# Optimal timing for generation investment with uncertain emission mitigation policy

**ABSTRACT** In view of the fact that different mechanisms for mitigating the CO2 emission have been employed or proposed in different countries or regions, and those already implemented are still in an evolutionary procedure, the future CO2 emission prices would be highly uncertain. Given this background, an effort is made for investigating the problem of generation investment decision-making in electricity market environment with uncertainties from the climate change policy for limiting the CO2 emission. According to the changing characteristics of the uncertain factors, the models of the fuel prices, electricity prices, and CO2 emission prices are respectively presented first. Next, under the existing real option approach (ROA) based methodological framework for the generation investment decision-making problem, a mathematical model accommodating multiple kinds of uncertainties and an efficient solving method are developed. Finally, the proposed model and method are illustrated by a numerical example with different scenarios. Copyright © 2010 John Wiley & Sons, Ltd.

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**ABSTRACT:**The generation business in the U.S. is currently undergoing a transition from a regulated monopoly toward an uncertain, competitive market. Under the competitive market, the price of electric power as well as the corresponding revenue may be much less certain than before. These market uncertainties have increased the significance of two critical factors in generation planning. These factors are financial risks and managerial flexibilities. In order to quantitatively and objectively address these two factors in generation planning, in this dissertation, we design and analyze a series of mathematical models based on the real options approach for generation planning. Hence, this dissertation can be viewed as a comprehensive study of the real options approach in generation planning. The dissertation begins with a simple multiple-project single-option model based on the Black-Scholes option-pricing formula. This is followed by a single-project multiple-option model based on geometric Brownian motion process, binomial lattice, and backward dynamic programming. Next, we design and analyze sophisticated multiple-project multiple-option models where the market values of the projects are assumed to be correlated. As before, we employ the backward dynamic programming over the lattice to determine the optimal options for the multiple projects and the corresponding values of the investment. Also, we investigate the roles of the correlation coefficients among projects in decision making and the value of an option. In addition, we construct and analyze a traditional generation planning model that incorporates forced customer outage costs and forced utility outage costs. By incorporating forced customer outage costs, we attempt to take customer satisfaction level into account. We compare and contrast the models from the real options approach as well as the traditional approach. We hope that the results of this dissertation will encourage utilities to effectively utilize the real options approach in generation planning under market uncertainties. As this approach can address the financial risks and managerial flexibility while the classical discounted cash flow approaches can not, we also hope that generation planning can be performed more quantitatively and objectively under the new economic uncertainties. Typescript (photocopy). Thesis (Ph. D.)--Iowa State University, 2001. Includes bibliographical references. - [Show abstract] [Hide abstract]

**ABSTRACT:**The European Union Emissions Trading Scheme (EU ETS) is the world's first large experiment with an emissions trading system for carbon dioxide (CO2) and it is likely to be copied by others if there is to be a global regime for limiting greenhouse gas emissions. After providing a brief discussion of the origins of the EU ETS, its relation to the Kyoto Protocol, and its precedents in Europe and the U.S., this paper focuses on allowance allocation—the process of deciding who will receive the newly limited rights to emit CO2. We describe how allowances were allocated in the EU ETS, with particular emphasis on the issues and problems encountered, including the lack of readily available installation-level data, the participants in the process, the use of projections, the choices of Member States with respect to auctioning, benchmarking, and new entrant provisions, and the difficult issue of deciding to whom the expected shortage was to be allocated. Finally, we discuss the recently available data on 2005 emissions and what they indicate concerning over-allocation, trading patterns, and abatement. We conclude with some observations about the broader implications of the EU ETS, what seems to be unique about CO2, and the fact that non-economic considerations inform the allocation of allowances.Review of Environmental Economics and Policy 01/2007; 1(1):66-87. · 2.15 Impact Factor -
##### Article: Optimal investments in power generation under centralized and decentralized decision making

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**ABSTRACT:**This work presents a novel model for optimization of investments in new power generation under uncertainty. The model can calculate optimal investment strategies under both centralized social welfare and decentralized profit objectives. The power market is represented with linear supply and demand curves. A stochastic dynamic programming algorithm is used to solve the investment problem, where uncertainty in demand is represented as a discrete Markov chain. The stochastic dynamic model allows us to evaluate investment projects in new base and peak load power generation as real options, and determine optimal timing of the investments. In a case study, we use the model to compare optimal investment strategies under centralized and decentralized decision making. A number of interesting results follow by varying the assumptions about market structure and price response on the demand side.IEEE Transactions on Power Systems 03/2005; · 3.53 Impact Factor

Page 1

Optimal timing for generation investment with

uncertain emission mitigation policy

Guozhong Liu1, Fushuan Wen2*,yand Iain MacGill3

1School of Electrical Engineering, South China University of Technology, Guangzhou 510640, China

2School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

3The Centre for Energy and Environmental Markets (CEEM) and School of Electrical Engineering

and Telecommunications, The University of New South Wales, Sydney 2052, Australia

SUMMARY

In view of the fact that different mechanisms for mitigating the CO2emission have been employed or

proposed in different countries or regions, and those already implemented are still in an evolutionary

procedure, the future CO2emission prices would be highly uncertain. Given this background, an effort is

made for investigating the problem of generation investment decision-making in electricity market

environment with uncertainties from the climate change policy for limiting the CO2emission. According

to the changing characteristics of the uncertain factors, the models of the fuel prices, electricity prices, and

CO2emission prices are respectively presented first. Next, under the existing real option approach (ROA)

based methodological framework for the generation investment decision-making problem, a mathematical

model accommodating multiple kinds of uncertainties and an efficient solving method are developed.

