Energy Conversion and Management 51 (2010) 1099–1110

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Energy Conversion and Management

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Thermodynamic evaluation of combined cycle plants

Nico Woudstra *, Theo Woudstra, Armando Pirone, Teus van der SteltDelft University of Technology, Energy Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands

a r t i c l e i n f o

Article history:Received 19 June 2008Received in revised form 18 May 2009Accepted 13 December 2009Available online 21 January 2010

Keywords:Combined cycle plantsExergy analysisInternal exergy efficiencyExergy flow diagramsValue diagramsCycle-Tempo

0196-8904/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.enconman.2009.12.016

* Corresponding author. Tel.: +31 15 278 2178; faxE-mail address: n.woudstra@tudelft.nl (N. Woudst

a b s t r a c t

The application of the exergy concept for the thermodynamic evaluation of energy conversion systemsand chemical plants is steadily growing. However the general application of this concept is complicatedby the large variety of parameters that is used to present the results of such evaluations. Easily under-standable diagrams that offer a quick overview of the main results of such an evaluation will be veryhelpful.

Large power plants, as for example combined cycle plants, consist of a large number of apparatuses.The thermodynamic modeling of these plants requires the computation of the thermodynamic propertiesat inlets and outlets of all apparatuses. These results allow for the calculation of the exergy values at allconsidered points after defining an appropriate environment. Using these exergy values exergy losses andefficiencies of all considered apparatuses can be determined.

However, additional parameters and methods for presenting losses are necessary to understand theorigin of exergy losses and the options for further improvements. Exergy efficiencies of power cyclesshow the actual losses but do in general not clearly indicate the potential for improvement. The use ofthe so-called internal exergy efficiency of a power cycle will be helpful to understand this potential. Alsovalue diagrams and exergy flow diagrams are very useful to understand the thermodynamic performanceof complicated systems.

In this paper the application of these tools is demonstrated for the evaluation of alternative designs ofcombined cycle plants. Three system designs are established for this purpose and modeled using thecomputer program Cycle-Tempo. The considered combined cycles use the same gas turbine but have dif-ferent steam bottoming cycles. Differences do originate from the number of pressure levels at whichsteam is generated in the HRSG (Heat Recovery Steam Generator). The evaluation includes respectivelya single pressure, double pressure and triple pressure HRSG. The steam pressures are optimized withregard to overall plant efficiency using a multi-parameter optimization procedure.

The evaluation shows that the application of the internal exergy efficiency of a power cycle is in par-ticular useful if the temperature of heat transfer from the cycle will be affected by the cycle performance,i.e. in the case of gas turbine cycles. The value diagrams show how the increasing number of pressure lev-els of steam generation will reduce the losses due to heat transfer in the HRSG but also the exergy lossdue to the exhaust of flue gas to the stack. The exergy flow diagrams show that the main exergy lossesof combined cycle plants occur in the combustion process. Possibilities to reduce these losses are limited.Serious improvement of the efficiencies of future combined cycle plants is conceivable by applying hightemperature fuel cells.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Exergy analysis is frequently used for the thermodynamic eval-uation of power plants. In general an exergy analysis will provideadditional knowledge about the thermodynamic losses in the sys-tem. However the significance of an exergy analysis depends onthe insight that will be achieved with regard to the origin of lossesand the options for loss reductions. Therefore, graphs that allow a

ll rights reserved.

: +31 15 278 2460.ra).

simple presentation of the main losses in complex systems will bevery helpful; together with appropriate parameters that clearlyindicate the thermodynamic performance and the improvementpotential, they are essential during the search for system optimiza-tion. In this paper unusual methods to present system performanceand exergy losses like exergy flow diagrams, value diagrams andthe internal exergy efficiency of thermal power cycles are de-scribed and demonstrated for the evaluation of alternative designsof Combined Cycle (CC) plants.

The combination of a gas turbine with a steam turbine cycle in aso-called CC plant appeared to be very successful. The combined

Nomenclature

ex specific exergy (kJ/kg)Ex exergy (kJ)Exloss exergy loss (kJ)ExQ exergy of an amount of heat (kJ)h specific enthalpy (kJ/kg)LHVfuel lower heating value of the fuel (kJ/kg)m mass (kg)Q heat (kJ)s specific entropy (kJ/kg K)T temperature (K)TC temperature of heat transfer from the cycle (K)TH temperature of heat transfer to the cycle (K)T0 temperature of the environment (K)T thermodynamic equivalent temperature of heat transfer

(K)TC thermodynamic equivalent temperature of heat transfer

from the cycle (K)TH thermodynamic equivalent temperature of heat transfer

to the cycle (K)W work (kJ)Wrev work from a reversible power cycle (kJ)

gth, rev thermal efficiency of a reversible power cycle (–)gex, intern internal exergy efficiency of an irreversible power cycle

(–)

Indicesbc bottoming cycleC coldH hotin inletout outlettc topping cycle

AbbreviationsCC Combined CycleGT gas turbine (cycle)HP high pressureHRSG Heat Recovery Steam GeneratorIP intermediate pressureLP low pressureST steam turbine (cycle)

1100 N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110

cycle became popular in particular in countries where natural gasis sufficiently available for electricity generation. Combined cycleplants can achieve thermal efficiencies up to 60%, based on theLHV of the fuel, with present day gas turbine technology. The re-cent increase of fuel prices will stimulate the search for furtherimprovements. Detailed insight in the thermodynamic perfor-mance of combined cycle plants is necessary for the evaluationof the various options proposed to improve the system efficiency.A variety of system improvements is investigated in Refs. [1–12].In almost all papers any kind of exergy evaluation, based on pre-ceding flow sheet calculations, is used to elucidate the effects ofsystem modifications. Only in [2] no explicit results of exergy cal-culations are shown. The added value of the exergy evaluations isnot always obvious.

