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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)

Therefore (3.6)

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 is the heat input to the steam cycles

Now from eq. (3.6) =

(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 ms = 29.235 kg/s

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) (3.17)

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CONSIDERING HRSG (HEAT RECOVERY STEAM GENERATOR)

Let the pinch point difference

T5 T4, mg

T12, ms 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)

HRSG

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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.