Because of the fast development of wind and solar photovoltaic power plants, as well as the multiplication of high voltage direct current links, the analysis and simulation of large transmission systems with a high penetration of power electronic converters have become necessary. In this situation, reduced models of converters are needed to make the simulation faster and the stability analysis more straightforward. These reduced models need to be accurate enough, depending on the needed accuracy, and they have to keep the physical structure of the converter full model to be easily implemented on classical analysis software. A structure-preserving method to reduce the state order of a grid forming converter model is presented here. It is based on a modal analysis to remove the fastest poles of the system while keeping the slowest almost unchanged.