Multi-horizon optimization for domestic renewable energy system design under uncertainty

In this paper we address the challenge of designing optimal domestic renewable energy systems under multiple sources of uncertainty appearing at different time scales. Long-term uncertainties, such as investment and maintenance costs of different technologies, are combined with short-term uncertainties, including solar radiation, electricity prices, and uncontrolled load variations. We formulate the problem as a multistage multi-horizon stochastic Mixed Integer Linear Programming (MILP) model, minimizing the total cost of a domestic building complex's energy system. The model integrates long-term investment decisions, such as the capacity of photovoltaic panels and battery energy storage systems, with short-term operational decisions, including energy dispatch, grid exchanges, and load supply. To ensure robust operation under extreme scenarios, first- and second-order stochastic dominance risk-averse measures are considered preserving the time consistency of the solution. Given the computational complexity of solving the stochastic MILP for large instances, a rolling horizon-based matheuristic algorithm is developed. Additionally, various lower-bound strategies are explored, including wait-and-see schemes, expected value approximations, multistage grouping and clustering schemes. An extensive computational experiment validates the effectiveness of the proposed approach on a case study based on a building complex in South Germany. We tackle models with over 43 million constraints and 12 million binary, 700 hundred integer and 10 million continuous variables; they are solved with up to 0.32% optimality gap in reasonable computing time, where the value of the stochastic decisions as well as the benefit of the integrated risk-averse measures are quantified.