Thermo-Economic-Environmental Multiobjective Optimizationof a Gas Turbine_Ahmadi

INTERNATIONAL JOURNAL OF ENERGY RESEARCH

Int. J. Energy Res. 2011; 35:389–403

Published online 23 March 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1696

Thermo-economic-environmental multiobjectiveoptimization of a gas turbine power plant withpreheater using evolutionary algorithm

H. Barzegar Avval1, P. Ahmadi2,�,y, A. R. Ghaffarizadeh3 and M. H. Saidi2

1Energy-Optimization Research and Developement Group, Tehran, Iran2Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology (SUT), PO Box

11155-9567, Tehran, Iran3Young Researchers Club, Department of Computer Science, Azad University of Arak, Arak, Iran

SUMMARY

In this study, the gas turbine power plant with preheater is modeled and the simulation results are compared withone of the gas turbine power plants in Iran namely Yazd Gas Turbine. Moreover, multiobjective optimization hasbeen performed to find the best design variables. The design parameters of the present study are selected as: aircompressor pressure ratio (rAC), compressor isentropic efficiency (ZAC), gas turbine isentropic efficiency (ZGT),combustion chamber inlet temperature (T3) and gas turbine inlet temperature. In the optimization approach, theexergetic, economic and environmental aspects have been considered. In multiobjective optimization, the threeobjective functions, including the gas turbine exergy efficiency, total cost rate of the system production includingcost rate of environmental impact and CO2 emission, have been considered. The thermoenvironomic objectivefunction is minimized while power plant exergy efficiency is maximized using a genetic algorithm. To have a goodinsight into this study, a sensitivity analysis of the results to the interest rate as well as fuel cost has been performed.In addition, the results showed that at the lower exergetic efficiency in which the weight of thermoenvironomicobjective is higher, the sensitivity of the optimal solutions to the fuel cost is much higher than the location of ParetoFrontier with the lower weight of thermoenvironomic objective. Copyright r 2010 John Wiley & Sons, Ltd.

KEY WORDS

multiobjective optimization; gas turbine plant; exergy analysis; thermoeconomics; thermal modeling; exergy destruction; genetic

algorithm

Correspondence�P. Ahmadi, Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology (SUT), PO

Box 11155-9567, Tehran, Iran.yE-mail: [email protected], [email protected]

Received 29 July 2009; Revised 17 January 2010; Accepted 26 January 2010

1. INTRODUCTION

The optimization of power generation systems is one of

the most important subjects in the energy engineeringfield. Due to the high prices of energy and thedecreasing fossil fuel recourses, the optimum applica-

tion of energy and the energy consumption manage-ment methods are very important. In the thermalsystem engineering, gas turbines (GTs) have beenemployed in three applications: first one is open cycle

GTs, which produces only power, second is cogenera-tion systems in which heat and power are producedtogether and third is combined cycle (CC) systems in

which GTs and steam turbines are used together. TheGT is known to feature low capital cost to power ratio,high flexibility, high reliability without complexity,

short delivery time, early commissioning and commer-cial operation and very short-time start-up andrunning. Moreover, the CC uses the exhaust heat from

the GT engine to increase the power plant output andboost the overall efficiency to more than 50% [1,2].Recently, exergy and exergoeconomic analyses havebeen used in thermal systems especially power plants. It

is well known that the exergy can be used to determinethe location, type and true magnitude of exergy loss(or destruction). Therefore, it can play an important

Copyright r 2010 John Wiley & Sons, Ltd.

issue in developing strategies and in providing guide-lines for more effective use of energy in the existingpower plants [3,4]. Thermoeconomics combines the

exergy analysis with the economic principles andincorporates the associated costs of the thermodynamicinefficiencies in the total product cost of an energy

system. These costs may conduct designers to under-stand the cost formation process in an energy systemand it can be utilized in optimization of thermodynamicsystems, in which the task is usually focused on

minimizing the unit cost of the system product [5].Several researchers carried out the exergy and exergoe-conomics in which GT played a significant part. Sahin

and Ali [6] carried out an optimal performance analysisof a combined Carnot cycle (two single Carnot cycles incascade), including internal irreversibilities for steady-

state operation. They obtained the maximum powerand efficiency analytically and demonstrated the effectsof irreversibility parameters on maximum power out-put. Ameri et al. [7] performed the exergy analysis of

the supplementary firing in heat recovery steamgenerator in a CC power plant. Their results showedthat if a duct burner is added to heat recovery steam

generator, the first and second law efficiencies arereduced. Nevertheless, the results show that the CCpower plant output power increases when the duct

burner is used. Although exergy and exergoeconomicanalyses are so important and indispensable in powergeneration, they cannot find the optimal design

parameters in such systems. Therefore, using theoptimization procedure with respect to thermodynamiclaws as well as thermoeconomics is essential. In fact,objectives in this regard involved in the design

optimization process are as follows [8]: thermodynamic(e.g. maximum efficiency, minimum fuel consumption,minimum irreversibility and so on), economic (e.g.

minimum cost per unit of time, maximum profit perunit of production) and environmental (e.g. limitedemissions, minimum environmental impact). Some

researchers have carried out the optimization in powerplant and CHP systems. They usually use evolutionaryalgorithm in their studies. Sahoo [9] carried out the

exergoeconomic analysis and optimization of a cogen-eration system using evolutionary programming. Heconsidered a cogeneration system, which produced50MW of electricity and 15 kg s�1 of saturated steam at

2.5 bar. He optimized the unit using exergoeconomicprinciples and evolutionary programming. The resultsshowed that for the optimum case in the exergoeco-

nomic analysis, the cost of electricity and productioncost are 9.9% lower in comparison with the base case.Sayyaadi and Sabzaligol [10] performed the exergoe-

conomic optimization of a 1000-MW light waterreactor power generation system using a geneticalgorithm (GA). They considered 10 decision variables.Moreover, it was shown that by optimization techni-

ques considered in their research although fuel cost ofoptimized system is increased in comparison with the

base case plant, nevertheless this shortcoming ofoptimized system is compensated by larger monetarysaving on other economic sectors. Sanaye et al. [11]

analyzed the optimal design of a CHP plant in Iran.Although they used the single objective functionrepresenting the total cost of the plant in terms of

dollar per second, results showed that by increasing thefuel cost, the numerical values of decision variablesusing GA in the thermoeconomically optimal designtend to those of the thermodynamically optimal design.

On the contrary, there are some studies in the literaturecarried out by considering the environmental aspect ofthermal systems. Dincer [12] considered the environ-

mental and sustainability aspects of hydrogen and fuelcell systems.Dincer also analyzed the exergetic and environ-

mental aspects of drying systems [13]. In addition to theexergetic and monetary costs of mass and energystreams in the thermal systems, environomic considersthe costs related to flows of pollutants [14]. However,

by applying the unit damage cost related to NOx andCO emissions [15], this objective function is formulatedin the cost terms and it can be considered as an addi-

tional economic objective. In this sense, the non-ab-breviated term thermoenviroeconomic would be moreappropriate, as recognized by Frangopoulos [14].

Ehyaei and Mozafari [16] performed the optimizationof micro-GT by exergy, economic and environmental.They performed their analysis for various fuels. The

results showed that optimization results are little af-fected by the type of fuel considered and trends ofvariations of second law efficiency and cost rate ofowning and operating the whole system are in-

dependent of the fuels.Suresh et al. [17] performed the 3E analysis of

advanced power plants based on high ash coal.

