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INVESTMENT IN NEW POWER GENERATION UNDER UNCERTAINTY: BENEFITS OF CHP VS CONDENSING PLANTS

IN A COPULA-BASED ANALYSIS

ENERDAY – 6th Conference on Energy Economics and TechnologyDresden, April 8, 2011

Günther Westner and Reinhard MadlenerRWTH Aachen University

April 2011 | Günther Westner and Reinhard Madlener | 2

Scope and research motivation

Scope of our research• Investments under uncertainty in new large-scale fossil-fired power plants• Comparison between condensing plants and combined heat and power (CHP)

plants• Impact of CHP on the investment decision

Research question• Is it possible to reduce the uncertainty for investors through the specific

characteristics of CHP generation?• What is the impact of CHP generation on the selection of construction sites for

new large-scale power plants?

Approach• Real options theory • Spread-based financial modeling• Application of copula functions to describe the dependence structure between the

input parameters


Benefits of Combined Heat & Power (CHP) generationPrimary energy savings and emission reduction

Combined Heat & Powere. g. Engine-CHP

Power

Heat

Primary Energy

Engine-CHP

100

ηel = 34 %

ηth = 56 %

34

56

10

10(Losses)

Primary energy savings:

62

162 = 38 %

Conventional GenerationCondensing plant + Heat boiler

Primary Energy

ηel = 36 %

ηth = 90 %

Power Plant

100

HeatBoiler

62

2

64

6

72(Losses)

In total: 162


Typically operated in heat control mode

Privileged allocation of emission allowances according to the double benchmark principle (allocation for power and heat)

In many European countries governmental support for highly efficient CHP generation

Dependent on the heat utilization of the plant

CHP plants

Typically operated in power control mode

Specific characteristics of power plant operation

Allocation for power only (in many European countries reduction factor on the free allocated certificates is applied)

Allocation of CO2 allowances within the EU ETS

NoneGovernmental support and promotion schemes

NoneAdditional revenues through heat sales

Condensingpower plants

CHP generation versus condensing power plants Energy economic specifics of CHP generation


Selected generation technologiesFocus on large-scale fossil-fired power plants

CCGT technology(Combined-Cycle Gas Turbine)

Hard coal technology

380 gCO2/kWhel380 gCO2/kWhel800 gCO2/kWhel800 gCO2/kWhelCO2 emission factor

0.35-0.18-Heat efficiency

0.500.600.420.45Power efficiency

Heat controlPower controlPower controlPower controlOperation mode

Combined-cycle gas turbine

Combined-cycle gas turbine

Steam turbineSteam turbineTechnology

400 MW400 MW800 MW800 MWElectrical capacity

CHP plantCondensing plantCHP plantCondensing plant


Description of the real options model appliedThe theory behind

Option Value[€/MW]

Aggregated annual spread [€/MW]

Value of waiting

Value of the investment

Break evenpoint

Model assumptions:

• Reference parameter of our model is the aggregated annual spread (AASi) of each investigated technology i. The AASi is defined as:

dzσdtαAAS

dAASii AASAAS

i

i +=

• The option value is calculated based on the Bellman Equation

E(dF(V))ρF(V)dt =

= −∫ dte(t)AASΕV ρt

T

0

iti

• The value of the investment is equal to the discounted AASi

0ρF(V)(V)VF'α(V)²V²Fσ21

ii AAS''

AAS =−+

1βAVF(V) =

• The stochastic characteristic of the AASi is assumed by a continuous-time process based on the Geometric Brownian motion

AASi = Specific Spread x Power Utilization


Aggregated annual spread [€/MW el] =

Specific spread [€/MWh el] x Power utilization [h]

Si Specific spread of plant i in [€/MWhel]PE Market price for electric power in [€/MWhel]RH Revenues through heat sales in [€/MWhel]PCHP Promotion for CHP generation in [€/MWhel]CF Fuel cost in [€/MWhth] ηel Electrical efficiency λF CO2 emission factor of the used fuel in [tCO2/MWhel]πP Free allocation of CO2 allowances for power in [tCO2/MWhel]πH Free allocation of CO2 allowances for heat in [tCO2/MWhel]CCO2 Market price for CO2 allowances in [€/tCO2]

Specific spread of condensing plants

Specific spread of CHP plants

2COPF

el

FECond )Cπ(λη

CPS −−−=

2COHPF

el

FCHPHECHP )Cππ(λ

η

CPRPS −−−−++=

Specific clean spark spread in €/MWhel

23.831.1Std. deviation**29.815.6Mean*

CHP plantCondensing plant[€/MWhel]

* Period: 01-10-2007 till 31-09-2009** Chosen approach tends to overestimates the volatility of the specific spread

