The airflow (W) in the gas turbine is given as

\mathit{W}={\mathit{W}}_{\mathit{a}}\frac{{\mathit{P}}_{\mathit{a}}}{{\mathit{P}}_{\mathit{ao}}}\frac{{\mathit{T}}_{\mathit{io}}}{{\mathit{T}}_{\mathit{i}}}

(1)

Where Ti is ambient temperature and P_{a} denotes the atmospheric pressure. *W*_{
a
} is air flow with the assumption that *P*_{
a
} = *P*_{a 0}.

The compressor discharge temperature is given as

{\mathit{T}}_{\mathit{d}}={\mathit{T}}_{\mathit{i}}\left(1+\frac{\mathit{x}-1}{{\mathit{\eta}}_{\mathit{c}}}\right)

(2)

\mathit{x}={\left({\mathit{P}}_{\mathit{ro}}\mathit{W}\right)}^{\mathit{\gamma}-\frac{1}{\mathit{\gamma}}}

(3)

*P*_{
ro
} is the design compressor pressure ratio and y is the ratio of specific heats.

The gas turbine inlet temperature T_{f} (K) is given by (Kakimoto & Baba 2003)

{\mathit{T}}_{\mathit{f}}={\mathit{T}}_{\mathit{d}}+\left({\mathit{T}}_{\mathit{fo}}-{\mathit{T}}_{\mathit{do}}\right)\frac{{\mathit{W}}_{\mathit{f}}}{\mathit{W}}

(4)

Where W_{f} is fuel flow per unit its rated value, ‘o’ denotes rated value, W denotes the airflow and T_{d} denotes the compressor discharge temperature.

Gas Turbine exhaust temperature T_{e} (K) is given by (Kakimoto & Baba 2003)

{\mathit{T}}_{\mathit{e}}={\mathit{T}}_{\mathit{f}}\left[1-\left(1-\frac{1}{\mathit{x}}\right){\mathrm{\eta}}_{\mathit{t}}\right]

(5)

Where *η*_{
t
} is turbine efficiency. The exhaust gas flow is practically equal to the airflow.

The efficiency of a combined cycle (unfired) is given as, Horlock (Horlock 2003)

{\mathrm{\eta}}_{\mathit{cc}}={\mathrm{\eta}}_{\mathit{gt}}+{\mathrm{\eta}}_{\mathit{st}}\left(1-{\mathrm{\eta}}_{\mathit{gt}}\right)

(6)

Where *η*_{
cc
}is the efficiency of the combined cycle, *η*_{
gt
} is the efficiency of Gas Turbine and *η*_{
st
} is the efficiency of Steam Turbine. The thermal efficiency of the simple gas turbine cycle is given as (Al-Zubaidy & Bhinder 1996)

\mathrm{\eta}=\frac{\left(1-\frac{1}{{\mathit{p}}_{\mathit{p}}}\right)\left(\mathit{a}-{\mathit{p}}_{\mathit{p}}\right)}{{\mathrm{\eta}}_{\mathit{c}}\left({\mathit{k}}_{1}-1\right)-{\mathit{p}}_{\mathit{p}}+1}

(7)

Where, *a* = *η*_{
c
}*η*_{
t
}*k*_{1}.

Where *p*_{
p
} is the isentropic temperature ratio (T_{2}/T_{1}), k_{1} is the cycle maximum temperature ratio (T_{3}/T_{1}).

Differentiating (6) gives (Kehlhofer et al. 2009)

\frac{\partial {\mathit{\eta}}_{\mathit{cc}}}{\partial {\mathit{\eta}}_{\mathit{gt}}}=1+\frac{\partial {\mathit{\eta}}_{\mathit{st}}}{\partial {\mathit{\eta}}_{\mathit{gt}}}\left(1-{\mathit{\eta}}_{\mathit{gt}}\right)-{\mathit{\eta}}_{\mathit{st}}

(8)

The overall efficiency improves with the increase in gas turbine efficiency if

\frac{\partial {\mathit{\eta}}_{\mathit{cc}}}{\partial {\mathit{\eta}}_{\mathit{gt}}}>0

(9)

From equation (8) and (9) one obtains:

-\frac{\partial {\mathit{\eta}}_{\mathit{st}}}{\partial {\mathit{\eta}}_{\mathit{gt}}}<\left(\frac{1-{\mathit{\eta}}_{\mathit{st}}}{1-{\mathit{\eta}}_{\mathit{gt}}}\right)

(10)

The above calculations were done using the following parameters: Pressure Ratio: 8 to 16; Air Fuel Ratio: 50 to 65; Plant Rating: 122 MW for Steam Turbine and 104 MW for Gas turbine.