Results from exergy calculations are usual presented as exergylosses (frequently called exergy destruction) in system compo-nents (like combustors, heaters, compressors and expanders) orsubsystems and relative exergy losses (exergy destruction rates).Relative exergy losses are usually defined as the exergy loss di-vided by the total exergy supplied to the system by the fuel. Sev-eral references present (relative) mainly exergy losses ofsubsystems [4,5,7,8,10]. Data are presented in tables or bar graphs.More detailed results of exergy calculations are tabulated in[1,3,12]. In Refs. [3,9] the exergy concept has been used also foran economic assessment of system alternatives. It is obvious thata final optimization of energy conversion systems has to be basedon economic considerations. However, a separate thermodynamicevaluation will be useful to understand the thermodynamicstrengths and weaknesses of the system configurations under con-sideration. Furthermore, the selection of arbitrary data for avoid-able thermodynamic inefficiencies and cost numbers, needed forthe exergoeconomic analysis, might hamper the credibility of theresults. Nevertheless, an exergoeconomic evaluation is consideredto be a useful but additional step in the final phase of plantoptimization.

A graphical presentation of results from exergy calculations ap-pears not to be very common. In [4] the results are summarized incombined energy and exergy diagrams. In [11] the magnitudes ofthe exergy flows are shown in a simplified system flow diagram.Refs. [5,6,10] show trends in (summarized) exergy values and exer-

gy destruction ratios as a function of the considered variable. In [7]T,h-diagrams are used to illustrate the results of HRSG optimiza-tion. However, these diagrams do not explicitly show exergy valuesor exergy losses.

Exergy efficiencies, also called second law efficiencies, are notused abundantly in the referred papers. Refs. [3,5] show well spec-ified exergy efficiencies of plant components. Many of the otherreferences mainly present exergy efficiencies of power cyclesand/or the considered power plants. With respect to thermal plantand cycle efficiencies, the added value of exergy efficiencies is verylimited. For a comparison of the performance of plants and plantcomponents well specified exergy efficiencies can be useful. With-out clear specification exergy efficiencies, like other efficiencies,are mainly causing confusion.

In this paper an attempt is made to present a comprehensiveand systematic evaluation of the thermodynamic performance ofpower plants. For this purpose three system designs of CC plantsare established and modeled by using Cycle-Tempo [13], a flowsheeting program for the evaluation and optimization of energyconversion systems, developed at the Delft University of Technol-ogy. Since 1982 the program is applied by various universities, re-search organizations and industries worldwide. Calculationprocedures are based on the first and second of thermodynamics.Irreversibility’s have to be specified by the user; for specific appa-ratuses the program can provide default values. Optimization rou-tines are available for multi-parameter optimization and thecalculation of exergy values is done by a postprocessor. The graph-ical user interface allows the user to establish easily various dia-grams (T,s-diagrams, T,Q-diagrams and value diagrams) that willvisualize the calculated results. Comprehensive information,including the program manual, is available from the Cycle-Tempowebsite [13].

The system designs are based on the same gas turbine, but differwith regard to the steam turbine cycle. Steam cycles are derived forrespectively single pressure, double pressure and triple pressureHRSG’s. The steam pressures are optimized using a multi-parame-ter optimization routine as available in the program. Cycle-Tempoalso calculates exergy values of all fluid flows of the system byusing the composition of air from the environment, saturated withwater vapor, at a temperature of 15 �C as the reference state.

hot reservoir

N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110 1101

Furthermore, the program calculates exergy losses and efficienciesof all apparatuses as specified for the system, and is able to drawvalue diagrams. Also exergy flow diagrams are presented for theconsidered plants.

Before presenting the results of the system calculations theinternal exergy efficiency of power cycles and the value diagramwill be described first. Internal exergy efficiencies have to be calcu-lated by using the thermodynamic equivalent temperature of heattransfer to and from the cycle. Therefore it is also discussed howthis parameter can be calculated or estimated.

2. Concepts for the evaluation of thermal power systems

2.1. The internal exergy efficiency of power cycles

The general system for the evaluation of power cycles is shownin Fig. 1. From the second law of thermodynamics we know thatthe efficiency of a reversible cycle depends only on the tempera-tures at which heat is transferred to and from the cycle. By apply-ing the thermodynamic temperature (Kelvin temperature) thethermal efficiency of a reversible power cycle can be calculatedusing the following equation:

gth; rev ¼W rev

Q H¼ 1� TC

THð1Þ

For real systems the efficiency will always be lower because of fric-tion and other losses in the cycle. If the effect of all losses in the cy-cle is included in the so-called internal exergy efficiency (gex, intern)the thermal cycle efficiency can be written as:

gth ¼WQH¼ gex; intern � 1� TC

TH

� �ð2Þ

The Eqs. (1) and (2) show that the internal efficiency is actually de-fined as:

gex; intern ¼W

W revð3Þ

This means that the internal exergy efficiency is defined as the ratioof two amounts of work. The internal exergy efficiency can be usedto assess the thermodynamic quality of a power cycle or a combina-tion of power cycles. In other papers this efficiency is also called‘‘second law efficiency” (i.e. [19]) but as efficiencies based on thesecond law can be defined in different ways a more specific nameis preferred.

The work derived from an amount of heat can determined for areversible cycle respectively an irreversible cycle then becomes:

QH

QC

W

hot reservoir

cold reservoir

TH

TC

Fig. 1. General model of thermal power cycles.

W rev ¼ 1� TC

TH

� �� QH ð4Þ

W ¼ gex; intern � 1� TC

TH

� �� Q H ð5Þ

Heat transfer to and from a power cycle in general does not occur atconstant temperatures. However to enable the universal use of Eqs.(1), (2), (4), and (5) the constant temperatures of heat transfer haveto be replaced by the thermodynamic equivalent temperature (T).Then the general equation for the efficiency of a thermal power cy-cle becomes:

gth ¼ gex; intern � 1� TC

TH

!ð6Þ

The combination of two cycles can be considered as shown in Fig. 2.In this system all heat transferred from the topping cycle is trans-ferred to the bottoming cycle. However the temperatures of heattransfer are not the same. Thus an exergy loss will occur in theintermediate reservoir due to heat transfer.

Eq. (2) can be applied for the separate cycles as well as for thecombined cycle. For the combined cycle can be written:

gth ¼W tc þWbc

Q H; tc¼ gex; intern; CC � 1� TC

TH

!

¼ gex; intern; CC � gth; rev ð7Þ

Thus the internal efficiency of the combined cycle (gex, intern, CC) notonly includes the losses of the separate power cycles but also thelosses of the intermediate reservoir.

