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

TL;DR

This paper develops a multistage stochastic MILP model for designing domestic renewable energy systems that accounts for multiple uncertainties across different time scales, optimizing costs and ensuring robustness.

Contribution

It introduces a novel multi-horizon stochastic MILP framework with risk-averse measures and a rolling horizon matheuristic for large-scale problems, advancing energy system design under uncertainty.

Findings

Successfully applied to a large case study with over 43 million constraints.

Achieved solutions with up to 0.32% optimality gap within reasonable time.

Quantified the value of stochastic decisions and risk-averse measures.

Abstract

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.