htj21051

Thermo-economic Optimization of Gas Turbine Power Plant withDetails in Intercooler

Ehsan Khorasani Nejad,1 Farzaneh Hajabdollahi,2 Zahra Hajabdollahi,3 and Hassan Hajabdollahi4 1Mechanical Engineering Department, Behbahan Branch, Islamic Azad University, Behbahan, Iran

2Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran3Mechanical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran4Mechanical Engineering Department, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

In this paper a gas turbine power plant with intercooler is modeled andoptimized. The intercooler is modeled in details using the NTU method. Aircompressor pressure ratio, compressor isentropic efficiency, gas turbine isentropicefficiency, turbine inlet temperature, cooling capacity of the absorption chiller, recu-perator effectiveness as well as eight parameters for configuration of the intercoolerare selected as design variables. Multi-objective genetic algorithm is applied tooptimize the total cost rate and total cycle efficiency simultaneously. Two plantsincluding an intercooler and with/without air preheater are studied separately. It isobserved that the air compressor pressure ratio in the HP compressor is higher thanthe LP compressor in both cases and its differences are higher for a plant without anair preheater. Actually the air compressor pressure ratio is found to be about 8.5%lower than the ideal value and 9.5% higher than the ideal value in the LP compressorand HP compressor, respectively, in the case with an air preheater. Moreover, acorrelation for intercooler pressure drop in terms of its effectiveness was derived inthe optimum situation for each case. 2013 Wiley Periodicals, Inc. Heat Trans AsianRes, 42(8): 704723, 2013; Published online 5 June 2013 in Wiley Online Library(wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21051

Key words: gas turbine, intercooler, efficiency, total cost rate, NSGA-II

1. Introduction

The optimization of power generation systems is one of the most important subjects in theenergy engineering field. Owing to the high prices of energy and the decreasing fossil fuel resources,the optimum design of energy consumption management methods is important. Recently, thermo-economic and multi-objective analysis and optimization of thermal systems have become a keysolution in providing a better system in optimal energy consumption and optimal system configuration[1]. Rosen and Dincer [2] used thermo-economic analysis of power plants and applied it to a coal-fired electricity generating power plant. Ameri et al. applied exergy and genetic algorithm tools forthermal modeling and optimal design of a steam cycle power plant [3]. Ahmadi and Dincer appliedmulti-objective optimization for a gas turbine and combined cycle power plant [47]. Yildirim andGungor performed the exergoeconomic analysis for a combined heat and power (CHP) system and

2013 Wiley Periodicals, Inc.

Heat TransferAsian Research, 42 (8), 2013

704

obtained the exergoeconomic factors for each component in the CHP system [8]. Chen et al. carriedout the modeling and optimization of a simple gas turbine with recuperator to achieve the maximumpower output [9]. The power output was optimized by adjusting the mass flow rate and the distributionof pressure losses along the flow path. Chaquet et al. applied a genetic algorithm for efficiencyoptimization of a gas turbine by adjusting through flow geometry [10]. Hajabdollahi et al. performedthe multi-objective optimization for a steam cycle power plant by considering the total cost rate andcycle efficiency as two objective functions [11]. They considered the total cost and exergy efficiencyor rate of exergy destruction as two objective functions. Sahin and Ali [12] performed an optimalperformance analysis of a combined Carnot cycle in a cascade form, including internal irreversibilityfor steady-state operation. Koch et al. used the genetic algorithm to find the optimum designconfiguration and process variables in a combined cycle power plant [13]. Bracco and Siri optimizeda combined cycle power plant with a single pressure HRSG from an exergy point of view [14]. Valdeset al. applied the genetic algorithm to find the optimum thermodynamic parameters of a heat recoverysteam generator (HRSG) in a combined cycle power plant [15]. Aljundi performed an energy andexergy analysis of a steam power plant to find the points with energy and exergy losses [16]. Ashleyand Sarim investigate the effect of ambient temperature on efficiency and net output power of a gasturbine [17]. They found that for every K rise in ambient temperature above ISO conditions the gasturbine loses 0.1% in terms of thermal efficiency and 1.47 MW of its gross (useful) power output.Abdallah et al. performed the exergetic optimization of an intercooled gas turbine [18]. Theyoptimized the location of the intercooler, and the reheat combustion chamber as well as the overallpressure ratio. Yi et al. optimized a solid oxide fuel cell and an intercooled gas turbine (SOFCICGT)hybrid cycle to reach the maximum efficiency using the design of the experiment optimization method[19]. Chen et al. maximized the power of an intercooled regenerated Brayton cycle by researchingthe optimum intercooling pressure ratio and the optimum heat conductance distributions among thefour heat exchangers [2022]. Moreover, Hajabdollahi et al. performed thermo-economic modelingand optimization of a shell and tube, plate fin, condenser, and fin tube heat exchangers by maximizingthe effectiveness and minimizing the total annual cost [2327].