Although they considered the environmental impact,they did not optimize the cycle. In their study,the environmental impact of the power plants is esti-

mated in terms of specific emissions of CO2, SOx, NOx

and particulates. They concluded that the maximumpossible plant energy efficiency under the Indian

climatic conditions using high ash Indian coal isabout 42.3%.In the present study, which is the extended and de-

veloped version performed by Ahmadi co-workers

[18,19], the simulation and multiobjective optimizationof a GT power plant with preheater is performed.Three objective functions including the GT exergy ef-

ficiency, total cost rate of the system product and thecost rate of environmental impact have been con-sidered. Furthermore, the environmental impact has

been integrated with the thermoeconomic objectivefunction and defined as a new objective function inthis study. The thermoenvironomic objective functionis minimized while power plant exergy efficiency is

maximized using a GA. Moreover, to have a good in-sight into this analysis, the amount of CO2 emission is

Thermo-economic-environmental Multi-objective OptimizationH. B. Avval et al.

390 Int. J. Energy Res. 2011; 35:389–403 r 2010 John Wiley & Sons, Ltd.

DOI: 10.1002/er

considered as another objective function. Hence, thisobjective function is minimized while exergy efficiencyis maximized. Accordingly, the design parameters are

compressor pressure ratio (rAC), compressor isentropicefficiency (ZAC), GT isentropic efficiency (ZGT), com-bustion chamber inlet temperature (T3) and gas turbine

inlet temperature (TIT). Moreover, the sensitivityanalysis is performed to have a good insight into thisresearch.In summary, the following are the contribution of

this study in the subject:

� The GT modeling output was compared with the

experimental dada obtained from actual runningGT power plant with preheater.

� Three objective functions, including exergy

efficiency, total cost rate of the plant (includingfuel cost, purchase cost, cost of exergy destructionand the cost rate of environmental impact)and CO2 emission of the plant, have been

considered.� A modified version of evolutionary algorithm

(i.e. GA) is developed for multiobjective

optimization.� This code, which is developed based on GA, has

been applied to find the set of Pareto optimal

solution [8] with respect to aforementioned objec-tive functions.

� Proposing a new closed form equation for the

exergy efficiency in term of total cost rate at theoptimal design point.

� To provide a very helpful tool for the optimaldesign of the GT plant, the equation was derived

for the Pareto optimal points curve.� Showing Pareto optimal solution curves for

various fuel costs and interest rates.

2. THERMAL MODELING

To find the optimum physical and thermal designparameters of the system, a simulation program wasdeveloped in Matlab software. The temperature profile

in GT, input and output enthalpy and exergy of eachline in the plant were estimated to study the multi-objective optimization of the plant. The energy-balance

equations for various parts of the GT plant as shown inFigure 1 are as follow:

� Air compressor:

T2 ¼ T1 111

ZAC

½rðga�1Þ=gac � 1��

ð1Þ

_WAC ¼ _ma � CpaðT2 � T1Þ ð2Þ

The Cpa in this analysis is considered to be atemperature variable function as [1]:

CpaðTÞ ¼ 1:04841�3:8371T

104

� �1

9:4537T2

107

� �

�5:49031T3

1010

� �1

7:9298T4

1014

� �ð3Þ

� Air preheater:

_maðh3 � h2Þ ¼ _mgðh5 � h6ÞZAP ð4Þ

P3

P2¼ ð1� DPaphÞ ð5Þ

� Combustion chamber (cc):

_mah31 _mfLHV ¼ _mgh41ð1� ZccÞ _mfLHV ð6Þ

P4

P3¼ ð1� DPccÞ ð7Þ

Combustion equation is

lCx1Hy11ðxO2O21xN2

N21xH2OH2O

1xCO2CO21xArArÞ

! yCO2CO21yN2

N21yO2O2

1yH2OH2O1yNONO1yCOCO1yArAr

yCO2¼ ðl� x11xCO2

� yCOÞ

yN2¼ xN2

� yNO

yH2O ¼ xH2O1l� y1

2

yO2¼ xO2

� l� x1 �l� y1

4�yCO2�

yNO

2

yAr ¼ xAr

l ¼nfna

ð8Þ

� Gas turbine:

T5 ¼ T4 1� ZGT 1�P4

P5

� �1�gg=gg" #( )

ð9Þ

Figure 1. Schematic diagram of the GT power plant.

Thermo-economic-environmental Multi-objective Optimization H. B. Avval et al.

Int. J. Energy Res. 2011; 35:389–403 r 2010 John Wiley & Sons, Ltd.

DOI: 10.1002/er

391

_WGT ¼ _mgCpgðT5 � T4Þ ð10Þ

_WNet ¼ _WGT � _WAC ð11Þ

_mg ¼ _mf1 _ma ð12Þ

The Cpg in this analysis is considered to be atemperature variable function as [1]:

CpgðTÞ ¼ 0:99161516:99703T

105

� �

12:7129T2

107

� ��

1:22442T3

1010

� �ð13Þ

These combinations of energy- and mass-balance

equations were numerically solved and the temperatureand enthalpy of each line of the plant were predicted.It should be noted that the utilized thermodynamic

mode is developed based on the following basic as-sumptions [11,18,19]:

� All the processes in our study are considered basedon the steady-state model.

� The principle of ideal gas mixture is applied for the

air and combustion products.� The fuel injected to the combustion chamber is

assumed to be natural gas.� Heat loss from the combustion chamber is

considered to be 3% of the fuel lower heatingvalue. Moreover, all the other components areconsidered adiabatic.

� The dead state is P0 5 1.01 bar and T0 5 293.15K.� In the preheater, 4% pressure drop is considered.

In addition, 3% pressure drop is considered in the

combustion chamber.

3. EXERGY ANALYSIS

Exergy can be divided into four distinct components.The two important ones are the physical exergy andchemical exergy. In this study, the two other compo-

nents, which are kinetic exergy and potential exergy,are assumed to be negligible as the elevation and speedhave negligible changes [20–24]. The physical exergy is

defined as the maximum theoretical useful workobtained as a system interacts with an equilibriumstate [20]. The chemical exergy is associated with the

departure of the chemical composition of a system fromits chemical equilibrium. The chemical exergy is animportant part of exergy in combustion process.Applying the first and the second laws of thermo-

dynamics, the following exergy balance is obtained:

_EQ1Xi

_miei ¼Xe

_meee1 _Ew1 _ED ð14Þ

It should be noted that in Equation (14), subscripts eand i are the specific exergy of control volume inletand outlet flow, respectively and ED is the exergy

destruction. Other terms in this equation are asfollows [20,25]:

_EQ ¼ 1�T�Ti

� �_Qi ð15Þ

_Ew ¼ _W ð16Þ

eph ¼ ðh� h�Þ � T�ðS� S�Þ ð17Þ

_EQ and _Ew are the corresponding exergy of heattransfer and work, which cross the boundaries of thecontrol volume, T is the absolute temperature (K) and

(1) the ambient conditions. In Equation (14), term E isdefined as follows:

_E ¼ _Eph1 _Ech ð18Þ

where _E ¼ _me.The mixture chemical exergy is defined as follows

[20,25–27]:

exchmix ¼Xni¼1

Xiexchi1RT0

Xni¼1

XiLnXi1GE

" #ð19Þ

GE, which is the excess free Gibbs energy, is negligibleat low pressure at a gas mixture.

