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Modeling and exergy and exergoeconomic optimization of a gas turbine power
plant using a genetic algorithm
Soheil. Fouladi
MS.c student, School of Mechanical Engineering, Iran University of Science & Technology, Tehran, Iran
[email protected]
Hamid. Saffari
Assistant Professor, School of Mechanical Engineering, Iran University of Science & Technology, Tehran, Iran
[email protected]
ABSTRACT In this paper, the thermodynamic modelling of a gas
turbine power plant in Iran is performed. Also, a
computer code has been developed based on Matlab
software. Moreover, both exergy and exergoeconomic
analysis of this power plant have been conducted. To
have a good insight into this study, the effects of key
parameters such as compressor pressure ratio, gas
turbine inlet temperature (TIT), compressor and turbine isentropic efficiency on the total exergy destruction,
total exergy efficiency as well as total cost of exergy
destruction have been performed. The modelling
results have been compared with an actual running
power plant located in Yazd city, Iran. The results of
developed code have shown reasonable agreement
between the simulation code results and experimental
data obtained from power plant. The exergy analysis
revealed that the combustion chamber is the must
exergy destructor in comparison with other
components. Also, its exergy efficiency is less than
other components. This is due to the high temperature
difference between working fluid and burner
temperature. In addition, it was found that by the
increase of TIT, the exergy destruction of this
component can be reduced. On the other hand, the cost
of exergy destruction is high for the combustion chamber. The effects of design parameters on exergy
efficiency have shown that increase in the air
compressor ratio and TIT, increases the total exergy
efficiency of the cycle. Furthermore, the results have
revealed that by the increase of TIT by 3500 C, the cost
of exergy destruction is decreased about 22%.
Therefore, TIT is the best option to improve the cycle
losses. In addition, an optimization using a genetic
algorithm has been conducted to find the optimal
solution of the plant.
Keywords: Steam power plant, Exergy analysis,
Efficiency, Exergy destruction.
1 INTRODUCTION Energy systems involve a large number and various types of interactions with the world outside their
physical boundaries.
Therefore, designer must face many issues, which deal
primarily with the energy, economy and environment.
In this area, gas turbines (GT) are the best option
because they are widely used as both single gas turbine
cycles and combined cycles. Hence, thermodynamic
modeling and performance analysis of gas turbine
power plant is one of the significant subjects for
thermal system designers. The combined cycle power
plants (CC) use the exhaust heat from the gas turbine
engine to increase the power plant output and boost the
overall efficiency to more than 50%.
The new methodology is exergy analysis and its
optimization component is known as thermodynamic
optimization, or entropy generation minimization
(EGM). This new approach is based on the simultaneous application of the first law and the second
law in analysis and design [1].
The energy crisis of the 1970s and the continuing
emphasis on efficiency (conservation of fuel resources)
have led to a complete overhaul of the way in which
power systems are analyzed and improved
thermodynamically [2].
Today, many electrical generating utilities are striving
to improve the efficiency (or heat rate) at their existing
thermal electric generating stations, many of which are
over 25 years old. Often, a heat rate improvement of
only a few percent appears desirable as it is thought that
the costs and complexity of such measures may be more
manageable than more expensive options. Thus, a better
understanding is attained when a more complete
thermodynamic view is taken, which uses the second
law of thermodynamics in conjunction with energy analysis, via exergy methods.
The most commonly-used method for evaluating the
efficiency of an energy-conversion process is the first-
Proceedings of the ASME 2010 International Mechanical Engineering Congress & Exposition IMECE2010
November 12-18, 2010, Vancouver, British Columbia, Canada
IMECE2010-39577
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law analysis. Analysis of power generation systems are
of scientific interest and also essential for the efficient
utilization of energy resources. In addition, there are
numerous research papers in the literature which have
presented exergy and exergoeconomic analysis.
However, they usually don't pay much attention to the
effect of key parameters on the cycle components
specially cost of exergy destruction. It is well-known
that the exergy can be used to determine the location, type and true magnitude of exergy loss (or destruction).
Thus, it can play an important role in developing
strategies and in providing guidelines for more effective
use of energy in the existing power plants [3].