In this paper after the thermo-economic modeling of an intercooled gas turbine power plant,this equipment is optimized by maximizing the cycle thermal efficiency as well as minimizing thetotal cost rate of the cycle simultaneously.

As a summary, the following are the contributions of this paper on this subject:

Thermo-economic modeling of an intercooled gas turbine power plant system with details onintercooled heat exchanger modeling.

Applying multi-objective optimization for this system with total cycle efficiency and total costrate as two objectives using NSGA-II.

Selecting the air compressor pressure ratio in each stage, compressor isentropic efficiencies,gas turbine isentropic efficiency, gas turbine inlet temperature, capacity of the absorptionchiller, recuperator effectiveness as well as eight geometrical parameters of an intercooled heatexchanger (ICHE) as 16 design parameters (decision variables).

705

Performing the optimization for two states, an intercooled gas turbine with air preheater and anintercooled gas turbine without air preheater.

Proposing a closed form equation for ICHE pressure drop in terms of effectiveness in anoptimum situation.

Investigating the optimum compressor pressure ratio in each stage and comparison with its idealsituation.

Investigating the effect of ICHE pressure drop, temperature differences, and effectiveness ontotal cycle efficiency.

Nomenclature

Atot total heat transfer area of heat exchanger (m2)Aflow minimum free-flow area (m2)a annualized factor ()Z.

inv investment cost ($/hour)Z.

env environmental cost ($/hour)Z.

fuel fuel cost ($/hour)Z.

total total cost rate ($/hour)cf cost of fuel per unit of energy ($/Mj-1)COP coefficient of performance ()do tube outside diameter (m)dc fin collar outside diameter (m)Dh hydraulic diameter (m)f friction factor ()h specific enthalpy (kJ/kg)i interest ratej Colburn number ()G mass flux (kg/m2s)LHV lower heating value (kJ/kg)m.

mass flow rate (kg/s)P pressure (bar)pf fin pitch (mm)Q. heat transfer rate (kW)T temperature (C)TPZ adiabatic temperature in the primary zone of combustion chamber (K)L1 cold stream flow length (m)L2 hot stream flow length (m)L3 no-flow length (m)n depreciation time (year)Np number of tube passes ()Nr number of tube row ()Re Reynolds number ()rp compressor pressure ratioXl longitudinal pitch (m)

706

Xt transversal pitch (m)W. power (kW)

Greek Symbols

specific volume (m3/kg)P pressure drop (Pa) efficiency or effectiveness specific heat ratio maintenance factor total cycle thermal efficiency heat exchanger porosity

Subscripts

ave averagea airamb ambientAP air preheaterAC air compressorCC combustion chamberchil chillerc coldD destructione exit conditionenv environmentGT gas turbineh hotICHE intercooler heat exchangerf fuelg combustion gasesHE heat exchangerHRSG heat recovery steam generatorin inlet conditionk componentout outlettot totalT turbine! reference ambient condition

2. Energy Analysis

The energy balance equations for various parts of the gas turbine system as shown in Fig. 1are as follows:

(1)Absorption chiller

707

where cp,a is considered a temperature variable function as follows [28]:

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Air preheater

Fig. 1. Schematic diagram of an intercooler gas turbine (ICGT). [Color figure can be viewed in theonline issue, which is available at wileyonlinelibrary.com/journal/htj.]

