Axiomatics of the blondel-park transformation

The doubly-fed induction generator (DFIG) is a key constituent of energy conversion plants. The control of a DFIG is a challenge, whenever the primary energy supply (e.g., the wind velocity field) is characterised by intermittency. The mathematical model and control of a DFIG rely on the Blondel-Park transformation, which is known to simplify the governing equations. The distinctive feature of this contribution consists of showing how the Blondel-Park transformation derives from a set of conditions to be met by a group. Such a group is shown to exist and to continuously depend on one parameter. The uniqueness of its infinitesimal generator is also shown. As an application, the well-known electric torque theorem is proved in a simple way, which relies on a "product of matrices" formula. The latter, in turn, is a by-product of the axiomatic deduction of the Blondel-Park transformation.