Finally, the proposed model and method are illustrated by a numerical example with different scenarios.

Copyright # 2010 John Wiley & Sons, Ltd.

key words:

generation investment decision-making; electricity market; climate change policy; CO2

emission mitigation; real options; uncertainty

1. INTRODUCTION

The power industry worldwide is suffering or going to encounter three major challenges: significantly

fluctuating fuel prices, power industry restructuring for introducing competition, and Greenhouse Gas

(GHG) mitigation. These three factors could bring significant uncertainties for generation investment

decision-making. Investment risks caused by the fluctuating fuel prices and power industry

restructuring have been investigated in a few publications[1–5], mainly based on the well-established

real options approach (ROA). For instance, in Reference [1] the impact of various uncertainties

(i.e., the electricity price, load demand, natural gas price) on the net-present value of two power plant

investments is investigated by using ROA. In References [2,3], in the ROA based framework, a two-

branch modelandafour-branch lattice modelare developed tofind thevaluesof generation investment

options. In Reference [4], the ROA is extended to consider the situation of a large generation company

and it is shown that the uncertainty of the electricity price has to be considered in the investment

analysis if the company is not able to hedge the price effect in the financial markets and if there is no

competition on the investment opportunity. In Reference [5], the ROA is employed to determine the

optimal investment strategies for capacity expansion where the investment can be carried out or

delayed under market uncertainties.

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER

Euro. Trans. Electr. Power 2011; 21:1015–1027

Published online 6 September 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/etep.493

*Correspondence to: Professor Fushuan Wen, School of Electrical Engineering, Zhejiang University, Hangzhou 310027,

China.

yE-mail: fushuan.wen@gmail.com

Copyright # 2010 John Wiley & Sons, Ltd.

Page 2

GHG emissions have resulted in the global warming of 1.38C since the age of industrialization. It is

estimated that if the global climate increases 28C further, dangerous consequences could be happened

[6,7].Hence,thewell-knownKyotoProtocol thataims tolimitglobalGHG emissions wasagreedonin

October1997 and tookeffect on February16, 2005[8].Up tonow,more than 140 countrieshave joined

the Kyoto Protocol and the GHG emissions of the member countries in the Protocol have exceeded

55% of the global total volume. According to the Kyoto Protocol, by 2012, the reduced emission

amount by industrialized countries should reach at least 5% compared to the baseline in 1990. In

addition, in view that the first commitment period would be due in 2012 and the following reduction

plan is still not confirmed, some countries or regions have already established mid- and long-term

emission reduction plans. For instance, the Europe Union (EU) has planned to reduce the emissions by

20% at least and up to 30% through collaboration with other countries by 2020; at the same time, the

long-term target by 2050 has also been set with the emission reduction to 60–80% as compared to the

baseline in 1990 [9].

In order to fulfill the commitments, several instruments were developed in Kyoto Protocol such as

Carbon Emission Right Trading Scheme, Joint Implementation and Clean Development Mechanism.

Some counties have implemented one or more of these schemes. For instance, the overall reduction

obligation was distributed within the EU following a Burden Sharing Agreement (BSA). EU member

states would face a cap on annual emissions, namely the quantity of allowances that are allocated to

each country. Henceforth each member state developed its own National Allocation Plan (NAP). First,

this allocates the country’s total BSA target between the trading sectors and the non-trading sectors.

Secondly, it specifies how the permits in the trading sector will be distributed among the individual

sources [10,11].

ConsideringthattheimpactofGHGemissionsontheglobalclimatewarmingisbecomingafocusof

extensive concern from the public around the world, it is anticipated that more and more climate

change policies or protocols will be gradually introduced in different countries to limit the GHG

(mainly CO2) emissions [8]. Allowances for the CO2emissions would be introduced into the Carbon

Emissions Trading Market and become a new market product with market values and prices. As far as

the powerindustryisconcerned, coalisstillthemostpopularenergysourceinmostcountries.Itiswell

known that coal firing produces a great deal of CO2. As a result, when CO2emissions are strictly

restricted, the power industry would inevitably be significantly affected. Hence, in making future

generation investment decisions for generation companies or potential investors, the uncertainty of

CO2emissionpricesandtherelatedinvestmentriskscausedbyclimatechangepoliciesshouldbetaken

into account. Up to now, research work in this area is still very preliminary.

