Unification of field and circuit theories of electrical machines

The field in the airgap of an idealised model induction motor is derived from Maxwell´s equations, and the result is extended to give the stator and rotor field equations of the practical machine. It is shown that, if each term of the voltage equation of the machine, referred to stationary axes, be multiplied by the quantity K = (1/2k1N1¿) sin p¿1 where N1 is the number of primary terms per phase, k1 is the distribution factor, ¿ is the axial length, in metres, and p is the number of pole pairs, each term of the field equation will be obtained. Since the voltage equation concerned applies generally to all types of machine, the unification also appears to be general. As an illustration of its consequences, the commutator (Park´s) transformation of circuit theory is shown to be equivalent to the Lorentz transformation of field theory.