Moreover, another important issue to improve the
existing system is the origin of the exergy loss and
components in which the most exergy destruction take
place. Hence, a clear picture, instead of only the
magnitude of exergy loss in each section, is required.
According to literature, exergy analysis is a
methodology for the evaluation of the performance of
devices and processes, and involves examining the
exergy at different points in a series of energy-
conversion steps [2-5]. Among the useful analysis
techniques that are available, exergy analysis is
important because it is a useful, convenient and
straightforward method for assessing and improving thermal power plants.
Exergy analysis results can aid efforts to improve the
efficiency, and possibly the economic and
environmental performance of GT power plants.
Thermoeconomic analysis combines the exergy analysis
with the economic principles and incorporates the
associated costs of the thermodynamic inefficiencies in
the total product cost of an energy system. These costs
may conduct designers to understand the cost formation
process in an energy system and it can be utilized in
optimization of thermodynamic systems, in which the
task is usually focused on minimizing the unit cost of
the system product [5]. Several researchers carried out
the exergy and exergoeconomics in which gas turbine
played a significant part. Sahin and Ali [6] carried out
an optimal performance analysis of a combined Carnot
cycle (two single Carnot cycles in cascade), including internal irreversibilities for steady-state operation.
Ameri and Ahmadi [3] performed the exergy analysis
of the supplementary firing in heat recovery steam
generator in a combined cycle power plant. Their
results showed that if a duct burner is added to heat
recovery steam generator (HRSG), the first and second
law efficiencies are reduced.
Also, Ameri et al. [2] performed the energy, exergy and
exergoeconomic analysis for one of the largest steam
power plant in Iran. It was found that boiler was a most
significant component which should be considered for
any improvements. The reason of the greatest exergy
destruction in this part is due to the combustion and
heat transfer processes which take palace across large
temperature differences between burner temperature
and working fluid. The same results were obtained in
another research performed by Ameri et al. [4]. It was
found that in combined cycle power plants, combustion
chamber destroy the inflow exergy because of the high
temperature difference. However, that article did not
pay much attention the effects of key parameters.
The present study is the extended version of earlier
research [1, 3]. The following points are the specific
contribution of the current paper in this subject:
Complete thermodynamic modeling of one of the greatest gas turbine power plants in Iran
has been performed.
Exergy analysis of the GT plant has been
performed.
Exergoeconomic analysis of the GT power
plant has been carried out.
The effects of key parameters on both exergy
and exergoeconomic performance of the cycle
have been conducted.
2 Exergy analysis Exergy is composed of two important parts. The first
one is the physical exergy and the second one is the
chemical exergy. In this study, the kinetic and potential
parts of exergy are negligible [4]. The physical exergy
is defined as the maximum theoretical useful work
obtained as a system interact with an equilibrium state.
The chemical exergy is associated with the departure of the chemical composition of a system from its chemical
equilibrium. The chemical exergy is an important part
of exergy in combustion process. It is important to
observe that unlike energy, exergy is exempt from the
law of conservation [5]. Irreversibility associated with
actual processes cause exergy destruction.
In order to do the exergy analysis, mass and energy
balances on the system are required to be determined. If
one applies the first second laws of thermodynamics,
one can find the formula for exergy balance as the
following [4]:
Continuity equation:
eimm
(1)
Energy equation:
i
ie
ehmhmWQ
(2)
Exergy balance equation:
i e
DWeeiiQ EEememE
(3)
Where subscripts i and e refer to streams entering and
leaving the control region, respectively. The exergy rate
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of a stream of substance (neglecting the potential and
kinetic components) can be written in the form:
chph EEE (4)
where:
emE
The mixture chemical exergy is defined as follows [6]:
n
i
n
i
E
ii
ch
i
ch
mix GLnXXRTexXex i
1 1
0
(5)
The last term,EG , which is the excess free Gibbs
energy is negligible at low pressure at a gas mixture. One can generalize the chemical exergy concept of fuel
to every ONHC component [7]. The molar
chemical exergy ch
cex of such a component will be:
)( 0,
e
cc
ch
cex
(6)
Where e
c refers to the chemical potential of the component at the restricted dead state.
e
O
e
N
e
OH
e
co
e
c
2
222
)2/4/(
)2/()2/(
(7)
0,c represents the chemical potential of the
components at their thermo-mechanical equilibrium
state with the standard ambient.
