Comparison of Enhanced Benders Decomposition Methods for Stochastic Optimization of Energy System Models and Challenges for the Application to High Performance Computing

Kurzfassung

Long term capacity expansion planning requires making decisions now, which have an impact on the energy system over several decades, however uncertainty prevails with regard to exogenous parameters such as fuel prices, CO2 prices, market regulation and renewable feed-in. Stochastic optimization over a large set of scenarios can incorporate this uncertainty into the decision process. This paper compares different enhanced Benders decomposition methods implemented in an energy system model (ESM) with regard to computation time, memory used during calculation and number of iterations. When considering flexibility options like electrical energy storage, demand side management and electric mobility in energy system models, a high spatial and temporal resolution of the modelled energy system is required. Consequently, the implementation of stochastic optimization into high resolution optimizing energy system models will lead to an increased complexity, due to the additional scenario dimension. This makes traditional stochastic optimization approaches like the formulation of the deterministic equivalent impossible to solve due to memory restrictions. This problem can be tackled using decomposition approaches such as enhanced Benders decomposition in order to guarantee achieving the global optimum while taking computational constraints into account. Challenges arise especially regarding CPU load balancing for the application to high performance computing. The work is part of the BEAM-ME project, a German funded research project aiming at developing speed-up methods by improving the modelling, underlying algorithms and application of ESM on high performance computing. The presentation will discuss the modelling approaches in order to extend the existing energy system model REMix, developed at the German Aerospace Center, as well as the comparison of different algorithmic decompositions improvements implemented in order to accelerate convergence and achieve parallelization. These methodological improvements include the types of optimality cuts, application of trust-regions and achieving asynchronous solving of master and sub problem. The preliminary results indicate substantial improvements are possible compared to the traditional Benders Decomposition and computational constraints can be overcome. Furthermore these methods may be improved by applying energy system model specific information.