For the evaluation of the fuel exergy, the aboveequation cannot be used. Thus, the corresponding ratioof simplified exergy is defined as:

x ¼exf

LHVfð20Þ

Due to the fact that for most usual gaseous fuels, theratio of chemical exergy to lower heating value is

usually close to 1, one may write it as [28]:

xCH4¼ 1:06

xH2¼ 0:985

ð21Þ

For gaseous fuel with CxHy, the following experi-mental equation is used to calculate x [28]

x ¼ 1:03310:0169y

x�

0:0698

xð22Þ

In this study, for the exergy analysis of the plant, the

exergy of each line is calculated at all states and thechanges in the exergy are determined for each majorcomponent. The source of exergy destruction (or irre-versibility) in combustion chamber is mainly combus-

tion or chemical reaction and thermal losses in the flowpath, respectively [7,23]. However, the exergy destruc-tion in the heat exchanger of the system, i.e. air pre-

heater is due to the large temperature differencebetween the hot and cold fluids.The exergy destruction rate and the exergy efficiency

for each component in the base case and for the wholesystem in the power plant (Figure 1) are summarized inTable I. The operating conditions for base case of

the GT power plant, such as fuel mass flow rate andcalorific value, output electrical power and efficienciesof compressor and GT, are summarized in Table II.



DOI: 10.1002/er

4. EXERGOECONOMIC ANALYSIS

4.1 Economic model

Due to finite natural resources and world increasingenergy demand by developing countries, it becomesincreasingly important to recognize the mechanisms

that degrade energy and resources and to developsystematic approaches for improving the design ofenergy systems and reducing the impact on the

environment. The second law of thermodynamicscombined with economics represents a very powerfultool for the systematic study and optimization ofenergy systems. This combination forms the basis of the

relatively new field of thermoeconomics (exergoeco-nomics). Moreover, the economic model takes intoaccount the cost of the components including the

amortization and maintenance and the cost of fuelcombustion. To define a cost function that depends onoptimization parameters of interest, component cost

should be expressed as a function of thermodynamicdesign parameters [21]. The first study in this regardwas proposed in the study called CGAM problem

[29–31], which considered the thermoeconomic analysisof a cogeneration plant to produce 14 kg s�1 water at20 bar. On the contrary, exergy costing involves costbalance usually formulated for each component sepa-

rately. A cost balance applied to the kth systemcomponents shows that the sum of cost rates associated

with all the existing exergy stream equals the sum ofcost rates of all the entering exergy streams plus theappropriate charges due to capital investment and

operating and maintenance expenses. The sum of thelast two terms is denoted by _Zk. For each flow line in thesystem, a parameter called flow cost rate C (dollar per

second) was defined and the cost-balance equation ofeach component in the following form is used.Accordingly, for a component that receives heat

transfer and generates power, one can write [21]:Xe

_Ce;k1 _Cw;k ¼ _Cq;k1Xi

_Ci;k1 _Zk ð23Þ

The cost balances are generally written so that all termsare positive. Using Equation (23), one can write [10,21]:X

ðce _EeÞk1cw;k _Wk ¼ cq;k _Eq;k1Xðci _EiÞk1 _Zk ð24Þ

_Cj ¼ cjEj ð25Þ

The cost-balance equations for all the components ofthe system construct a set of nonlinear algebraicequations, which was solved for Cj and cj.In this analysis, it is worth mentioning that the fuel

and product exergy should be defined. The exergyproduct is defined according to the components underconsideration. The fuel represents the source that is

consumed in generating the product. Both product andfuel are expressed in terms of exergy. The cost ratesassociated with the fuel ( _Cf) and product ( _CP) of a

component are obtained by replacing the exergy rates( _E). For example, in a turbine, fuel is difference be-tween input and output exergy and product is thegenerated power of the turbine.

In the cost-balance formulation Equation (23), thereis no cost term directly associated with exergy de-struction of each component. Accordingly, the cost

associated with the exergy destruction in a componentor process is a hidden cost. Thus, when combine theexergy balance and exergoeconomic balance together,

one can obtain the following equations:

_EF;k ¼ _EP;k1 _ED;k ð26Þ

where _EF;k represents the fuel exergy rate for kthcomponent, and _EP;k stands for the product exergy rate

of kth component, _EL;k and _ED;k are the exergy loss andexergy destruction rate of that component, respectively.For example, _EL;k is the useful energy (exergy) that iswasted to the environment without converting to the

useful form of energy, and _ED;k is the exergy destruc-tion due to the irreversibilities. For the turbines, if theyare assumed to be adiabatic, _EL;k is equal to zero. In

addition, if the pumps are supposed to be adiabatic, _EL

is equal to zero. Moreover, for the heaters, if they aresupposed to operate adiabatically, _EL;k is equal to zero.

For each flow line in the system, a parameter that iscalled flow cost rate _C(dollar per second) is defined.

cP;k _EP;k ¼ cf;k _EF;k � _CL;k1 _Zk ð27Þ

Table I. The exergy destruction rate and exergy efficiency

equations for plant components.

Components Exergy destruction Exergy efficiency

Compressor ED;AC ¼ E1 � E2 � Ew;AC Zex;AC ¼E2 � E1

WAC

CC ED;CC ¼ E31E9 � E4 Zex;CC ¼E4

E31E9

GT ED;GT ¼ EC � ED �WGT Zex;GT ¼WGT

EC � ED

AP ED;AP ¼Pi;AP

E�Pe;AP

E Zex;AP ¼ 1�ED;APPi;AP

E

Table II. Operating conditions of the Yazd Power Plant.

Name Unit Value

Natural gas mass flow rate

to combustion chamber

kg s�1 9.01

Air mass flow rate kg s�1 352.3

Lower heating value of natural gas kJ kg�1 45 059.43

Compressor isentropic efficiency % 0.83

Gas turbine isentropic efficiency % 0.87

Air preheater effectiveness % 0.81

Compressor pressure ratio — 10.59

Gas turbine pressure ratio — 10.1

Output power MW 106



DOI: 10.1002/er

393

If one eliminates _EF;k from Equations (19) and (20),one can obtain the following relations:

cP;k _EP;k ¼ cf;k _EP;k1ðcf;k _EL;k � _CL;kÞ1 _Zk1cf;k _ED;k

ð28Þ

Eliminating _EP;k, from Equation (28), we find:

cP;k _EF;k ¼ cf;k _EF;k1ðcP;k _EL;k � _CL;kÞ1 _Zk1cP;k _ED;k

ð29Þ

The last term on the RHS Equation (29) involves therate of exergy destruction. As discussed before, if one

assumes that the product _EP;k is fixed and that the unitcost of fuel cF;k of the kth component is independent ofthe exergy destruction, one can define the cost of exergy

destruction by the last term of Equation (23).

_CD;k ¼ cf;k _ED;k ð30Þ

More details of the exergoeconomic analysis, cost-bal-ance equations and exergoeconomic factors are com-pletely discussed in References [4,9,10,21].

