Mathematical optimization of a solar photovoltaic system for a single-family detached home

This paper presents a mathematical sizing algorithms of a stand alone and grid-connected photovoltaic-battery system for a residential house. The objective is to minimize the total storage capacity with cost of electricity. The proposed methodology is based on a Linear and Non-linear programming involving a real data collected through one year with reference to Hradec Kralove meteorological data and typical load profile in Czech Republic. The algorithm jointly optimizes the sizes of the photovoltaic and the battery systems by adjusting the battery charge and discharge cycles according to the availability of solar resource and a time-of-use tariff structure for electricity. The results show that jointly optimizing the sizing of battery and photovoltaic systems can significantly reduce electricity imports and the cost of electricity for the household. However, the optimal capacity of such photovoltaic battery varies strongly with the electricity consumption profile of the household, and is also affected by electricity and battery prices.This paper presents a mathematical sizing algorithms of a stand alone and grid-connected photovoltaic-battery system for a residential house. The objective is to minimize the total storage capacity with cost of electricity. The proposed methodology is based on a Linear and Non-linear programming involving a real data collected through one year with reference to Hradec Kralove meteorological data and typical load profile in Czech Republic. The algorithm jointly optimizes the sizes of the photovoltaic and the battery systems by adjusting the battery charge and discharge cycles according to the availability of solar resource and a time-of-use tariff structure for electricity. The results show that jointly optimizing the sizing of battery and photovoltaic systems can significantly reduce electricity imports and the cost of electricity for the household. However, the optimal capacity of such photovoltaic battery varies strongly with the electricity consumption profile of the household, and is also affected by electricity and battery prices.