Using Fuzzy Real Options Valuation for Assessing Investments in NGCC and CCS Energy Conversion Technology
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FCN Working Paper No. 3/2009
Using Fuzzy Real Options Valuation for Assessing
Investments in NGCC and CCS Energy Conversion
Technology
Christian Kraemer and Reinhard Madlener
November 2009
Institute for Future Energy Consumer
Needs and Behavior (FCN)
Faculty of Business and Economics / E.ON ERCFCN Working Paper No. 3/2009
Using Fuzzy Real Options Valuation for Assessing Investments in IGCC and CCS
Energy Conversion Technology
November 2009
Authors’ addresses:
Christian Kraemer
Institut für Elektrische Anlagen und Energiewirtschaft
Schinkelstraße 6
52062 Aachen, Germany
E-mail: ck@iaew.rwth-aachen.de
Reinhard Madlener
Institute for Future Energy Consumer Needs and Behavior (FCN)
Faculty of Business and Economics / E.ON Energy Research Center
RWTH Aachen University
Mathieustrasse 6
52074 Aachen, Germany
E-mail: rmadlener@eonerc.rwth-aachen.de
Publisher: Prof. Dr. Reinhard Madlener
Chair of Energy Economics and Management
Director, Institute for Future Energy Consumer Needs and Behavior (FCN)
E.ON Energy Research Center (E.ON ERC)
RWTH Aachen University
Mathieustrasse 6, 52074 Aachen, Germany
Phone: +49 (0) 241-80 49820
Fax: +49 (0) 241-80 49829
Web: www.eonerc.rwth-aachen.de/fcn
E-mail: post_fcn@eonerc.rwth-aachen.deUsing Fuzzy Real Options Valuation for Assessing Investments
in NGCC and CCS Energy Conversion Technology
Christian Kraemera and Reinhard Madlenerb,∗
a
Institute of Power Systems and Power Economics (IAEW), RWTH Aachen University,
Schinkelstrasse 6, 52056 Aachen, Germany
b
Institute for Future Energy Consumer Needs and Behavior (FCN), Faculty of Business & Economics/
E.ON Energy Research Center, RWTH Aachen University, Mathieustrasse 6, 52074 Aachen, Germany
November 2009
Abstract
In this paper we study the relative advantage of investing in a natural gas combined-
cycle (NGCC) power plant versus a coal-fired power plant with and without carbon cap-
ture and storage (CCS) technology. For the investment analysis under uncertainty, we
apply fuzzy real options theory. Three different price scenarios for fuel input and CO2
emission permits are taken into consideration. For the assumptions made, we find evidence
that the NGCC and (to a lesser degree) the conventional hard coal-fired power plant are
the most cost-effective options, followed by the two CCS technologies ‘Oxyfuel’ and ‘Pre-
combustion’. In contrast, due to high specific investment costs and significant losses in
conversion efficiency, the third CCS option ‘Post-combustion’ remains uneconomical. The
sensitivity analysis reveals that already at moderate cost reductions, ‘Pre-combustion’
and ‘Oxyfuel’ both become economically viable and, at sufficiently low CO2 permit prices
or interest rates, even the preferred options.
Key words: Real options analysis, Fuzzy sets, NGCC, Coal combustion, CCS;
JEL Classification Nos.: G11, Q42
∗
Corresponding author. Tel. +49-241-80 49 820; Fax: +49-241-80 49 829; E-mail: rmadlener@eonerc.rwth-
aachen.de (R. Madlener).
11 Introduction
Sustainability considerations of power generation have moved up the agenda of policy-makers,
alongside the growing worries about the impacts of climate change, dwindling fossil fuel
supplies, and considerable investment needs in the power generation sector. Moreover, with
climate policy instruments, such as the European Union Emissions Trading System (EU ETS),
(avoided) carbon dioxide emissions become valuable and make conventional fossil-fired power
generation technologies relatively less attractive than other power generation technologies,
especially the very CO2 -intensive ones. Natural gas has a CO2 emission factor of about
0.222 t/MWhth , compared to hard coal with about 0.338 t/MWhth , so that the specific CO2
emissions of NGCC plants are only about half of those of comparable coal technologies.
In this paper, we study the relative advantage of investing in a natural gas combined-
cycle (NGCC) power plant versus a conventional coal-fired power plant with and without
carbon capture and storage (CCS) technology. We consider three different price scenarios
for fuel input and CO2 emissions adopted from the literature. Since CCS technology is not
commercially available yet, we consider an investment project that will be completed in the
year 2020.
For the analysis, we apply fuzzy real options (FRO) theory, which has so far hardly been
used in energy economics (a rare example is Tao et al., 2007, on information technology
investment for nuclear power plants). From a methodological perspective, we demonstrate
that FRO modeling is a useful way for valuing competing power generation investment al-
ternatives. FRO modeling as such has become increasingly popular in recent years, see e.g.