Air compressor

Combustion chamber (CC)

(9)(10)

708

where cp,g is considered a temperature variable function as follows [28]:

Heat recovery steam generator

These combinations of energy and mass balance equations are numerically solved and the temperatureas well as enthalpy of each line of the plant is predicted based on the following basic assumptions:

All the processes in our study are considered based on 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 released energy.Moreover, all other components are considered adiabatic.

The thermophysical properties of air and water such as specific heat are considered as temperatureand/or pressure dependent.

Intercooler heat exchanger details modeling

In this paper, a cross-flow plain fin and tube heat exchanger with both fluids unmixed is usedas the intercooler (Fig. 2). The NTU method is applied to estimate the heat exchanger pressure dropand effectiveness. Moreover, longitudinal pitch (Xl), transversal pitch (Xt), fin pitch (pf), number of

Turbine

(12)

(13)

(14)

(15)

(11)

(16)

(17)

(18)(19)

709

tube pass (Np), outside tube diameter (do), cold stream flow length (L1), no-flow length (L3), and hotstream flow length (L2) are considered as eight design parameters for the design of a fin and tube heatexchanger as an intercooler. The Fanning factor f and Colburn factor j (respectively representativeof pressure drop and of its thermal performances), for plain flat fins on staggered tube banks areestimated as follows [27]:

The above equations are valid for 300 < Re < 20,000 and for 6.9 dc 13.6 mm, 1.3 Dh 9.37 mm, 20.4 Xt 31.8 mm, 12.7 Xt 32 mm, 1.0 pf 8.7 mm, and 1 Nr 6. The proposedcorrelations for the Colburn number and Fanning friction factor are accurate within 15% [27].

Furthermore, the pressure drop is also estimated from [27]:

where is the ratio of minimum free-flow area to frontal area and f is the Fanning friction factor.

More details for intercooler heat exchanger modeling and verification can be found in Ref. 27.

3. Genetic Algorithm for Multi-objective Optimization3.1 Multi-objective optimization

A multi-objective problem consists of optimizing (i.e., minimizing or maximizing) severalobjectives simultaneously, with a number of inequality or equality constraints. GAs are semi-stochas-

(21)

(20)

(22)

Fig. 2. Schematic diagram of plain fin and tube heat exchanger as intercooler. [Color figure can beviewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]

710

tic methods, based on an analogy with Darwins laws of natural selection [29]. The first multi-objec-tive GA, called vector evaluated GA (or VEGA), was proposed by Schaffer [30]. An algorithm basedon non-dominated sorting was proposed by Srinivas and Deb [31] and called non-dominated sortinggenetic-algorithm (NSGA). This was later modified by Deb et al. [32] which eliminated highercomputational complexity, lack of elitism, and the need for specifying the sharing parameter. Thisalgorithm is called NSGA-II which is coupled with the objective functions developed in this studyfor optimization.

3.2 Tournament selection

Each individual competes in exactly two tournaments with randomly selected individuals, aprocedure which imitates survival of the fittest in nature.

3.3 Controlled elitism sort

To preserve diversity, the influence of elitism is controlled by choosing the number ofindividuals from each subpopulation, according to the geometric distribution [33]

to form a parent search population, Pt + 1 (t denotes the generation), of size S, where 0 < c < 1 and wis the total number of ranked non-dominated.

3.4 Crowding distance

The crowding distance metric proposed by Deb [34] is utilized, where the crowding distanceof an individual is the perimeter of the rectangle with its nearest neighbors at diagonally oppositecorners. So, if individual X(a) and individual X(b) have the same rank, a larger crowding distance isbetter.

3.5 Crossover and mutation

Uniform crossover and random uniform mutation are employed to obtain the offspringpopulation, Qt + 1. The integer-based uniform crossover operator takes two distinct parent individualsand interchanges each with corresponding binary bits with a probability, 0 < pc 1. Followingcrossover, the mutation operator changes each of the binary bits with a mutation probability,0 < pm < 0.5.

