Post on 24-Jan-2017
transcript
Stochastic Simulation of PhotoVoltaic Costsand Investment
by
Ignacio Maulen.
Dept. of Economics and Business Management.Universidad Rey Juan Carlos, Madrid, Spain.
ignacio.mauleon@urjc.es
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
Introduction & index.
Static long run simulation of energy and climate models:
But parameters are estimated => random.
Stochastic simulations (Monte Carlo).
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Stochastic simulations (Monte Carlo).
Distant horizons: 2030, 2050 => Feasible?
Results relevant for investors and policy makers.
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
Index:
PV Cost Model Estimation.
Simulating PV Module Prices.
Simulating Total Investment.
Risk Analysis.
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Risk Analysis.
Capacity Simulations.
Summary & Implications.
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
PV Cost Model Estimation.
Learning by doing, PV costs & Installed Capacity.
2.5
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4.5
MODULE PRICES w.r.t. CAPACITY O.L.S. regression (logs.) & Learning Rate (LR)
Log(P)=3.98-0.33*Log(Cap) (45.) (26.)
R2=0.95, D.W.=0.44 LR=20% (23.1)
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1981
19821983
19841985
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0 2 4 6 8 10 12
Log(
mod
ule
pric
es)
Log(Installed capacity)
19851986
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19881989
199019911992
199319941995
1996199719981999
20002001 20022003
20042005
2006 2007 2008
2009
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20122013
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
Econometric estimation refinements:
Dynamics.
Sample size.
Silicon prices.
Two equation model for PV and silicon prices.
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Two equation model for PV and silicon prices.
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
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Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
CAPACITY FORECASTS
(world Gw.)
IEA GP-BAU IRENA Cu30%
2020 370 161 220 777
2030 1.764 234 500 10.709
Simulating PV Module Prices.
Parameter uncertainty (randomness).
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2030 1.764 234 500 10.709
2050 4.548 471 2.035.314
IEA: International Energy Association.
GP-BAU: Green Peace - Business As Usual.
IRENA: International Renewable Energy Association.
Cu30%: Capacity up 30% annually ( historical average 1993-2013).
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.MODULE PRICES
(1w., US $)
IEA GP-BAU IRENA Cu30% EPd3% IEA-pnr
2020 mean 0.410 0.531 0.429 0.327 0.379 0.280
(50%) 0.259 0.349 0.285 0.202 0.255 0.270
(80%) 0.598 0.782 0.627 0.479 0.560 0.336
(90%) 0.868 1.140 0.923 0.692 0.805 0.376
2030 mean 0.174 0.431 0.203 0.078 0.144 0 .107
(50%) 0.101 0.257 0.118 0.037 0.085 0.103
(80%) 0.247 0.631 0.290 0.112 0.210 0.128
(90%) 0.393 0.912 0.440 0.178 0.323 0.144
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2050 mean 0.088 0.292 0.163 0.005 0.061 0.048
(50%) 0.046 0.185 0.082 0.001 0.030 0.047
(80%) 0.126 0.397 0.227 0.004 0.070 0.058
(90%) 0.205 0.609 0.373 0.010 0.129 0.065
IEA: International Energy Association.
GP-BAU: Green Peace - Business As Usual.
IRENA: International Renewable Energy Association.
Cu30%: Capacity up 30% annually ( historical average 1993-2013).
EPd3%: Energy Prices down 30% annually.
IEA-p.n.r: IEA & non random parameters.
Price of 1 w. in 2013, 0,75 US $
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.p.
d.f.
val
ue
Module Prices (w. US$)
A) PROBABILITY DENSITY FUNCTIONS(Kernel smoothed) Module Prices (2030) ; (w. US$)
Median
Mean
Legend
p.d.f. 2030
50% Probability
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0 0.101 0.174 0.2 0.3 0.4 0.5 0.6
50%Probability p.
d.f.
val
ue
Module Prices (w. US$)
B) PROBABILITY DENSITY FUNCTIONS: RANDOM v. NON RANDOM PARAMETERS(Kernel smoothed) Module Prices (2030)
Non random param p.d.f.
Random param p.d.f.
Legend
Random param.
Non random param.
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Mom
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& P
rob.
int.
Mo
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nts
& P
rob
. in
t.