Zimmermann (2001), Magni et al. (2001), Carlsson and Fullér (2001), Carlsson and Fullér
(2003), Rothwell (2006), Mathews et al. (2007), Angelou and Economides (2007), Yang et al.
(2008), Collan et al. (2009), and Sheen (2009). In contrast to other studies, we account for
areas where the fuzzy number actually takes negative values.
The remainder of this paper is organized as follows. Section 2 describes the economic
model for the power plants studied, section 3 presents the FRO model specification applied,
section 4 reports on the data and assumptions used, section 5 presents the results obtained,
and section 6 concludes.
22 Power plant characterization
2.1 Costs and revenues
At the beginning of a power plant project, there is a high capital outlay that is typically
spread over several years. These investment costs comprise costs for planning, construction,
and putting into operation.
Over the lifetime of a plant, fixed and variable operating costs arise. The former comprise
capital-dependent costs, such as taxes, insurance, or capital costs. Depreciation costs are
not considered here. Other fixed costs include repair and maintenance costs, personnel costs,
social costs, and administrative overhead costs. In our analysis, we consider all fixed costs as
one block, because our main focus is on the variable costs per MWh of electricity generated
by the different types of plants. For simplicity reasons, we assume that the fixed costs amount
to 3–5% of the investment costs, which are discounted to the base year in order to be able to
add them to the investment costs.
All plant types considered are fired with fossil fuels, which have to be purchased in the
respective markets before use. Fuel costs account for the largest share of the annual variable
costs of plant operation. For both natural gas and coal, spot and futures markets exist where
these commodities are traded.
Another variable cost component is the CO2 costs, which depend on the CO2 intensity
of the fuel. Additionally, other variable costs arise, denoted as co , such as flue gas cleaning,
variable staff costs, and miscellaneous other costs.
For a conventional power plant, we can thus define the marginal costs as
1 1
c= · pi + · pCO2 · ni + co i = {gas, coal}, (1)
ηi ηi
where ηi is the conversion efficiency of plant type i, pi the price of input fuel i, pCO2 the
price of CO2 permits, ni the CO2 intensity of fuel i, and co other costs.
For obvious reasons, power plants with different fuel costs pi and different efficiencies ηi
can be expected to have different marginal costs, c. Natural gas, for instance, is typically more
expensive but features higher conversion efficiencies. Likewise, even if conversion efficiencies
were the same, a coal-fired power plant would emit more CO2 than a gas-fired power plant
would. A CCS-equipped power plant can avoid CO2 emissions by ξ percent, but then the
3CO2 has to be transported to and stored in a suitable reservoir, causing additional costs,
cCCS . Hence we can expand (1) and write
1 1
c= · pi + · pCO2 · n · (1 − ξ) + co + cCCS i = {gas, coal}. (2)
ηi ηi
The liberalization of the European electricity market has changed the goals of electricity
generation and of transmission companies regarding the operation of power generation units
from cost minimization to profit maximization. Therefore, we use an approach that is based on
a price duration curve in order to also include revenues in the model. The profit-maximizing
owner of a power plant will try to minimize costs and maximize revenues. Electrical energy
is traded either based on standardized contracts at the power exchange (such as the EEX in
Leipzig) or by means of individual long-term (so-called over-the-counter, OTC) contracts.
2.2 Spread and profit margin
If hourly prices are sorted in ascending order over a year, we obtain for each price level the
number of hours for which at least this price is paid for electricity. The resulting graph is
commonly referred to as price duration curve (Figure 1), which we use for the valuation of
the power plant.
For determining the profit margin of a power generation unit, we consider the difference
between the spot price of electricity, pS,el , and the marginal costs of the power plant, defined
as the spread S (referred to as ‘dark spread’ for coal and ‘spark spread’ for natural gas) as
1
Si = pS,el − · pS,i i = {gas, coal}, (3)
ηi
where pF,el denotes the projected future price of electricity, η the conversion efficiency,
and pF,i the projected future price of natural gas and coal, respectively. Since the cost of CO2
emissions is not included yet, we have to modify the spread function accordingly in order to
get the clean spread CS:
1 1
CSi = pF,el − · pF,i − · n · pF,CO2 i = {gas, coal}. (4)
ηi ηi
The additional term describes the CO2 certificate cost for total auctioning (see section 4.1),
4Figure 1: Ordered price duration curve for the EEX spot market in 2008
Source: Data from EEX (2009), own illustration
depending on the CO2 intensity of the fuel under consideration (CO2 factor n), conversion
efficiency ηi of the plant, and the projected future price of the CO2 emissions, pF,CO2 . If
S is positive, the power plant is utilized, and electricity is sold profitably. In contrast, if
S is negative or zero, the plant should be shut down, as each kWh of electricity produced
incurs a loss or a zero profit, respectively. S can be computed for each individual hour of the
year and thus determines the level of the revenues. Note that the assumptions for the unit
commitment do not include thermal constraints, such as start-up costs and minimum up and
down times, or ramping limits. Because a gas-fired power plant can usually be operated more
flexibly than a coal-fired power plant, the model used tends to underestimate the value of the
gas-fired power plant. Integration of the difference between p(t) and the marginal cost c (i.e.
