A what is the average rate of price reduction per

a. What is the average rate of price reduction per year (keep 2 significant digits for final
answers) for the Si wafer PV modules between 1985 and 2011? What is the average rate of cost
reduction per year for the thin film PV modules between 2006 and 2013? Hint: ?
?
=
?
0
(1 − ?) ?
. [10 points]
ANS:
Cost reduction-Si wafer: 1 − (
1.455 $/?
12.526 $/?
)
1
2011−1985
= 7.95% ≈ 8.0% per year [5 points]
Cost reduction-thin film: 1 − (
0.614 $/?
1.586 $/?
)
1
2013−2006
= 12.7% ≈ 13% per year [5 points]

b. Based on the learning curve model
?
?
0
= (
?
?
0
)
−?
or log
10
? − log
10
?
0
= −? ⋅ (log
10
? −
log
10
?
0
) . What is the progress ratio (keep 4 significant digits for final answers) for Si wafer PV
modules and thin film PV modules, respectively. Hint: progress ratio = 2
−?
. [10 points]
ANS:
Si wafer: ? = −
log
10
1.455−log
10
12.526
log
10
56.872−log
10
0.107
= 0.34304 [3 points]
Progress ratio 2
−0.34304
= 0.78838 ≈ 0.7884 [2 points]
Thin film: ? = −
log
10
0.614−log
10
1.586
log
10
8.823−log
10
0.110
= 0.21643 [3 points]
Progress ratio 2
−0.21643
= 0.86069 ≈ 0.8607 [2 points]
c. The U.S. Department of Energy has set the SunShot goal of reaching $0.50/W for PV module
prices. In which year (whole number such as 2013), the goal for the Si wafer PV modules and
the thin film PV modules would be reached, respectively? Note that the thin film PV module
data in the figure is presented in cost rather than prices. Assume that for a targeted price of
$0.50/W for thin film PV module, the corresponding cost is $0.40/W. Further assume that the
annual installation for Si wafer PV module and thin film PV module will be 20. GW and 1.6 GW,
respectively. Neglect inflation on prices. Hint: use the learning curve model in part b) to project
the price for Si wafer PV modules from its 2011 data, and project the cost for thin film PV
modules from its 2013 data. [10 points]
ANS:
Si wafer:
For a target price of $0.50/W, the required cumulative installation is
log
10
? = log
10
?
0
+
(log
10
?−log
10
?
0
)
−?
= log
10
0.107 +
(log
10
0.50−log
10
12.526)
−0.34304
= 3.1072
Cumulative installation ? = 10
3.1072
= 1280.0?𝑊 [3 points]
For an annual installation of 20.0 GW, the year to reach SunShot Goal:
2011 +
1280.0𝐺?−56.872𝐺?
20.0𝐺?/????
= 2072.2 = Year 2073 [2 points if within +- 1 year; 1 point if within +-5 years]
Thin film:
For a target cost of $0.40/W, the required cumulative installation is
log
10
? = log
10
?
0
+
(log
10
?−log
10
?
0
)
−?
= log
10
0.110 +
(log
10
0.40−log
10
1.586)
−0.21643
= 1.8055
Cumulative installation ? = 10
1.8055
= 63.900?𝑊 [3 points]
For an annual installation of 1.6 GW, the year to reach SunShot Goal:
2013 +
63.90𝐺?−8.823𝐺?
1.6𝐺?/????
= 2047.4 = Year 2048 [2 points if within +- 1 year; 1 point if within +-5 years]
d. [ER200/PP284 only] Assuming that the annual installation for each type of PV modules grows
at 30.0%/year, in which year (whole number such as 2013) would the SunShot goal be reached?
For example, the annual installation for Si wafer PV module is 20.GW in 2012, 20.GW*(1+30%)
in 2013, and so on. The annual installation for thin film PV module is 1.6 GW in 2014 and
1.6*(1+30%) in 2015, and so on. Hint: summation of geometric series
∑
??
𝑖 ?−1
𝑖=0
=
?(1−?
𝑛
)
1−?
. For
? ? = ? , ? =
log
10
?
log
10
?