Thoroughly, several methods have been suggestedto express the purchase cost of equipment in terms ofdesign parameters in Equation (23) [10,21]. However,

we have used the cost functions that are suggested byAhmadi co-workers [4,32] and Roosen et al. [33].Nevertheless, some modifications have been made totailor these results to the regional conditions in Iran and

taking into account the inflation rate. For converting thecapital investment into cost per time unit, one may write:

_�Zk ¼ �Zk � CRF � j=ðN� 3600Þ ð31Þ

where N is the annual number of the operating hours ofthe unit, and j5 1.06 [11] the maintenance factor, Zk is

the purchase cost of kth component in US dollar. Theexpression for each component of the GT plant andeconomic model is presented in Appendix A. Thecapital recovery factor (CRF) depends on the interest

rate as well as estimated equipment lifetime. CRF isdetermined using the relationship [21]:

CRF ¼ið11iÞn

ð11iÞn � 1ð32Þ

where i is the interest rate and n the total operating

period of the system in years.Finally, to determine the cost of exergy destruction

of each component, the value of exergy destruction,

ED,k, is computed using exergy-balance equation in theearlier section.

4.2. Cost-balance equations

As we know for estimating the cost of exergy

destruction in each component of the plant, first weshould initially solve the cost-balance equations foreach component. Therefore, in application of the

cost-balance equation (Equation (23)), there is usuallymore than one inlet and outlet streams for somecomponents. In this case, the numbers of unknown cost

parameters are higher than the number of cost-balanceequations for that component. Auxiliary exergoeco-nomic equations are developed to solve this problem

[21,34]. Implementing Equation (23) for each compo-nent together with the auxiliary equations forms asystem of linear equations as follows:

½ _Ek� � ½ck� ¼ ½ _Zk� ð33Þ

Here, ½ _Ek�, ½ck� and ½ _Zk� are the matrix of exergy rate

which were obtained in exergy analysis, exergetic costvector (to be evaluated) and the vector of _Zk factors(obtained in economic analysis), respectively.

_E1 0 0 0 0 0 0 0 0

_E1 � _E2 0 0 0 0 _E7 0 0

0 _E2 � _E3 0 � _E5 � _E6 0 0 0

0 0 _E3 � _E4 0 0 0 0 _E9

0 0 0 _E4 � _E5 0 � _E7 � _E8 0

0 0 0 1 �1 0 0 0 0

0 0 0 0 0 0 1 �1 0

0 0 0 0 1 �1 0 0 0

0 0 0 0 0 0 0 0 1

26666666666666666666666664

37777777777777777777777775

�

c1

c2

c3

c4

c5

c6

c7

c8

c9

26666666666666666666666664

37777777777777777777777775

¼

0

� _ZAC

� _ZAP

� _Zcc

� _ZGT

0

0

0

Fc

26666666666666666666666664

37777777777777777777777775

ð34Þ

Therefore, by solving these sets of equations, one canfind the cost rate of each line in Figure 1. Moreover,they are used to find the cost of exergy destruction in

each component of the plant.

5. THERMOENVIRONOMICMODELING

To minimize the environmental impacts, a primarytarget is to increase the efficiency of energy conversionprocesses and, thus, decrease the amount of fuel and

the related overall environmental impacts, especiallythe release of carbon dioxide, which is one of themain components of greenhouse gases. Therefore,



DOI: 10.1002/er

optimization of thermal systems based on this fact hasbeen an important subject in recent years. Althoughthere are a lot of studies in the literature, which are

dealing with optimization of power plants, generallythey do not pay much attention to environmentalimpacts. For this reason, one of the major goals of the

present study is to consider the environmental impactsas producing the CO and NOx. As it was discussedin [35], the adiabatic flame temperature in the primaryzone of the combustion chamber is derived as follows:

Tpz ¼ Asa expðbðs1lÞ2Þpx�yy�cz� ð35Þ

where p is dimensionless pressure (P/Pref), y the

dimensionless temperature (T/Tref), c the H/Catomic ratio, s5f for fp1 (f is mass or molar ratio)and s5f�0.7 for fX1. Moreover, x, y and z are

quadric functions of s based on the followingequations:

x� ¼ a11b1s1c1s2 ð36Þ

y� ¼ a21b2s1c2s2 ð37Þ

z� ¼ a31b3s1c3s2 ð38Þ

In Equations (35)–(38), parameters A, a, b, l, ai, bi andci are constant parameters. More details are presentedin [7,36]. All the parameters in Equations (36)–(38) are

listed in Table III.As it is stated in the literature, the amount

of CO and NOx produced in the combustion chamber

and combustion reaction also change mainly bythe adiabatic flame temperature. Accordingly, based onReference [37], to determine the pollutant emission in

grams per kilogram of the fuel, the proper equations

are proposed as follows:

_mNOx¼

0:15E16t0:5 expð�71100=TpzÞP0:053 ðDP3=P3Þ

ð39Þ

_mCO ¼0:179E99 expð7800=TpzÞ

P23tðDP3=P3Þ

ð40Þ

where t is the residence time in the combustionzone (t is assumed constant and is equal to 0.002 s);Tpz is the primary zone combustion temperature;

P3 is the combustor inlet pressure; DP3=P3 is the non-dimensional pressure drop in the combustion chamber.

6. OPTIMIZATION (OBJECTIVEFUNCTIONS, DESIGN PARAMETERSAND CONSTRAINTS)

6.1. Definition of the objectives

Three objective functions including exergy efficiency(to be maximized), the total cost rate of product andenvironmental impact (to be minimized) and CO2

emission (to be minimized) are considered for multi-objective optimization. The second objective functionexpresses the environmental impact as the total

pollution damage (dollar per second) due to CO andNOx emission by multiplying their respective flow ratesby their corresponding unit damage cost (CCO and

CNOxare equal to 0.02086 dollar per kilogram CO and

6.853 dollar per kilogram NOx) [36]. In the presentstudy, the cost of pollution damage is assumed to be

added directly to the expenditures that must be paid.Therefore, the second objective function is sum of thethermodynamic and environomic objectives. Due to theimportance of environmental effects, the third objective

function is considered as CO2 emission, which isproduced in the combustion chamber. This amount ofCO2 (kgMWh�1) emission is obtained from combus-

tion equation discussed in Section 2.The objective function for this analysis is considered as:� GT power plant exergy efficiency:

ZTotal ¼_WNet

_mf;cc � LHV� xð41Þ

where WNet, mf,cc and x are GT net output power, massflow rate of fuel injected to the combustion chamber,respectively, and x ¼ 1:03310:0169ðy=xÞð0:0698=xÞ forgaseous fuel with CxHy formula.� Total cost rate:

_CTot ¼ _Cf1Xk

_Zk1 _CD1 _Cenv ð42Þ

where

_Cenv ¼ CCO _mCO1CNOx_mNOx

_Cf ¼ cf _mf � LHV ð43Þ

where _Zk, _Cf and _CD are purchase cost of each

Table III. Constants for Equations (36)–(38).

0.3pjp1.0 1.0pjp1.6

Constants 0.92pyp2 2pyp3.2 0.92pyp2 2pyp3.2

A 2361.7644 2315.752 916.8261 1246.1778

a 0.1157 �0.0493 0.2885 0.3819

b �0.9489 �1.1141 0.1456 0.3479

l �1.0976 �1.1807 �3.2771 �2.0365

a1 0.0143 0.0106 0.0311 0.0361

b1 �0.0553 �0.045 �0.078 �0.085

c1 0.0526 0.0482 0.0497 0.0517

a2 0.3955 0.5688 0.0254 0.0097

b2 �0.4417 �0.55 0.2602 0.502

c2 0.141 0.1319 �0.1318 �0.2471

a3 0.0052 0.0108 0.0042 0.017

b3 �0.1289 �0.1291 �0.1781 �0.1894

c3 0.0827 0.0848 0.098 0.1037



DOI: 10.1002/er

395

component, fuel cost and cost of exergy destruction,respectively. In addition, _mCO and _mNOx

are calculatedfrom Equations (39) and (40).