the clean spread CS) over time yields the profit margin, P M , defined as
∫ T
PM = [p(t) − c]dt. (5)
0
Note that all three price variables of particular interest here, i.e. fuel price, electricity
price, and the price of CO2 permits, are not known ex ante and hence have to be estimated.
53 Fuzzy real options model
Following Collan (2008), we use fuzzy numbers instead of a revenue distribution function. To
this end, we define a triangular fuzzy number, henceforth referred to as the fuzzy net present
value (NPV) set A = (a, α, β), comprising all possible NPVs. Similar to the Datar-Mathews
approach (Datar and Mathews, 2004, hereafter DM) two scenarios address the extreme cases
with the NPVs (a − α) and (a + α), respectively, whereas a third scenario tackles the NPV
reference case. The fuzzy real options value, F ROV , can then be calculated as (cf. Collan
et al., 2009, p.7): ∫∞
0 µA (x)dx
F ROV = ∫ +∞ E(A+ ). (6)
−∞ µA (x)dx
The integral in the denominator represents the area determined by the fuzzy NPV and
the integral in the numerator the part of it that yields a positive NPV. Hence the ratio tells
us at what probability the project is profitable. E(A+ ) denotes the fuzzy mean of the positive
part of A, which for triangular fuzzy numbers with a − α < 0 < a can be stated as (cf. Collan
et al., 2009, p.8):
(α − a)3 β−α
E(A+ ) = 2
+a+ . (7)
6α 6
For the determination of the F ROV , given a triangular fuzzy number A = (a, α, β), we
obtain the following functional form (for details, see Appendix A):
a + β−α
6 , 0≤a−α
a
(α+β)−(1− α )(a−α) [ (α−a2 ) + a +
3
β−α
(α+β) 6α 6 ], a−αconstruction starts, however, no investment in CCS power plants will take place, and hence
the negative contribution to today’s technology can be neglected.
Such a procedure is, of course, applied implicitly even today. By means of scenario analysis
different market developments are modeled. Depending on the forecast, the most profitable
power plant technology will be chosen. Hence a preferred technology can be assigned to each
scenario.
In our real options analysis, the selection process is reversed. Individual investment al-
ternatives are assigned a value that considers the different scenario-dependent states of the
world in the future. If, over time, it becomes clear that the technology cannot be operated
profitably, then it will be abandoned. The resulting flexibility is attributed to the power plant
as a real options value and leads to a more realistic assessment of the technologies considered.
Abandonment of a technology is only sensible if future developments of markets and prices
are evolving. However, shortly before construction begins, a better forecast can be made than
today (in our analysis, construction of a plant put into operation has to start in 2015, so that
then more information will be available than in our base year 2009).
4 Data and assumptions
For a consistent valuation of the technological options, we have to make certain assumptions.
These concern mainly fuel costs, CO2 emission costs, and the annual values and hourly
schedules of the electricity price. Since CCS technology is not expected to be available
commercially before 2020, we need to consider a time horizon until 2060, given the expected
lifetime of a coal-fired power plant of forty years.
4.1 Plant characteristics
Table 1 shows the data used for the analysis. The conventional hard coal-fired power plant
used as a reference is one which, in 2008, is operated in the medium-load segment (5,000
full-load hours p.a.) and which has a conversion efficiency of 38%. The conversion efficiency
is assumed to increase by 0.2–0.3% per annum, from 38% in 2008 to 40% in 2020.
We assume a construction period of five years and that the investment costs are spread
equally across this period of time. Technical restrictions, such as ramp-up and shut-down
7Table 1: Parametrization of the power plants studied
Convent. CCS
Parameter Unit NGCC hard coal Pre-comb. Oxyfuel Post-comb.
Capacity [MW] 600 600 600 600 600
Investment cost [million e/MW] 0.5 1.25 1.8 2.0 2.14
Conversion efficiency [%] 60 40 41 40 36
CO2 sequestr. rate [%] - - 88 95 88
Fixed O&M cost p.a. [% of inv. cost] 5.0 5.2 5.8 3.7 5.0
Variable cost [e/MWh] 2.7 1.2 2.0 4.5 2.0
CO2 transport
& storage cost [e/t] - - 5.0 5.0 5.0
Sources: Damen et al. (2006), p.222f; BMU (Ed.) (2008), p.179; Grünberg (2007);
Damen et al. (2007); and Krautz (2004)
times, are ignored for simplicity. In order to ensure comparability of results, we use the same
installed capacity for the generating units of each vintage.