2.2. The thermodynamic equivalent temperature of heat transfer

Heat transfer to or from a fluid flow will in general change thetemperature of the flow; only in case of phase changes of pure flu-ids the temperature will remain constant. The exergy of the trans-ferred heat can be determined with the following equation:

ExQ ¼Z out

in1� T0

T

� �� dQ ð8Þ

The thermodynamic equivalent temperature (T) is defined suchthat, if the same amount of heat is transferred to the system at thatspecific temperature, the exergy transferred to the system will bethe same as in the case of the varying temperature, thus:

cold reservoir

intermediate reservoir

TH

TC

QC

Wtoppingcycle

bottomingcycle

W

QH

QH,bc

QC,tc TC,tc

TH,bc

tc

bc

Fig. 2. General model of a combined cycle system.

ex

Q

in ex out

Fig. 3. System of heat transfer to a fluid.

1102 N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110

ExQ ¼Z out

in1� T0

T

� �� dQ ¼ 1� T0

T

� �� Q ð9Þ

In Fig. 3 a system for heat transfer to a fluid is shown. The exergybalance for this system can be written as follows:

DEx ¼ m � ðexout � exinÞ ¼ ExQ � Exloss ð10Þ

In such a system exergy losses are caused only by friction of thefluid flow. The exergy loss due to friction is almost negligible inmost technical applications. Combining Eqs. (9) and (10) andneglecting the exergy loss in the system will result in the followingequation:

m � ½ðhout � hinÞ � T0 � ðsout � sinÞ� ¼ 1� T0

T

� ��m � ðhout � hinÞ ð11Þ

From this equation it appears that the thermodynamic equivalenttemperature of heat transfer becomes:

T ¼ hout � hin

sout � sinð12Þ

Further simplification of this equation is possible if the fluid can beconsidered to be an ideal gas with constant specific heat (cp). Underthese circumstances Eq. (12) can be written as follows:

T ¼ Tout � T in

ln ToutT in

ð13Þ

Unfortunately the concept of the internal exergy efficiency doesnot easily allow for the exact calculation of efficiency values. Bydefinition the internal cycle efficiency compares the power fromthe irreversible cycle with the corresponding reversible cycle (seeEq. (3)). However inlet and outlet conditions will never be thesame for these cycles since the conditions of the real cycle are af-fected by the irreversibility’s in the cycle. This can be demonstratedby considering a simple (closed cycle) gas turbine cycle as shownin Fig. 4. The outlet temperatures of the compression and expan-

T

1

2

3

4

s

4'

2'

p2

p1

p > p2 1

T0

0

Fig. 4. Simple gas turbine cycle (closed cycle).

sion processes of the real (irreversible) cycle (points 2 and 4) arehigher than the corresponding values of the reversible cycle (points20 and 40). When applying Eq. (13) it will be obvious that the ther-modynamic equivalent temperature of heat transfer to the cycle,resulting in the temperature increase from point 2 to point 3, willbe higher in the case of the irreversible cycle than in the case of thereversible cycle. The same must be concluded with regard to thethermodynamic equivalent temperature of heat transfer from thecycle. The effect will be quantified for some of the considered cy-cles in Section 3.2.1.

2.3. The value diagram

Value diagrams can be very useful to discuss the performance ofthermal power plants [14]. In Fig. 5 the value diagram of an open,internal combustion gas turbine cycle is shown, assuming thatcompression and expansion occurs in a reversible way, thus with-out friction. As the length of the horizontal axis equals the specificexergy of the fuel supplied to the gas turbine and the length of thevertical axis is one (with T0 as the origin and T = infinite as theupper limit) the total area of the diagram equals the specific exergyof the fuel. In the case of natural gas the specific exergy of the fuelis somewhat higher than the lower heating value (LHVfuel) of thefuel. The upper curve in the diagram represents the temperatureincrease of the gases in the combustor, assuming that air and fuelenter the combustor at the same temperature. The area below thiscurve equals the exergy of the heat that is transferred to the gasturbine cycle (see Eq. (8)). Then it must be concluded that theslantly shaded area is the difference in exergy between the situa-tion before and after combustion; thus this area represents theexergy loss of combustion. As the lower curve represents the tem-perature decrease of the flue gas during cooling from gas turbineexit temperature to ambient temperature T0, the area below thiscurve represents the exergy of the heat from the flue gas leavingthe gas turbine. In the case of a single gas turbine cycle the exergyof the flue gas will be lost as the exhaust gases are cooled by mix-ing with ambient air. In CC plants the exergy from the flue gas isutilized in a bottoming steam cycle as shown in Fig. 6 for a singlepressure steam cycle. The vertical shaded area represents the exer-gy losses due to heat transfer in the Heat Recovery Steam Genera-tor (HRSG) and due to the residual heat of the flue gas which isdischarged to the atmosphere. In the case of a single pressure

Ex loss, combustion

W shaft Q flue gas

LHVex fuel

Ex flue gas

T0

T(1- )

1

0

Fig. 5. Value diagram of a simple gas turbine cycle.

Q steam

Exloss, combustion

1

0

Exloss, heat transfer

Ex loss, stack

Wshaft, GT

Wshaft, ST

Ex loss, condenser

T0T

(1- )

LHVfuel

exfuel

Fig. 6. Value diagram of a single pressure combined cycle.

Table 1Overall results and some characteristic data of the combined cycle plants.

Units 1 press. 2 press. 3 press.

Overall resultsNet electrical power MWe 364.26 374.84 379.13Thermal efficiency – 0.5514 0.5674 0.5739Increase in efficiency – – 0.0160 0.0225

Gas turbine cycleFuel flow MW 660.62 660.62 660.62Pressure ratio – 17.12 17.12 17.12Turbine inlet temp. (ISO) �C 1227.81 1227.81 1227.81GT outlet temp. �C 581.60 582.43 583.92Stack temperature �C 160.78 119.03 81.88

Steam turbine cycleHP inlet temp. �C 550.00 549.75 550.40HP inlet press. Bar 41.54 112.9 175.0IP inlet temp. �C 550.22 550.96 552.31IP inlet press. Bar 9.261 11.62 31.45LP inlet temp. �C 226.68LP inlet press. Bar 2.711Condenser press. Bar 0.02643 0.02643 0.02643

876543210 9876543210Entropy [kJ/kg.K]

9

500

400

300

200

100

600

500

400

300

200

100Tem

pera

ture

[°C

]

600

876543210 9876543210

Entropy [kJ/kg.K]9

500

400

300

200

100

600

500

400

300

200

100Tem

pera

ture

[°C

]

600

876543210 9876543210

Entropy [kJ/kg.K]9

500

400

300

200

100

600

500

400

300

200

100Tem

pera

ture

[°C

]

600

a

b

c

Fig. 7. (a) T,s-diagram of the single pressure steam cycle. (b) T,s-diagram of thedouble pressure steam cycle. (c) T,s-diagram of the triple pressure steam cycle.

