Large-scale hydropower models in StochasticPrograms.jl

Abstract

We present three large-scale hydropower planning models implemented in our open-source software framework StochasticPrograms.jl developed using the Julia programming langugage. The framework provides an expressive syntax for formulating stochastic programming models and has distributed capabilities that can handle large-scale instances. The three models describe different case studies of the hydroelectric power plants in the Swedish river Skellefte\"alven. The models are two-stage stochastic programs with sampled scenarios that describe uncertain electricity prices and local water inflows. The first model is a day-ahead planning problem that concerns how to determine optimal order strategies in a day-ahead energy market. We pose this problem from the perspective of a hydropower producer, who participates in the Nordic day-ahead market and operates in the Swedish river Skellefte\"alven. We implement the day-ahead model using our computational tools and then solve large-scale instances of the problem in a distributed environment. A statistically significant value of running stochastic planning is obtained using a sample-based algorithm. Next, we consider a variation of the day-ahead problem that includes preventive maintenance scheduling. We show how intricate coordination between the submitteed market orders and the maintenance schedule results in a larger value of the stochastic solution than the day-ahead problem. The final model is a capacity expansion problem with a long planning horizon. The same methodology is applied as when solving the first two hydropower problems. However, the planning horizon is considerably longer, from one year up to 20 years compared to a 24 hour horizon. We note that the relative significance of the value of the stochastic solution is much greater when comparing to the extra profits incurred from the capacity expansion instead of the total profit.