A common challenge in promoting PV systems in residential areas is determining the optimal size of solar panels and batteries for each house. Though it might appear straightforward, finding the best solution for many homes quickly becomes computationally demanding. This complexity increases further when considering uncertain factors like variations in average solar radiation, energy consumption patterns, and potential energy sharing between homes.
Addressing this issue, a research team from Japan, including Professor Takeshi Hatanaka from the Tokyo Institute of Technology, has developed a new and efficient method to solve this optimization problem. Their approach, detailed in a paper published in IEEE Access on June 6, 2024, aims to realize net-zero energy houses (ZEHs)-homes designed to have an annual net energy consumption close to zero. This research was conducted in collaboration with Waseda University and the University of Toyama.
The researchers formulated the optimization problem as a system of mathematical equations and inequalities to determine the optimal sizing of PV panels and batteries in terms of cost and carbon neutrality. They considered scenarios where each home generates its energy and where energy sharing between homes is allowed, known as a 'sharing economy.'
The primary challenge was that such complex optimization problems are typically nonconvex, meaning solver algorithms can settle for suboptimal solutions. To overcome this, the researchers applied transformations to convert the original problem into a linear programming (LP) problem, which is more manageable.
The team tested their approach on a Japanese neighborhood with available energy consumption and solar generation data for 134 households. They successfully found optimal solutions for both individual and sharing economies. "Our numerical examples leveraged real-world data instead of relying on synthetic data, enhancing the authenticity of our findings," highlights Hatanaka. "We demonstrated that attaining ZEH status does not significantly elevate costs, which implies that it is a feasible goal for residential houses in Japan."
The experiment also showed that commercial solvers could not solve the original optimization problem due to its complexity. "When considering about two months of data, the original problem becomes computationally challenging, taking up to 14 hours to be solved by commercial solvers. In contrast, the full problem can be solved in less than ten seconds using our LP transformations,".
These findings could greatly facilitate the adoption of renewable energy systems in residential neighborhoods by helping planners determine the appropriate size of solar panels and batteries. Hopefully, these efforts will lead to cities filled with ZEHs.
Research Report:Net-Zero Energy House-Oriented Linear Programming for the Sizing Problem of Photovoltaic Panels and Batteries
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Tokyo Institute of Technology
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