The annual average insolation (energy of sunlight per unit area) striking a fixed solar panel in Buffalo, New York, is 200 W?m?2, while in Phoenix, Arizona, it is 270 W?m?2. In each location, the solar panel converts 15% of the incident energy into electricity. Average annual electricity use in Buffalo is 6000 kW?h at an average cost of $0.15 kW?h, while in Phoenix it is 11,000 kW? h at a cost of $0.09 kW? h.
(a) In each city, what area of solar panel is needed to meet the average electrical needs of a residence?
(b) In each city, what is the current average annual cost of electricity?
(c) If the solar panel has a lifetime of 20 years, what price per square meter of solar panel can be justified in each location? Assume that future increases in electricity prices offset the cost of borrowing funds for the initial purchase, so that you need not consider the time value of money in this analysis.
a. One way to figure this out is to find the annual average usage by taking the total annual usage (in kW-h) and dividing by the number of hours in a year to get an average usage in kW. For Buffalo, we have (6000 kW-h/yr)/(8766 h/yr) = 0.684 kW. In Pheonix, it is 11000/8766 = 1.255 kW. In Buffalo, we get 0.15*200 = 30 W m2 of solar panel, while in Phoenix we get 0.15*270 = 40.5 W m-2. The total area needed in Buffalo is therefore 684/30 = 22.8 m2, while the total area needed in Pheonix is 1255/40.5 = 31.0 m2.
b. In Buffalo, it is 6000 kW h * 0.15 $/(kW h) = $900
In Pheonix, it is 11000 kW h * 0.09 $/(kW h) = $990
c. Neglecting the time value of money, we need the solar panels in each case to cost less than 20 years worth of electricity. Thus, in Buffalo, we require the total cost to be less than 20*$900 = $18000 and in Phoenix we require it be less than 20*$990 = $19800. Dividing these by the total area needed in each location gives:
Buffalo: $18000/22.8 m2= $790 m-2
Phoenix: $19800/31.0 m2= $639 m-2
This must include the total installed cost in each case, not just the panels themselves. Support structures, power inverters, etc. will be required. Sizing the panels based on average insolation assumes that electricity can be stored and retrieved for indefinite periods of time at no additional cost. This might be the case if the local electricity supplier allows the homeowner to feed power into the grid and be fully credited against any power drawn from the grid at other times (net metering).
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