It is found in Reference [12] that returns on investment in a nuclear plant will be higher in a scenario

with uncertain carbon prices than in a world with certain prices. In References [13–15], the influences

of future uncertain emissions trading and CO2penalties are investigated within a ROA setup. In these

models, the design of emissions trading schemes and the number of allowances that are freely

distributed are their main features. It is shown in Reference [16] that the uptake of various generation

technologies varies significantly depending on the investors’ views on the carbon price uncertainty.

However, in these papers, only the carbon price uncertainty is considered. While in actual situations,

more uncertainties will be encountered by investors in making generation investment decisions in the

electricity market environment.

The major purpose of this paper is to illustrate explicitly how the market uncertainties, which results

inthe fluctuations offuelpricesandelectricityprices,andtheclimatechangepolicyuncertainty,which

can lead to the CO2price fluctuation more significantly, influence the investment decision-making of

generation companies. The mathematical model developed can accommodate multiple kinds of

uncertainties and the impacts arising from these different uncertainties are contrasted in a relatively

simpleandtransparentframework.Thefindingsshowthattheuncertainties,whichhavegenerallybeen

deemed to lead to the delay of investment, may result in higher probability to exercise an investment

option under some conditions.

This paper is organized as follows. First, the real options theory for investments under uncertainty is

briefly introduced in Section 2. In Section 3, the stochastic motion models are presented for the

uncertain fuel price, electricity price and CO2emission price. In Section 4, the ROA is employed to

compute the value of the investment option and a Monte Carlo based solving approach presented for

Copyright # 2010 John Wiley & Sons, Ltd.Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

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G. LIU, F. WEN AND I. MacGILL

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finding the optimal investment strategy. A method for computing the annual profit of a generation

company is developed in Section 5. An illustrative example and test results for different scenarios are

served for demonstrating the essential features of the developed model and method in Section 6.

Finally, the concluding remarks are given in Section 7.

2. THE REAL OPTIONS APPROACH

The real option approach (ROA), as comprehensively described in Reference [17], has been developed

over the last two decades specifically for evaluating investments under uncertainty. According to ROA,

if an investment is irreversible and the timing of the investment is flexible, the opportunity to invest

can be considered as a real option. The ROA claims that the optimal timing of an investment does

not occur until the value of the project itself exceeds the value of the option to invest in the future.

In mathematical terms, the real options valuation is based on a stochastic dynamic optimization.

ComparedtoatraditionalstaticNetPresentValue(NPV)evaluationofexpectedfuturecashflowsfrom

an investment project, the real options paradigm adds two important analytical dimensions to the

problem. First, a dynamic representation of the timing of the investment decision is used. Secondly,

important uncertain factors are represented as stochastic processes. The ROA usually gives a more

restrictive investment strategy since the value of waiting for information about uncertain future trends

is taken into account. The ROA also suggests the use of contingent claims analysis or risk-neutral

valuation to bypass the problem of determining an appropriate risk-adjusted discount rate. The

advantage is that a risk-free interest rate can be used for discounting. These methods are based on

the assumption that a portfolio can be constructed in the financial markets, which exactly replicate

the uncertainties in the investment project. This is a strong assumption, since investment projects can

involve a number of uncertainties that are not necessarily traded or replicated in any financial market.

3. THE FRAMEWORK FOR GENERATION INVESTMENT

DECISION-MAKING UNDER UNCERTAINTY

Suppose that generation company X possesses a relatively inefficient coal-fired power plant with CX

MW installed capacity. During the operation process, the generation company has been suffering an

ever-increasing amount of burdens, such as the increasing environmental pressure, rapidly rising coal

prices and the restriction of CO2emissions. On the other hand, for a Combined Cycle Gas Turbine

(CCGT) plant, the natural gas has been regarded as clean energy and advocated to be utilized for

generating electricity in a lot of countries. The emitted CO2amount for per MWh generation by a

CCGTpowerplantonlyaccountsfor33%ofthatbyacoal-firedpowerplant;whilefornitrogenoxides,

the number is only 0.5%. In addition, a CCGT power plant basically does not produce SO2. Compared

with a coal-fired power plant, it is obvious that the CCGT power plant is much more environment-

friendly.

The transition from a coal-fired power plant to a CCGTone does not generally require complicated

inspection and approval procedures and basically new space is not required; most devices of the coal-

fired power plant can continue to be utilized. Compared to the construction of a new power plant, the

cost for the transition is also relatively low. Given these considerations, it is assumed that the

generation company X would consider investing to transform the coal-fired plant to a CCGT one. In

fact, some transitions have already been made in China because of the above-mentioned reasons.

