Problem 4: Costs of installing rooftop solar PV (50 points)

In this problem, you calculate out-of-pocket costs and payback time for a rooftop solar installation. Assume that this PV system measures 6 m x 5 m and that the panels are 20% efficient.

1. (a) Peak power rating: The solar industry describes the peak wattage of a PV system as its power output during hypothetical irradiance of 1000 W/m2. Whats the peak wattage (in W) of this PV system? (4 pts)
2. (b) Total installation costs: Peak wattage is used by the industry to estimate installation costs. Assume that total installation costs (including panels, parts, permits, and labor) are $4.00/W where the W refers to peak wattage. How much will this PV system cost to install? (4 pts)
3. (c) Out-of-pocket costs: Fortunately, the government has programs to reduce this cost. The federal tax credit for solar PV is 30% of installation (in other words, the U.S. government reimburses homeowners for 30% of the installation cost). In addition, Arizona provides an additional tax rebate of $1000. When these one-time subsidies are deducted from the installation costs, what are the net out-of-pocket costs for this system? (4 pts)

2 According to the U.S. Energy Information Administrations State Energy Data System (SEDS), specifically Table C9 at http://www.eia.gov/state/seds/sep_use/notes/use_print.pdf, Arizonas total annual electricity consumption in 2013 was 1,091 trillion Btu. I multiplied that by a conversion factor (1 kWh/3412 Btu) to get kWh/year, then divided by 365 to get kWh/day.

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(d) Annual generation: Now lets calculate how much electricity the PV system will actually generate in a year (as opposed to peak wattage, which is a hypothetical number). Phoenixs average daily insolation is 5.38 kWh/m2/day. For the sake of simplicity, assume that this energy is entirely captured by the panels (in other words, dont worry about the pitch of the roof or the direction of the panels). What is this PV systems annual electricity output (in kWh)? (8 pts)

(e) Payback time: If Arizonas electricity price is 12 cents/kWh, what is the payback time of this PV system (in years to two decimal places)? Hint: think about the electricity generated by the PV system as saving you the cost of buying electricity from the grid. (10 pts)

(f) Geographic variation: Now compare to another geographic location: the great city of Hartford, CT, which happens to be your professors hometown. Electricity there is an expensive 20 cents/kWh. The state of Connecticut offers a one-time rebate of 67.5 cents/W of installed capacity (where installed capacity refers to the peak wattage of the whole system). Assume the same panel efficiency, installation costs, and federal tax credit as we used for Arizona. You can look up annual average daily insolation on the chart you used in problem 2. Based on these parameters, in Connecticut what would be this systems:

i. ii. iii.

Out-of-pocket installation cost (in $)? (6 pts) Annual electricity generation (in kWh)? (4 pts) Payback time (in years)? (10 pts)