Optimal consumer capacity investment in solar panel system under supply and demand uncertainty

Our paper analyzes the optimal capacity investment in solar panels system for consumers. During the daytime, solar panel system absorbs energy from the sun and supplies the energy generated to the building structure. Our model takes into consideration the variations in the daily consumption of electricity and the variations in the daily available sun energy. We model these variations in our paper as uncertainty in energy demand and uncertainty in energy supply. Excessive usage of electricity that is beyond the energy generation of the solar panels are bought at a higher price from the utility company than the payment received from the utility company for excess energy sold to the grid. We analytically solve for the optimal quantity of solar panels to purchase and install. Our paper fills the research gap in quantifying the impact changes in solar energy yield rate, consumption, and sell -back rate has on the consumer's optimal investment decision in solar panels. We find that the optimal quantity of solar panels increases with the cost of energy during the daytime and payment for excess energy sold to the grid. Interestingly, when solar yield increases, the optimal solution only increases initially, and then it will eventually decrease. Furthermore, our analytical models provide consumers with a decision support system to determine the optimal number of solar panels to purchase and install while taking into consideration the random yield of solar panels, variations in energy consumption, and potential for sell back of excess unused energy generated under complex billing structures from the utility company. Our mathematical models are adaptable to policy changes such as rebates and purchase and sell back rates for electricity. Our numerical study validates the mathematical models and further analyzes the impact changes in solar energy yield rate, energy consumption, and sell -back coefficient have on the consumer's capacity investment decision in solar panels. Our numerical studies find that the lower the reliability factor of solar yield, the more impact the daytime energy cost has on the optimal quantity. When the sell -back coefficient exceeds a certain threshold, the optimal quantity of solar panels increases exponentially.