We further assume that (i) CO2 permits are to be 100% auctioned (i.e. EU Directive
2003/87/EG is effected such that after 2013 grandfathering will have ceased completely),
that (ii) for the time horizon of our study (i.e. until 2060) hard coal and natural gas are
available in sufficient quantity to secure continuous operation of the plants, and that (iii)
CO2 storage capacities are sufficient and hence no limiting factor.
Next, we determine the number of hours where, for given marginal costs c, the power
plant yields a positive profit margin (linearized as V (c), see also Figure 2):
8760 − c · (8760 − Vlin0 )
c < plin0
c · mlin + ylin + δv plin0 < c < plin1
V (c) = (9)
Vlin1 + (c − plin1 )/(plin1 − ppeak ) · ppeak plin1 < c < ppeak
0 ppeak < c
with Vlin0 , plin0 , mlin , ylin , δv , Vlin1 , plin1 , ppeak .
This allows us to compute the profit margin, P M , of each generation technology
∫ V (c) ∫ V (c)
PM = [p(t) − c]dt = p(t)dt − c · V (c) (10)
0 0
for the three scenarios considered (index i is dropped for simplicity of exposition).
This integral describes the level of the annual surpluses generated for an installed capacity
8ppeak  Ȗ)(1+ȡ)
ȡ : escalation factor for peak power prices
ppeak  Ȗ)
Ȗ : shift factor, determined by coal price
ppeak ȣ : elongation factor for load hours
140
120 Base:
Electricity price EUR / MWh
EEX 2008
p0m  Ȗ) p(t) in 2020+
Electricity price p(t) [€/MWh]
plin1100
p(t) in 2008
80
P0m
60
58 €/MWh
plin0 40
20
0
0 1000 2000 3000 4000 5000 6000 7000 8000 8760
V0 V0 Â Ȟ) Full load
Full-load hours
hours /a
V [1/a]
Figure 2: Shift of the price duration curve over time
of 1 MW. For each hour in which the power plant yields a positive profit margin these margins
are aggregated for the entire year. Based on the linearization of p(t) the integral can be
9conveniently decomposed into triangles and rectangles, as shown in (11):
0.5(ppeak − plin1 )V (plin1 ) + plin1 V (plin1 )
+0.5(plin1 − plin0 )V (plin0 ) + plin0 [V (plin0 ) − V (plin1 )]
+(plin0 − c)[V (c) − V (plin0 )] − c · V (c)
c < plin0
0.5(ppeak − plin1 )V (plin1 ) + plin1 V (plin1 )
P M (c) = (11)
+0.5(plin1 − c)(V (c) − V (plin1 ) + −V (plin1 ))
−c · V (c) plin0 < c < plin1
0.5(ppeak − c)V (c) plin1 < c < ppeak
0 ppeak < c
with ppeak , plin1 , plin0 and V (c) as shown in Figure 2.
From this we can determine the annual profit margins per technology i that are dependent
on the calculated marginal cost ci . The profit margins computed for each year between 2020
and 2060 are discounted with 8% to the year 2020. The net present value can then be obtained
by multiplying P M with the installed capacity Capi as
∑
2060
P Mt (ci,t )
NPV = · Capi . (12)
(1 + i)2020−t
t=2020
4.2 Price scenarios considered
For the analysis with the FRO modeling method, we have defined three different price sce-
narios. From the World Energy Outlook 2008 of the International Energy Agency (IEA,
2008) and the EIA scenarios (EIA, 2009) we get projections for fuel prices until 2030, while
BMU (Ed.) (2008) has published price scenarios until 2050. Transportation costs, fuel storage
costs, and potential allocation costs of power plants are neglected, as these are relatively small
compared to the absolute price level.
We distinguish between a price trajectory A, which assumes a marked increase of the
prices and which we take as the reference case (dubbed Medium). We further assume a price
trajectory B with a more moderate price development (dubbed Low). Finally, we have defined
a high price trajectory C, where fuel prices rise linearly by a factor of 1.5 (in 2020) and 2.0 (in
10Table 2: Price trajectories for the construction of the price duration curve, by scenario
Scenario / Price Unit 2020 2025 2030 2040 2050 2060
Low
Natural gas [e/MWhth ] 32 35 38 42 45 49
Hard coal [e/MWhth ] 16 17 19 21 22 24
CO2 [e/t] 30 33 35 40 45 50
Medium
Natural gas [e/MWhth ] 40 46 52 61 69 76
Hard coal [e/MWhth ] 20 23 25 31 36 42
CO2 [e/t] 40 45 50 60 70 75
High
Natural gas [e/MWhth ] 60 72 84 107 128 153
Hard coal [e/MWhth ] 30 35 41 55 68 83
CO2 [e/t] 39 45 51 62 74 85
Source: Own compilation, based on data from BMU (Ed.) (2008)
2060) compared to the Medium scenario (dubbed High). Table 2 depicts the price trajectories
assumed for the different scenarios (linear interpolation between the marker years). Assuming
the fuel and CO2 costs, the marginal cost of a single power plant of each technology can be
computed for each of the price scenarios considered. The resulting costs are summarized in
Appendix B.
