Net-Zero Energy House-Oriented Linear Programming for the Sizing Problem of Photovoltaic Panels and Batteries

The global drive towards carbon neutrality has led to a significant increase in the number of power plants based on renewable energy sources (RES). Concurrently, numerous households are adopting RES to generate their own energy, aiming to decrease both electricity costs and carbon footprints. To support these users, many papers have been devoted to developing optimal investment strategies for residential energy systems. However, there is still a significant gap as these studies often neglect important aspects like carbon neutrality. For this reason, in this paper, we explore the concept of net-zero energy houses (ZEHs) - houses designed to have an annual net energy consumption around zero - by presenting a constrained optimization problem to find the optimal number of photovoltaic panels and the optimal size of the battery system for home integration. Solving this constrained optimization problem is difficult due to its nonconvex constraints. Nevertheless, by applying a series of transformations, we reveal that it is possible to find an equivalent linear programming (LP) problem which is computationally tractable. The attainment of ZEH can be tackled by introducing a single constraint in the optimization problem. Additionally, we propose a sharing economy approach to the investment problem, offering a strategy that could potentially reduce investment costs and facilitate the attainment of ZEH more efficiently. Finally, we apply the proposed frameworks to a neighborhood in Japan as a case study, demonstrating the potential for long-term ZEH attainment. The results show that, under the right incentive, users can achieve ZEH, reduce their electricity costs and have a minimal impact on the main grid.