When the Norwegian government introduced the CO2 tax for hydrocarbon fuels, the challenge became to improve the performance of off-shore power systems. An oil and gas platform typically operates on an island (stand-alone system) and the power demand is covered by two or more gas turbines. In order to improve the plant performance, a bottoming cycle unit can be added to the gas turbine topping module, thus constituting a combined cycle plant. This paper aims at developing and testing the numerical model simulating the part-load and dynamic behavior of a novel power system, composed of two gas turbines and a combined gas turbine coupled with an air bottoming cycle plant. The case study is the Draugen off-shore oil and gas platform, located in the North Sea, Norway. The normal electricity demand is 19 MW, currently covered by two gas turbines generating each 50% of the power demand, while the third turbine is on stand-by. During oil export operations the power demand increases up to 25 MW. The model of the new power plant proposed in this work is developed in the Modelica language using basic components acquired from ThermoPower, a library for power plant modelling. The dynamic model of the gas turbine and the air bottoming cycle turbogenerator includes dynamic equations for the combustion chamber, the shell-and-tube recuperator and the turbine shafts. Turbines are modelled by the Stodola equation and by a correlation between the isentropic efficiency and the non-dimensional flow coefficient. Compressors are modelled using quasi steady-state conditions by scaling the maps of axial compressors employing a similar design point. The recuperator, which recovers the exhaust heat from the gas turbine, is modelled using correlations relating the heat transfer coefficient and the pressure drop at part-load with the mass flow rate. Thermodynamic variables and dynamic metrics, such as the rise time and the frequency undershooting/ overshooting, are predicted. Considering a load ramp of 0.5 MW/s, an undershooting of 4.9% and an overshooting of 3.0% are estimated. The rise time is approximately 30 s. Moreover, findings suggest that decreasing the core weight of the recuperator leads to limiting the frequency fluctuations, thus minimizing the risk of failure of the power system.