Hence, the corresponding decision-making process would be analyzed by simulation methods in this

work. Suppose thatthisproject investmentmaytake placeinaspecificyear tin[t0,Texp]andthe capital

investment is a constant IX($). Here, t0refers to the current year and usually set to zero. During any

year of [t0, Texp], the generation company X can choose to invest immediately, wait for better

investment opportunities or abandon investment opportunities forever. In view of the fact that the

investment plan can be exercised in any year, thus the investment opportunity can be viewed as an

American-style call option. The value of the investment plan is identical to the value of the underlying

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

OPTIMAL TIMING FOR GENERATION INVESTMENT

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asset; the investment capital is identical to the exercising price of the call option. The year Texpis the

last time to invest and can be identical to the maturity date of the call option.

For thegeneration companyX,the investmentprofitwould be dominated by three factorsas follows:

(1) the future fuel price; (2) the future electricity price under the electricity market environment; and

(3) the future climate policies for GHG emissions. Hence, the three uncertain factors will be modeled

below using the stochastic process.

3.1. Modeling fuel price uncertainties

Generally speaking, the variance of the fuel price in the future is a stochastic process, and this means

that the price would rise or decline stochastically based on the present price. Based on the uncertain

pricemodelformulatedbyDixitandPindyck inReference [17],the fuelpriceismodeledhereby using

the well-established Geometric Brownian Motion (GBM), as detailed below:

dpfuel;t¼ mfpfuel;tdt þ sfpfuel;tdwt

(1)

dwt¼ "t

ffiffiffiffi

dt

p

(2)

where pfuel,tis the fuel price in the tth year; mfis the expected growth rate of pfuel,t; sfis the expected

volatility rate of pfuel,tand expressed as a percentage change; dwtis the increment of a wiener process

which is used to simulate the shock of the stochastic market change on the fuel price; "tobeys the

standard normal distribution, namely "t?Nð0;1Þ; dt is the time step and set to 1 year in this work.

According to Equations (1) and (2), the fuel price in the studied time horizon Tcan be represented as

follows:

pfuel;t¼ pfuel;t?1expfðmf?0:5sf2Þdt þ sf"t

ffiffiffiffi

dt

p

g

(3)

Note that whether or not GBM is appropriate to model the uncertainties in risk management and

option pricing has been discussed in some books and papers [17,18]. In fact, some motion models such

as the Geometric Brownian Motion, mean-reverting motion, and Poisson motion are suitable for

modeling some uncertainties according to the statistic characteristics of the problem studied. By

analyzing historical data, we found that GBM is a good candidate for modeling the fuel price. Besides,

up to now, it is still an open question that if there exists one motion model which would be absolutely

accurate for modeling the change of uncertainties.

3.2. Modeling the future electricity price

In the electricity market environment, the load level is one of the main factors having impacts on the

electricity price. Hence, it is supposed here that the uncertainties of the electricity price mainly come

from the load growth, and again the GBM is employed to simulate the load motion as formulated

below:

dLmax;t¼ mLLmax;tdt þ sLLmax;tdwt

(4)

dwt¼ "t

ffiffiffiffi

dt

p

(5)

where Lmax,tis the maximum load in the tth year; mLis the expected growth rate of Lmax,t; sLis the

expected volatility rate of Lmax,t; mLand sLcan be estimated by using historical data; the meanings of

dwt, "t, and dt are the same as those defined before.

According to Equations (4) and (5), the maximum load in the tth year can be represented as

Lmax;t¼ Lmax;t?1expfðmL?0:5sL2Þdt þ sL"t

ffiffiffiffi

dt

p

g

(6)

It is obvious that the investment strategies employed by the other generation companies or investors

will have significant impacts on the optimal investment decision-making of the generation company X.

Copyright # 2010 John Wiley & Sons, Ltd.Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

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G. LIU, F. WEN AND I. MacGILL

Page 5

Whileintheelectricitymarketenvironment,investmentstrategiesaresurelyprivateissuesandcould

notbebroadcastedtothepublicbeforetheinvestmentisimplemented.Thus,itwillbenecessaryforthe

generation company X to estimate the investment strategies of rivals based on available information,

for instance, the generation planning established by the regulators or system operators, the historical

investment strategies of the rivals and other related market information. For the convenience of

presentation, the other generation companies are aggregated as a large company and named as the

generation company A. Suppose that the current installed capacity CA,0of the company A is public

information and the installed capacity increasing rate~kA obeys a normal distribution, namely

~kA?NðmA;sAÞ, thus the installed capacity of the company A in the tth year can be represented as,

CA;t¼ ð1 þ~kAÞCA;t?1

(7)

Based on the weekly weighted average electricity price and the weekly average system capacity

adequacy of the PJM day-ahead energy market in 2001 (detailed data can be found in Reference [19]),

it is discovered that a cubic equation is suitable for describing the relationship between the electricity

price and the capacity adequacy as detailed below,

pe;t;w¼ ar3

t;wþ br2

0?pe;t;w?pe

t;wþ crt;wþ d

s:t:

(8)

where a, b, c, and d are constant coefficients and in the following analysis their estimated values from

historical data in the PJM electricity market are employed: a¼?18632, b¼31728, c¼?17912,

d¼3414. pe,t,wand rt;w¼ ðCt;w?Lt;wÞ=Ct;wrespectively represent the average electricity price and

the average capacity adequacy in the wth week of the tth year; peis the price cap set by the

market regulator to prevent the market power from being abused; Lt,wis the average load in the wth

week, and can be calculated by employing the typical historical load curve and a sampled value of

the maximum load; Ct,wis the average installed capacity in the wth week of the tth year, and is

represented as

Ct;w¼ Ctð1?~kdÞ

(9)

Where:~kdis the escaping rate of the generation capacity from the studied electricity market, and is

supposed to obey the normal distribution, namely~kd?Nðmd;sdÞ; Ctis the total installed capacity

including CX,tMW from the generation company X and CA,tMW from the generation company A.