4.3 Scenario-dependent modeling of the price duration curve
In the scenarios considered, the fuel and emission permit costs rise in different ways, which
also impacts the electricity price and results in scenario-dependent shifts of the price duration
curve (Ockenfels et al., 2008). Thus, we need to model the price duration curve in a way
that the annual price levels are endogenized. Specifically, we define a reference power plant,
which is operated about 5,000 hours a year (mid-load) and which has an average conversion
efficiency of 38% (typical hard coal power plant). If we correct for increases in conversion
efficiency and the possible addition of CCS, this reference plant determines a factor γs,t ; s ∈
{low, medium, high}, t ∈ [2020, 2060] that determines the increase in price levels in each year
and scenario. Furthermore, a factor αs,t describes the upward shift from the original 2008
curve. In the higher price scenarios, we assume that a certain share of the power plants has
integrated CCS, so that CO2 prices do not have to be taken fully into the shift. We assume
that the average conversion efficiency of an existing coal-fired power plant is raised from 38%
in 2008 to 40% in 2020, after which it rises, depending on the scenario concerned, between 0.2–
0.3% per annum. This enables a scenario-adequate annual upward shift of the price duration
11Table 3: Parametrization of the price duration curve, by scenario
Parameter Low Medium High
Shift factor γ in 2020 1.19 1.43 1.84
Shift factor γ in 2060 1.73 2.44 3.88
Price escalation factor ρ (rise of peak power price) 0.05 0.10 0.20
Elongation factor ν (rise of peak power full-load hours) 0.00 -0.01 -0.05
curve. In order to take account of the increasing share of renewable energy (for which reserve
capacity has to be provided), we assume further that over time more and more peak power
has to be provided. This is taken care of by an elongation factor ν, which raises the full-load
hours during which peak power has to be produced. At the same time, a price escalation
factor ρ safeguards that the price for these peak hours is raised. The factors of the price
duration curve introduced must be determined in advance and are here derived from market
price simulations of the European electricity market (Mirbach, 2009). The assumptions for
the various factors are summarized in Table 3.
5 Results
5.1 NPVs and FROVs
Table 4 depicts the present values of the fixed cost and the profit margin for the three scenarios.
As can be seen, coal plants with Post-combustion always have a negative NPV, irrespective
of the scenario, and would thus never be realized. To some extent this is due to the relatively
high investment costs (about e200 million higher than for Pre-combustion as the second most
expensive option). On the other hand, the loss in conversion efficiency is significant, and the
resulting efficiency of 36% leads to markedly higher fuel consumption.
Both Pre-combusion and Oxyfuel show a similar cost-effectiveness, but investment costs
for Pre-combustion power plants are higher. Its NPV is therefore negative in the Low price
scenario. However, the marginally higher conversion efficiency of 41% versus 40% somewhat
dampens the impact of the higher investment costs.
NGCC power plants can yield high positive NPVs for both low and medium price increases.
Even the high gas prices in scenario High, due to the very high conversion efficiency and the
relatively lowest specific investment costs, do not lead to a negative NPV.
Conventional hard coal power plants can be operated profitably in all price scenarios. On
12Table 4: (Net) Present value and FROV of the power plant technologies considered, by
scenario
[million e] Convent. CCS
PV / NPV / FROV NGCC hard coal Pre-comb. Oxyfuel Post-comb.
A. Present value investment and fixed O&M cost:
Investment cost 348.1 870.3 1,253.2 1,399.4 1,489.9
Discounted fixed cost 298.7 776.5 1,247.2 888.5 1,278.3
Sum 646.8 1,646.8 2,500.4 2,287.4 2,768.2
B. Present value profit margin:
Low 1,113.7 1,750.7 2,470.4 2,322.0 1,870.5
Medium 1,174.2 1,866.2 2,938.6 2,865.1 2,131.2
High 800.3 2,036.1 2,753.7 2,610.1 1,728.6
C. NPV power plant (C = B − A):
Low 466.9 103,8 -30.0 34.1 -987.8
Medium 527.4 219.4 438.2 577.2 -637.0
High 153.5 389.3 253.3 322.2 -1,039.7
Fuzzy RO value 424.7 228.4 235.3 316.7 0.0
the one hand, the high conversion efficiency of 49% and the relatively low specific investment
costs are responsible for this outcome. Furthermore, we have assumed a coal-fired power plant
as a reference for the shift of the price duration curve, which ensures that this type of power
plant is always cost-effective.
