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The study of the performance of a gas turbine power plant involves complex components. One of the most important component in the modeling of a gas turbine is an axial compressor as in the first few stages involve variable vanes to regulate the flow and avoid surging. Furthermore, a single shaft gas turbine cogeneration plant maintains the exhaust gas temperature for the sake of steam production by regulating the variable vanes. Associated with that compressor performance maps are changing continuously as the blades' angle change. Therefore, this paper studies the compressor characteristics including the variable stator vanes effect using appropriate scaling law and empirical formulae. Simulation is used to study the effect of variable stator vanes on the performance of the axial compressor working in a single shaft gas turbine cogeneration plant. Fixed geometry and variable geometry compressor air flow regulation, turbine exhaust temperatures are compared. The other results include both the accessible experimental data and the simulation output.