-40

0

40

80

120

160

01.10.07 01.04.08 01.10.08 01.04.09

CHP plant

Condensing plant

160

120

80

40

0

- 40

Definition of the aggregated annual spread (I)Specific spread: Differentiation between condensing and CHP plants


Aggregated annual spread [€/MW el] =

Specific spread [€/MWh el] x Power utilization [h]

Definition of the aggregated annual spread (II)Power utilization: Differentiation between power control and heat control mode

0

20

40

60

80

100

120

140

160

Power Price[€/MWh]

100

80

60

40

20

0

Capacity Utilization [%]

Power Price

01-01-2009 31-01-2009

Capacity Utilization

15-01-2009

January 2009

0

20

40

60

80

100

120

140

160

Power Price[€/MWh]

100

80

60

40

20

0

Capacity Utilization [%]

Power Price

01-01-2009 31-01-2009

Capacity Utilization

15-01-2009

January 2009

Power control mode Heat control mode

The amount of power production depends on the price of electrical power

Power production is independent from the price of electrical power


Correlation between specific spread and utilizationCoherence between specific spread and applied generation capacity

power control

0.620

CHP[€/MWhel]

power control

0.620

Condensing [€/MWhel]

Coal-fired plant Gas-fired plant

heat controlpower controlOperation mode

00.522Correlation coefficient

CHP [€/MWhel]

Condensing[€/MWhel]

0

2.500

5.000

7.500

10.000

12.500

15.000

-100 -80 -60 -40 -20 0 20 40 60 80 100

Specific spread [€/MWh]

Gen

erat

ion

capa

city

[MW

]

Hard-coal generation(Correlation 0.620)

Gas generation(Correlation 0.522)

0

2.500

5.000

7.500

10.000

12.500

15.000

-100 -80 -60 -40 -20 0 20 40 60 80 100

Specific spread [€/MWh]

Gen

erat

ion

capa

city

[MW

]

Hard-coal generation(Correlation 0.620)

Gas generation(Correlation 0.522)

(Data exemplarily for December 2009)


Copula functions Describe the dependence structure between two independent random variables

• Copula functions are able to reproduce the complex dependence structure between two input variables (like specific spread and plant utilization) more accurately

• Copula functions are able to consider tail dependence and asymmetric correlation between the distributions considered

• The fundamental theory behind all copula-based analysis is known as Sklar’s Theorem (Sklar, 1959)

Sklar stated that if F: Rd → (0,1) is a joint distribution function with margins X1, X2, …, Xd, then there exists a copula C: (0,1)d → (0,1) such that for all x ϵ Rd and u ϵ (1,0)d there exists a joint distribution function

Conversely, if C:(0,1)d → (0,1) is a copula and F1, …, Fd are distribution functions, then there exists a joint distribution function F with margins F1, …, Fd such that for all x ϵ Rd and u ϵ (1,0)d there exists a copula function

The copula function C is unique if F, F1, …, Fd are continuous distribution functions.

C(u))}(xF),...,(xC{FF(x) dd11 ==

)}(uF),...,(uF{F)u,...,C(u d1

d11

1n1−−=


Dependence structure Empirical dependence structure vs. simulated structure via copula functions

Dependence structure between specific spread and utilization for gas-fired power plants

1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

a) Original data b) Simulated data via empirical fitted copula function

• The distribution of the original data is inhomogeneous within the considered interval • The chosen copula function reproduces the complex dependence structure between the two

input variables (1) specific spread and (2) plant utilization quite accurately


Exceedance correlations Describe the deviations between empirical data and simulation results

1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

a) Coal-fired power plants b) Gas-fired power plants

Empirical dataEmpirically fitted copulaNormal distribution

Quantiles

Exc

eeda

nce

corr

elat

ion

Exc

eeda

nce

corr

elat

ion

Quantiles


1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

1.00

0.80

0.60

0.40

0.20

0.000.00 0.20 0.40 0.60 0.80 1.00

a) Coal-fired power plants b) Gas-fired power plants



Quantiles

Exc

eeda

nce

corr

elat

ion

Exc

eeda

nce

corr

elat

ion

Quantiles



• Exceedance correlations describe the deviations between the dependence structure of empirical data and the dataset modeled by applying either copula functions or correlation coefficients

• The deviations between the empirical dependence structure and the results gained by application of copula functions are less significant compared to the results gained with correlation coefficients

• Therefore, the copula-based approach leads to more accurate results compared to linear correlation coefficients


Gas-fired CHP plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900

Gas-fired condensing plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900

Coal-fired CHP plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900

Coal-fired condensing plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900

Probability Distribution [%]




Aggregated annual spread [ € / kW ]