It can also be seen that the RO value is zero for Post-combustion power plants, which
is trivial. In none of the scenarios is an investment profitable, so that waiting for more
information has no added value. For the other technologies, the RO value is strongly positive.
Note, however, that these values are not directly comparable due to their differences in project
size. In order to avoid this problem, we have also calculated the difference investments.
5.2 Calculation in differences
In this section, we calculate a fictitious investment project that represents the switching from
one technology to another. As the base technology we choose a hard coal power plant, since
this already served as a reference for the price scenarios. Given a lead time of five years,
construction of a plant to be ready in 2020 has to be started in 2015. Table 5 shows the
advantage of switching from the decision to build a hard coal power plant to an alternative
technology. 2020 values are discounted to the base year 2009 with a 5% discount rate , in
order to compare the projects based on current values.
Notice that for the Low price scenario, the NGCC power plant is more competitive than
13Table 5: Present value and FROV when switching from a conventional hard coal plant to
NGCC or CCS technology (difference calculation), by scenario
[million e] CCS
Scenario NGCC Pre-comb. Oxyfuel Post-comb.
Low 212.3 -78.3 -40.8 -585.6
Medium 180.1 127.9 209.2 -500.7
High -137.9 -79.5 -39.2 -835.5
Fuzzy RO value 113.4 8.2 24.6 0.0
the others and is the only one that shows a highly positive NPV. For the Medium price
scenario, the situation is less clear, although the result indicates that the Oxyfuel technology
should be chosen. Finally, for the High price scenario, it is optimal to stick to the hard coal
power plant. At first sight this seems paradox, as with higher CO2 prices it is expected that
the CCS technology will become economically more attractive (since it features lower CO2
emissions, although at the expense of a lower energy efficiency). Due of the lower efficiency,
the higher fuel costs actually overcompensate the cost savings due to avoided (lower) CO2
emissions. Table 5 also displays the RO value, i.e. the value that arises from keeping the
option to switch to another technology alive.
For Post-combustion, this RO value is zero, i.e. switching does not pay in any of the
scenarios considered. For the two other CCS technologies, switching is profitable in the
Medium price scenario. The NGCC power plant, with a fuzzy RO value of e113 million, is
economically more attractive than the CCS options that feature an RO value of e8 million
(Pre-combustion) and e25 million (Oxyfuel), respectively.
5.3 Sensitivity analyses
In order to check the robustness of the results presented above, we also performed some
sensitivity analyses by means of parameter value variation. An important parameter is the
risk-adjusted interest rate. Figure 3 shows the sensitivity of the fuzzy RO value when the
interest rate is varied between 3–15%. At low interest rates of up to 6.6%, Oxyfuel and Pre-
combustion CCS are more favorable than NGCC, while the latter becomes more profitable at
an interest rate higher than 7.1% (the RO value for the Post-combustion plant remains zero).
Next, we have varied CO2 prices for all scenarios at the same level between 0 100 e/t
and 100 e/t. Figure 4 shows that NGCC plants have a positive and steadily increasing RO
value beyond a CO2 price of 20 e/t, since NGCC has a lower CO2 emission factor than
14Figure 3: Sensitivity analysis for the interest rate (3–15%)
Figure 4: Sensitivity analysis for the CO2 price (0–100 e/t)
the conventional coal plant. For the CCS technologies, the fuzzy RO value becomes positive
at about 45 e/t (Oxyfuel and Pre-combustion only). Beyond 50 e/t Oxyfuel, is the most
preferred technology option, while Post-combustion is never cost-effective (F ROV = 0). The
relative advantage of Oxyfuel over Pre-combustion is minor, though, and arises from the lower
fixed costs of 3.7 e/MW of Oxyfuel plants, compared to 5.0 e/MW for Pre-combustion.
15Figure 5: Sensitivity analysis for the investment costs (+/-30%)
As a further sensitivity check, we have altered investment costs in 5% steps from -30%
to +30% for each technology, leaving the other ones unchanged (Fig. 5). While we do not
expect major changes in the development of investment costs and conversion efficiencies of
conventional hard coal plants and NGCC technology, we do for CCS. The results depicted in
Figure 5 show that for Post-combustion plants a cost reduction of 6% is needed for making
these profitable, whereas for Pre-combustion and Oxyfuel, a 10% reduction suffices.
Finally, we have varied conversion efficiency from -5% to +10% for the CCS technologies,
as their conversion efficiencies are more uncertain than those of the NGCC or hard coal power
plants, which can be estimated more easily and, therefore, do not need to be altered. As Figure
6 shows, a modest 1.5% increase for Oxyfuel and a 2% increase for Pre-combustion makes
these two CCS technologies economically more attractive than NGCC. At the same time, a
minor reduction in efficiency pulls the fuzzy RO value down to zero. For Post-combustion,
the RO value only starts to rise at a conversion efficiency higher than 43%.
