The embedded energy conversion systems onboard vehicles impose strong constraints on power density (low weight and volume) and robustness. Several solutions can be used to achieve these objectives which consist in acting either on the design of the static converter or on the electric machine. In this paper, we propose to act on the two systems together. Thus, the increase in the power density of the converter will be achieved by using wide band-gap semiconductor power devices like the SiC or GaN. These components are very small and able to operate at high frequency, thus reducing the dimensions of passive components and of the cooling system used. To increase the reliability of the electric machine, a multiphase PMSM is used. In this paper, the proposed design method of the integrated GaN inverter into a machine is presented. It will be used for the realization of an integrated GaN inverter into a multiphase PMSM.