Year ; Forecasting Period
C) MEAN, VARIANCE & PROBABILITY INTERVALS Module Prices (w. US$)
Variance
median
meanmax. 80%
max. 90%
LegendMeanVarianceMedianMax. 80%Max. 90%
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2015 2020 2025 2030 2035 2040 2045 2050
Var
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ku
rto
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Year ; Forecasting Period
D) VARIANCE, SKEWNESS & KURTOSIS Log(Module Prices)
Variance
SkewnessKurtosis
LegendVarianceSkewnessKurtosis
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2015 2020 2025 2030 2035 2040 2045 2050
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Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.p.
d.f.
val
ue
PROBABILITY DENSITY FUNCTIONS(Kernel smoothed) Module Prices (2030) ; (w. US$)
Median
Mean
Legend
p.d.f. 2030
50% Probability
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p.d.
f. v
alue
Module Prices (w. US$)
0
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0 0.101 0.174 0.2 0.3 0.4 0.5 0.6
50%Probability
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.p.
d.f.
val
ue
PROBABILITY DENSITY FUNCTIONS (Kernel smoothed): RANDOM & NON RANDOM PARAMETERS Module Prices (2030) ; (w. US$)
Non random param p.d.f.
Legend
Random param. p.d.f. 2030
Static param. p.d.f. 2030
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p.d.
f. v
alue
Module Prices (w. US$)
Random param p.d.f.
Median random (0.101)
Mean random (0.174)
Median n.random (0.103)
Mean n.random (0.107)
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Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.M
om
ents
& P
rob. in
t.
Mom
ents
& P
rob. in
t.
MEAN, VARIANCE & PROBABILITY INTERVALS Module Prices (w. US$)
max. 80%
max. 90%
LegendMeanVarianceMedianMax. 80%Max. 90%
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Mom
ents
& P
rob. in
t.
Mom
ents
& P
rob. in
t.
Year ; Forecasting Period
Variance
median
mean
max. 80%
0
0.2
0.4
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2015 2020 2025 2030 2035 2040 2045 2050
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.Variance
& s
kew
ness
kurt
osi
s
VARIANCE, SKEWNESS & KURTOSIS
Log(Module Prices)
Variance
LegendVarianceSkewnessKurtosis
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Variance
& s
kew
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kurt
osi
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Year ; Forecasting Period
Skewness
Kurtosis
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2015 2020 2025 2030 2035 2040 2045 2050
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Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
Simulating Total Investment.
Total amount of funds vs. unitary price.
Price depends on investment.
( ) TIPI nn tt =1
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( ) TIPI ntt =1 It , increase in capacity.
Pt , module price.
TIn , total accumulated investment; years 1 to n.
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
ACCUMULATED TOTAL INVESTMENT
(billions US $)
IEA GP-BAU IRENA Cu30% EPd3% IEA-pnr
2020 mean 126 21 103 293 118 89
(50%) 88 15 70 196 84 88
(80%) 178 31 148 422 170 100
(90%) 254 43 208 606 242 108
2030 mean 455 56 351 1.488 397 296
(50%) 287 38 234 948 266 293
(80%) 668 81 509 2.153 573 327
(90%) 973 117 757 3.185 852 346
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2050 mean 759 137 20.140 638 480
(50%) 453 91 8.780 350 477
(80%) 1.091 191 26.330 920 516
(90%) 1.676 292 43.890 1.427 557
IEA: International Energy Association.
GP-BAU: Green Peace - Business As Usual.
IRENA: International Renewable Energy Association.
Cu30%: Capacity up 30% annually ( historical average 1993-2013).
EPd3%: Energy Prices down 30% annually.
IEA-p.n.r: IEA & non random parameters.
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.p.
d.f.
val
ue
Total Investment (b. US$)
A) PROBABILITY DENSITY FUNCTIONS (Kernel smoothed; 2030)
Median
Mean
Legend
p.d.f. 2030
50% Probability
0
0.0005
0.001
0.0015
0.002
0.0025
0 100 260 391 600 800 1000 1200 1400 1600
50% Pro- bability
Pro
babi
lity
valu
e
Total Investment (b. US$)
B) PROBABILITY FUNCTIONS (2030)
Observed
Theoret.
