Analytical calculation of the induced EMF in PM-machines with arbitrary arranged surface mounted magnets using the winding function theory

In the following paper, an analytical approach for the calculation of the the induced emf in windings of electrical machines is provided. This method uses the complex Fourier series that describe the stator winding function and the magnetic flux density distribution in the air gap that is caused by the rotor permanent magnets. By using a special case of the Parseval´s theorem, the induced emf can be computed in an easy and straight-forward way. The practical implementation of the calculation scheme only uses sums of the product of the Fourier coefficients and therefore the computation is very fast. The proposed procedure is used for calculating the induced emf in a machine with two different PM rotors. One rotor uses a symmetrical magnet distribution, the other one uses an asymmetrical magnet distribution. The calculation delivers two different shapes of the induced voltage in the identical stator winding system. The air gap flux density is approximated in a simple way and expressed by an exponential function term. The analytically calculated results are compared with the results of a transient FEM simulation and, in case of the asymmetrical rotor with the measured emf on a sample machine validating in this way the proposed computation procedure.