We consider a gamma type free piston engine with the MARTINI configuration for electric power generation. A dynamic simulation of this engine has been developed using a decoupled analysis. The equation of motion of the free piston induces a strong coupling between the electrical load and the thermodynamics inside the free piston Stirling engine. From the thermodynamics point of view, the piston-displacer phase lag is an important parameter. We point out that, if the electrical circuit elements (R-L-C) are constants, the phase lag between the free pistons and displacer motions is far from the optimum for the engine considered. For both cases of stand-alone engine with an independent electrical load, or grid-connected engine, it is shown how, by varying the instantaneous value of the electrical resistance, one can in a very simple way multiply the net electrical power by a factor 4 to 6, and the efficiency by a factor 1.25 to 2, without any engine geometry modification.