Final answer:
The number of square meters of PV cells needed to meet a person's yearly electricity needs is calculated based on average daily solar radiation and PV efficiency. Payback time for a PV system is determined by the system cost, electricity prices, and daily electricity production. A $20,000 system at $0.09 per kWh, assuming daily needs are met for a four-person household, will take about 12.3 years to reach $20,000 of electricity generation.
Step-by-step explanation:
Calculating a person's residential electricity needs for a year involves looking at an electricity bill, dividing the total kWh by the number of people and the number of days in the billing period. The average American uses 12 kWh per day. To calculate the solar radiation per square meter for one year, one would use regional data, typically in the range of 4-6 kWh/m²/day. Factoring in a photovoltaic (PV) conversion efficiency of 10%, and then improving it to 40%, will change the number of square meters needed for PV cells to supply that person's electricity for the year.
The calculation of payback time for a commercially available household photovoltaic system presupposes knowledge of the total system costs, electricity prices, and average daily sunlight hours. At a system cost of $20,000 and electricity prices of $0.09 per kWh, with a system providing enough kWh for a four-person household, the payback time can be computed by dividing the system cost by the daily electricity value production in dollars.
Given the average household consumption of 30 kWh per day and an estimated full-sun-equivalent yield of 6 hours per day at a cost of $0.09 per kWh, a $20,000 system would take about 12.3 years to generate $20,000 of electricity ($20,000 / ($0.09 * 30 kWh * 365 days) = 12.3 years). This calculation does not take into account potential federal and state incentives that could reduce the payback period.