2020/09/22 by Niklas L. P. Lundström, Lundström, Niklas L. P., Marcus Olofsson +3 · 2 citations
Engineering · Environmental Science · Mathematics · #35K45 #49N90 #90B50 #Electric Power System Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Water resources management and optimization #Water-Energy-Food Nexus Studies #math.OC #msc:35K45 #msc:49N90 #msc:90B50
paper · pdf · doi:10.48550/arxiv.2009.10554
28 pages
arxiv created 2020/09/22 · openalex publication_date 2020/09/22 · arxiv updated 2020/09/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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 set of production planning problems related to hydropower plants. In particular, we study two different cases involving small run-of-river hydropower plants and show how optimal switching can be used to create fully automatic production schemes in these cases, with non-zero cost of switching between different states of production. Along the way of deriving these schemes, we also create a model for the random flow of water based on stochastic differential equations and fit this model to historical data. This stochastic flow model, which should be of independent interest, mimics the long term seasonal behaviour of the flow while still allowing for stochastic fluctuations and can incorporate a given forecast to damp the impact of such fluctuations in near time. 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.