For the evaluation of the fuel exergy, the above formula
cannot be used. Thus, the corresponding ratio of
simplified exergy is defined as the following [8]:
ff LHVex
(8)
Due to the fact that for the most of usual gaseous fuels,
the ratio of chemical exergy to the Lower Heating
Value is usually close to 1, one may write [4]:
985.0
06.1
2
4
H
CH
(9)
For gaseous fuel with CxHy, the following experimental
equation is used to calculate ξ [4]:
xx
y 0698.00169.0033.1
(10)
In this formula (3), (e) is the total specific exergy and
DE
is the exergy destruction.
i
i
Q QT
TE
1
(11)
WEW
(12)
)()( SSThheph (13)
Where T is the absolute temperature (K) and subscripts
(i) and (o) refer to inlet and ambient conditions
respectively.
In the exergy analysis of power plants, the exergy of
steam should be calculated at all states and the changes
in the exergy are determined for each major component.
Unlike energy, exergy is not conserved but destroyed in
the system. In the components of the plant, exergy is
dissipated during a process because of friction, mixing,
combustion, heat transfer, etc. The source of exergy
destruction (or irreversibility) in boiler and steam turbine is mainly combustion (chemical reaction) and
thermal losses in the flow path respectively [9].
However, the exergy destruction in the heat exchangers
of the system i.e. condenser, feed water heater, is due to
the large temperature difference between the hot and
cold fluid.
The objective of present study is to perform an exergy
and exergoeconomic analysis and the simulation of Gas
turbine power plant which is a common cycle to
produce power in Iran. Thus, for this reason after
simulation and thermodynamic modeling of this cycle,
the exergy balance for each component is calculated to
find the exergy destruction in each component.
3 Exergoeconomic analysis Exergoeconomic or thermo-economic is the branch
of engineering that appropriately combines, at the level of system components, thermodynamic evaluations
based on an exergy analysis with economic principles,
in order to provide the designer or operator of a system
with useful information for the design and operation of
a cost-effective system which is not obtainable by
regular energy or exergy analysis and economic
analysis [10]. When exergy costing is not applied,
researchers should use a different term (e.g., thermo-
economic). Thermo-economic is a more general term
and characterizing any combination of a
thermodynamic analysis with an economic one [11, 12].
In order to define a cost function which depends on
optimization parameters of interest, component cost
should be expressed as functions of thermodynamic
design parameters [12].
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For each flow line in the system, a parameter called
flow cost rate C ($ s-1
) is defined, and the cost balance
equation of each component is written as:
k
i
kikqkw
kee
ZCCCC
,,,
,
(14)
The cost balance equation of each component is written
as:
kkiikqkqkkwkee
ZEcEcWcEc )()(,,,
(15)
jjj EcC (16)
In this analysis it is worth mentioning that the fuel and
product exergy should be defined. The exergy product
is defined according to the components under
consideration. The fuel represents the source that is
consumed in generating the product. Both the product
and fuel are expressed in terms of exergy. The cost rates
associated with the fuel (
FC ) and product (
PC ) of a
component are obtained by replacing the exergy rates
(
E ). For example, in a turbine, fuel is the difference
between input and output exergy and product is the generated output power of the turbine.
In the cost balance formulation (Eq.14), there is no cost
term directly associated with exergy destruction of each
component. Accordingly, the cost associated with the
exergy destruction in a component or process is a
hidden cost. Thus, if one combines the exergy balance
and exergoeconomic balance together, one can obtain
the following equations:
KDKPKF
EEE,,,
(17)
Accordingly, the expression for the cost of exergy
destruction is defined as it follows:
kDkFkD EcC
,,,
(18)
Further details of the exergoeconomic analysis, cost
balance equations and exergoeconomic factors are
completely discussed in references [3, 12 and 13].
In addition, several methods have been suggested to
express the purchase cost of equipments in terms of
design parameters in Eq. (14). However, we have used the cost functions which are suggested by Ameri et al.
[2]. Nevertheless, some modifications have been made
to tailor these results to the regional conditions in Iran
and taking into account the inflation rate. To convert
the capital investment into cost per time unit, one may
write:
)3600(..