N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110 1103

steam cycle these losses are still substantial. Further reduction ofthese losses is possible by generating steam at two or more pres-sure levels in the HRSG.

3. The combined cycle plants

3.1. Plant designs

System configurations have been established for three differentcombined cycle plants. The plants are characterized by the numberof pressure levels for steam generation in the HRSG. The same gasturbine data, based on published data of the Siemens V94.3A [15],are used for all plants. The gas turbine is fuelled with natural gas(Slochteren quality). Overall results and some characteristic dataof the plants are presented in Table 1.

The results confirm that increasing the number of pressure lev-els at which steam is generated in the HRSG will result in signifi-cant higher overall thermal efficiencies (1.60% and 2.25% (points)).

The gas turbine has a compressor pressure ratio of 17.12 and aturbine inlet temperature (ISO temperature) of 1227.81 �C. It isarbitrarily assumed that the increased complexity of the HRSG willresult in a higher pressures loss of the flue gases. The increasedpressure loss of the 2 and 3 pressure alternatives has caused some-what higher GT outlet temperatures.

Steam turbine data are chosen without considering construc-tional limitations. The steam turbine cycles are single reheat cycleswith steam turbine inlet temperatures of 550 �C. The slight devia-tions from this temperature are caused by the calculation process.Steam pressures are the result of a multi-parameter optimizationthat minimizes the overall exergy losses. In the case of the singlepressure steam cycle steam is generated only at a pressure levelcorresponding to the HP turbine inlet pressure. After expansionin the HP turbine steam is reheated in the HRSG and further ex-panded in the IP and LP turbine. In the HRSG of the double pressuresystem steam is generated at pressure levels corresponding withthe inlet pressure of the HP and IP turbines. Expanded steam fromthe HP steam turbine is mixed with steam from the IP steam gen-erator before it is reheated to the IP turbine inlet temperature. In

403403

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4

3

2

1

Dearator

DA-evap

LPTIPTHPT

Stack

IP-EVAP

IP-SHHP-ECO 3

IP-ECO 1

HP-ECO 1

LP-EVAP

LP-ECO

HP-ECO 2

HP-EVAP

IP-ECO 2

LP-Super Heater

Fig. 8. CC plant with 3 pressure HRSG.

1104 N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110

the case of the triple pressure system steam is generated in theHRSG at three pressure levels corresponding with the inlet pres-

sure of the HP, IP and LP steam turbines. Steam from the LP steamgenerator is mixed with the IP outlet flow. The temperature of the

Table 3Results of the steam turbine cycles.

Steam turbine cycle Units 1 press. 2 press. 3 press.

Overall cycle dataHeat flow from GT exhaust gas MW 400.28 400.90 402.02Heat flow to ST cycle MW 300.73 329.72 355.91Net electrical power from cycle MW 112.90 124.09 129.48gth, ST – 0.3754 0.3763 0.3638TH; ST K 522.7 529.7 526.6

TC K 295.2 295.2 295.2gth, rev, ST – 0.4352 0.4427 0.4394gex, intern, ST – 0.8626 0.8501 0.8279

Exergy balanceExergy from HRSG to ST cycle MW 133.51 149.27 160.32Net electrical power MW 112.90 124.09 129.48Exergy from ST cycle to condenser MW 4.38 4.79 5.27Internal exergy loss MW 16.23 20.39 25.57gex, ST cycle – 0.8743 0.8589 0.8351

Table 2Results of the gas turbine cycles.

Gas turbine cycle Units 1 press. 2 press. 3 press.

Overall cycle dataHeat flow to cycle (LHV) MW 660.62 660.62 660.62Net electrical power from cycle MW 251.36 250.75 249.65gth, GT – 0.3805 0.3796 0.3779TH K 1040.0 1040.0 1040.0

TC; GT K 521.1 521.4 521.9

gth, rev, GT – 0.4989 0.4987 0.4982gex, intern, GT – 0.7626 0.7612 0.7586

Exergy balanceCombustorFuel exergy MW 691.48 691.48 691.48Exergy loss combustor MW 204.61 204.61 204.61Exergy transferred to GT cycle MW 486.87 486.87 486.87

GT cycleInternal exergy loss MW 41.27 41.20 41.10Net electrical power MW 251.36 250.75 249.5Exergy of exhaust gas MW 194.24 194.92 196.12gex, GT cycle – 0.8590 0.8589 0.8586

N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110 1105

LP steam (approx. 227 �C) almost equals the outlet temperature ofthe IP steam turbine. The condenser pressure is based on the avail-ability of cooling water of 12 �C at condenser inlet and a tempera-ture increase of 7 K. The three steam turbine cycles are presentedin the T,s-diagram in Fig. 7a–c.

Detailed system models have been established which are ap-plied for design point calculations. Fig. 8 shows the configurationof the system model of the CC plant with 3 pressure HRSG. Steamturbine efficiencies are calculated by Cycle-Tempo. The applied cal-culation method is based on [17] and results in somewhat conser-vative values for the steam turbine efficiencies.

3.2. Evaluation of system results

3.2.1. Gas turbine cycleThe amount of fuel supplied per second to the gas turbine

(17.387 kg/s) is the same for all three systems. The correspondingheat flow (660.62 MW) is based on the lower heating value of thefuel. The exergy flow of the fuel, as shown in Table 2, is691.48 MW. The exergy loss due to combustion is 204.61 MW; thismeans that 29.59% of the exergy transferred to the plant is lost dur-ing combustion. The exergy efficiency of the combustion process isthen 70.41%. Table 2 shows that the generated net electrical powerby the gas turbine cycle is not the same for the three systems. Thedifferences in net electrical power result from differences in GToutlet pressure. It was arbitrarily assumed that a higher numberof pressure levels should result in higher gas side pressure lossesof the HRSG. The assumed overall pressure losses are 24, 29 and38 mbar respectively. Therefore the thermal cycle efficiency (gth,

GT) slightly decreases if the number of pressure levels increases.The thermal efficiency of the cycle (gth, GT) represents the fractionof the heat flow to the cycle that is converted into electrical power.

