Fig. 3
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Rowen’s model for gas turbine representation.
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Rowen’s model is shown in Fig. \ref{ttps://www.authorea.com/users/227193/articles/433220-untitled-document?mode=edit#author-label-fig:3} and the values of the transfer functions are taken from \citep{rowen1992simplified}. The model assumes no heat recovery in the system and operates at a constant speed of 95% to 107%. The input and output signals are generated in per unit (p.u), where the operation signal is divided by the rotor speed nominal signal, \(N\) . The model consists of three main control components. The first component is the speed governor. It controls the speed of a system and manoeuvers the frequency, exhaust temperature and compressor output as necessary by the load demand. The second component is the fuel temperature control. It regulates the output temperature to be lower than the constant maximum or it increases the temperature for more energy when the demand increases. The third component is the IGV temperature control which plays a major role in balancing the temperature by opening or closing of the air intake.
The  simulation functions are the turbine exhaust temperature as calculated in Equation \eqref{eq:1}, with T R as the turbine rated exhaust temperature, 950°F, N is the speed signal line and W f  is the fuel flow line,
\[f_{1}=T_{R}-\left(700\left(1-W_{f}\right)+550\left(1-N\right)\right)\label{eq:1}\]
turbine torque is calculated from Equation \eqref{eq:},
\[f_{2}=1.3\left(W_{f}-0.23\right)+0.5\left(1-N\right)2\label{eq:}\]
and turbine exhaust flow calculation as in Equation \eqref{eq:3} with \(L_{IGV}\) as the IGV opening and \(T_{a}\)
is the ambient temperature, 59°F.
\[f_{3}=N\left({L_{IGV}}^{0.257}\right)\left(\frac{519}{T_{a}+460}\right)\label{eq:3}\]
This model provides a basis for DLE gas turbine fuel system which needs to be modelled in the form of a transfer function.

DLE Gas Turbine Fuel System