# Two-stage stochastic, large-scale optimization of a decentralized energy system: a case study focusing on solar PV, heat pumps and storage in a residential quarter

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## Abstract

The expansion of fluctuating renewable energy sources leads to an increasing impact of weather-related uncertainties on future decentralized energy systems. Stochastic modeling techniques enable an adequate consideration of the uncertainties and provide support for both investment and operating decisions in such systems. In this paper, we consider a residential quarter using photovoltaic systems in combination with multistage air-water heat pumps and heat storage units for space heating and domestic hot water. We model the investment and operating problem of the quarter’s energy system as two-stage stochastic mixed-integer linear program and optimize the thermal storage units. In order to keep the resulting stochastic, large-scale program computationally feasible, the problem is decomposed in combination with a derivative-free optimization. The subproblems are solved in parallel on high-performance computing systems. Our approach is integrated in that it comprises three subsystems: generation of consistent ensembles of the required input data by a Markov process, transformation into sets of energy demand and supply profiles and the actual stochastic optimization. An analysis of the scalability and comparison with a state-of-the-art dual-decomposition method using Lagrange relaxation and a conic bundle algorithm shows a good performance of our approach for the considered problem type. A comparison of the effective gain of modeling the quarter as stochastic program with the resulting computational expenses justifies the approach. Moreover, our results show that heat storage units in such systems are generally larger when uncertainties are considered, i.e., stochastic optimization can help to avoid insufficient setup decisions. Furthermore, we find that the storage is more profitable for domestic hot water than for space heating.

## Keywords

Large-scale energy system optimization Stochastic programming Uncertainty modeling Markov process## Notes

### Acknowledgements

The authors acknowledge support by the state of Baden-Württemberg through bwHPC and the Germany Research Foundation (DFG) through Grant No INST 35/1134-1 FUGG. This research has been supported by KIC InnoEnergy. KIC InnoEnergy is a company supported by the European Institute of Innovation and Technology (EIT), and has the mission of delivering commercial products and services, new businesses, innovators and entrepreneurs in the field of sustainable energy through the integration of higher education, research, entrepreneurs and business companies. Valentin Bertsch acknowledges funding from the Energy Policy Research Centre of the Economic and Social Research Institute.

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