The thermodynamic equivalent temperature of heat transfer tothe GT cycle (TH) is calculated by applying Eq. (13), with the com-pressor outlet temperature as Tin and the turbine inlet temperatureas Tout. Because of the combustion process it is not possible to ap-ply Eq. (12). Therefore, and because of the high temperature in-crease due to combustion, the calculated value is not veryaccurate. The inaccuracy can be checked by comparing the exergyefficiency of combustion. The exergy efficiency of combustion canbe calculated using the data from the system calculation; then:gex, combustion = 0.7041. But the exergy efficiency of combustioncan also be estimated by using the thermodynamic equivalenttemperature of heat transfer; the estimated value then becomes:

gex, combustion, estimated = 0.7229. The difference between the actualvalue and the estimated value based on TH appears to be less than3% (relative).

The thermodynamic equivalent temperature of heat transferfrom the cycle (TC; GT) is also calculated by applying Eq. (13) usingthe turbine outlet temperature as Tin and the temperature of theenvironment (288.15 K) as Tout. A more accurate value can be ob-tained by applying Eq. (11). The differences between these valueshave only a limited effect on the exergy values that will result fromthese temperatures (about 1%). For this evaluation the accuracy ofthe presented values is supposed to be sufficient. Because of thedifferent exhaust pressures of the three cases, the gas turbine exittemperatures and therefore also the thermodynamic equivalenttemperatures of heat transfer from the cycle are slightly different.

The thermal efficiencies of the reversible cycle (gth, rev, GT) arecalculated using the temperatures TH and TC; GT. The determinationof these values is based on temperatures of the irreversible process.This is in principle not correct, but it is the only available data fromthe system calculation. The inaccuracies resulting from this ap-proach are discussed in chapter 4.

The internal exergy efficiency of the cycle (gex, intern, GT) is calcu-lated as the ratio between the irreversible and the reversible ther-mal efficiency (see Eq. (7)). Differences between the values of thealternative plants are only due to the differences in gas turbineoutlet temperature caused by the difference in pressure loss ofthe HRSG’s. The internal exergy efficiency of the gas turbine cyclesis approximately 76% when using the calculated values for gth, rev,

GT and gth, GT.In Table 2 also some calculated exergy values are shown. The

fuel exergy, the exergy loss of combustion and the exergy trans-ferred to the gas turbine cycle are the same for the consideredcases. The exergy loss of the gas turbine cycle, the net electricalpower and the exergy of the exhaust gas show slight differencesdue to the differences in the gas turbine exhaust temperature.The exergy efficiency of the cycle is calculated using the followingequation:

gex;GT cycle ¼Exproduct

Exsource¼ Pelectr; net

Exto GT cycle � Exexhaust gasð14Þ

The calculated values of the exergy efficiencies of the gas turbinecycle are almost 86% which is much higher than the values calcu-lated for the internal exergy efficiencies of the cycles. The differ-ences between these parameters are discussed in chapter 4.

3.2.2. Steam turbine cycleThe results of the calculations of the steam turbine cycle are

shown in Table 3. The heat flow that can be obtained from the

Table 4Results of the combined cycle plants.

Combined cycle plant Units 1 press. 2 press. 3 press.

Overall cycle dataHeat into cycle MW 660.62 660.62 660.62Net electrical power MW 364.26 374.84 379.13gth, CC – 0.5514 0.5674 0.5739TH K 1040.0 1040.0 1040.0

TC K 295.2 295.2 295.2gth, rev, CC – 0.7162 0.7162 0.7162gex, intern, CC – 0.7699 0.7923 0.8014gex, CC – 0.8070 0.8157 0.8195

Exergy balanceFuel exergy MW 691.48 691.48 691.48Net electrical power MW 364.26 374.84 379.13Overall exergy loss MW 327.22 316.64 312.35Exergy efficiency CC plant – 0.5268 0.5421 0.5483

1106 N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110

GT exhaust gas by cooling this gas to ambient temperature is basedon the assumption that water vapor in the flue gas will remain inthe vapor phase. Then, approximately 400 MW of heat can be ex-tracted from the gas turbine exhaust gas. In the case of the singlepressure system only 300.73 MW from 400.28 MW is transferredto the steam turbine cycle. The net electrical power from the steamturbine cycle is 112.90 MW which results in a thermal efficiency ofthe (irreversible) steam cycle (gth, irrev, ST) of 0.3754. This efficiencyis determined by dividing the net electrical power from the ST cy-cle by the heat transferred to the ST cycle. It appears that the partof the heat from the GT exhaust gas that is transferred to the ST cy-cle is strongly affected by the number of pressure levels at whichsteam is generated in the HRSG. In the case of the triple pressuresystem the heat flow to the ST cycle is about 18% higher then inthe case of the single pressure system. The increase of heat ex-tracted in the HRSG results in a lower outlet temperature of theflue gas (=stack temperature, see Table 1) and in a strong reductionof the heat lost through the stack. However the generated net elec-trical power is not only determined by the heat transferred to thecycle. It appears that also the thermal efficiency of the cycle (gth, ST)is affected by the number of pressure levels; Table 3 shows that ithas a higher value in the case of the double pressure system and alower value in case of the triple pressure system.

The thermodynamic equivalent temperature of heat transfer tothe cycle (TH; ST) is calculated by applying Eq. (12). As heat is trans-ferred to the cycle in different heat exchangers, this equation has tobe modified into:

T ¼P

Um � ðhout � hinÞPUm � ðsout � sinÞ

ð15Þ

It appears that the double pressure system enables a somewhathigher temperature of heat transfer to the cycle (529.7 K); the tem-perature of the triple pressure system however appears to beslightly lower than for the double pressure system (526.6 K), mainlydue to the larger decrease of the flue gas temperature. Heat is trans-ferred from the ST cycle at constant temperature in the condenser.Then, the condenser temperature is the temperature of heat trans-fer from the ST cycle (TC). This temperature is the same for all cases.The thermal efficiency of the reversible cycle (gth, rev, ST) is calcu-lated by using the thermodynamic equivalent temperatures of heattransfer to and from the cycle. As the temperature of heat transferfrom the cycle is constant, the thermal efficiency of the reversiblecycle is only a function of the thermodynamic equivalent tempera-ture of heat transfer to the cycle (TH; ST). Thus the highest value isobtained for the two pressure case.