4. Objective Functions, Design Parameters, and Constraints

In this study, efficiency and total cost rate of the gas turbine cycle are considered as twoobjective functions. The total efficiency of the system is estimated as

(24)

(23)

711

in which Wnet and m.

f are the gas turbine net output power and mass flow rate of fuel.

The total cost rate includes investment cost rate (Z.

inv), operating (fuel) cost rate (Z.

f) , andenvironmental related cost rate (Z

.

env) as follows:

where Z.

inv, Z.

f, and Z.

env are:

in which Z k is the purchase cost of the k-th component in U.S. dollars. The expression for investmentcost rate of each component of the plant is listed in Appendix A [24, 27, 35, 36], where the annualcost coefficient a is defined as

in which i is the interest rate and n is the system life time in years.

In Eq. (26), N is the annual number of the operating hours of the unit, is the maintenancefactor, and cf is the cost of fuel per unit of energy.

The amount of CO and NOx produced in the combustion chamber is changed mainly by themaximum flame temperature; to determine the pollutant emission in grams per kilogram of fuel, thefollowing equations are proposed [37]:

where is the residence time in the combustion zone ( is assumed to be constant, equal to 0.002 s);P3 is the combustor inlet pressure; P3/P3 is the non-dimensional pressure drop in the combustionchamber, and Tpz is the primary zone combustion temperature which is estimated as follows [37]:

(25)

(29)

(32)

(30)

(31)

(26)

(27)

(28)

712

where is the atomic ratio of H/C and Iso represents the standards conditions and A, , , , x, y, zare constants, which depend on values of fuel and T/TIso [37]. In this study the air compressor pressureratio (for two compressors), compressor isentropic efficiency (for two compressors), gas turbineisentropic efficiency, gas turbine inlet temperature, nominal capacity of absorption chiller, recuperatoreffectiveness as well as eight design parameters related to the geometrical configuration of intercoolerare considered as 16 design parameters.

Furthermore, the following usual inequality constraints are also satisfied:

The last constraint is applied for keeping the stack temperature above the dew point temperature andavoiding the formation of sulfuric acid.

5. Case Study

Optimum design parameters of the gas turbine system are obtained for a situation with anambient temperature of 25 C which could provide 100 MW of electric power. The system isoptimized for depreciation time n = 15 years and interest rate i = 0.1. Furthermore, the maintenancefactor = 1.1 is considered in this case. Moreover, CCO and CNO

x are assumed to be 0.02086 $/kg

and 6.853 $/kg, respectively [38]. It is worth mentioning that the chiller COP was supposed constant(0.7) in the range of 8002000 kW cooling capacity. In addition the optimization results are performedfor two states including an intercooled gas turbine with an air preheater and an intercooled gas turbinewithout an air preheater, named Case I and Case II, respectively.

6. Optimization Results

6.1 Intercooled gas turbine with air preheater (Case I)

Design parameters (decision variables) and the range of their variations are listed in Table 1.The genetic algorithm optimization is performed for 800 generations, using a search population sizeof M = 150 individuals, crossover probability of pc = 0.85, gene mutation probability of pm = 0.035,and controlled elitism value c = 0.55. The Pareto front is depicted in Fig. 3 that clearly reveals theconflict between two objectives, the efficiency and total cost rate. Any change in design parametersare listed in Table 1 that increases the efficiency, leads to an increase in the total cost rate, and viceversa. This shows the need for multi-objective optimization techniques in optimal design of thisequipment. It is shown in Fig. 3 that the maximum efficiency exists at design point A (0.485), whilethe total cost rate is the biggest at this point. On the other hand, the minimum total cost rate occurs atdesign point E (2611$/hour), with the smallest efficiency value (0.464) at that point. Design point Ais the optimal situation at which efficiency is a single objective function, while design point E is theoptimum condition at which total cost rate is a single objective function. The optimum values of two

(33)

(34)

(35)

713

objectives for five typical points from A to E (Pareto-optimal fronts) along with fuel cost, investmentcost, and pollution cost for input values given in Table 1 are listed in Table 2. It is observed that bythe increase of total cost rate, the rate of change in investment cost is higher than the fuel cost.