Observed: 1170
95% interval
Theoret.: 1094
95% interval
Legend
Observed 2030
Equiv. Log Normal 0.1
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p.d.
f. v
alue
Total Investment (b. US$)
C) PROBABILITY DENSITY FUNCTIONS(Kernel smoothed; 2030)
Observed
Theoretical
Legend
Observed p.d.f. 2030
Theoretical Log Normal
0
0.0005
0.001
0.0015
0.002
0.0025
0 250 500 750 1000 1250 1500 1750 2000
p.d.
f. v
alue
Total Investment (b. US$)
D) PROBABILITY DENSITY FUNCTIONS (Kernel smoothed; 2020/30/40/50)
p.d.f. 2020
p.d.f. 2030p.d.f. 2040
p.d.f. 2050
Legend
p.d.f. 2020
p.d.f. 2030
p.d.f. 2040
p.d.f. 2050
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Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.p.
d.f.
val
ue
PROBABILITY DENSITY FUNCTIONS(Kernel smoothed) Total Investment (2030) ; (b. US$)
Median
Mean
Legend
p.d.f. 2030
50% Probability
0.0015
0.002
0.0025
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p.d.
f. v
alue
Total Investment (b. US$)
Mean
0
0.0005
0.001
0 200 260 391 600 800 1000 1200 1400 1600
50% Probability
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.P
roba
bilit
y va
lue
PROBABILITY FUNCTIONS Total Investment (2030) ; (b. US$)
Observed
Theoret.
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Pro
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lity
valu
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Total Investment (b. US$)
Observed
95% interval
Theoret.
95% interval
Legend
Observed C.D.F. 2030
Theoretical Log Normal
0.1
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0.5
0 250 500 750 1000 1094 1170 1250 1500 1750 2000
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Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.p.
d.f.
val
ue
PROBABILITY DENSITY FUNCTIONS(Kernel smoothed) Total Investment (2030) ; (b. US$)
Observed
Theoretical
Legend
Observed p.d.f. 2030
Theoretical Log Normal
0.0015
0.002
0.0025
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p.d.
f. v
alue
Total Investment (b. US$)
Theoretical
0
0.0005
0.001
0 250 500 750 1000 1250 1500 1750 2000
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.p.
d.f.
val
ue
PROBABILITY DENSITY FUNCTIONS (Kernel smoothed) Total Investment (years 2020/30/40/50); (b. US$)
p.d.f. 2020
Legend
p.d.f. 2020
p.d.f. 2030
p.d.f. 2040
p.d.f. 2050
0.004
0.005
0.006
0.007
0.008
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p.d.
f. v
alue
Total Investment (b. US$)
p.d.f. 2020
p.d.f. 2030
p.d.f. 2040
p.d.f. 2050
0
0.001
0.002
0.003
0.004
0 200 400 600 800 1000
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
Risk Analysis.
Expected Investment at Risk (EIR):
Expected Investment, if prices rise above a given high value.
[ ][ ]
xxob =Pr
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[ ][ ] EIRxxxE
xxob
==
|
Pr
e.g., valuexupperx ,,,%,90=TI, Total Investment
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
EXPECTED INVESTMENT 'AT RISK'
(billions of US $)
IEA GP-BAU IRENA Cu30% EPd3% IEA-pnr
2020
(80%) 312 51 252 726 292 110
(90%) 404 67 329 936 376 116
2030
(80%) 1.176 140 911 4.032 1.058 348
(90%) 1.557 178 1.170 5.562 1.392 384
2050
(80%) 2.082 361 66.657 1.773 539
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(80%) 2.082 361 66.657 1.773 539
(90%) 2.709 450 1.017.00 2.343 561
IEA: International Energy Association.
GP-BAU: Green Peace - Business As Usual.
IRENA: International Renewable Energy Association.
Cu30%: Capacity up 30% annually ( historical average 1993-2013).
EPd3%: Energy prices down 3% annually.
IEA-p.n.r: IEA & non random parameters.
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
Capacity Simulations.
Grid Parity: PV energy price, competitive.
Question: Capacity needed to achieve that price reduction.
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Reverse simulations.
Stoch. Simul. of PV Costs & Inv.Stoch. Simul. of PV Costs & Inv.
Summary & implications.
PV cost model estimated with up-to-date econometric methods.
Parameter uncertainty (randomness), accounted for in simulations.
Results:
Simulations still valid, though more uncertain.
Useful prob. intervals at long horizons (2030, 2050).
Framework for risk analysis.
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Framework for risk analysis.
Implications:
Analysis applicable to other renew. energy sources, and climate models.
PV energy set to become major player in transition to a more
sustainable, equitable, and cleaner energy model.