Polyphase electrical machine with n phases, n≥3, including a casing defining a longitudinal axis, a stator and a rotor including a mechanical drive shaft, the electrical machine being equipped with a power electronics and a coolant circuit and the power electronics is formed of n power electronic modules evenly distributed over an inner circumference of a longitudinal extension of the casing whose outer circumference is covered with a single annular DC bus decoupling capacitor electrically connected to the n power electronic modules, the coolant circuit including a plurality of U-shaped tubes with a tubular outgoing part extending over an entire length of the casing and including the longitudinal casing extension and a shorter tubular return part, extending over a casing length excluding the longitudinal casing extension.