To provide a useful tool for the optimal design of the gas turbine, the following equation forefficiency versus the total cost rate is derived for the Pareto curve (Fig. 3):

(36)

Fig. 3. The distribution of Pareto-optimal points solutions usig NSGA-II in Case I. [Color figurecan be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]

Table 1. The Design Parameters and Their Range of Variation

714

which is valid in the range of 0.363 < < 0.485 for efficiency. The interesting point is that consideringa numerical value for the efficiency in the mentioned range, provides the minimum total cost rate forthat optimal point along with other optimal design parameters.

Each point on the Pareto front has the potential of final optimum design. However, selectionof a final solution among the optimum points existing on the Pareto front needs a process ofdecision-making. In fact, this process is mostly carried out based on engineering experiences and theimportance of each objective for decision makers. The process of decision-making is usuallyperformed with the aid of a hypothetical point in Fig. 3, named the equilibrium point, where bothobjectives have their optimal values independent of the other objectives [23, 25]. It is clear that it isimpossible to have both objectives at their optimum point, simultaneously, and as shown in Fig. 3,the equilibrium point is not a solution located on the Pareto front. The closest point of the Pareto frontto the equilibrium point (design point C) might be considered as a desirable final solution with the0.4827 efficiency and 2858 $/hour total cost rate.

Distribution of optimum compressor pressure ratio (rp) for two stages is shown in Fig. 4. It isobserved that rp2 > rp1 for all optimum design points and rp2 is about 20% higher than rp1 in theoptimum situation. The value of optimum rp, for maximum cycle efficiency, in each compressor withideal assumptions such as no pressure drop in intercooler, is estimated as rp,id = rp1 rp2 . This is

Table 2. The Optimum Values of Efficiency and Total Cost Rate for Design Points A to E inPareto-Optimal Front (Case I)

Fig. 4. Scattering of compressor pressure ratios for the Pareto-optimal front in Case I. [Colorfigure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]

715

shown in Fig. 4 [39]. It is observed that the rp in a low pressure (LP) compressor is about 8.5% lowerthan the ideal rp. On the other hand, the rp in a high pressure (HP) compressor is about 9.5% higherthan the ideal rp. Variation of total cycle efficiency and total cost rate versus each compressor pressureratio for final optimum design (design point C) are shown in Figs. 5 and 6, respectively. By increasingthe compressor pressure ratio the efficiency increases initially and then decreases. The efficiency hasits maximum value at rp1 = 2.61 and rp2 = 3.05 where rp2 > rp1. On the other hand the cost is increasedby an increase of both compressors pressure ratios as shown in Fig. 6. In addition, total cycleefficiency is depicted versus intercooler pressure drop in Fig. 7. It is generally observed from Fig. 7that by increasing the intercooler pressure drop, the total cycle efficiency decreased because the workof the second compressor increased. Consequently the fuel mass flow rate increased to overcome the

Fig. 5. Variation of total cycle efficiency versus compressor pressure ratio for optimum designpoint C (Case I). [Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com/journal/htj.]

Fig. 6. Variation of total cost rate versus compressor pressure ratio for optimum design point C(Case I). [Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com/journal/htj.]

716

increment of second compressor work and as a result the total cycle efficiency decreased. The resultsof optimum ICHE pressure drop and effectiveness shown in Fig. 8 can be fitted with a maximum10% error as follows:

PICHE(%) = 12.754ICHE 9.278 (37)

where ICHE is ICHE effectiveness and varies in the range of 0.840.88. Actually using thiscorrelation, the total gas turbine cycle with intercooler can be modeled and optimized without thedetails of the intercooler and ICHE is just a new design parameter.

Fig. 7. Scattering of total cycle efficiency versus intercoolor pressure drop for the Pareto-optimalfront in Case I. [Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com/journal/htj.]

Fig. 8. Scattering of intercoolor pressure drop versus intercoolor effectiveness for thePareto-optimal front in Case I. [Color figure can be viewed in the online issue, which is available

at wileyonlinelibrary.com/journal/htj.]

