CHEPTER-3
EFFECT OF OPERATING VARIABLES ON THERMAL
EFFICIENCY OF COMBINED CYCLE POWER PLANT
3.1 THERMAL EFFICIENCY OF THE COMBINED CYCLE: In combined cycle power plants if power in gas turbine and steam turbine is Pgt and Pst
respectively and heat supplied in combustion chamber is Qc, then according to general
definition of thermal efficiency.
(3.1)
If there is a supplementary firing in HRSG, then
(3.2)
For gas turbine process
(3.3)
For steam turbine process
(3.4)
Q1 is the heat exchange in HRSG from exhaust gases
Now from equation (3.3)
(3.5)
(3.6)
Therefore
Substituting the value of
from equations (3.3) and (3.6) in equation (3.2)
Now,
(3.7)
3.2 THE EFFECT OF SUPPLEMENTARY FIRING IN THE HRSG ON
OVERALL THERMAL EFFICIENCY
Supplementary firing in the HRSG improves the overall thermal efficiency of combined
cycle power plant whenever
(3.8)
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Differentiating the eq. (3.7) w.r.t QSF
From eq. (3.7) the RHS term is ηo
Now
The term
Now from eq. (3.6)
is the heat input to the steam cycles
=
(3.9)
Eq. (3.9) shows that with supplementary firing of fuel in HRSG, the power output of
steam cycle (Pst) as well as its efficiency (
) increase and so the increase in the overall
efficiency diminishes. Therefore, supplementary firing is becoming less and less
attractive. Generally it is more profitable to burn the fuel in the combustor of gas turbine
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plant itself since the heat is supplied to the system at a temperature higher than that in
steam cycle.
If there is no supplementary firing then efficiency of combined cycle from eq.(3.7).
reduces to
)
(3.10)
Now,
We can find the effect of gas turbine efficiency on the overall efficiency of combined
cycle by differencing eq. (3.10) w.r.t. gas turbine efficiency ηgt
(3.11)
Increasing the gas turbine efficiency improves the overall efficiency, only if
From eq. (3.11)
(3.12)
Improving the gas turbine efficiency is helpful only if it does not cause much a drop in
the efficiency of steam process.
Table 3.1 Allowable reduction in steam process efficiency as a function of gas
turbine efficiency (steam process efficiency 0.25)
ηgt
0.2
0.3
0.4
.94
1.07
1.25
The table (3.1) shows that the higher the efficiency of the gas turbine, the greater may be
the reduction in efficiency of steam process. The proportion of the overall output being
provided by the gas turbine increases, reducing the effect of lower efficiency in the steam
cycle. But a gas turbine with a maximum efficiency still does not provided an optimum
combined cycle plant. (Rolf Kehlhofer; 1997)
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3.3 SYSTEM LAYOUTS: - There are so many plant layout exist of combined cycle
power plant. Few of them are listed below.
A. SINGLE PRESSURE SYSTEM:- The simplest arrangement for a combined
cycle plant is a single pressure system (Fig.3.1). This consists of one or more
gas turbine with a single pressure HRSG, a condensing steam turbine, a water
cooled condenser and single stage feed water pre heater in the deaerator. The
steam for deaerator is tapped from the steam turbine.
The HRSG consists of three parts.
•
The feed water pre heater (economizer), which is heated by flue gases.
•
The evaporator.
•
The super heater.
Fig. 3.1 Flow diagram of the single-pressure system
1
Compressor
6
Economizer
11
Feed water tank/deaerator
2
Gas turbine
7
Boiler drum
12
Feed water pump
3
Bypass stack
8
Steam turbine
13
Condensate pump
4
Super heater
9
Condenser
5
Evaporator
10
Steam bypass
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B. Single pressure system with a pre heating loop in the HRSG
C. Two pressure system fuel with sulpher
D. Two pressure system fuel with no sulpher
E. Limited a system with steam or water injection in to the gas turbine to reduce
nitrogen oxide emissions (NOX)
F. A system using a single waste heat boiler for two gas turbine
G. Combined cycle power plants with limited supplementary firing
H. Combined cycle power plants with maximum supplementary firing (Rolf
Kehlhofer; 1997)
3.4 CASE STUDY
PROBLEM STATEMENT:
The effect of operating variables on overall thermal efficiency of combined cycle
power plant, variables are as follows
Inlet condition of air to the compressor P1 bar, T1, k
= 1 bar, 298 k
Pressure ratio of the compressor rp
=8
Maximum gas temperature at inlet to the gas turbine T3, k
= 1173 k
Pressure drop in the combustion chamber
=3%
Efficiency of the compressor
= 0.88
Efficiency of gas turbine ηgt
= 0.88
Calorific value of fuel
=
Specific heat of air (Cpa)
=
Specific heat of gas (Cpg)
=
Specific heat ratio of gas
= 1.333
Specific heat ratio of air
= 1.4
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Condition of steam at inlet to steam turbine = P7 bar, T7, K (Corresponding Enthalpy h7)
40 bar, 698 k
Condenser pressure
= Pb bar, T8, K (Corresponding Enthalpy h8) .04 bar
Feed water temperature to the HRSG T12
= 443 k
Efficiency of steam turbine
= 0.82
Pressure drop of gas in the HRSG
= 0.0 5 bar
Steam Flow Rate
= 29.235 kg/s
ms
3.4.1 THERMODYNAMIC ANALYSIS: The
temperature
entropy
diagram
of
combined cycle is shown in fig. 3.2
Considering gas turbine plant:
PROCESS 1-2: Air is compressed from state 1 to 2 in compressor. The temperature of air
after compression is given by (Nag, P.K; 2010)
(3.13)
2
Fig. 3.2 Temperature-entropy diagram of combined cycle power plant
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Putting the value of
in eq. (3.13)
(3.14)
CONSIDERING COMBUSTOR PROCESS 2-3: Compressed air goes in to combustor
where combustion takes place.
