Multi-horizon optimization for domestic renewable energy system design under uncertainty
Giovanni Micheli, Laureano F. Escudero, Francesca Maggioni, Guzin Bayraksan
TL;DR
The paper tackles domestic renewable energy system design under uncertainty across long- and short-term horizons by formulating a multistage, multi-horizon stochastic MILP that co-optimizes PV/BESS investments with operational decisions. It introduces time-consistent risk-averse constraints based on first- and second-order stochastic dominance to guard against extreme discomfort, and develops a rolling-horizon matheuristic (SFR3) to obtain feasible solutions for large-scale instances. To gauge solution quality, it proposes multiple lower-bound schemes (SWS, SMG, SMC, MHEV, MHOEV) and evaluates them against a South Germany building-case study with up to millions of variables and constraints. Computational results show that direct solves are feasible only for small cases, while the SFR3 heuristic delivers near-optimal solutions for large problems within reasonable time; the bound schemes (especially SMG/SMC) provide reliable benchmarks. The study demonstrates the practical viability of robust multi-horizon RES design and highlights the influence of discomfort constraints on total costs, informing design decisions in residential-scale energy systems.
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. Extensive computational experiments validate the effectiveness of the proposed methods on a case study based on a building complex in South Germany, tackling models with over 20 million constraints, 5 million binary variables, and 6 million continuous variables.