The internal exergy efficiency of the steam cycle (gex, intern, ST) iscalculated again as the ratio between the irreversible and thereversible thermal efficiency. It appears that the internal cycle effi-ciency of the steam turbine cycle decreases if the number of pres-sure levels is increased. The accuracy of the internal efficiencies islimited since the exergy losses that are determining these efficien-cies strongly depend on assumed performance data. But it seems tobe plausible that the higher complexity of the 3 pressure steamcycle and the addition of steam at lower pressure and temperaturethan the live steam will result in higher internal losses of the cycle.As:

Pnet electr ¼ gex; intern; ST � gth; rev; ST � _QH to ST ð16Þ

it will be clear that the net generated electrical power is dominatedby the increase of heat transfer to the cycle. However the higherinternal losses mitigate the effect of the higher heat flow to theST cycle.

The exergy transferred in the HRSG to the steam cycle is calcu-lated by summarizing the exergy transfer to the steam cycle in allheat exchangers of the HRSG:

Exto ST in HRSG ¼X

i

Um;w exout; w � exin; w� �

ð17Þ

The values in Table 3 show that increasing the number of pressurelevels has a significant effect on the exergy flow to the steam tur-bine cycle (+12% in case of double pressure and +20% in case of tri-ple pressure). However also the transfer of exergy from the steamcycle to the condenser increases as well as the internal exergy lossof the steam cycle. Therefore the net generated electricity is notproportional to the exergy flow to the cycle.

The exergy efficiency of the steam turbine cycle is calculated inthe same way as for the gas turbine cycle. The following equation isused:

gex; ST cycle ¼Exproduct

Exsource¼ Pelectr; net

Exto ST cycle � Exto condenserð18Þ

The differences between the internal cycle efficiency (gex, intern, ST)and the exergy efficiency of the cycle (gex, ST cycle) are much lowerthan in the case of the gas turbine cycle.

3.2.3. Combined cycle plantThe CC plants are evaluated assuming that the gas turbine cycle

and the steam turbine cycle together are considered to be one ther-mal power cycle. The overall results of the CC plants are shown inTable 4. The net electrical power generated by the combined cycleequals the sum of the net electrical powers from the gas turbinecycle and the steam cycle. Then the thermal efficiency of the com-bined cycle increases from 0.5514 for the single pressure plant to0.5739 for the triple pressure plant.

Heat transfer to the combined cycle occurs only in the combus-tor of the GT; therefore the (thermodynamic equivalent) tempera-ture of heat transfer to the cycle is the same as for the gas turbinecycle (1040 K). Heat transfer from the combined cycle to the envi-ronment occurs in the steam condenser (at 295.2 K). Thus the heattransferred to the cycle as well as the thermal efficiency of thereversible cycle (gth, rev, CC) are the same for all the consideredcases. From Eq. (16) it will be clear that the differences in the ther-mal efficiencies of the irreversible cycles are caused only by the dif-ferences in the internal efficiencies of the cycles. Thereforeincreasing the number of pressure levels for steam generation inthe HRSG will increase the internal efficiencies (gex, intern, CC) from0.7699 for the single pressure case to 0.8014 for the triple pressurecase.

The exergy efficiency of the combined cycle can be calculated asbefore for the GT and the ST cycles. But in this case also the exergythat is discharged to the environment trough the stack has to besubtracted in the denominator. The following equation is used:

Table 5Exergy balance of the HRSG.

HRSG Units 1 press. 2 press. 3 press.

Exergy balanceExergy transferred from GT cycle MW 194.24 194.92 196.12Exergy transferred to ST cycle MW 133.51 149.27 160.32Exergy loss HRSG MW 29.64 23.12 18.99Exergy flue gas to stack MW 31.09 22.53 16.81

N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110 1107

gex; CC ¼Exproduct

Exsource¼ Pelectr; net

Exto GT cycle � Exto stack � Exto condenserð19Þ

The differences between the internal cycle efficiency (gex, intern, CC)and the exergy efficiency of the cycle (gex, CC) are again much lowerthan in the case of the gas turbine cycle.

The exergy balance of the combined cycle in Table 4 shows theresulting overall exergy losses and the exergy efficiencies of theconsidered plants. The overall exergy loss is the difference betweenthe fuel exergy and the net electrical power; the exergy efficiencyis calculated as the ratio of the net electrical power and the fuelexergy and increases from 0.5268 for the single pressure case to05483 for the triple pressure case.

The efficiency increase results from differences of the heattransfer in the HRSG. Therefore the exergy losses of the HRSG willbe discussed into more detail. The exergy balances of the HRSG’sare presented in Table 5. From the exergy transferred from theGT cycle (194.24 MW) in the single pressure case 29.64 MW is lostdue to heat transfer in the HRSG, 133.51 MW is transferred to thesteam cycle and the remainder (31.09 MW) is passed to the stack.It appears that by increasing the number of pressure levels thereduction of the exergy loss to the stack is even higher than thereduction of exergy loss due to heat transfer in the HRSG. Thereduction of exergy loss results in a significant higher exergy trans-fer to the steam cycle for the triple pressure case (+20% when com-pared to the single pressure case). However the effect on theoverall plant efficiency is somewhat mitigated by the slightly high-er exergy losses of the ST cycle as shown in Table 3.

The effect of the increased number of pressure levels is demon-strated into more detail by the value diagrams of the HRSG’sshown in Figs. 9 and 10 for the single and triple pressure cases.The shaded areas do represent the exergy loss. The temperaturecurve of the flue gas, if cooled to environmental temperature afterleaving the stack, shows clearly the effect of condensing the watervapor that is available in the flue gas.

An overview of all exergy losses and exergy flows of thecombined cycle plants is shown in the exergy flow diagrams(Grassmann diagrams) in Figs. 11 and 12. The diagrams show thereduced exergy losses of HRSG and stack for the triple pressurecase. However they also show that the larger exergy losses duecombustion and friction in the gas turbine cycle remain unaffected.

