An analytical calculation of the magnetic field of a salient-pole synchronous generator in 3D Cartesian coordinates based on the solution of the Laplace partial differential equation by separation of variables according to Fourier method is considered. The fundamental feature of the calculation consists in addressing the magnetization vector of the active ferromagnetic generator elements represented by double trigonometric series with unknown Fourier constants, whose periods amount to the doubled values of the pole division and the length of the stator core of the generator. The magnetization level of the yokes, the tooth layers of the stator and rotor, and the air gap itself have been geometrically considered as parallelepipeds superimposed onto each other. At the common boundaries between these parallelepipeds, well-known conditions for magnetic field should be met: the scalar magnetic potentials and the normal components of magnetic induction should not undergo a jump (discontinuity), and only the magnetic sheets of the windings positiomed at the boundaries should have a jump in magnetic potentials amounting to the total current of the magnetic sheet. These conditions make it possible to obtain a system of algebraic equations for to find Fourier constants. The geometric approach to the magnetization level of the rotor pole tips has led to the formation of required virtual configuration for the air gap for to provide the distribution of magnetic induction under the poles close to sinusoidal one. The magnetic field of the generator can be calculated as a combination of longitudinal and transverse fields, the latter being generated by the active current of the stator winding with the fixation of the generator load angle. It has been shown that radial ventilation ducts 7 mm wide in the stator core exert almost no effect on the distribution of magnetic induction in the air gap throughout the length of the rotor, this distribution being quite uniform.
A. A. Afanas’ev (Thu,) studied this question.