Let Pressure drop in combustor = 3%
therefore, p3 = 0.97p2
Let the flow rate of combustion gas be 1kg/s and that of fuel f kg/s so flow of air
= (1-f) kg/s
Therefore, by applying energy balance equation to combustor
f × CV = 1 ×Cpg (T3-T1) - (1-f)Cpa (T2-T1)
After solving it
(3.15)
Now
Air fuel ratio
(3.16)
CONSIDERING PROCESS 3-4: In process 3-4, combustion gases expend in gas turbine
(p5 =p1= 1 bar)
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(3.17)
CONSIDERING HRSG (HEAT RECOVERY STEAM GENERATOR)
Let the pinch point difference
T5
T12, ms
T4, mg
HRSG
T7
therefore,
Now applying energy balance equation for HRSG
(3.18)
(3.19)
Power output of steam turbine
Now,
Mass flow rate of Gas Turbine
(3.20)
Air flow rate entering the compressor
Power output from the gas turbine
Total Power Output
(3.21)
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Now,
Overall efficiency
(3.22)
After putting the value of
(3.23)
Where
(3.24)
3.5 EFFECT OF OPERATING VARIABLES ON OVERALL THERMAL
EFFICIENCY OF COMBINED CYCLE POWER PLANT
With the help of eq. 3.24 we can see the effect of variables like air inlet temperature in
compressor, gas turbine inlet temperature, pinch point etc.
3.5.1 EFFECT OF AIR INLET TEMPERATURE OF COMPRESSOR:
With the help of equation (3.24) we see the effect of different variables on the overall
efficiency.
1. We considered the variable air inlet temperature in the compressor, by putting the
given values of all variables in problem statement except air inlet temperature T1
in eq. 3.24 we get the equation
(3.25)
We make the program of this equation in C++ and get the results
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Fig.3.3. Effect of air inlet temperature of compressor on overall thermal efficiency
3.5.2
EFFECT OF GAS TURBINE INLET TEMPERATURE:
We considered the variable gas turbine inlet temperature T3, by putting the given values
of all variables in problem statement except gas turbine inlet temperature T3 in eq. 3.24
we get the eq.
(3.26)
Fig.3.4. Effect of Gas turbine inlet temperature on overall thermal efficiency
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3.5.3
EFFECT OF PINCH POINT:
By putting the value of all variables which is given in problem statement in eq. 3.24
except pinch point we get the following eq.
(3.27)
Fig.3.5. Effect of pinch point on overall thermal efficiency
3.5.4
EFFECT OF INLET TEMPERATURE AND PRESSURE OF STEAM
TURBINE:
By putting the value of all variables which is given in problem statement in eq. 3.24
except enthalpy of inlet steam in the turbine we get the following eq.
(3.28)
Fig.3.6. Effect of inlet temperature and pressure of steam turbine on overall thermal
efficiency of combined cycle
CONCLUSION:
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1.
From eq. 3.24 and graph we can conclude that if air temperature increases the
overall efficiency of the combined cycle plant decreases. because
•
Increasing the air temperature reduces the density of air, and there by reduces the
air mass flow drawn in.
•
The power consumed by the compressor increases in proportion to the inlet
temperature without their being a corresponding increase in the output from the
turbine.
•
In combined cycle plant as a function of air temperature with ambient conditions
remaining otherwise unchanged. As its shows, an increasing in air temperature
even has a slightly positive effect on the efficiency of the combined cycle power
plant, since the increase temperature in the gas turbine exhaust raises the
efficiency of steam process enough to more than compensate for the reduce
efficiency of the gas turbine unit.
2.
As we increase the inlet temperature of the gas turbine the overall efficiency of
combined cycle power plant increases. Because gas turbine efficiency and steam
process efficiency increases.
3.
It is clear from the graph as we decrease the pinch point the overall efficiency of
combined cycle plant increases. This is an important parameter, by reducing the
pinch point the rate of energy utilization in the HRSG can be influenced within
certain limits. However the surface of the heat exchanger increases exponentially
which quickly sets in limit for the utilization rate.
4.
The graph shows, the steam temperature and pressure increases the efficiency will
be increased. But in combined cycle plant, a high live steam pressure does not
necessarily mean a high efficiency. A higher pressure does indeed bring an
increase efficiency of the water steam cycle due to the greater enthalpy gradient in
the turbine. The rate of waste heat energy utilization in the exhaust gases however
drops off sharply. The overall efficiency of the steam process is the product of the
rate of energy utilization and the efficiency of the water steam cycle. There is an
optimum at approx. 30 bar.
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