NCRFZZ
kk
(19) Where, Zk is the purchase cost of kth component in US
$. The Capital Recovery Factor (CRF) depends on the
interest rate as well as estimated equipment life time.
CRF is determined using the following equation [2]:
n
n
i (1 i)CRF
(1 i) 1
(20)
In which i is the interest rate and n is the total operating
period of the system in years.
In Eq.19, N is the annual operation hours of the unit,
and φ (1.06) is the maintenance factor [2, 12]. Finally, in order to determine the cost of exergy
destruction of each component, the value of exergy
destruction, ED,k , is estimated using exergy balance
equation in the previous section.
3.1 Cost balance Equations
As we know for estimating the cost of exergy
destruction for each component of the power plant, first
we should solve the cost balance equations for each
component. Therefore, for the application of the cost
balance equation (Eq.14), there is usually more than
one inlet and outlet streams for some components. In
this case, the number of unknown cost parameters is
higher than the number of cost balance equation for that
component. Auxiliary exergoeconomic equations are
developed to solve this problem [2, 12]. Implementing
Eq.15 for each component together with the auxiliary equations forms a system of linear equations as it
follows:
kkKZcE
(21)
Where
KE ,
kc and
kZ are the matrix of
exergy rate (obtained in exergy analysis), exergetic cost
vector (to be evaluated) and the vector of
kZ factors
(obtained in economic analysis), respectively. The cost
function for each component in the cycle is presented in
table 1. After estimation of C i, the cost of exergy
destruction will be calculated based on Eq.18.
c
GT
CC
AP
AC
F
Z
Z
Z
Z
c
c
c
c
c
c
c
c
c
EEEE
EEE
EEEE
EEE
E
0
0
0
0
100000000
000110000
011000000
000011000
00000
000000
00000
000000
00000000
9
8
7
6
5
4
3
2
1
8754
943
6532
721
1
(22)
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Therefore, by solving these sets of equations, one can
find the cost rate of each flow line of GT (Fig.1).
Moreover, they are used to find the cost of exergy
destruction in each component of the plant.
4 Thermodynamic Modeling To find the optimum physical and thermal design parameters of the system, a simulation program was
developed in Matlab software. The cycle power plant
(CCPP), properties are found by using this code, which
are input and output enthalpy and exergy of each flow
line in the plant were estimated to study energy, exergy
and exergoeconomic analysis. The energy balance
equations for various parts of the CCPP (Fig.1) are as
follows:
Air compressor
1r1
1TTa
a 1
cAC
12 (23)
)TT(C.mW 12a,paAC (24)
(2)
Where Cpa is considered to be a temperature variable
function as the following [1]:
2
4 7
3 4
10 14
3.8371 9.4537( ) 1.04841 ( ) ( )
10 10
5.49031 7.9298( ) ( )
10 10
Pa
T TC T
T T
(25)
Combustion Chamber (CC)
2 3 (1 )a f g cc fm h m LHV m h m LHV (26)
3
2
(1 )cc
PP
P (27)
Gas turbine
1
34 3
4
1 1
g
g
GT
pT T
p
(28)
, 4 3. ( )GT g p gW m C T T (29)
ACGTNetWWW (30)
afg mmm
(31)
Where Cpg is taken as a temperature variable function as
it follows [1]:
5
2 3
7 10
6.99703( ) 0.991615 ( )
10
2.7129 1.22442( ) ( )
10 10
Pg
TC T
T T
(32)
4 Case Study
To verify the results of our simulation code, they are
compared with the actual data from an operating gas
turbine power plant in Yazd Power Plant. This power
plant is located near the Yazd city which is one of the
middle provinces in Iran. The schematic of this power
plant is shown in Fig.1. The incoming air has a
temperature of 17.100C and a pressure of 0.874 bar
using the power plant data gathered in 2006. The pressure increases to 10.593 bar through the
compressor, which has an isentropic efficiency of 83%.
The turbine inlet temperature is 10730C. The turbine
has an isentropic efficiency of 87%. The fuel (natural
gas) is injected at 17.100C and 30 bar.
4. Results and Discussions 4.1 Exergy Analysis Results The performance analysis of the GT cycle is
investigated considering actual conditions such as
temperature and pressure for each component. The air
conditions at the compressor inlet are set at 0.874 bar
and 2980K. In this case the output power of the gas
turbine cycle is 106 MW. In addition, the heat losses
across the combustion chamber are assumed to be 3%.
