Management strategies for run-of-river hydropower plants -an optimal switching approach

Abstract

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.

A Simple Model on Streamflow Management with a Dynamic Risk Measure

“…River is a dynamic environment driven by stochastic streamflow. Stochastic differential equations (SDEs) of the Ornstein-Uhlenbeck types driven by Gaussian [1] and Poisson noises [2][3] have been efficient models representing streamflow time series. Recently, a tempered stable Ornstein-Uhlenbeck model [4] has been proposed as a more realistic alternative to represent both continuous and jump noises in the streamflow time series [5].…”

Systems of fully nonlinear parabolic obstacle problems with Neumann boundary conditions

“…Then, naturally, the process can only take values between 0 and some X max , the latter being the capacity of the dam. (In case the power plant is of run-of-river type, i.e., has no dam, the problem can be reduced to Ω = R n and an application of the theory in this setting was recently studied in Lundström-Olofsson-Önskog [21].) When the dam is full, additional increase of water must be spilled, keeping the amount of water in the dam constant.…”