Energy System Analysis

Energy System Analysis


The problem of Energy Systems is as follows. The power market faces increasing challenges toward inegrating the growing share of Renewable Energy Sources (RES) due to the fluctuating nature of wind and solar insolation. Hence the conventional power plants must provide the flexibility to adjust to the fluctuating residual load resulting from the gap between power demand and the preferential feed-in from RES. Since the peak power production of renewable energy carriers such as solar power or wind power do not coincide with peak demands, the occurance of times with overproduction and time periods where fossile power plants are needed to cover power demand are unavoidable. To compensate overproductions, we include energy storages, such as batteries, pumped hydro storages or power to gas storages. This leads to a time expanded tuning of the charging and discharging of storages and the control of the fossile power plants to cover the fluctuating residual load, with the objective to minimize the electricity price resulting from the power production costs according to the merit order effect. In order to ensure system security we must include balancing power which must be held available by conventional power plants. Under the restrictions of the just explained unit commitment problem and the targets set by the government such as, at least 50% of the power demand must be satisfied by renewable energy carriers, we further suggest a power capacity expansion plan for the given planning period. The capacity expansion problem arises due to the fact that the nuclear plants will be turned off at specific times during the planning period. For extension power plants we include integrated gasification combined cycle power plants, gas turbines, wind power, hydro power, solar power and geothermal power. Mathematically this problem leads to a stochastic mixed integer nonlinear program, where the stochasticity results form the fluctuating feed in of renewable energy carriers. The nonlinearity results from the efficiency factors of the power plants and storages. The combinatorial aspects arise due to the switching processes of the conventional plants the charging status of the energy storages and the extension decisions.

People involved

Alexander Martin
Christoph Thurner


For further details about this project please contact Christoph Thurner (christoph.thurner [at]

Supported by

Bayerisches Staatsministerium für Wirtschaft und Medien,Energie und Technologie
Bayern Innovativ / Cluster Energietechnik


FAU Erlangen-Nürnberg Lehrstuhl Informatik 7
FAU Erlangen-Nürnberg Lehrstuhl für Elektrische Energiesysteme
AÜW (Allgäuer Überlandwerk GmbH)
Thüga AG
infra Fürth
SWU Stadtwerke Ulm/Neu-Ulm GmbH
WVV (Würzburger Versorgungs- und Verkehrs-GmbH)


A. Bärmann, A. Heidt, A. Martin, S. Pokutta, C. Thurner: Opens external link in
new windowPolyhedral Approximation of Ellipsoidal Uncertainty Sets via Extended Formulations — a computational case study –, Tech. Report. (submitted 2013)
M. Pruckner, C. Thurner, A. Martin, R. German: Opens external link in
new windowA Coupled Optimization and Simulation Model for the Energy Transition in Bavaria, MMB & DFT 2014 (Veranst.): Proceedings of the International Workshop on Demand Modeling and Quantitative Analysis of Future Generation Energy Networks and Energy Efficient Systems (FGENET 2014, Bamberg, Germany, March 19, 2014).
A. Bärmann, F. Liers, A. Martin, M. Merkert, C. Thurner, D. Weninger: Opens external link in
new windowSolving Network Design Problems via Iterative Aggregation, Mathematical Programming Computation: Volume 7, Issue 2 (2015), Page 189-217