The isentropic efficiency of the compressors is taken as
83%, and the isentropic efficiency of the gas and steam
turbines is fixed at 87%. The gas turbine inlet
temperature is varied between 1100 0K and 1450
0K and
the operation range for the compressor pressure ratio is
chosen from 10 to 20 in this study. The results from exergy analysis show that for the
above conditions, combustion chamber is the most
significant exergy destructor in the combined cycle
power plant. It is due to the fact that the chemical
reaction and the large temperature difference between
the burners and working fluid are the main source of
irreversibility. In fact, its exergetic efficiency is less
than other components. The exergy destruction of the
whole components in the GT is shown in Fig.2.
Figure 3 shows the effect of changes in the compressor
pressure ratio on the exergy efficiency. Results show
that for a gas turbine inlet temperature of 14500K, the
GT cycle exergy efficiency increases with the pressure
ratio.
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Figure 4 presents the effect of compressor pressure ratio
on the CC exergy destruction. It is shown that higher-
pressure ratio results in lower exergy destruction in the
whole GT cycle power plant, which results in less fuel
supplied to the gas turbine cycle. It means that any
saving in the fuel has a significant impact on the total
exergy destruction of the GT cycle. The exergy of the
fuel consists of physical and chemical exergy.
However, the chemical exergy has significant impact on the total exergy of fuel when compared with the
physical exergy.
Figure 5 shows the effect of gas turbine inlet
temperature variation on the gas turbine exergy
efficiency. It shows that increase in the TIT leads to
increase in the GT exergy efficiency due to the fact that
the GT turbine output increases. Figure 6 confirms that
by increase of the TIT, the exergy destruction decreases
as it was concluded by Fig.5. Therefore, it was found
that TIT is the most important parameter in designing
the GT cycle due to decrease in the exergy destruction
as well as increase in the cycle exergy efficiency.
Optimization Results: In this part, to have a good insight into this study, the
optimization of the power plant has been performed.
The optimization procedure is an evolutionary algorithm (i.e. Genetic Algorithm). The optimization
program is developed in Matlab Software
programming. Therefore; like each optimization
problem, the design Parameters of the plant, were
chosen as: compressor pressure ratio (rc), compressor
isentropic efficiency (ηC), gas turbine isentropic
efficiency (ηGT), combustion chamber inlet temperature
(T3), and turbine inlet temperature (T5). In order to
optimally find the design parameters a thermoeconomic
approach has been followed. An objective function,
representing the total cost of the plant in terms of dollar
per second, was defined as the sum of the operating
cost, related to the fuel consumption.
The objective function here is
.f f k
O F c m LHV Z (33)
For calculating the rate of operating cost equation, we
have:
LHVmcC fff (34)
In which c = 0.003 $/MJ is the regional cost of fuel per
unit of energy, fm is the fuel mass flow rate, and LHV
= 50000 kJ/kg is the lower heating value of Methane.
The objective function which is given to evolutionary
algorithm (i. e Genetic Algorithm) is considered here.
As it was discussed, the objective function is a
summation of three important parts. The convergence
of objective function is shown in figure (8). As it is
shown in this figure the objective function is reached to the final amount after almost 70 generations. It looks as
if our developed code has a powerful converge and it is
well-developed. Moreover, the variation of each
decision variable versus number of generation is shown
in figure(9-12). As it is clear in these mentioned figures,
in first 50 generations the variation of decision
variables are much more than other generation numbers
because searching in first intervals are more sensitive.
Thus, after some generations the objective function
finds the real decision variables. The optimization code
which is Genetic Algorithm is so accessible because the
number of generation is considered as an input. This
input generation number strongly depends on the
configuration of power cycle and our constraints. Therefore, the number of generations almost 300 is
found suitable for this problem.
5 Conclusion In the present study both thermodynamic modeling
and exergy and exergoeconomic analysis of a GT cycle
were performed.
The results from exergy analysis showed that
combustion chamber is the most significant exergy
destructor in GT cycle power plant which is due to the
chemical reaction and the large temperature difference
between the burners and working fluid and. Moreover,
the results showed that by increase of TIT, the GT
exergy efficiency increases due to the increase in the
output power of turbine as well as decrease in the
combustion chamber losses.
