On a probability distribution model combining household power consumption, electric vehicle home-charging and photovoltaic power production

In this paper we develop a probability distribution model combining household power consumption, electric vehicle (EV) home-charging and photovoltaic (PV) power production. The model is set up using a convolution approach to merge three separate existing probability distribution models for household electricity use, EV home-charging and PV power production. This model is investigated on two system levels: household level and aggregate level of multiple households. Results for the household level show the power consumption/production mismatch as probability distributions for different time bins. This is further investigated with different levels of PV power production. The resulting yearly distribution of the aggregate scenario of multiple uncorrelated households with EV charging and PV power production is shown to not be normally distributed due to the mismatch of PV power production and household power consumption on a diurnal and annual basis.