Stochastic simulation of photovoltaic costs

Stochastic Simulation of PhotoVoltaic Costsand Investment

by

Ignacio Maulen.

Dept. of Economics and Business Management.Universidad Rey Juan Carlos, Madrid, Spain.

[email protected]

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).

2I.Maulen (Univ. Urjc, Madrid)

Stochastic simulations (Monte Carlo).

Distant horizons: 2030, 2050 => Feasible?

Results relevant for investors and policy makers.


Index:

PV Cost Model Estimation.

Simulating PV Module Prices.

Simulating Total Investment.

Risk Analysis.


Risk Analysis.

Capacity Simulations.

Summary & Implications.


PV Cost Model Estimation.

Learning by doing, PV costs & Installed Capacity.

2.5

3

3.5

4

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)

1978

1979

1980

1981

19821983

19841985


-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12

Log(

mod

ule

pric

es)

Log(Installed capacity)

19851986

1987

19881989

199019911992

199319941995

1996199719981999

20002001 20022003

20042005

2006 2007 2008

2009

2010

2011

20122013


Econometric estimation refinements:

Dynamics.

Sample size.

Silicon prices.

Two equation model for PV and silicon prices.


Two equation model for PV and silicon prices.


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).


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


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





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

0

1

2

3

4

5

6

0 0.101 0.174 0.2 0.3 0.4 0.5 0.6

50%Probability p.

d.f.

val

ue


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.

0

2

4

6

8

10

12

14

16

0 0.1 0.2 0.3 0.4 0.5 0.6


Mom

ents

& P

rob.

int.

Mo

me

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%

0

0.2

0.4

0.6

0.8

1

1.2

1.4

2015 2020 2025 2030 2035 2040 2045 2050

Var

ianc

e &

ske

wne

ss

ku

rto

sis


D) VARIANCE, SKEWNESS & KURTOSIS Log(Module Prices)

Variance

SkewnessKurtosis

LegendVarianceSkewnessKurtosis

-3

-2

-1

0

1

2

3

4

5

2015 2020 2025 2030 2035 2040 2045 2050

3

14

25

36

47

58


d.f.

val

ue

PROBABILITY DENSITY FUNCTIONS(Kernel smoothed) Module Prices (2030) ; (w. US$)

Median

Mean

Legend

p.d.f. 2030

50% Probability

3

4

5

6


p.d.

f. v

alue


0

1

2

3

0 0.101 0.174 0.2 0.3 0.4 0.5 0.6

50%Probability


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

8

10

12

14

16


p.d.

f. v

alue


Random param p.d.f.

Median random (0.101)

Mean random (0.174)

Median n.random (0.103)

Mean n.random (0.107)

0

2

4

6

8

0 0.05 0.1 0.15 0.2 0.25

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%

0.8

1

1.2

1.4


Mom

ents

& P

rob. in

t.

Mom

ents

& P

rob. in

t.


Variance

median

mean

max. 80%

0

0.2

0.4

0.6

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

1

2

3

4

5

36

47

58


Variance

& s

kew

ness

kurt

osi

s


Skewness

Kurtosis

-3

-2

-1

0

1

2015 2020 2025 2030 2035 2040 2045 2050

3

14

25


Simulating Total Investment.

Total amount of funds vs. unitary price.

Price depends on investment.

( ) TIPI nn tt =1


( ) TIPI ntt =1 It , increase in capacity.

Pt , module price.

TIn , total accumulated investment; years 1 to n.


ACCUMULATED TOTAL INVESTMENT

(billions US $)


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


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





EPd3%: Energy Prices down 30% annually.



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


B) PROBABILITY FUNCTIONS (2030)

Observed

Theoret.

Observed: 1170

95% interval

Theoret.: 1094

95% interval

Legend

Observed 2030

Equiv. Log Normal 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 0.95

1

0 250 500 750 1000 1250 1500 1750 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 0.95 1


p.d.

f. v

alue


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


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

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0 200 400 600 800 1000


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


p.d.

f. v

alue


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.

0.5

0.6

0.7

0.8

0.9

0.95

1

0.5

0.6

0.7

0.8

0.9

0.95

1


Pro

babi

lity

valu

e


Observed

95% interval

Theoret.

95% interval

Legend

Observed C.D.F. 2030


0.1

0.2

0.3

0.4

0.5

0 250 500 750 1000 1094 1170 1250 1500 1750 2000

0.1

0.2

0.3

0.4

0.5


d.f.

val

ue

PROBABILITY DENSITY FUNCTIONS(Kernel smoothed) Total Investment (2030) ; (b. US$)

Observed

Theoretical

Legend

Observed p.d.f. 2030


0.0015

0.002

0.0025


p.d.

f. v

alue


Theoretical

0

0.0005

0.001

0 250 500 750 1000 1250 1500 1750 2000


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


p.d.

f. v

alue


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


Risk Analysis.

Expected Investment at Risk (EIR):

Expected Investment, if prices rise above a given high value.

[ ][ ]

xxob =Pr


[ ][ ] EIRxxxE

xxob

==

|

Pr

e.g., valuexupperx ,,,%,90=TI, Total Investment


EXPECTED INVESTMENT 'AT RISK'

(billions of US $)


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


(80%) 2.082 361 66.657 1.773 539

(90%) 2.709 450 1.017.00 2.343 561





EPd3%: Energy prices down 3% annually.



Capacity Simulations.

Grid Parity: PV energy price, competitive.

Question: Capacity needed to achieve that price reduction.


Reverse simulations.


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.


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.

Date post:	24-Jan-2017
Category:	Economy & Finance
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Stochastic simulation of photovoltaic costs

Economy & Finance