� CO2 emission. To have a complete optimization inthis study, the CO2 emission, which produces in com-bustion chamber, is considered as an objective func-

tion. Therefore, by using the combustion equationdiscussed in Equation (8), one can find the CO2 emis-sion of the plant.

e ¼_mCO2

_WNet

ð44Þ

6.3. Decision variables

The decision variables (design parameters) in this study

are compressor pressure ratio (rAC), compressorisentropic efficiency (ZAC), GT isentropic efficiency(ZGT), combustion chamber inlet temperature (T3) and

gas TIT. Although the decision variables may be variedin the optimization procedure, each decision variablesis normally required to be within a reasonable range.The list of these constraints and the reasons of their

applications are briefed based on [11] and summarizedin Table IV.

6.4. Evolutionary algorithm

6.4.1.GA. Evolutionary algorithms apply an iterative

and stochastic search strategy to find an optimalsolution (Figure 2) [38]. Principles of biologicalevolution are imitated in a very simplified manner.

Characteristic feature of an evolutionary algorithm is a

population of individuals.An individual consists of the values of the decisionvariables (here, structural and process variables)and is a potential solution to the optimization

problem [38].

6.4.2. Multiobjective optimization. A multiobjective

problem consists of optimizing (i.e. minimizing ormaximizing) several objectives simultaneously, with anumber of inequality or equality constraints. The

problem can be formally written as:

Find x ¼ ðxiÞ 8 i ¼ 1; 2; . . . ;NPar such as ð45Þ

fiðxÞ is a minimum (respectively, maximum) 8i ¼1; 2; . . . ;NObj

Subject to gjðxÞ ¼ 0 8 j ¼ 1; 2; . . . ;M ð46Þ

hkðxÞp0 8 k ¼ 1; 2; . . . ; k ð47Þ

where x is a vector containing the Npar design

parameters, ðfiÞi¼1;...;Nobjthe objective functions and

Nobj the number of objectives. The objective functionsðfiÞi¼1;...;Nobj

return a vector containing the set of Nobj

values associated with the elementary objectives to be

optimized simultaneously. The GAs are semi-stochasticmethods, based on an analogy with Darwin’s laws ofnatural selection [39]. The first multiobjective GA,

called vector evaluated GA (or VEGA), was proposedby Schaffer [40]. An algorithm based on non-dominated sorting was proposed by Srinivas and Deb

[41] and called non-dominated sorting GA (NSGA).This algorithm is called NSGA-II, which is coupledwith the objective functions developed in this study for

optimization.

6.4.3. Non-dominated sorting. Following the definitionby Deb [42], an individual X(a) is said to constrain-

dominate an individual X(b), if any of the followingconditions are true:

(1) X(a) and X(b) are feasible, with

ðaÞ XðaÞ is no worse than XðbÞ in all

objective and

ðbÞ XðaÞ is strictly better than XðbÞin at

least one objective: ð48Þ

(2) X(a) is feasible while individual X(b) is not.(3) X(a) and X(b) are both infeasible, but X(a) has a

smaller constraint violation.

Here, the constraint violation L(x) of an individualX is defined to be equal to the sum of the violated

Table IV. The list of constraints for optimization [11].

Constraints Reason

TITo1550 K Material temperature limit

P2/P1o20 Commercial availability

ZACo0.9 Commercial availability

T74400 1K To avoid formation of sulfuric acid

in exhaust gases

Figure 2. Basic concept of evolutionary algorithm (i.e. GA).



DOI: 10.1002/er

constraint function values

LðXÞ ¼Xj¼1

gðgjðXÞÞ � gjðxÞ ð49Þ

where g is the Heaviside step function.

6.4.4. Tournament selection. Each individual competesin exactly two tournaments with randomly selectedindividuals, a procedure that imitates survival of thefittest in nature.

6.4.5. Crowding distance. The crowding distance metricproposed by Deb and co-workers [42,43] is utilized,

where the crowding distance of an individual is theperimeter of the rectangle with its nearest neighbors atdiagonally opposite corners. Hence, if individual

X(a)and individual X(b) have same rank, each one hasa larger crowding distance is better.

6.4.6. Crossover and mutation. Uniform crossover andrandom uniform mutation are employed to obtain theoffspring population, Qt11. The integer-based uniformcrossover operator takes two distinct parent individuals

and interchanges each corresponding binary bits with aprobability, 0oPco1. Following crossover, the muta-tion operator changes each of the binary bits with a

mutation probability, 0oPmo0.5.

7. CASE STUDY

To have a good verification results from our simulation

code, the results in this study are compared with theactual running GT power plant in Yazd Power Plant,Iran. This power plant is located near the Yazd city,

one of the middle provinces in Iran. The schematicdiagram of this power plant is shown in Figure 1. Fromthe power plant data gathered in 2006, the incoming airhas a temperature of 17.11C and a pressure of

0.874 bar. The pressure increases to 10.593 bar throughthe compressor, which has an isentropic efficiency of83%. The turbine inlet temperature is 10731C. The

turbine has an isentropic efficiency of 87%. Theregenerative heat exchanger has an effectiveness of81%. The pressure drop through the air preheater is

considered 4% of the inlet pressure for both the flowstreams and through the combustion chamber is 3% of

the inlet pressure. The fuel (natural gas) is injected at17.11C and 30 bar. The results of thermodynamicproperties of the cycle form the modeling part and

the power plant data are summarized in Table V.It should be noted that the results show that the

average of difference between the numerical and the

measured values of parameters is about 2.93% withmaximum of 4.2% in combustion chamber mass flowrate. This verifies the correct performance of developedsimulation code to model this GT power plant.

8. RESULTS AND DISCUSSION

8.1. Optimization results

Figure 3 shows the Pareto frontier solution for a GTpower plant with objective functions indicated inEquations (41)–(44) in multiobjective optimization.

As shown in this figure, while the total exergy efficiencyof the cycle is increased to about 41%, the total costrate of products increases very slightly. Increasing the

total exergy efficiency from 41 to 43.5% is correspond-ing to the moderate increasing in the cost rate ofproduct. In addition, increase in the exergy efficiency

from 43.5% to the higher value leads to a drasticincreasing of the total cost rate.It is shown in Figure 3 that the maximum exergy

efficiency exists at design point (C) (43.89%), while thetotal cost rate of products is the biggest at this point.On the contrary, the minimum value for total cost rateof product occurs at design point (A). Design point C is

the optimal situation at which efficiency is a singleobjective function, while design point A is the optimumcondition at which total cost rate of product is a single

objective function. Specifications of these three sampledesign points A–C in Pareto optimal fronts are sum-marized in Table VI.

In multiobjective optimization, a process of decision-making for the selection of the final optimal solutionfrom the available solutions is required. The process of

Table V. Results between the power plant data and

simulation code.

Unit Measured data Simulation code Difference (%)

T2 1C 347.8 342.92 1.4

T6 1C 557.3 593.5 6.5

T7 1C 448 414.48 7.48

ma kg s�1 352.3 352.20 0.020

Zex % 24.63% 27.16% 10.27Figure 3. Pareto frontier: best trade off values for the objective

functions.



