The story: The Civil Engineering Department would like to have solar panels installed on the roof of Ghausi Hall to supply some of its electricity use - after all there is plenty of space on the roof and plenty of sun in Davis. Based on cost constraints the department decides it can install a 4.0 kWp system (the subscript p refers to rated power). Given the solar radiation in Davis (an annual average 5.47 kWh/m^2/day) the system could produce 7986.2 kWh/year. However, PV panels produce direct current (DC), which needs to be converted to alternating current through an inverter prior to use. Unfortunately this conversion is only 77% efficient (this is often refered to as a ‘derate factor'). There are additional inefficiencies due to (i) temperature effects on panel performance, (ii) increased inverter inefficiency at
high loads, and (iii) reflectivity of the panel surface. Summed on an average annual basis, these inefficiencies lead to an additional 10% loss of efficiency.
The photovoltaic panels: PV system manufacturing requires approximately 2300 kWh of primary (i.e. life cycle) energy per kW of rated power (2300 kWh/kWp).
Though most PV panels sold in the U.S. are produced in China, the brand selected by department are produced in Rochester MI, USA, and are transported by truck to Davis - a total distance of 2,330 miles. PV systems weigh approximately 300 lb/kWp. Freight truck energy intensity is approximately 0.025 gallons of diesel per ton-mile (assume U.S. short tons). Diesel has an energy content of 124,000 BTU/gal. In addition, 15,000 BTU of energy is used in the production of 1 gallon of diesel. Useful conversion: 1 kWh = 3412.14 Btu.
1. PV Production
a. Calculate the production energy required for a 4 kWp system. Report your answer in units of kWh.
b. Calculate the total transport energy required to deliver the PV system to the department in Davis. Report your answer in units of kWh.
c. Trains use about 1/10th the energy as trucks to move 1ton of freight 1 mile (0.025 gal/tonmi). Recalculate part b. assuming panels travel 180 miles by truck, and 2150 miles by train. Report your answers in kWh.
2. PV Electricity Production
a. Based on the location in Davis and the panel efficiency information, calculate the annual electricity production from the 4 kWp panel array.
3. Energy Indicators
a. Calculate the energy payback time - in other words - how many years does it take to produce as much energy as went into producing and transporting the PV system?
i. Assuming truck transport as in 1.b.
ii. Assuming combined truck and rail trainsport as in 1.c.
b. Assuming the PV system has a productive life of 20 years, and that there are no losses in efficiency over time, what is the net energy ratio for the system? Assume truck transport only (as in 1.b.).
c. Calculate the fossil energy intensity of PV-generated electricity (on a per-kWh basis) using the same assumptions as in 3.b. Your units will be kWh_Fossil /kWh_Generated.