thermo-economic-environmental multiobjective optimizationof a gas turbine_ahmadi
TRANSCRIPT
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.
Thermo-economic-environmental Multi-objective OptimizationH. B. Avval et al.
392 Int. J. Energy Res. 2011; 35:389–403 r 2010 John Wiley & Sons, Ltd.
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
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
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,
Thermo-economic-environmental Multi-objective OptimizationH. B. Avval et al.
394 Int. J. Energy Res. 2011; 35:389–403 r 2010 John Wiley & Sons, Ltd.
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
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
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).
Thermo-economic-environmental Multi-objective OptimizationH. B. Avval et al.
396 Int. J. Energy Res. 2011; 35:389–403 r 2010 John Wiley & Sons, Ltd.
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.
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
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
Thermo-economic-environmental Multi-objective OptimizationH. B. Avval et al.
398 Int. J. Energy Res. 2011; 35:389–403 r 2010 John Wiley & Sons, Ltd.
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 %
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
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).
Thermo-economic-environmental Multi-objective OptimizationH. B. Avval et al.
400 Int. J. Energy Res. 2011; 35:389–403 r 2010 John Wiley & Sons, Ltd.
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
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
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
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