717

6.2 Intercooled gas turbine without air preheater (Case II)

The genetic algorithm is run again for an intercooled gas turbine without an air preheater andPareto-optimal fronts are obtained and shown in Fig. 9. The Pareto front in Case II shifted to the leftand up in comparison with Case I which means that optimization for Case I provided greater efficiencyand a lower total cost rate. Furthermore the optimum values of objective functions along with fuelcost, investment cost, and pollution cost for this case are listed in Table 3. The optimum resultspresented in Fig. 9 are fitted using the following correlation:

Z.

total($/hour) = 253.2 2 263.9 + 64.84

2 206.2 + 81.52 104

(38)

Based on the definition of equilibrium point in the previous section, the design point C with an 0.3939efficiency and 4079 $/hour total cost rate is selected as the final optimum solution. Actually theefficiency decreases 18.4% and the total cost rate increases 42.7% when the air preheater is eliminated.Distribution of optimum compressor pressure ratio (rp) for the two stages along with an idealcompressor pressure ratio rp,id = rp1rp2 is shown in Fig. 10. It is observed that rp2 > rp1 but itsdifference is greater than the case with an air preheater. Variation of total cycle efficiency and totalcost rate versus each compressor pressure ratio for final optimum design (design point C) are shownin Figs. 11 and 12, respectively.

By increasing the compressor pressure ratio the efficiency increases initially and thendecreases next for the first compression stage and increases continuously for the second compressionstage. On the other hand, the cost is increased by the increase of the first compression stage and isdecreased by an increase of the second compression stage as shown in Fig. 12. As a result, bothobjectives improved by increasing rp2 and the maximum allowable rp2 is suitable in the thermo-eco-nomic optimization of an intercooled gas turbine without an air preheater as shown in Fig. 10. On theother hand, rp1 has an optimum value corresponding with the maximum efficiency of the cycle asshown in Fig. 10.

Fig. 9. The distribution of Pareto-optimal points solutions using NSGA-II in Case II. [Color figurecan be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]

718

Table 3. The Optimum Values of Efficiency and Total Cost Rate for Design Points A to E inPareto-Optimal Front (Case II)

Fig. 10. Scattering of compressor pressure ratios for the Pareto-optimal front in Case II. [Colorfigure can be viewed in the online issue, which is available at wileyonlinelibrary.com/journal/htj.]

Fig. 11. Variation of total cycle efficiency versus compressor pressure ratio for optimum designpoint C (Case II). [Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com/journal/htj.]

719

In addition, total cycle efficiency is depicted versus intercooler pressure drop in Fig. 13. Asin Case I it is generally observed from Fig. 13 that by increasing intercooler pressure drop, the totalcycle efficiency is decreased. The results of optimum ICHE pressure drop and effectiveness shownin Fig. 14 can be fitted with a maximum 15% error as follows:

PICHE(%) = 11.046 ICHE 7.9766 (39)

Fig. 12. Variation of total cost rate versus compressor pressure ratio for optimum design point C(Case II). [Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com/journal/htj.]

Fig. 13. Scattering of total cycle efficiencyversus intercoolor pressure drop for the

Pareto-optimal front in Case II. [Color figurecan be viewed in the online issue, which is

available atwileyonlinelibrary.com/journal/htj.]

Fig. 14. Scattering of intercoolor pressure dropversus intercooler effectiveness for the

Pareto-optimal front in Case II. [Color figurecan be viewed in the online issue, which is

available atwileyonlinelibrary.com/journal/htj.]

720

where IHE is ICHE effectiveness and varies in the range of 0.820.85. Actually using this correlation,the total gas turbine cycle with an intercooler can be modeled and optimized without the details ofthe intercooler where IHE is just a new design parameter.

