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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
April 2011 | Günther Westner and Reinhard Madlener | 3
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
April 2011 | Günther Westner and Reinhard Madlener | 4
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
April 2011 | Günther Westner and Reinhard Madlener | 5
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
April 2011 | Günther Westner and Reinhard Madlener | 6
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
April 2011 | Günther Westner and Reinhard Madlener | 7
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
April 2011 | Günther Westner and Reinhard Madlener | 8
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
April 2011 | Günther Westner and Reinhard Madlener | 9
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)
April 2011 | Günther Westner and Reinhard Madlener | 10
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−−=
April 2011 | Günther Westner and Reinhard Madlener | 11
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
April 2011 | Günther Westner and Reinhard Madlener | 12
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
Empirical dataEmpirically fitted copulaNormal distribution
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
Empirical dataEmpirically fitted copulaNormal distribution
Quantiles
Exc
eeda
nce
corr
elat
ion
Exc
eeda
nce
corr
elat
ion
Quantiles
Empirical dataEmpirically fitted copulaNormal distribution
Empirical dataEmpirically fitted copulaNormal distribution
• 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
April 2011 | Günther Westner and Reinhard Madlener | 13
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 [%]
Probability Distribution [%]
Probability Distribution [%]
Probability Distribution [%]
Aggregated annual spread [ € / kW ]
Aggregated annual spread [ € / kW ]
Aggregated annual spread [ € / kW ]
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
Probability Distribution [%]
Probability Distribution [%]
Probability Distribution [%]
Probability Distribution [%]
Aggregated annual spread [ € / kW ]
Aggregated annual spread [ € / kW ]
Aggregated annual spread [ € / kW ]
Aggregated annual spread [ € / kW ]
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
Std. deviation[€/kWel]
Mean [€/kWel]
167.57
101.57
Std. deviation[€/kWel]
Mean [€/kWel]
191.54
249.50
Std. deviation[€/kWel]
Mean [€/kWel]
April 2011 | Günther Westner and Reinhard Madlener | 14
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
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
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
Aggregated annual spread [€/kW]
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
April 2011 | Günther Westner and Reinhard Madlener | 15
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
April 2011 | Günther Westner and Reinhard Madlener | 16
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.
April 2011 | Günther Westner and Reinhard Madlener | 17
Thank you for your attention – any questions?
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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
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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
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