Furthermore, the results from exergoeconomic analysis
showed that like exergy analysis, combustion chamber
had the greatest cost of exergy destruction in
comparison with other components. In addition, the results showed that by increasing TIT, the GT cost of
exergy destruction was decreased.
Nomenclature amb Ambient
Cond Condenser
C Cost per unit of exergy ($/Mj-1
)
Cp Specific heat (kJ kg-1
K-1
)
CD Cost of exergy destruction ( $/hr)
Cf Cost of fuel pet unit of energy
($/Mj-1
)
E Exergy (kJ)
e Specific exergy (kJ kg-1
)
G Generator
GE Excess free Gibbs energy (kJ)
h Specific enthalpy (kJ/kg)
DE Exergy Destruction (kJ)
LHV Lower Heating Value (kJ/kg)
m Mass Flow rate (Kg/hr)
P Pressure (bar)
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Q Heat Transfer (kJ)
R Gas constant (kJ/kg.0K)
S Specific entropy (kJ kg-1
K-1
)
T Temperature (0C)
TIT GT inlet temperature (K)
W Work (kJ)
Greek symbols
ζ Specific exergy loss
Efficiency defect
ηe Exergy Efficiency
Subscripts and Superscripts
Ch Chemical
D Destruction
f Fuel
e Exit Condition
GT Gas Turbine
i Inlet Condition
k Component
L Loss
gi Gas Inlet
ge Gas Outlet
p Pump
ph Physical
T Turbine
tot Total
Reference ambient
condition
Rate
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Fig.1 schematic of a gas turbine power plant.
0
50
100
150
200
250
compressor combustion
chamber
Turbine(G.T) Air Preheater Total Gas
Turbine Cycle
exerg
y D
estr
ucti
on
(M
W)
Fig.2 Exergy destruction of each component of the cycle.
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9
Fig.4 Effect of compressor pressure on the PP exergy destruction.
Fig.5 Effect of TIT variation on the GT cycle exergy efficiency.
Fig.3 Effect of compressor pressure on the cycle exergy efficiency.
Fig.5 Effect of TIT variation on the GT cycle exergy efficiency.
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Fig.6 Effect of TIT variation on the GT exergy destruction.
Fig.7 The total cost of exergy destruction versus TIT.
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11
1.14
1.16
1.18
1.2
1.22
1.24
1.26
1.28
1.3
0 50 100 150 200 250 300
Number of Generations
Ob
jecti
ve F
un
cti
on
($/s
)
Figure (8): Convergence of objective function
after each generation.
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
0 50 100 150 200 250 300
Number of Generations
Co
mp
resso
r P
ressu
re R
ati
o
Figure (9): Variation of compressor pressure
ration with generations
0.795
0.8
0.805
0.81
0.815
0.82
0.825
0.83
0.835
0.84
0.845
0 50 100 150 200 250 300
Number of Generations
Co
mp
resso
r Is
en
tro
pic
Eff
icie
ncy (
%)
880
900
920
940
960
980
1000
1020
1040
1060
0 50 100 150 200 250 300
Number of Generations
Co
mb
usti
on
Ch
am
ber
Inle
t
Tem
pera
ture
(K
)
Figure (10): Variation of combustion chamber
inlet temperature with generations
0.845
0.85
0.855
0.86
0.865
0.87
0.875
0.88
0.885
0 50 100 150 200 250 300
Number of Generations
GT
Tu
rbin
e I
sen
tro
pic
Eff
icie
ncy (
%)
Figure (11): Variation of gas turbine inlet
temperature with generations
Figure (12): Variation of gas turbine isentropic
efficiency with generations
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12
Capital or investment cost functions System
Component
11
12 AC
a 2 2AC
1 1
c m p p1n
c p p
AC
2423
3
4
22
21 1 CTCEXP
p
pc
mcTIT
a
CC
CC
C
D
31 gGT 33 3 34
32 T
pc min 1 EXP c T c
c p
GT
5 6
0.6g(h h )
AP 41LMTD
mC
U T
AP
Table1: Purchase cost function of each component in Gas
turbine power plant.
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