4. Discussion of results

4.1. Exergy flow diagram and value diagram

The exergy flow diagrams of the CC plants and the value dia-grams of the HRSG’s give a clear and useful overview of all exergylosses. The exergy flow diagrams (Figs. 11 and 12) show that morethan 35% (205 + 41 MW) of the fuel exergy entering the CC plant islost due to combustion and friction in the gas turbine cycle. Theexergy losses in HRSG, stack and steam cycle together are only11% (30 + 31 + 16 MW) in the case of the single pressure systemand are reduced to 9% for the triple pressure case. The increaseof the number of pressure levels at which steam is generated in

the HRSG obviously influences only the losses in the system partsthat have limited effect on the overall exergy loss of the CC plant.

More detailed insight into the effect of an increased number ofpressure levels can be obtained from the value diagrams of theHRSG’s. The value diagram for the single pressure case (Fig. 9)shows that substantial exergy losses occur in most of the heatexchangers and in particular in the stack. The value diagram forthe triple pressure case (Fig. 10) shows that further reductions ofthe exergy losses in the HRSG and stack are possible. But it alsomakes clear that further attempts to reduce these losses will haveonly little effect.

4.2. Internal exergy efficiencies and exergy efficiencies of the cycles

Different parameters are applied in the previous chapters toindicate the performance of (sub)systems. The internal exergy effi-ciency of the cycle as well as the exergy efficiency are used for thepower cycles. The reason for this is that different questions have tobe answered during the evaluation of power cycles. The perfor-mance of real cycles is affected by irreversibility’s. The extent ofthese irreversibility’s is expressed by the exergy efficiency of thecycle. But this efficiency does not clearly show what the differenceis between the actual generated power and the power that wouldhave been generated in the case of a reversible cycle. For this pur-pose the internal cycle efficiency has been introduced. The internalefficiency is by definition lower than the exergy efficiency of thecycle.

The relevance of these efficiencies can be demonstrated bycomparing the exergy efficiencies and the internal exergy efficien-cies of respectively the GT cycle, the ST cycle and the combined cy-cle. It appears that the differences between these efficiencies arerather small for the ST cycle and the combined cycle. Howeverlarge differences are calculated for the GT cycle: the internal exer-gy efficiency for the single pressure case is 0.7626 whereas theexergy efficiency is 0.8590. It indicates that the difference in powerfrom a reversible GT cycle and the real GT cycle is much higherthan the exergy loss of the real cycle. This is caused by the fact thatin the case of a reversible cycle the temperature of the GT exhaustgas will be lower and consequently the exergy that is transferred tothe GT exhaust gas will be far less than in the case of the real GTcycle. Thus the difference between the internal efficiency and theexergy efficiency will become higher if the exergy transfer fromthe cycle is more affected by the performance of the cycle.

In the case of a steam cycles with near environmental condens-ing temperature the exergy transfer from the cycle is almost inde-pendent of the cycle efficiency. Then the internal efficiency is veryclose to the exergy efficiency. In that case the exergy efficiencyindicates the achievable improvement rather well. This is also truein the case of a combined cycle; however, it appears that the differ-ences between the internal efficiencies and the exergy efficienciesof the combined cycles are somewhat higher (for the single pres-sure case: gex, CC � gex, intern, CC = 0.8070 � 0.7699 = 0.0371) thanin the case of the steam cycles (gex, ST cycle � gex, intern, ST =0.8743 � 0.8626 = 0.0117). The higher difference in the case ofthe combined cycle is caused by the fact that the combined cycledischarges exergy to the environment not only in the condenserbut also through the stack.

Thus, the exergy efficiency of the cycle (or combined cycle) rep-resents the extent of exergy losses in the cycle while the internalexergy efficiency indicates the differences between the reversibleand the irreversible cycle.

4.3. Further developments

The exergy efficiencies of the CC plants differ from 0.5268 forthe single pressure case to 0.5483 for the triple pressure case;

Heat Exchgr. 309D.A. evapora 342

HP ECO 315IP ECO 1 352LP-ECO 362

LP Evaporato 365LP-superheat 366

IP-ECO 2 354HP-ECO 2 317

IP Evaporato 357IP superheat 358

HP end ECO 319HP Evaporato 322

Reheater 303HP Superheat 323

value diagram 3 press. HRSG

35633232231831631528328027024020419815410359.1

Transmitted heat [MW]

0 467

0

0.5

1

1 - T

0 / T

[-]

100

200

300

400

500 600 700 800

Tem

pera

ture

[°C

] 15

Stack 15

Fig. 10. Value diagram of the HRSG with steam generated at 3 pressure levels.

Grassmann diagram combined cycle(single pressure HRSG)

to GT cycleEx = 487 MW

fuelEx = 691 MW

combustion Ex = 205 MWloss

GT cycle Ex = 41 MWloss

P = 251 MWGT

Ex = 194 MWto HRSG

stack Ex = 31 MWloss

HRSG Ex = 30 MWlossEx = 134 MWto SC

steam cycle Ex = 16 MWloss

P = 113 MWSTP = 364 MWe

condenser Ex = 4 MWloss

Fig. 11. The exergy flow diagram (Grassmann diagram) of the CC plant with 1pressure HRSG.

Grassmann diagram combined cycle(triple pressure HRSG)

to GT cycleEx = 487 MW

fuelEx = 691 MW

combustion Ex = 205 MWloss

GT cycle Ex = 41 MWloss

P = 250 MWGT

Ex = 196 MWto HRSG

stack Ex = 17 MWloss

HRSG Ex = 19 MWlossEx = 160 MWto SC

steam cycle Ex = 26 MWloss

P = 129 MWSTP = 379 MWe

condenser Ex = 5 MWloss

Fig. 12. The exergy flow diagram (Grassmann diagram) of the CC plant with 3pressure HRSG.

Preheater 308DA evap 342

HP-ECO 313

HP Evaporato 316

Reheater 303HP Superheat 317

value diagram 1 press. HRSG

30128227422333.7 92.5

Transmitted heat [MW]0 465

0.5

0

1

0.5

0

1 - T

0 / T

[-]

1

700 600 500

400

300

200

100

800 700 600 500

400

300

200

100

Temperature [°C

]

15

800

Stack 107

Fig. 9. Value diagram of the HRSG with steam generated at 1 pressure level.

