Added Value of Scenario Tree Based Stochastic Optimization in Long and Medium Term Planning of Hydro Power Systems

Georg Ostermaier^*

The changes in the dynamics of power prices in Germany within the last few years have implied significant decreases of revenues of pumped storage hydro systems. The earnings from daily peak/offpeak price spreads have declined whereby at the same time long term management of large reservoirs has even more difficult due hardly predictable power price and inflow evolutions. \newline Stochastic Optimization has been applied for hydro system management for a long time already, but only recently operators expect additional benefits given the changed and even more uncertain power market situation. Besides stochastic dual dynamic programming, scenario tree based methods are meanwhile applied, which so far have hardly been used for complex hydro systems due to the curse of dimensionality in stochastic programming. \newline We apply efficient discretization methods for the generation of multi-dimensional scenario trees of power prices and inflows, based on moment matching and multinomial distributions. Furthermore, by using increased hardware efficiency it is meanwhile possible to set up and solve scenario tree based stochastic optimization models for even complex pumped storage systems. Ex post analyses have shown that outperformance over deterministic optimization in the range of 1-5 percent is achievable.

Mathematics Subject Classification: 60H30

Keywords: Hydro power systems, long term planning, price scenario trees, inflow scenario trees, stochastic optimization

Minisymposion: Stochastic Models for Optimization of Electric Power Systems