3.3. Modeling the CO2price jumping

In the future, the uncertainties of the CO2emission price come from three major aspects: (1) The price

fluctuation in the short term; (2) the price drifting in the long term; and (3) the price jumping caused by

the change of emission mitigation policies.

In a competitive market environment, the price fluctuation in the short term does not have much

impact on the long-term investment decision-making, and hence needs to be considered.

The long-term price drifting process could still be modeled by the GBM. New emission mitigation

policies or the change of GHG emission mechanisms could lead to the CO2price jumping. Up to now,

the post-2012 carbon agreements are still under debate. The 2009 United Nations Climate Change

Conference, commonly known as the Copenhagen Summit, was held in Copenhagen, Denmark,

between 7 December and 18 December. The conference included the 15th Conference of the Parties

(COP 15) to the United Nations Framework Convention on Climate Change and the 5th Meeting of the

Parties (MOP 5) to the Kyoto Protocol. According to the Bali Road Map, a framework for climate

change mitigation beyond 2012 was to be agreed there. However, only a ‘‘meaningful agreement,’’ the

Copenhagen Accord, had been reached. The agreement only recognized that climate change is one of

the greatest challenges of the present day and that actions should be taken to keep any temperature

increases to below 28C. The document is not legally binding and does not contain any legally binding

commitments for reducing CO2emissions, but many countries and non-governmental organizations

were still opposed to this agreement.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

OPTIMAL TIMING FOR GENERATION INVESTMENT

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Page 6

The post-2012 carbon agreements may or may not result in commitments with stricter levels of the

emission reduction and higher CO2prices. Given such considerations, it is assumed that a new

mitigation mechanism for CO2emissions would be implemented in a particular year t so as to

investigate the potential impacts of such a policy change. Thus, before the t th year, the CO2price

fluctuation could still be modeled by the GBM; while at the t th year, in addition to the GBM, there

should be an extra stochastic process to model the price jump; after the t th year, the price will follow

the GBM again, but at a new level. The models are detailed below:

?

dpco2;t¼

mco2pco2;tdt þ sco2pco2;tdwtþ hpco2;tð2dy?1Þ

mco2pco2;tdt þ sco2pco2;tdwt

t ¼ t

t6¼t

(10)

dwt¼ "t

ffiffiffiffi

dt

p

(11)

where pco2;tis the CO2emission price in the tth year; mco2is the expected growth rate of pco2;t; sco2is

theexpectedvolatilityrateofpco2;texpressedasapercentage change;the meaningsofdwt,"tanddtare

already defined before; dy is an uniformly distributed random number between 0 and 1; and h is a scale

factor.

According to Equations (10) and (11), the CO2price in the studied time horizon T can be formulated

as

?

pco2;t¼

pco2;t?1expfðmco2?0:5sco22Þdt þ sco2"t

pco2;t?1expfðmco2?0:5sco22Þdt þ sco2"t

ffiffiffiffi

dt

p

þ hð2dy?1Þg

ffiffiffiffi

dt

p

g

t ¼ t

t6¼t

(12)

FromEquation(12),givent¼9,threetypicalmotionprocessesfortheCO2priceintheyearsfrom0

to 19 are illustrated in Figure 1.

4. A GENERATION INVESTMENT DECISION-MAKING METHOD

The uncertainties of the fuel price, electricity price and CO2emission price could cause the generation

company X to defer an investment so that it can get more information for reducing the investment risk.

Hence, for the generation company X, choosing the optimal investment time or evaluating the value of

deferring investment, i.e., the value of an investment option, has emerged as a crucial problem in the

decision-making.

In this work, a Monte Carlo based approach is employed to evaluate the value of an investment

option and obtain the optimal investment strategies. The main steps are as follows:

Step 1: Input the required parameters including the specified sampling times N, and stochastic

motion parameters such as mf; sf; mL; sL; md; sd; mA; sA; mco2; sco2; Lmax;0; pco2;0; pfuel;0; t.

Step 2: Set counter k¼1.

Step 3: Sample the random values of Lmax,t, pfuel,t, and pco2(t¼t0,...,Texp) according to their

respective motion models.

Step 4: Sample the random values of CA,tand Ct,waccording to Equations (7) and (9).

Figure 1. Modeling of the uncertain CO2prices.