DOI: 10.1002/er

397

decision-making is usually performed with the aid of

a hypothetical point in Figure 3 named as equilibriumpoint where both the objectives have their optimalvalues independent of the other objectives. It is clear

that it is impossible to have both the objectives attheir optimum point, simultaneously and as shown inFigure 3, the equilibrium point is not a solution located

on the Pareto Frontier. The closest point of ParetoFrontier to the equilibrium point might be consideredas a desirable final solution. Nevertheless, in this case,the Pareto optimum Frontier has weak equilibrium, i.e.

a small change in exergetic function due to variationof operating parameters causes a large variation in thecost rate of product. Therefore, the equilibrium point

cannot be utilized for decision-making in this problem.In selection of the final optimum point, it is desired toachieve the better magnitude for each objective than its

initial value of the base case problem. Because of this,as the optimized points in the B–C region have themaximum exergy efficiency increment about 1% and

minimum total cost rate increment 82.53% relativeto the design C, this region was eliminated from thePareto curve remaining just the region of A–B as shownin Figure 4.

It should be noted that in multiobjective optimiza-tion and the Pareto solution each point can be theoptimized point. Therefore, selection of the optimum

solution is depending on preferences and criteria ofeach decision-maker. Hence, each decision-maker mayselect a different point as optimum solution that better

suits with his/her desires.

8.2. Total cost rate and exergy efficiency

To provide a very helpful tool for the optimal design ofthe GT cycle, the following equation was derived for

the Pareto optimal points curve (Figure 3).

_CTot ¼7:42189Z3116:3579Z2 � 18:7497Z14:45071

Z4121:3513Z3 � 7:18236Z2 � 6:40907Z12:35422

ð50Þ

This equation is valid in the range of 0.38oZo0.44.

8.3. Total cost rate and CO2 emission

In this part, two objective functions including totalcost and CO2 emission are considered. The result ofmultiobjective optimization is shown in Figure 5.

As it is shown in this figure, if one wants to reducethe CO2 emission of the cycle, which is mainly asso-

ciated with thermodynamic properties of the cyclecomponent such as compressor and GT isentropic ef-ficiency, the purchase cost of each equipment in the

cycle should be selected as high as they can. Therefore,the total cost rate increases although based on highefficient components. On the contrary, it is clear that byselecting the best component as well as using the low

mass fuel flow rate injected to the combustion chamber,the environmental impacts will decrease. Hence, toprovide the trend of this curve, the equation is fitted to

all the points obtained by multiobjective optimization.This equation is as follows:

_CTot ¼10:8572e4�1968:00e3�457:707e2�7:86003e10:712843

e3�284:365e2118608:6e1287:330ð51Þ

where e is the CO2 emission per net output power

(kgCO2MWh�1).

8.4. Comparison between optimization andYazd GT power plant

Table VII compares the cost rate of product, exergyefficiency and CO2 emission of the actual running

Figure 4. Selecting the optimal solution from Pareto frontier.

Figure 5. Pareto frontier for total cost rate versus CO2 emission.

Table VI. Optimum design values for A to C Pareto optimal

fronts for input value

Property Unit A B C

Zex % 39.59 43.5 43.89

CD,PP $ h�1 1227.1 1354.6 2309.6

CO2 kg MWh�1 201.5 183.4 181.8

Cenv $ h�1 16.92 11.88 11.78



DOI: 10.1002/er

power plant in Iran (i.e. Yazd Power Plant) and theresults from multiobjective optimization. It should benoted that the values for multiobjective is estimated

based on point (B) in Figure 3, because this point is thebest point in comparison with other points in thePareto solution. This point has the high efficiency and

the low total cost rate. Therefore, all the values arebased on this point. According to Table VII, theoptimization leads to the 43.4% increment in the totalexergy efficiency of the cycle. Moreover, the optimiza-

tion results show that by using these design parameters,one can decrease the total cost of exergy destruction byalmost 31.53%. One thing that is important is

decreasing the cost of environmental impact.Table VII shows that the difference between theoptimized data and the base case lead to decrease the

cost of CO and NOx by 44.78%. In addition, this tableshows that by using multiobjective GA, the amount ofCO2 obtained from optimization leads to 42.73%decrease in this objective function in comparison with

the actual running power plant.Table VIII represents the design parameters for both

optimization point and case study. It is worth men-

tioning that the optimization data are based on point

(B) in Figure 3. In addition, Table IX represents someimportant exergoeconomic parameters for the GTpower plant. From this table, it is understood that ex-

ergoeconomic factor is an important thermoeconomicparameter that shows the relative importance of acomponent cost to the associated cost of exergy de-

struction in that component. Accordingly, the highervalue of exergoeconomic factor implies that the majorsource of the cost for the component under con-sideration is related to the capital investment and op-

erating and maintenance costs. The lower value ofexergoeconomic factor states that the associated costsof thermodynamic inefficiencies are much more sig-

nificant than the capital investment and operating andmaintenance costs for the component under con-sideration. In this regard, it can be found out from

Table IX that for combustion chamber, the related costof exergy destruction is significantly higher than theowning and operating cost of this component, and theinefficiency cost for this component is dominant for

both base case and optimized systems. This is due tothe very high exergy destruction in the combustionprocess of combustion chamber. It is worth mentioning

that the greatest amount of exergy destruction for bothbase case and optimized case takes place at the com-bustion chamber because of the chemical reaction and

the large temperature difference between the burnersand the working fluid. In fact, its exergy efficiency isless than other components in the cycle. Furthermore,

it can be found from Table IX that the optimizationincreases the overall exergoeconomic factor of thesystem from 32.79 to 62.24%, implying that optimiza-tion process leads to decrease in cost of exergy de-

struction. Furthermore, Table IX also denotes that inthe all fields, the optimization process improves thetotal performance of the system in a way that the ex-

ergy destructions is reduced about 23.17%, the relatedcost of the system inefficiencies decreases about12.29%.

8.5. Sensitivity analysis

In each optimization problem to have a good insightinto the study, a sensitivity analysis should beperformed. This analysis, which is carried out based

Table VIII. Comparison of design variables between the

optimization and case study.

Decision variable Case study Optimization results

rComp 10.59 13.93

ZComp 0.83 0.86

ZGT 0.87 0.91

TIT (1K) 1346.15 1351.23

T3 (1K) 763.56 790.46

Table IX. Comparison of thermoeconomic parameters of the different components in a power plant for base case and final selected

optimum solution.

ED (MW) ED/ED,Tot CD ($ h�1) Z/(Z1CD)

Component BC Opt BC Opt BC Opt BC Opt

AC 7.8 2.48 6.67 2.76 88.2 55 61.33 90.04

CC 86.46 73.5 74.01 81.90 1028.6 927.7 0.86 0.64

GT 12.65 7.7 10.82 8.58 180.7 145.4 46.9 91.47

AP 9.9 6.06 8.47 6.75 131.1 125.5 34.57 57.58

Total 116.81 89.74 100 100 1428.5 1253 32.79 62.24

Table VII. Comparison between actual power plant parameters

and optimized data in this study.