7. Conclusions

A gas turbine system was optimally designed using a multi-objective optimization techniquewith an air preheater and intercooler. The design parameters (decision variables) were air compressorpressure ratio, compressor isentropic efficiency, gas turbine isentropic efficiency, gas turbine inlettemperature, capacity of the absorption chiller, recuperator effectiveness, as well as eight designparameters for configuration of the intercooler. In the present optimization problem, the total cycleefficiency and total cost rate were considered as two objective functions. The optimization problemwas developed for two plants, a gas turbine with both air preheater and intercooler system, and a gasturbine with intercooler and without air preheater. A set of Pareto-optimal front points was obtainedusing NSGA-II for each case. The results revealed the level of conflict between the two objectives ineach case. An 18.4% decrease in efficiency and a 42.7% increase in total cost rate were found whenan air preheater was eliminated. It is observed that the air compressor pressure ratio in the HPcompressor is higher than the LP compressor in each case and its differences is much greater in thecase without an air preheater. The air compressor pressure ratio is about 8.5% lower and 9.5% higherthan the ideal value in LP and HP compressor, respectively, in the case with an air preheater. Moreover,a relation for intercooler pressure drop in terms of its effectiveness was derived in the optimumsituation for each case. These relations enable a designer to model and optimize an intercooler gasturbine with more accuracy and without the details of the intercooler modeling.

Literature Cited

1. Hajabdollahi H, Ahmadi P, Dincer I. An exergy-based multi objective optimization of a heatrecovery steam generator (HRSG) in a combined cycle power plant (CCPP) using evolutionaryalgorithm. Int J Green Energy 2010;8:867879.

2. Rosen M, Dincer I. Exergoeconomic analysis of power plants operating on various fuels. ApplTherm Eng 2003;23:643658.

3. Ameri M, Ahmadi P, Hamidi A. Energy, exergy and exergoeconomic analysis of a steam powerplant: A case study. Int J Energy Res 2009;33:499512.

4. Ahmadi P, Dincer I. Thermodynamic analysis and thermoeconomic optimization of a dualpressure combined cycle power plant with a supplementary firing unit. Energ Convers Manage2011;52:22962308.

5. Ahmadi P, Dincer I. Exergoenvironmental analysis and optimization of a cogeneration plantsystem using Multimodal Genetic Algorithm (MGA). Energy 2010;35:51615172.

6. Ahmadi P, Dincer I. Thermodynamic and exergoenvirnmental analyses, and multi-objectiveoptimization of a gas turbine power plant. Appl Therm Eng 2011;31:25292540.

7. Avval HB, Ahmadi P, Ghaffarizadeh AR, Saidi MH. Thermo-economic-environmental mul-tiobjective optimization of a gas turbine power plant with preheater using evolutionaryalgorithm. Int J Energy Res 2011;35(5):389403.

8. Yildirim U, Gungor A. An application of exergoeconomic analysis for a CHP system. Int JElectrical Power Energy Systems 2012;42(1):250256.

9. Chen L, Li Y, Sun F, Wu C. Power optimization of open-cycle regenerator gas-turbinepower-plants. Appl Energy 2004;78(2):199218.

721

10. Chaquet JM, Carmona EJ, Corral R. Using genetic algorithms to improve the thermodynamicefficiency of gas turbines designed by traditional methods. J Appl Soft Comput2012l;12(11):36273635.

11. Hajabdollahi F, Hajabdollahi Z, Hajabdollahi H. Soft computing based multi-objective opti-mization of steam cycle power plant using NSGA-II and ANN. J Appl Soft Comput2012;12:36483655.

12. Sahin B, Ali K. Thermo-dynamic analysis of a combined Carnot cycle with internal irre-versibility. Energy 1995;20(12):12851289.

13. Koch C, Cziesla F, Tsatsaronis G. Optimization of combined cycle power plants usingevolutionary algorithms. Chem Eng Process 2007;46:11511159.

14. Bracco S, Sir S. Exergetic optimization of single level combined gasesteam power plantsconsidering different objective functions. Energy 2010;35:53655373.

15. Valdes M, Duran MD, Rovira A. Thermoeconomic optimization of combined cycle gas turbinepower plants using genetic algorithms. Appl Therm Eng 2003;23:21692182.