Copyright # 2010 John Wiley & Sons, Ltd.Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

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G. LIU, F. WEN AND I. MacGILL

Page 7

Step 5: Compute rt,wand then obtain the value of pe,t,wthrough Equation (8).

Step 6: Compute the investment profit Vinv

the CCGT plant in the tth year, respectively. The transition from the coal-fired plant to the CCGT plant

issupposedtobecompletedattheyear Tld,andduring thetransitionprocess theprofitofthegeneration

company X is supposed to be At. Then should the generation company X invest in the tth year, the

expected profit will be

t. Define Atand Btas the profits of the coal-fired plant and

Vtinv¼

X

tþTld?1

n¼t

e?ðn?tÞrdtAnþ

X

Tlf

n¼tþTld

e?ðn?tÞrdtBn?Ix

where r is the risk-free interest rate and Tlfis the lifetime of the power plant.

Step 7: Compute the profit of waiting to invest Vwait

for a better investment opportunity, then the expected profit of waiting would be

t

. If the generation company X continues to wait

Vtwait¼ Atþ e?rdtV?

ðtþ1Þ

where V?(tþ1)represents the maximum profit when the generation company X has chosen an optimal

investment time during the time period [tþ1, Texp]

Step 8: Obtain the optimal investment strategy. In the year Texp, if the expected profit of investing

would exceed that of waiting, then the generation company X should implement the investment plan;

otherwise, it would abandon the investment opportunity forever. Hence, the value of the investment

option in the year Texpwould be

(

max

X

TexpþTld?1

n¼Texp

e?ðn?TexpÞrdtAnþ

X

Tlf

n¼TexpþTld

e?ðn?TexpÞrdtBn?Ix;

X

Tlf

n¼Texp

e?ðn?TexpÞrdtAn

)

In any year t (t¼t0,..., Texp?1), the investment option value Ftcan be obtained by comparing the

expected value of exercising the option versus that of waiting for a better investment opportunity

through the backward recursive method as detailed below:

(

P

:

Define LTexpand Ltrespectively as the criteria for identifying whether the option should be exercised

in the year Texp, and whether the option should be exercised in the year t (t¼t0..., Texp?1):

1VTexpinv?VTexpwait>0

0

Ft¼

max

P

TexpþTld?1

n¼Texp

e?ðn?tÞrdtAnþ

P

Tlf

n¼TexpþTld

e?ðn?TexpÞrdtBn

)

?Ix;

Tlf

n¼Texp

maxfVtinv;Vtwait?

e?ðn?TexpÞrdtAn

8

>

>

>

>

>

>

>

>

>

>

>

>

<

t ¼ Texp

0?t<Texp

(13)

LTexp¼

otherwise

?

(14)

Lt¼

1

0

Vtinv?Vtwait>0

otherwise

?

(15)

In Equations (14) and (15), ‘‘1’’ represents that the investment option should be exercised and ‘‘0’’

the opposite.

In order to maximize the investment profit, the generation company X would choose to invest

immediately when Ltequals to ‘‘1’’ for the first time, then the corresponding investment time is the

optimal t?. Before t?, Ltwould keep being ‘‘0,’’ and this means that the optimal strategy for the

generation company X is to hold the option and wait for a better investment opportunity; at t?, Ltequals

to ‘‘1,’’ and this means that investing immediately can get higher profit than waiting further.

Step 9: Set k¼k+1, if k<N, go back to Step 3; otherwise, go to the next step.

Step 10: Compute the distribution probability of the optimal timing and investment profit based on

the simulated data in a statistical way.

Copyright # 2010 John Wiley & Sons, Ltd.Euro. Trans. Electr. Power 2011; 21:1015–1027

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Page 8

5. COMPUTATION OF THE ANNUAL PROFIT OF THE GENERATION COMPANY

Certainly, different electricity market patterns would have different impacts on the profit of the

generation company and accordingly on the investment decision-making as well.

In an energy-only market, the cost recovery and profit making of the generation company depend on

the amount of the electricity sale in the spot market as well as in the bilateral contract market.

While in an electricity market with the capacity payment, the generation company could get profits

not only from the energy sale but also from its available generation capacity. Moreover, different

capacity mechanisms could lead to different profiting pattern. In Reference [20], the profit differences

under different market patters are compared, including the energy-only market, capacity payment,

capacityobligation,andcapacity subscription.Duetospace limitation, onlytheprofitofthegeneration

company in the energy-only market is presented below.

After having calculated thevalue of pe,t,wthrough Equation (8), the profitof the generation company

X in the tth year can be represented as

re;t¼

X

52

w¼1

168 maxfpe;t;w?Cvar;X;0gCX

(16)

Cvar;X¼ Cfuelþ Cfuel;co2þ Cvar;O&M;fuel

(17)

where Cvar,X, Cfuel, Cfuel;CO2, and Cvar,O&M,fuelare respectively the variable cost, the fuel cost, the CO2

emission cost, and the operation and maintenance cost, for per MWh generation of the plant.