6 Conclusion
Investments in power generation plants are subject to high uncertainty and irreversibility,
and sometimes can be postponed, which creates a value of waiting that is worth taking into
account. In this paper we have demonstrated how fuzzy real options theory can be applied in
16Figure 6: Sensitivity analysis for the conversion efficiency (-5%,+10%)
such a context. Specifically, a simple fuzzy function provides an intuitive solution for assessing
the real options concerned.
A conventional hard coal power plant is used as a reference, against which the other options
are benchmarked. We find that Post-combustion, due to high investment costs and efficiency
losses, is not a feasible option in any of the scenarios considered. In contrast, for higher
CO2 prices or lower interest rates, Pre-combustion and Oxyfuel turn out to be economically
attractive. The best performance is exhibited by NGCC technology, which turns out to be
profitable at CO2 prices higher than 25-50 e/t, or an interest rate of more than 7%.
In the RO analysis performed, the different full-load hours of the technologies are ignored
due to their differences in marginal cost. Specifically, CCS technologies are assumed to exhibit
some 8,000 full-load hours, while NGCC are used both for mid-load and peak-load. In our
model, investment decisions are taken on the basis of the fuzzy RO value derived from the
price duration function of the spot market only, i.e. the investor does not care about the use
patterns in actual operation as long as the return on investment is acceptable. In this respect,
accounting for the optimal dispatching under technical restrictions could be an interesting and
useful extension of the model.
Overall, NGCC technologies have the best prospects, while CCS technology requires po-
litical support. Intensive R&D is still underway for the membranes used in the Oxyfuel
technology and the hydrogen turbines for Pre-combustion, and it will be necessary that these
17R&D efforts result either in lower investment costs or higher conversion efficiencies, or both.
Finally, it should be noted that in our analysis we have assumed 100% auctioning of CO2
certificates. If this does not materialize, it will be to the disadvantage of the CCS technology.
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Appendix
Appendix A: Derivation of the fuzzy real options value (FROV)
Proof of eq. (8): For a triangular fuzzy number, the formula for the area of a triangle A =
0.5 · c · h generally applies (baseline c = α + β, height h = 1), so that we can write
∫ +∞
µA (x)dx = 0.5(α + β). (A.1)
−∞
Based on the considerations of Collan et al. (2009), we can distinguish the following cases,
where in different intervals of the fuzzy number the negative part is truncated:
Case 1: 0 ≤ a − α
This implies that the fuzzy number A is completely in the positive area. We use the formula
z3 β−α
E(A/z) = 6α2
+α+ 6 for some z which describes the distance of the truncation point of
the fuzzy number as a − α, E(A+ ) = E(A/z). Since A is completely positive, z = 0, and so
∫∞
0 µA (x)dx
∫∞
the quotient of the area of the positive part to the total area is trivial and equals
−∞ µA (x)dx
unity. From this it follows that
∫∞
0 µA (x)dx β−α
F ROV = ∫ +∞ · E(A+ ) = a + . (A.2)
6
−∞ µA (x)dx
Case 2: a − α < 0 ≤ a
The truncated part is in the left, ascending section of the fuzzy number. For this section,
3
E(A+ ) has already been derived in Collan et al. (2009) as [ (α−a)
6α2
+a+ β−α
6 ]. The total
area below the fuzzy number minus the truncated negative part, 0.5(1 − αa )(a − α), is then
20∫∞
0 µA (x)dx. From this we get
∫∞
0 µA (x)dx 0.5(α + β) − 0.5(1 − αa (a − α)) (α − a)3 β−α
F ROV = ∫ +∞ · E(A+ ) = ·[ 2
+a+ ].
0.5(α + β) 6α 6
−∞ µA (x)dx
(A.3)
Case 3: a < 0 ≤ a + β
The fuzzy number is truncated right of the middle a. The expected value of the positive
area can be calculated with (A.3) from Case 2. The height of the remaining triangle can be
ignored, since the top value is treated as unity (i.e. it is the a of fuzzy number A). For this
fuzzy number α′ = 0 and a′ = 0, since the truncation is exactly at zero. β ′ is determined as
the positive part of the distance from a to (a + β), i.e. as (a + β). Hence we obtain
a+β
E(A+ ) = . (A.4)
6
∫∞
The term 0 µA (x)dx is the remaining part of the triangle with the baseline (a + β) and the
height (1 + a/β). Thus we get
0.5(a + β) · (1 + βa ) a + β
F ROV = · . (A.5)
0.5(α + β) 6
Case 4: a + β < 0
The fuzzy number A would be totally in the negative area and the share of the positive part
would be zero, so that F ROV = 0.
q.e.d.
