2020/09/22 by Niklas L. P. Lundström, Lundström, Niklas L. P., Marcus Olofsson +3 · 1 citation
Engineering · Environmental Science · #35K45 #49N90 #90B50 #Electric Power System Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Water resources management and optimization #Water-Energy-Food Nexus Studies
paper · pdf · doi:10.48550/arxiv.2009.10554
openalex publication_date 2020/09/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The mathematical theory for optimal switching is by now relatively well\ndeveloped, but the number of concrete applications of this theoretical\nframework remains few. In this paper, we bridge parts of this gap by applying\noptimal switching theory to a set of production planning problems related to\nhydropower plants. In particular, we study two different cases involving small\nrun-of-river hydropower plants and show how optimal switching can be used to\ncreate fully automatic production schemes in these cases, with non-zero cost of\nswitching between different states of production. Along the way of deriving\nthese schemes, we also create a model for the random flow of water based on\nstochastic differential equations and fit this model to historical data. This\nstochastic flow model, which should be of independent interest, mimics the long\nterm seasonal behaviour of the flow while still allowing for stochastic\nfluctuations and can incorporate a given forecast to damp the impact of such\nfluctuations in near time. We benchmark the performance of our model using\nactual flow data from a small river in Sweden and find that our production\nscheme lies close to the optimal, within 2 % and 5 %, respectively, in a long\nterm investigation of the two plants considered.\n