Optimal Investment Decisions for a Zero Emission Building under Uncertainty: Stochastic BUTLER

This paper presents a two-stage stochastic mixed-integer linear (MILP) model for optimal design and operation of a zero emission building (ZEB). The stochastic MILP model considers both investments as well as operational decisions, and is able to account for short-term uncertainty of solar radiation, ambient temperatures, heat load of the building and electricity prices, that influences the building's operating pattern. A case study of a single family house situated in Norway has been performed, with the following technology choices at hand: building integrated PV (BIPV), air-source and ground-source heat pumps, biopellet boiler, heat storage, and battery. The results of the case study show that the optimal investment in a ZEB for Norwegian conditions is an air sourced heat pump combined with an electric top-up coil, heat storage and solar PV. The main objective of the paper is to identify the value of using the stochastic versus the deterministic approach, and to assess its benefits. A deterministic model often uses average climatic conditions as input parameters, and hence, do not provide a viable solution under extreme weather conditions. Results show that the stochastic model is advantageous to its deterministic counterpart to: (i) cover the heat demand of periods colder than the deterministic input data, and (ii) avoid over-sizing of the base-load heat technology. The results imply that a stochastic model provides a solution with lower total costs, that offers more flexibility in terms of an improved allocation of the installed capacity between base load, storage and top-up technologies compared to the deterministic solution.