the number of concrete applications of this theoretical framework remains few. In this paper, we bridge parts of this gap by applying optimal switching theory to a conceptual production planning problem related to hydropower. In particular, we study two examples of small run-of-river hydropower plants and provide an outline of how optimal switching can be used to create fully automatic production schemes for these. Along the way, we create a new model for random flow of water based on stochastic differential equations and fit this model to historical data. We benchmark the performance of our model using actual flow data from a small river in Sweden and find that our production scheme lies close to the optimal, within 2 and 5 %, respectively, in a long term investigation of the two plants considered.

目前，最优切换的数学理论已经相对完善，但该理论框架的具体应用数量仍然很少。在本文中，我们通过将最优切换理论应用于与水电相关的概念性生产规划问题来弥补这一差距。特别是，我们研究了两个小型径流式水力发电厂的例子，并概述了如何使用最佳切换来为这些发电厂创建全自动生产计划。在此过程中，我们基于随机微分方程为随机水流创建了一个新模型，并将该模型与历史数据进行了拟合。我们使用瑞典一条小河的实际流量数据对模型的性能进行基准测试，发现我们的生产方案接近最佳，分别在 2% 和 5% 以内，