The work in this article defines an innovative approach to evaluate the performances of gas turbine based systems. This approach allows to link the thermodynamic and mechanical model of a gas turbine with its control system while bypassing the necessity to model the electrical generator. A non-dimensional group, called Aergia number, has been experimentally correlated with the measured electrical power output through a linear function. The Aergia number reproduces with accuracy the electrical power output during both steady state and transient operation. Furthermore, the proven linearity of the model implies that, in principle, its implementation requires the knowledge of just two data points during steady state operation. The model has been validated using two experimental facilities within the ENEA Casaccia Research Center, each equipped with a Turbec T100 S3 micro gas turbine, but characterized by different gas paths. Furthermore, the same linearity relation has been confirmed for aeroderivative and heavy duty single-, dual-, and triple-shaft gas turbines with power outputs ranging from 2 to 330 MWel. In light of these findings, the non-dimensional group Aergia positions itself, at least, as a rule of thumb for evaluating gas turbine off-design power output and, on a broader perspective, as a valid performance indicator in the definition of a gas turbine digital twin.