Gas-fired CHP plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900

Gas-fired condensing plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900

Coal-fired CHP plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900

Coal-fired condensing plant

0,0%

2,0%

4,0%

6,0%

8,0%

-500 -300 -100 100 300 500 700 900









Distributions of the aggregated annual spread Results of the copula-based simulation

155.95

120.81

Std. deviation[€/kWel]

Mean [€/kWel]

144.95

125.29


Mean [€/kWel]

167.57

101.57


Mean [€/kWel]

191.54

249.50


Mean [€/kWel]


0

25

50

75

100

125

0 25 50 75 100 125 150

Aggregated annual spread [€/kW]

Opt

ion

valu

e [€

/kW

] Condensing plant

CHP plant

Intrinsic value

0

25

50

75

100

125

0 25 50 75 100 125 150


Opt

ion

valu

e [€

/kW

] Condensing plant

CHP plant

Intrinsic value

0

25

50

75

100

125

0 25 50 75 100 125 150


Opt

ion

valu

e [€

/kW

] Condensing plant

CHP plant

Intrinsic value

0

25

50

75

100

125

0 25 50 75 100 125 150


Opt

ion

valu

e [€

/kW

] Condensing plant

CHP plant

Intrinsic value

Option value for gas-fired plantsa) Calculation based on correlation coefficients b) Calculation based on copula function

• Option values of gas-fired condensing plants are higher compared to option values of CHP plants of the same technology

• Due to the higher option value it is more likely that investments in condensing plants are cancelled or postponed than investments in CHP plants

• The application of copula functions leads in comparison to correlation coefficients to less significant differences in the option values between condensing and CHP plants

Impact of CHP on the option value of gas-fired CCGT plantsCHP generation reduces the option value of investments


Impact of CHP on the option value of coal plantsA high degree of CHP generation decreases the option value

• The option value of coal-plants depends on the total fuel utilization • The total fuel utilization increases with an increased degree of CHP generation• Consequently, the higher the share of CHP generation, the lower is the option value of

coal-fired power plants • As the degree of CHP generation depends on the heat sink available, it is beneficial to

build new large-scale coal-fired power plants next to sites where the heat can be utilized

Option value of coal-fired plantsStd. deviation of the specific spread

0

5

10

15

20

25

30

0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90Fuel utilization ζ

Std

. dev

iatio

n of

spe

cific

sp

read

[€/M

Wh

el]

0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90

0

5

10

15

20

25

30

0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90Fuel utilization ζ

Std

. dev

iatio

n of

spe

cific

sp

read

[€/M

Wh

el]

0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.900

25

50

75

100

125

0 25 50 75 100 125 150Aggregated annual spread [€/kW]

Opt

ion

valu

e [ €

/ kW

]

Condensation plant (ζ =0,45)CHP plant (ζ = 0,6)CHP plant (ζ = 0,85)Intrinsic value

Condensing


Main results

Approach adopted:

• We chose the aggregate annual spread as basis of our real options investigation

• The aggregate annual spread is gained from the specific spreads and plant utilization, by applying independently to alternative approaches:

1. Description of the dependence structure via correlation coefficients

2. Description of the dependence structure via copula functions

• We compare the results of the two different approaches

Conclusions:

• A high degree of CHP generation reduces the risk exposure and the uncertainty for the investor

• As the possible degree of CHP generation depends significantly on the heat sink available, the question of heat utilization could become a more relevant criteria for the selection of plant sites.

• Our research could have an impact on the criteria for site evaluation of utilities that intend to invest in new large-scale fossil power plants.


Thank you for your attention – any questions?

References:Bastianin, A., 2009. Modelling asymmetric dependence using copula functions: an application to value-at-risk in the energy

sector. Working Paper 2009.24, Fondazione Eni Enrico Mattei.Dixit, A.K., Pindyck, R.S., 1994. Investment under Uncertainty. Princeton University Press, Princeton, NJ.Kumbaroğlu, G., Madlener, R., Demirel, M., 2008. A real options evaluation model for the diffusion prospects of new renewable

power generation technologies. Energy Economics, 30 (4), 1882–1908.Sklar, A., 1959. Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université

de Paris, Volume 8, 229–231.Westner, G., Madlener, R., 2010. The benefit of regional diversification of cogeneration investments in Europe: A mean-

variance portfolio analysis. Energy Policy 38 (12), 7911-7920.Westner, G., Madlener, R., 2011. Investment in new power generation under uncertainty: Benefits of CHP vs condensing

plants in a copula-based analysis. Energy Economics (in press).Wickart, M., Madlener, R., 2007. Optimal technology choice and investment timing: A stochastic model of industrial

cogeneration vs. heat-only production. Energy Economics 29 (4), 934-952.

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