Property Unit Case study Optimized Differences

Zex % 24.63 43.5 143.4%

CTotal $ h�1 8031.3 6105.8 �31.53%

CO2 kg MWh�1 320.27 183.4 �42.73 %

Cenv $ h�1 17.2 11.88 �44.78 %



DOI: 10.1002/er

399

on the change in a related parameter as well as someother modeling parameters, helps us to predict theresults while some modifications are necessary in

modeling and optimization. Therefore, the sensitivityanalysis of the Pareto optimum solution is performed tothe fuel-specific cost and the interest rate. Figure 6

shows the sensitivity of the Pareto optimal frontier tothe variation of specific fuel cost. This figure shows thatthe Pareto Frontier shifts upward as the specific fuelcost increases. At the lower exergetic efficiency in which

the weight of thermoenvironomic objective is higher, thesensitivity of the optimal solutions to the fuel cost ismuch higher than the location of Pareto Frontier with

the lower weight of thermoenvironomic objective. Infact, the exergetic objective does not have a significanteffect on the sensitivity to the economic parameters such

as the fuel cost and interest rate. Moreover, at higherexergy efficiency, the purchase cost of equipment in theplant is increased so that the cost rate of the plant alsoincreases. Furthermore, at the constant exergy efficiency

by increasing the fuel cost, the total cost rate of theproduct increases due to the fact that the fuel price playsa significant role in this objective function.

Figure 7 presents the sensitivity analysis of Paretooptimum solution of the CO2 emission and total costrate by change in the fuel cost rate. From this figure, it

is obvious that to have a cycle, which produces lessCO2, one may select the components that have higherthermodynamic properties like isentropic efficiency.

Therefore, it leads to increase of the purchase cost ofthe equipment. On the contrary, by increasing the fuelcost, the total cost rate of the product is increased be-cause of the important role of the fuel cost in this ob-

jective function.Similar behavior is observed for sensitivity of Pareto

optimal solution to the interest rate in Figures 8 and 9.

The final optimal solution that was selected in this re-search belongs to the region of Pareto Frontier withsignificant sensitivity to the costing parameters. How-

ever, the region with the lower sensitivity to the costingparameter is not reasonable for the final optimumsolution due to weak equilibrium of Pareto Frontierin which a small change in exergetic efficiency of plant

due to variation of operating parameters may leadto the danger of increasing the cost rate of product,drastically.

Figure 7. Sensitivity of Pareto optimum solution to the specific

fuel cost (i 5 13%).

Figure 6. Sensitivity of Pareto optimum solution to the specific

fuel cost (i 5 13%).

Figure 8. Sensitivity of Pareto optimum solution to the interest

rate (Cf 5 0.003 $ MJ�1).

Figure 9. Sensitivity of Pareto optimum solution to the interest

rate (Cf 5 0.003 $ MJ�1).



DOI: 10.1002/er

9. CONCLUSION

In this study, the thermodynamic modeling and multi-objective optimization of a GT power plant withpreheater are performed. In addition, to have a good

thermodynamic modeling, the results from the simula-tion code were compared with data obtained from theactual running GT power plant in Iran. The results

showed that the average of differences between thenumerical and the measured values of parameters isabout 5.134% with maximum of 10.27% in cycle

exergy efficiency. On the contrary, for the optimizationprocedure, an alternative to previously presentedcalculus-based optimization approaches, namely evolu-

tionary algorithm (i.e. GA), was utilized for multi-objective optimization of typical GT power plant. Theproposed evolutionary algorithm was shown to be apowerful and effective tool in finding the set of the

optimal solutions for the choice of optimum designvariables in the power plant in comparison with theconventional mathematical optimization algorithms.

Moreover, the need to quantify the environmentalimpacts lead to the introduction of pollution-relatedcosts in our economic objective function. In this regard,

the environmental objective is transformed to a costfunction encountered the cost of environmental im-pacts. The new environmental cost function was

merged in thermoeconomic objective and a newthermoenvironomic function was obtained. On thecontrary, to have a good insight of the CO2 emission inthe plant, the emission of this dangerous gas is

considered as distinguished objective function. It meansthat the CO2 emission per MWh of the plant should beminimized. Hence, the four-objective problem was

transformed to a three-objective optimization problemfacilitating the decision-making process. Furthermore,the comparison between the optimized plant and the

actual running power plant was performed. The resultsof optimization in comparison with actual power plantshowed that the optimization increases the overallexergoeconomic factor of the system from 32.79 to

62.24%, implying that optimization process mostlyimproved the associated cost of thermodynamic in-efficiencies. The sensitivity of obtained Pareto solutions

to the interest rate and fuel cost were studied. More-over, it was discussed that selection of the finaloptimum solution from the Pareto Frontier requires a

process of decision-making, which is depending onpreferences and criteria of each decision-maker.

NOMENCLATURE

C 5 cost per unit of exergy ($MJ�1)Cp 5 specific heat (kJ kg�1K�1)

CDv 5 cost of exergy destruction ($ h�1)Cf 5 cost of fuel pet unit of energy ($MJ�1)

E 5 exergy (kJ)e 5 specific exergy (kJ kg�1)GE 5 excess free Gibbs energy (kJ)

h 5 specific enthalpy (kJ kg�1)_ED 5 exergy destruction (kJ)LHV 5 lower heating value (kJ kg�1)

m 5mass flow rate (kg h�1)P 5 pressure (bar)Q 5 heat transfer (kJ)R 5 gas constant (kJ kg�1K�1)

S 5 specific entropy (kJ kg�1K�1)T 5 temperature (1C)Tpz 5 adiabatic temperature in the primary zone

of combustion chamber (K)W 5work (kJ)x 5molar fraction_Z 5 capital cost rate ($ s�1)Zk 5 purchase cost of the component ($)

Greek symbols

Z 5 efficiencyZGT 5 gas turbine isentropic efficiency

ZAC 5 air compressor isentropic efficiencye 5CO2 emission per net output power

(kgCO2MWh�1)

g 5 specific heat ratioj 5maintenance factorx 5 coefficient of fuel chemical exergy

Subscripts and Superscripts

a 5 air

amb 5 ambientAP 5 air preheaterAC 5 air compressor

cc 5 combustion chamberch 5 chemicalCRF 5 capital recovery factor

D 5 destructione 5 exit conditionenv 5 environment

GT 5 gas turbinef 5 fuelg 5 combustion gasseshr 5 hour

i 5 interest ratein 5 inlet conditionk 5 component

L 5 lossOpt 5 optimumph 5 physical

PP 5 power plantrC 5 compressor pressure ratioref 5 referencetot 5 total

1 5 reference ambient condition� 5 rate



DOI: 10.1002/er

401

APPENDIX A: PURCHASEEQUIPMENT COST FUNCTIONS [33]

System

component

Capital or investment

cost functions

AC ZAC ¼c11 _ma

c12 � ZAC

� �P2

P1

� �ln

P2

P1

� �

CC ZCC ¼c21 _ma

c22 �P4P3

!½11EXPðC23TTIT � C24Þ�

GT ZGT ¼c31 _mg

c32 � ZT

� �in

PC

PD

� �½11EXPðc33T3 � c34Þ�

AP ZAP ¼ C41_mgðh5�h6Þ

UDTLMTD

� �0:6

REFERENCES

1. Kurt H, Recebli Z, Gredik E. Performance analysis

of open cycle gas turbines. International Journal of

Energy Research 2009; 33(2):285–294.

2. Ameri M, Ahmadi P, Khanmohammadi S. Exergy

analysis of a 420 MW combined cycle power plant.

International Journal of Energy Research 2008;

32:175–183.

3. Dincer I, Al-Muslim H. Thermodynamic analysis of

reheats cycle steam power plants. International

Journal of Energy Research 2001; 25:727–739.

