In this paper, a complete methodology to design a modular brushless wound rotor synchronous machine is proposed. From a schedule of conditions and a chosen structure (with 7 phases, 7 slots and 6 poles), a non-linear and non-convex optimization problem is defined and solved using NOMAD (a derivative free local optimization code): the external volume is minimized under some constraints, which are the average torque equal to 5 Nm, the torque ripple less than 5%, the efficiency greater than 94%, and the surface temperature less than 85 • C. The constraints have to be computed using 2D-finite element simulations in order to reduce the CPU-time consumption for each NOMAD iteration. Moreover, a relaxation of this optimization problem makes it possible to provide an efficient starting point for NOMAD. Thus, a good optimal design is obtained, and it is then validated by using 3D electromagnetic and thermic numerical methods. These numerical verifications show that, inside the end-winding, the leakage flux is high. This yields a lot of iron losses in this machine. Moreover, the surface and coil temperature differences between the 2D and 3D numerical approaches are discussed. Finally, the machine prototype is built following the optimal dimensions and a POKI-POKI TM assembly technology. Preliminary experimental tests are carried out, and the results are devoted to the comparison of measured and predicted 3D numerical results.