1108 N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110

0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000

300

500

700

900

1100

1300

1500

1700

1900

temperature of heat transferred to the system (K)

effic

ienc

y

Carnot efficiency actual efficiency

Fig. 13. The effect of the temperature of heat transfer to the cycle on the efficiencyof a thermal power cycle (the actual efficiency is based on an internal cycleefficiency of 0.80).

N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110 1109

the corresponding thermal efficiencies are respectively 0.5514 and0.5739. These values are somewhat lower than the highest obtain-able values (about 0.60) today. Thus, it must be concluded thateven the best performing combined cycles are wasting more than40% of the available exergy from the fuel. Directions for furtherimprovements can be derived from Eq. (6) as well as from the exer-gy flow diagrams. The main options are: a further increase of thetemperature of heat transfer to the cycle and an increase of theinternal exergy efficiency (by reducing the exergy losses withinthe cycle).

The exergy losses within the cycle are the result of a trade-offbetween driving forces for heat transfer etc. and capital costs.Technology development and increased fuel prices will result ina gradual reduction of these losses. The internal exergy efficienciesof the combined cycles today are about 80%, the remaining spacefor further improvements is not very high. An increase of the inter-nal exergy efficiency to 85% or 90% will raise the plant thermal effi-ciency with roughly 4–7% points; the necessary efforts will takeprobably a long period of continued development.

The other option is the increase of the temperature of heattransfer to the cycle. This can be achieved in several ways: increas-ing the gas turbine inlet temperature (TIT), increasing the pressureratio and applying one or more reheats. The effect of increasedtemperatures of heat transfer is indicated in Fig. 13. The solid linerepresents the Carnot efficiency of a thermal power cycle thattransfers residual heat to the environment at environmental tem-perature; the dotted line represents the cycle efficiency if an inter-nal exergy efficiency of 0.80 is applied. The calculated temperatureof heat transfer to the cycle of the systems considered in this paperis 1040 K. Fig. 13 shows that with this temperature a thermal effi-ciency of somewhat less than 60% can be achieved. This corre-sponds rather well with the value calculated for the triplepressure plant. Temperatures higher than 1300–1400 K are neces-sary to reach efficiencies that are significantly higher than 60%. Athermodynamic equivalent temperature of heat transfer to the cy-cle of about 1350 K can be obtained with a pressure ratio of 40 anda TIT of 1700 �C in case of a gas turbine without reheat; this willresult into thermal efficiencies of CC plants of 62–63%. Raisingthe TIT to 1900 �C will increase the thermal efficiency with about1% point. Today the gas turbine with the highest TIT is the GE H-series (S109H, S107H) [16] with steam cooled blades. Further in-crease of the turbine inlet temperatures will require substantial ef-forts from gas turbine manufactures; because of the limitedbenefits it is not very likely that they will opt for this development.

The application of reheat is another option to increase the ther-modynamic temperature of heat transfer to the cycle. The intro-

duction of a reheat gas turbine by Alstom (GT26) [16] is the onlyattempt into this direction so far; further developments are not an-nounced. Therefore, the prospects of combined cycle efficienciessignificantly higher than 60% in the future seem to be limited.

Electrochemical conversion of fuels provides an opportunity toavoid the large exergy losses that are inherent to thermal fuel con-version. In particular high temperature fuel cells have the potentialto enable plant efficiencies over 80%. In [18] a study is presentedthat investigates the conditions under which these high efficien-cies are conceivable using SOFC–GT hybrid systems. The resultsshow that such high efficiencies can be achieved without bottom-ing cycle and with rather moderate conditions for the gas turbineas well as the fuel cell; the application of a bottoming cycle will en-able a further increase of the plant efficiency with 1–3% points.Overall plant power is dominated by the performance of the gasturbine, but can be much lower than for conventional power sta-tions. It is obvious that the present state of the art of SOFC technol-ogy is insufficient to build SOFC–GT hybrid plants, but theperspective of very high conversion efficiencies might justify sub-stantial development efforts today.

5. Conclusions

The application of combined cycles has resulted in a significantincrease of power plant efficiencies during the last decades. Overallplant efficiencies of about 60% are achievable today if heat from thegas turbine exhaust gases is efficiently used. The evaluation ofexergy losses in combined cycle plants shows that these lossesare mainly dominated by the exergy losses of thermal combustion.Possibilities to reduce these losses are limited. The exergy flow dia-grams (Figs. 11 and 12) show that the highest losses are caused by(thermal) combustion of the fuel. The further enhancement ofoverall power plant efficiencies to 70% or even higher will requirethe development of high temperature fuel cell systems like SOFC–GT hybrid systems

The comparison of CC plants with increasing number of pres-sure levels of steam generation in the HRSG shows that the effi-ciency gain of a triple pressure system in comparison with asingle pressure system is caused by the reduction of the exergy lossof heat transfer in the HRSG as well as the lower exergy of the fluegasses discharged to the stack. The last effect is even more impor-tant than the reduction of exergy losses due to heat transfer as canbe learned from the value diagrams of the HRSG’s (Figs. 9 and 10).In the case of the triple pressure system the remaining exergylosses of heat transfer and flue gas discharge together are about5% of the fuel exergy. A further increase of the number of steampressure levels in the HRSG does not seem to be really beneficial;it enables only a small reduction of the overall exergy loss of theplant.

Different parameters can be used to assess the thermodynamicperformance of power plants or the different cycles. The tradition-ally used thermal efficiency does not indicate thermodynamiclosses correctly as it does not consider for the temperature of heattransfer to and from the cycles. Therefore the application of exergyefficiencies should be recommended. Exergy efficiencies howeverjust show the actual losses in the considered situation but do notindicate clearly the difference with the ideal case. In order to seehow far the actual performance differs from the performance inthe ideal (reversible) case, the internal exergy efficiency of a cycleis a better indicator, in particular if the exergy transferred from thecycle is seriously influenced by the performance of the cycle itself.An estimated value of the internal exergy efficiency can be calcu-lated with limited accuracy using available data from system cal-culations. Very accurate values of the internal exergy efficiencywill require the additional computation of the reversible cycle.

1110 N. Woudstra et al. / Energy Conversion and Management 51 (2010) 1099–1110

However, the accuracy of the estimated values will be sufficient forusual evaluations.

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