4. Ahmadi P, Ameri M, Hamidi A. Energy, exergy

and exergoeconomic analysis of a steam power plant

(a case study). International Journal of Energy

Research 2009; 33:499–512.

5. Balli O, Aras H. Energetic and exergetic performance

evaluation of a combined heat and power system with

the micro gas turbine (MGTCHP). International

Journal of Energy Research 2007; 31(14):1425–1440.

6. Sahin B, Ali K. Thermo-dynamic analysis of a

combined Carnot cycle with internal irreversibility.

Energy 1995; 20(12):1285–1289.

7. Ameri M, Ahmadi P, Khanmohamadi S. Exergy

analysis of supplementary firing effects on the heat

recovery steam generator. Proceedings of the 15th

International Conference on Mechanical Engineering

2007, Paper no. 2053, Tehran, Iran, 2007.

8. Toffolo A, Lazzaretto A. Evolutionary algorithms for

multi-objective energetic and economic optimization

in thermal system design. Energy 2002; 27:549–567.

9. Sahoo PK. Exergoeconomic analysis and optimiza-

tion of a cogeneration system using evolutionary

programming. Applied Thermal Engineering 2008;

28(13):1580–1588.

10. Sayyaadi H, Sabzaligol T. Exergoeconomic optimi-

zation of a 1000MW light water reactor power

generation system. International Journal of Energy

Research 2009; DOI: 10.1002/er.1481.

11. Sanaye S, Ziabasharhagh M, Ghazinejad M. Opti-

mal design of gas turbine CHP plant. International

Journal of Energy Research 2009; 33(8):766–777.

12. Dincer I. Environmental and sustainability aspects

of hydrogen and fuel cell systems. International


13. Dincer I. On energetic, exergetic and environmental

aspects of drying systems. International Journal of

Energy Research 2002; 26:717–727.

14. Frangopoulos CA. An introduction to environomic

analysis and optimization of energy-intensive sys-

tems. Proceedings of the ECOS’92. New York:

ASME; 1992; 231–239.

15. Toffolo A, Lazzaretto A. Energy, economy and

environment as objectives in multi-criteria optimiza-

tion of thermal system design. Energy 2004;

29:1139–1157.

16. Ehyaei MA, Mozafari AA. Energy, economic and

environmental (3E) analysis of a micro gas turbine

employed for on-site combined heat and power

production. Energy and Buildings 2010;

42(2):259–264.

17. Suresh MVJJ, Reddy KS, Kolar AK. 3-E analysis of

advanced power plants based on high ash coal.

International Journal of Energy Research. DOI:

10.1002/er.1593.

18. Ahmadi P, Najafi AF, Ganjehei AS. Thermody-

namic Modeling and Exergy analysis of a Gas

Turbine Plant (Case Study in Iran). Proceedings of

the 16th International Conference of Mechanical

Engineering, 2008, Kerman, Iran, ISME 2243.

19. Avval HB, Ahmadi P. Thermodynamic modeling of

combined cycle power plant with gas turbine blade

cooling. Proceedings of the First Iranian Thermo-

dynamic Congress, Isfahan, Iran, 2007.

20. Kotas TJ. The Exergy Method of Thermal Plant

Analysis. Butterworths: London, 1985.

21. Bejan A, Tsatsaronis G, Moran M. Thermal Design

and Optimization. Wiley: New York, 1996.

22. Ameri M, Ahmadi P. The study of ambient

temperature effects on exergy losses of a heat

recovery steam generator. Proceedings of the Inter-

national Conference on Power Engineering, 2007,

Hang Zhou, China, 2007; 55–61.

23. Cihan A, Hacıhafızoglu O, Kahveci K. Energy-

exergy analysis and modernization suggestions for a

combined-cycle power plant. International Journal of

Energy Research 2006; 30:115–126.

24. Dincer I, Al-Muslim H. Thermodynamic analysis of

reheats cycle steam power plants. International




DOI: 10.1002/er

25. Ahmadi P. Exergy analysis of combined cycle power

plants (a case study), 2006, B.Sc. Thesis, Energy

Engineering Department, Power and Water Uni-

versity of Technology, Tehran, Iran, 2006.

26. Szargut J, Morris DR, Steward FR. Exergy analysis

of thermal, chemical, and metallurgical processes,

Hemisphere, New York, 1988.

27. Aljundi I. Energy and exergy analysis of a steam

power plant in Jordan. Applied Thermal Engineering.

DOI: 10.1016/j.applthermaleng.2008.02.029.

28. Balli1 O, Aras H. Energetic and exergetic performance

evaluation of a combined heat and power system with

the micro gas turbine (MGTCHP). International


29. Valero A, Lozano MA, Serra L, Tsatsaronis G, Pisa J,

Frangopoulos CA et al. CGAM problem: definition

and conventional solution. Energy 1994; 19(3):279–286.

30. Tsatsaronis G, Pisa J. Exergoeconomic evaluation

and optimization of energy systems: application to

the CGAM problem. Energy 1994; 19(3):287–321.

31. Frangopoulos CA. Application of thermoeconomic

optimization methods to the CGAM problem.

Energy 1994; 19(3):323–342.

32. Ahmadi P, Sanaye S. Optimization of combined cycle

power plant using sequential quadratic programming.

Proceedings of the ASME Summer Heat Transfer

Conference, Florida, U.S.A., 2008, HT2008-56129.

33. Roosen P, Uhlenbruck S, Lucas K. Pareto optimiza-

tion of a combined cycle power system as a decision

support tool for trading off investment vs. operating

costs. International Journal of Thermal Sciences

2003; 42:553–560.

34. Ozgur Colpan C, Yesein T. Energetic, exergetic and

thermoeconomic analysis of Bilkent combined cycle

cogeneration plant. International Journal of Energy

Research 2006; 30:875–894.

35. Gulder OL. Flame temperature estimation of con-

ventional and future jet fuels. Journal of Engineering

for Gas Turbines and Power 1986; 108(2):376–380.

36. Toffolo A, Lazzaretto A. Energy, economy and

environment as objectives in multi-criteria optimiza-

tion of thermal system design. Energy 2004; 29:

1139–1157.

37. Rizk NK, Mongia HC. Semi analytical correlations

for NOx, CO and UHC emissions. Journal of

Engineering for Gas Turbines and Power 1993;

115(3):612–619.

38. Ghaffarizadeh A. Investigation on evolutionary

algorithms emphasizing mass extinction. B.Sc. Thesis,

Shiraz University of Technology-Shiraz, Iran, 2006.

39. Goldberg DE. Genetic Algorithms in Search, Opti-

mization and Machine Learning. Addison-Wesley:

Reading, MA, 1989.

40. Schaffer JD. Multiple objective optimization with

vector evaluated genetic algorithms. Proceedings of

the International Conference on Genetic Algorithm

and their Applications, Boston, U.S.A., 1985.

41. Srinivas N, Deb K. Multiobjective optimization

using no dominated sorting in genetic algorithms.

Journal of Evolutionary Computation 1994; 2(3):

221–248.

42. Deb K. Multi-objective Optimization Using Evolu-

tionary Algorithms. Wiley: Chichester, 2001.

43. Deb K, Goel T. Controlled elitist non-dominated

sorting genetic algorithms for better convergence.

Proceedings of the First International Conference on

Evolutionary Multi-criterion Optimization, Zurich,

2001; 385–399.



DOI: 10.1002/er

403

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Thermo-Economic-Environmental Multiobjective Optimizationof a Gas Turbine_Ahmadi