21Appendix B: Marginal cost of power generation
Table 6: Marginal cost of power generation, by technology and scenario, 2020–2060
[e/MWh] Convent. CCS
Scenario / Year NGCC hard coal Pre-comb. Oxyfuel Post-comb.
Low
2020 66.53 54.07 47.01 49.04 53.14
2025 72.19 58.62 50.68 52.64 57.31
2030 77.52 63.18 54.35 56.25 61.48
2035 82.19 67.23 57.41 59.23 64.95
2040 86.85 71.28 60.47 62.21 68.42
2045 90.18 74.51 62.55 64.1 9 70.78
2050 93.51 77.74 64.63 66.16 73.14
2055 97.00 81.07 66.83 68.26 75.64
2060 100.55 84.44 69.08 70.41 78.19
Medium
2020 83.17 68.66 57.73 59.43 65.30
2025 94.06 77.90 65.08 66.65 73.66
2030 105.28 87.14 72.44 73.86 82.01
2035 115.25 96.68 80.16 81.46 90.78
2040 125.22 106.23 87.88 89.05 99.55
2045 132.86 114.66 94.26 95.26 106.80
2050 140.49 123.08 100.64 101.48 114.04
2055 147.83 130.31 107.54 108.40 121.88
2060 155.43 137.83 114.79 115.68 130.13
High
2020 116.58 88.41 81.70 84.04 92.61
2025 137.04 103.82 95.97 98.30 108.83
2030 159.18 119.94 111.09 113.43 126.02
2035 180.40 137.29 127.68 130.07 144.89
2040 202.66 155.40 145.17 147.63 164.78
2045 221.71 172.22 161.12 163.63 182.93
2050 241.51 189.66 177.81 180.37 201.91
2055 263.22 209.00 196.78 199.45 223.49
2060 286.27 229.62 217.28 220.09 246.81
Source: Own calculations
22List of FCN Working Papers
2009
Madlener R., Mathar T. (2009). Development Trends and Economics of Concentrating Solar Power Generation
Technologies: A Comparative Analysis, FCN Working Paper No. 1/2009, Institute for Future Energy
Consumer Needs and Behavior, RWTH Aachen University, November (revised September 2010).
Madlener R., Latz J. (2009). Centralized and Integrated Decentralized Compressed Air Energy Storage for
Enhanced Grid Integration of Wind Power, FCN Working Paper No. 2/2009, Institute for Future Energy
Consumer Needs and Behavior, RWTH Aachen University, November (revised September 2010).
Kraemer C., Madlener R. (2009). Using Fuzzy Real Options Valuation for Assessing Investments in NGCC and
CCS Energy Conversion Technology, FCN Working Paper No. 3/2009, Institute for Future Energy Consumer
Needs and Behavior, RWTH Aachen University, November.
2008
Madlener R., Neustadt I., Zweifel P. (2008). Promoting Renewable Electricity Generation in Imperfect Markets:
Price vs. Quantity Policies, FCN Working Paper No. 1/2008, Institute for Future Energy Consumer Needs and
Behavior, RWTH Aachen University, July (revised November 2011).
Madlener R., Wenk C. (2008). Efficient Investment Portfolios for the Swiss Electricity Supply Sector, FCN Working
Paper No. 2/2008, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University,
August.
Omann I., Kowalski K., Bohunovsky L., Madlener R., Stagl S. (2008). The Influence of Social Preferences on
Multi-Criteria Evaluation of Energy Scenarios, FCN Working Paper No. 3/2008, Institute for Future Energy
Consumer Needs and Behavior, RWTH Aachen University, August.
Bernstein R., Madlener R. (2008). The Impact of Disaggregated ICT Capital on Electricity Intensity of Production:
Econometric Analysis of Major European Industries, FCN Working Paper No. 4/2008, Institute for Future
Energy Consumer Needs and Behavior, RWTH Aachen University, September.
Erber G., Madlener R. (2008). Impact of ICT and Human Skills on the European Financial Intermediation Sector,
FCN Working Paper No. 5/2008, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen
University, September.
FCN Working Papers are free of charge. They can mostly be downloaded in pdf format from the FCN / E.ON ERC
Website (www.eonerc.rwth-aachen.de/fcn) and the SSRN Website (www.ssrn.com), respectively. Alternatively,
they may also be ordered as hardcopies from Ms Sabine Schill (Phone: +49 (0) 241-80 49820, E-mail:
post_fcn@eonerc.rwth-aachen.de), RWTH Aachen University, Institute for Future Energy Consumer Needs and
Behavior (FCN), Chair of Energy Economics and Management / Prof. R. Madlener, Mathieustrasse 6, 52074
Aachen, Germany.You can also read
