Optimizing PV-Battery Combinations for Sustainable Energy Solutions in Australian Households by Adjustable Robust Optimization

Achieving net-zero emissions by 2050 necessitates significant improvements in the environmental performance of buildings, which are responsible for approximately one-third of global energy consumption and greenhouse gas emissions. The integration of photovoltaic (PV) systems and battery storage is a vital strategy for addressing these challenges. PV technology plays a critical role in the transition to a low-carbon future by providing a feasible and efficient solution to enhance energy efficiency amidst the growing demand for sustainable energy. With a remarkable 34% penetration of PV systems, Australia stands as a leader in PV adoption. The long-term nature of decisions regarding the optimal sizing of PV systems and batteries for households is influenced by various parameters, particularly energy demand and generation rates, which present significant uncertainties. This research develops a novel model based on Adjustable Robust Optimization to determine the optimal PV-battery combination. Unlike traditional uncertainty sets, such as box and budget, which can be overly conservative, this model utilizes k-means-based data-driven uncertainty sets to more effectively address demand and generation rate uncertainties. The proposed two-stage model includes a “here-and-now” stage that considers all uncertainty variables, followed by a “wait-and-see” stage that also accounts for these variables. The model is applied to a case study of a household in Queensland, comprising two individuals in their 30 s, and its results are compared with those obtained from a linear optimization model.