In Equation (16), it is assumed that the generation unit will be fully dispatched if pe,t,w>Cvar,X, or

shutdown when pe,t,w?Cvar,X. This assumption is only used to highlight the basic characteristic of the

proposed method which is actually applicable to general situations.

The annual profit of the coal-fired plant and the CCGT plant, i.e., Atand Bt, can be formulated as

At¼

X

X

52

w¼1

168 maxfpe;t;w?Cvar;X;coal;0gCX

(18)

Bt¼

52

w¼1

168 maxfpe;t;w?Cvar;X;gas;0gCX

(19)

where Cvar,X,coaland Cvar,X,gasare respectively the variable costs of the coal-fired plant and the CCGT

plant for per MWh generation.

6. CASE STUDY

Suppose that the efficiencies of the coal-fired plant and the CCGT plant are 40 and 70%, and the CO2

emission factors from the coal-fired plant and the CCGT plant are 1.15 and 0.35ton/MWh,

respectively.Theinvestingplanningperiodis20yearsbetween[0,19].Othertechno-economicdataare

shown in Table I. These data are based on the average value of the plant costs given in Reference [21],

with minor modifications for coal-fired and CCGT plants based on discussions with people in

generation companies.

Table I. Techno-economic data of the two different power plants.

VariablesCoal-fired plant CCGT plant

Plant lifetime Tlf(Years)

Plant capacity Cx(MW)

Investment capital IX($)

Reconstruction time Tld(Years)

Variable operation and maintenance cost Cvar,O&M,fuel($/MWh)

20

600

0

2

3.3

25

600

2.5?108

0

1.5

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:1015–1027

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Page 9

In order to quantify the impact of the uncertainties on the investment profit and investment decision-

making, three scenarios have been analyzed, as detailed below.

In Scenario 1, the volatilities of the fuel price and the CO2emission price are assumed to be very

low (approaching zero), thus their future prices can be considered to keep increasing stably.

At the same time, assume that the electricity price fluctuates randomly. The specifications are

detailed below:

(1) The risk-free interest rate r is 5%.

(2) The initial coal price pcoal;0¼2500$/TJ with an annual growth rate mcoal¼1.2%, and annual

volatility rate scoal¼0.1%.

(3) The initial gas price pgas;0¼5500$/TJ with an annual growth rate mgas¼1.2%, and annual

volatility rate sgas¼0.1%.

(4) The initial maximum load Lmax;0¼54000MW with an annual growth rate mL¼2%, and annual

volatility rate sL¼4.5%; the initial installed capacity of the generation company A is

59000MW with an annual growth rate mA¼2%, and annual volatility rate sA¼4.5%; the

parameters associated with the escaping rate of the generation capacity mdand sdare 1.3 and

0.8%, respectively.

(5) The initial CO2emission price pco2;0is 15$/ton with an annual growth rate mco2¼5%, and an

annual volatility rate sco2¼0.1%; the scale factor h is 0.

In Scenario 2, the volatility of the CO2emission price is set to 20% and the scale factor h to 1. In

addition,itisassumedthattheemissionmitigationpolicieswouldhaveagreatchangeattheyeart ¼9.

The other specifications are the same as those in Scenario 1.

In Scenario 3, the annual volatility rate scoalis set to 2%, and sgasto 4%. The other specifications

are the same as those in Scenarios 1 and 2.

By using the method presented in Section 4, the probability and profit of the generation company X

to exercise the investment option can be calculated at any specified year under different scenarios. The

simulation results for Scenarios 2 and 3 are shown in Table II. In Scenario 1, the investment option

would not be triggered. The histograms of the probability distribution of the investment profit under

these three scenarios are shown in Figures 2–4.

Table II. The probabilities and profits of exercising the investment option.

Year Scenario 2 Scenario 3

Exercise

probability (%)

Exercise

profit (108$)

Exercise

probability (%)

Exercise

profit (108$)

0

1

2

3

4

5

6

7

8

9

0.0

0.0

0.0

0.5

0.4

0.5

0.4

0.3

3.6

4.1

3.2

0.7

0.4

0.6

0.7

0.4

0.3

0.2

1.6

1.9

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

3.4

5.8

4.5

2.8

2.7

3.6

3.6

4.2

3.6

3.4

3.8

2.9

6.25

6.42

6.58

6.72

6.92

7.05

7.27

7.43

7.78

7.22

7.37

7.14

8.31

8.05

8.12

8.22

8.14

8.35

8.49

8.63

9.12

9.43

9.26

9.48

10.02

11.45

11.32

11.55

10

11

12

13

14

15

16

17

18

19

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

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From Table II and Figures 2–4, the following points could be made:

(1) Scenario 1:If both the fuel and CO2prices are stable under thegivenprice specifications used in

the case study, the investment for transferring the coal-fired power plant to a CCGTone will not

take place. The current coal-fired power plant will have the profit of at least $4.615?108during

its lifetime. Given a confidence level of 95%, the profit of the existing coal-fired plant will not

exceed $ 5.44?108.

