Development of a Mathematical Model to Size the Photovoltaic and Storage Battery Based on the Energy Demand Pattern of the House

Abstract

Solar energy is used in buildings worldwide. However, because the efficiency of photovoltaic power generation varies with environmental fluctuations, it is difficult to control. Therefore, electricity generation from photovoltaics is often poorly matched to the electricity load of the house. The use of storage batteries and photovoltaic panels can effectively improve the stability of the energy supply; however, it also introduces the problem of higher initial costs. Generally, a larger photovoltaic area and battery capacity can lead to higher costs and more renewable energy; therefore, to determine a suitable size of photovoltaic and storage battery for a house, the energy demand of the house must also be considered. The traditional method for sizing photovoltaics and storage batteries mainly considers the daily average electricity demand and the useful area for installing photovoltaics. To size the photovoltaic in a more precise manner, we propose a mathematical model (nonlinear programming) for selecting a relatively optimal solution for the photovoltaic area, battery capacity, and photovoltaic installation angle by considering the hourly and annual demands for electricity from the grid. To validate this mathematical method, a detached house in Zhouzhi county, Shaanxi province, China, was selected to size the devices by the proposed method. Results show that the device sizes determined using the proposed mathematical model are significantly smaller than those determined using the traditional method, without suffering a significant increase in the demand for electricity from the grid. According to our economic analysis, although the proposed method for sizing devices reduces the device cost payback period by half compared to that of the traditional method, the payback period for the devices sized using the proposed method is still 10.6 years. The extremely low electricity price in China may contribute to the extended payback period and thus discourage residents from installing renewable energy devices.