reason it tastes so sweet to the Joneses next
door, who have just purchased a solar electric
system and are enjoying steady monthly bills.
As the price of the electricity one avoids buying
goes up, the time it takes to recoup the original
investment in the system — called the simple
payback time, or sometimes the “break-even”
time — goes down.
We can roughly estimate the payback for
a residential grid-tied system that is not a net-exporter to the grid by using this formula:
U
Simple Payback (SPB) = -----------------------------
(years) D*I*W*R*C
where U is the upfront system cost (not including any incentives), D is 365 days per year, I is
the average number of full-sun-hours per day (
insolation) at a given location, W is the system size
(kilowatts DC) degraded annually by 1 percent,
R is the system’s performance ratio (
conservatively set at 0.75), and C is the cost of electricity
(per kilowatt-hour) adjusted annually at plus 5
percent. For a commercial-sized application, solar generation that overlaps with peak kilowatt usage may shave down the demand charges as well.
But the simple payback is, at best, an approximation. Run it five times in five years and
one likely has five different numbers, due to
fluctuating power rates and the ebb and flow of
incentives (not included in the equation above).
Things get difficult when trying to choose the
right time to invest in such a system, factoring
in rebates and the price of electricity, along with
technology advances. Speaking in the language
of sustainability, a more useful number is the
energy payback period: the number of years it
takes for the solar panels’ energy production to
equal the initial energy inputs of manufacture
and installation and for net-positive production
to begin. The energy payback is fixed by the conversion efficiency of the PV cell, the methods of
manufacture, system construction and climate.
This can be stated as follows:
EM + EBOS
Energy Payback (EPB) = ---------------------
(years) D I W R
where EM is the energy required in the manufacture of the solar panels — for example, the
refining and crystallization of silicon and cutting it to wafer size. EBOS, “energy for balance of
Reducing the financial payback on a photovoltaic system is likely to require a variety of renewable
energy incentives and penalties for net-CO2-producing electricity generation. Shown, a sun-tracking
photovoltaic array at Sierra Nevada Brewing Co., Chico, Calif.
comparing Financial vs. energy payback
In this sample of large-scale photovoltaic installations,
simple (dollar) payback averaged five times as long as energy payback.
Institution
Location
Size
(k W DC)
Array
type
Date
Insolation1
(full-sun
hours/day)
5. 38
5. 2
5. 48
6
4. 4
4. 13
4. 48
4. 4
SPB
(yrs)
EPB2
(yrs)
Butte College 21 5
Napa Valley College 17 4
Loyola Marymount Univ. 20 3
Arizona State Univ. 35 5
Carnegie Mellon Univ. 39 5
University at Buffalo 25 6
Harvard University 32 5
Univ. Southern Maine 27 5
Average 27 4.75
Assuming (a) 5 percent electricity rate escalation3 (b) performance ratio of 0.754 (c) annual photovoltaic cell degradation
of 0.01 for monosilicon and polysilicon modules, 0.015 for amorphous silicon modules5 (d) single-axis tracking increases
output by 20 percent (e) peak demand is reduced more in warm climates (California, Arizona) than in cooler ones due to load
profiles (f) power generation never exceeds consumption, i.e., net-metering regulations do not factor.
Oroville, Calif.
Napa, Calif.
Los Angeles
Tempe, Ariz.
Pittsburgh
Buffalo, N. Y.
Cambridge, Mass.
Portland, Maine
1,055
1,158
723
30
12
74
36
8
Ground
Ground, tracking
Rooftop
Parking awning
Rooftop
Rooftop
Rooftop
Rooftop
2005
2006
2003
2005
2005
2006
2003
2005
1 National Renewable Energy Laboratory (2008) U. S. photovoltaic solar resource: flat plate tilted at latitude. Map,10- by 10-kilometer resolution. Units are
full-sun hours per day.
2 Alsema E. A. (2000) Energy pay-back time and CO2 emissions of PV systems. Progress in Photovoltaics: Research and Applications 8: 17–25.
3 Energy Information Administration (2007) Electric Power Annual – State Data Tables. eia.doe.gov/cneaf/electricity/epa/epa_sprdshts.html Cited 15 May
2008.
4 Mohr N. J., Schermer J.J., Huijbregts M. A., Meijer A., Reijnders L. (2007) Life cycle assessment of thin-film GaAs and GaInP/GaAs solar modules. Progress in
Photovoltaics: Research and Applications 15:163-179.
5 Marion B., Adelstein J., Boyle K., Hayden H., Hammond B., Fletcher T., Canada B., Narang D., Shugar D., Wenger H., Kimber A., Mitchell L., Rich G. and
Townsend T., (2005) Performance Parameters for Grid-Connected PV Systems. Proceedings of the 31st IEEE Photovoltaics Specialists Conference and Exhibition, Lake Buena Vista, Fla.