(2) Scenario 2: If only the fuel price is stable while the CO2emission price is highly volatile, then

the investment for transferring to a CCGT may occur in the 3rd year. Taking into account of the

investment cost, the happening probability of an investment loss is about 1.9%. The maximum

value of the loss can reach $80 million, accounting for 32.2% of the investment capital. On the

other hand, however, the probability of a profitable investment is 98.1%, and the probability of

having more profits than the maximum probable profit in Scenario 1 is 44%.

(3) Scenario 3: If both the fuel price and CO2emission price are highly volatile, the investment for

transferring to a CCGT plant may be happened in the 9th year. The probability of the investment

loss is about 2.4%, and the maximum value of the loss could reach $1.08?108, and this

accounts for 43.1% of the investment capital. If the confidence level is given at 95%, the profit

will not exceed $ 9.96?108, representing 3.98 times of the investment capital. The investment

profit will have an 62.7% probability of more than the maximum possible profit in Scenario 1.

Figure 2. The profit and associated probability distribution in Scenario 1.

Figure 3. The profit and associated probability distribution in Scenario 2.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

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G. LIU, F. WEN AND I. MacGILL

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(4) The uncertainties of the fuel price and CO2emission price have significant impacts on the

uncertainties of the investment profit. The degree of the uncertainties in Scenario 3 is obviously

higher than that in Scenario 1. The range of the profit in Scenario 1 is from $4.615?108to

$5.578?108, while in Scenario 3 it is from ?$1.078?108to $11.854?108. This means that

the more significant the uncertainties are, the wider the range of the investment profit will be.

(5) When thevolatilities of the fuel and CO2emission prices are set to bevery low (Scenario 1), the

investment options would not be triggered. However, when the volatility of the CO2emission

price is set to be high, the options would be triggered, for instance, in the 3rd year. Should the

investment have been taken place, the generation company would have 0.5% chance for

achieving a profit of up to 2.5 times of the investment cost ($6.25?108). The probability of

transforming the coal-firedpowerplanttothe CCGTplantoverthewhole planning time horizon

is not high (only 19.8%). However, if all the prices (including natural gas, coal, electricity, and

CO2) are highly volatile during the whole planning period as shown in Scenario 3, the

investment will become much more attractive. The total probability of transforming the

coal-fired power plant to the CCGT plant over the whole planning time horizon is over

44%, which is much higher than the probabilities in Scenarios 1 and 2.

7. CONCLUSION

Inthiswork, giventhatthe CO2emission priceisuncertainresulting fromthe uncertainclimatechange

policies, a new methodological framework for generation investment decision-making is presented

based on the well-developed ROA, with the uncertain electricity prices and uncertain fuel prices in the

electricity market environment taken into account. In this way, the impact of the uncertainties on

generation investment can be quantified and this has been illustrated with a numerical example.

As a preliminary work, the investment activities from other generation companies and their

interactions have not yet been modeled in detail, and represent our future research efforts.

ACKNOWLEDGEMENTS

This work is supported by ARC Discovery Grant of Australia.

8. LIST OF SYMBOLS AND ABBREVIATIONS

8.1. Symbols

mco2

mf

Expected growth rate of pco2;t

Expected growth rate of pfuel,t

Figure 4. The profit and associated probability distribution in Scenario 3.

Copyright # 2010 John Wiley & Sons, Ltd.Euro. Trans. Electr. Power 2011; 21:1015–1027

DOI: 10.1002/etep

OPTIMAL TIMING FOR GENERATION INVESTMENT

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mL

sco2

sf

sL

Expected growth rate of Lmax,t

Expected volatility rate of pco2;t

Expected volatility rate of pfuel,t

Expected volatility rate of Lmax,t

8.2. Abbreviations

At

Bt

CA;t

Cfuel

Cfuel,CO2

Cvar,X

Cvar,O&M,fuel

Cvar,X,coal

Cvar,X,gas

CX

dwt

IX

~kA

Lmax,t

pe,t,w

pfuel,t

pco2;t

r

rt;w

t0

Texp

Vinv

t

Tlf

Vwait

t

V?(tþ1)

Profits of the coal-fired plant in the tthyear

Profits of the CCGT plant in the tthyear

Installed capacity of Company A in the tthyear

Fuel cost of the power plant

CO2emission cost of the power plant

Variable cost of the power plant

Operation and maintenance cost of the power plant

Variable costs of the coal-fired plant

Variable costs of the CCGT plant

Installed capacity of generation company X

The increment of a Wiener process

Capital investment

Installed capacity increasing rate

Maximum load in the tthyear

Average electricity price in the wthweek of the tthyear

Fuel price in the tthyear

CO2emission price in the tthyear

Risk-free interest rate

Average capacity adequacy in the wthweek of the tthyear

Current year

Last time to invest

Investment profit

Lifetime of the power plant

Profit of waiting to invest

Maximum profit when an optimal investment time is chosen during the time period

[tþ1, Texp]

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