Uncertainty modeling with the open source framework urbs

The transition of the energy system to a renewable energy source based system requires methods on how to incorporate uncertainty in modeling the energy system. There are different approaches starting from mainly variation based approaches up to including stochastic programming. For this work, a modified version of stochastic dual dynamic programming (SDDP) has been implemented into the open source framework urbs. The framework consists of a linear optimization for energy dispatch and expansion planning and has been extended to include uncertain inputs for volatile energy sources like wind or solar. Different paths on how much these sources are providing for the feed-in can be modeled by packing one or more time steps to so-called realizations with different probabilities. The solution algorithm itself is based on a modified Benders decomposition approach, which is adapted to the constraints specifically relevant for power system analysis. The relation of SDDP and Benders decomposition is used to overcome the exponential growth of variables typically involved in classic stochastic programming. The novel approach is tested on a case study of Germany and shows how a more realistic economic dispatch can be calculated with a stochastic approach compared to a deterministic one.