When the generators of a coherent group in a power system are equivalenced for transient stability studies, it is logical that the associated controllers—excitation controllers and the speed governing systems—are also equivalenced. Depending upon various design features and capacity, the time constants of the transfer functions of different controllers may be different. This paper presents a Walsh function approach for equivalencing the controllers in multi-machine power systems, taking into account the above differences. The approach has an elegant mathematical base and provides any desired level of accuracy.