The non-linear characteristics of AC machines based on the calculation of magnetic field co-energy

Non-linear characteristics, as relations between linked fluxes and currents of individual machine coils, are sought for in the so called circuit models of saturated electrical machines. Their determination can be based on the cc-energy of the magnetic field only, which is a multivariable function of all coil currents and rotor position angle. The author proposes the calculation of co-energy values at necessary points by the FEM and the interpolation of the results by a suitable multivariable spline function. The functions of linked fluxes are generated as the first derivatives of the spline. This way could be used to separate the circuit calculation from the field calculation when saturated machines are modelled. An example of a wound rotor induction machine is used to show the elementary problems of the calculation of the non-linear characteristics.