16. Aljundi IH. Energy and exergy analysis of a steam power plant in Jordan. Appl Therm Eng.2009;29:324328.

17. De Sa A, Al Zubaidy S. Gas turbine performance at varying ambient temperature. Appl ThermEng 2011;31:27352739.

18. Abdallaha H, Facchinib B, Danesc F, De Ruyck J. Exergetic optimization of intercooled reheatchemically recuperated gas turbine. Energ Convers Manage 1999;40:16791686.

19. Yi Y, Rao AD, Brouwer J, Samuelsen GS. Analysis and optimization of a solid oxide fuel celland intercooled gas turbine (SOFCICGT) hybrid cycle. J Power Sources 2004;132:7785.

20. Wang W, Chen L, Sun F, Wu C. Power optimization of an irreversible closed intercooledregenerated brayton cycle coupled to variable-temperature heat reservoirs. Appl Therm Eng2005;25:10971113.

21. Wang W, Chen L, Sun F, Wu C. Power optimization of an end reversible closed intercooledregenerated Brayton cycle. Int J Therm Sci 2005;44:8994.

22. Chen L, Wang J, Sun F. Power density analysis and optimization of an irreversible closedintercooled regenerated Brayton cycle. Math Comput Model 2008;48:527540.

23. Hajabdollahi H, Ahmadi P, Dincer I. Multi-objective exergetic optimization of shell and tubeheat recovery heat exchangers using a genetic algorithm. Heat Transf Eng 2012;33(7):618628.

24. Ahmadi P, Hajabdollahi H, Dincer I. Cost and entropy generation minimization of a cross flowplate-fin heat exchanger (PFHE) using multi-objective genetic algorithm. J Heat Trans-TASME 2010; DOI: 10.1115/1.4002599.

25. Hajabdollahi H, Tahani M, Shojaee fard MH. CFD modeling and multi-objective optimizationof compact heat exchanger using CAN method. Appl Therm Eng 2011;31:25972604.

26. Hajabdollahi H, Ahmadi P, Dincer I. Thermoeconomic optimization of a shell and tubecondenser using evolutionary algorithm. Int J Refrig 2011;34:10661076.

27. Hajabdollahi H, Ahmadi P, Dincer I. Modeling and multi-objective optimization of plain finand tube heat exchanger using evolutionary algorithm. J Thermophys Heat Tr (2011), DOI:10.2514/1.49976.

28. Kurt H, Recebli Z, Gredik E. Performance analysis of open cycle gas turbines. Int J EnergyRes 2009;33(2):285294.

29. Goldberg DE. Genetic algorithms in search, optimization and machine learning. Reading, MA:Addison-Wesley; 1989.

30. Schaffer JD. Multiple objective optimization with vector evaluated genetic algorithms. In: ProcInternational Conference on Genetic Algorithm and Their Applications, 1985.

722

31. Srinivas N, Deb K. Multi-objective optimization using non-dominated sorting in geneticalgorithms. J Evol Comput 1994;2(3):221248.

32. Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multi-objective genetic algorithm:NSGA-II. IEEE Trans Evol Comput 2002;6(2):182197.

33. Deb K, Goel T. Controlled elitist non-dominated sorting genetic algorithms for better conver-gence. In: Proceedings of the First International Conference on Evolutionary Multi-criterionOptimization. Zurich;2001. pp. 385399.

34. Deb K. Multi-objective optimization using evolutionary algorithms. Chichester: John Wileyand Sons Ltd.; 2001.

35. Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: Wiley; 1996.36. Tichi SG, Ardehali MM, Nazari ME. Examination of energy price policies in Iran for optimal

configuration of CHP and CCHP systems based on particle swarm optimization algorithm.Energ Policy 2010;38:62406250.

37. Glder. Flame temperature estimation of conventional and future jet fuels. J Eng Gas TurbPower 1986;108(2):37680.

38. Toffolo A, Lazzaretto A. Energy, economy and environment as objectives in multi-criteriaoptimization of thermal system design. Energy 2004;29:11391157.

39. El-Wakil MM. Power plant technology. McGraw-Hill; 2002.

APPENDIX

"F F F"

723