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

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 (PV) systems in combination with multi-stage 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 (SMILP) 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 (DFO). The subproblems are solved in parallel on high-performance computing (HPC) 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.

Self-consumption through power-to-heat and storage for enhanced PV integration in decentralised energy systems

“…The methodology relates to Schwarz et al (2017) who describe a module-based model chain including stochastic programming to take into account weather-related uncertainties, e.g., PV supply, energy demand or electricity prices, and to endogenously determine optimal investment in the system's components. The model framework is explained in Section 3.1, the data generation and optimisation process are explained in detail in Section 3.2 and 3.3.…”

“…This study demonstrates the optimisation of a residential quarter modelled as a stochastic program with a temporal resolution of 15 min and a 20-year time horizon. The approach is related to Schwarz et al (2017) and extended by endogenising investment decisions into PV, power-to-heat technology and electrical storage as well as the consideration of different tariffs including a dynamic electricity price generation module (see Section 3).…”

“…This paper uses the comprehensive approach of Schwarz et al (2017) that consistently models and propagates uncertainties through a model chain comprising three layers (see Fig. 2): a) input layer, b) transformation layer and c) optimisation layer.…”

“…In the light of these developments and the statements by the EU promoting self-consumption as a means to support RE integration, the question arises (from a consumer perspective) what flexibilities to shift load and increase self-consumption are most profitable and how to optimally combine different sources of flexibility in the presence of uncertainty. Some researchers, however, also hold critical views on self-consumption (Khalilpour and Vassallo, 2015;Simshauser, 2016;Bertsch et al, 2017). Their criticism is not directed at selfconsumption and PV expansion as such, but mainly raises distributional concerns.…”

A Discussion of Mixed Integer Linear Programming Models of Thermostatic Loads in Demand Response

“…The authors in [8] develop an approach based on a partial-differential equation model of thermal diffusion to determine the thermostat settings to minimize the electricity bill for a consumer with energy time-of-use and power prices, in which the optimal thermostat programming for HVAC is formulated as a constrained dynamic optimization problem. The authors in [9] consider the optimization of the investment and operation planning of a decentralized energy system, which is subject to different sources of uncertainties, encompassing photovoltaic generators and load flexibility using heat pumps in combination with thermal energy storage units for space heating and domestic hot water, which is tackled by two-stage stochastic programming.…”