The article presents a method for calculating the magnetic system using the finite difference method for the axisymmetric system. The finite difference method for constructing a model of the generator's magnetic field allows integrating differential equations into partial derivatives by reducing the equations in finite differences. A special feature of the presented calculation method is the automation of determining the boundaries of the media interface, by taking into account the magnetic resistance of adjacent nodes relative to the calculated node. The main characteristic of a magnetic field is magnetic induction, which is a vector quantity. Magnetic induction is calculated based on the distribution pattern of the magnetic potential. Based on the Poisson and Laplace equations presented in the article, a computer program was developed for automating the calculation of the magnetic induction vector. The results of the program for calculating the magnetic field pattern on the example of a synchronous generator with a two-circuit magnetic system used as a part of a wind generator are presented. Graphical dependences of the change in the value of magnetic induction inside the stator coil of a synchronous generator are constructed for a rotor with an external magnetic circuit, for a rotor with an internal magnetic circuit, and for a rotor with two magnetic circuits simultaneously. In the calculation of the magnetic system, as presented in article, by the method of the example synchronous generator with dual magnetic system, the maximum value of magnetic induction, penetrating the winding of the synchronous generator along the axis r, when the internal circuit is 0.21 T, using the external loop, the value of the magnetic induction vector is 0.283 T. When using a two-circuit system, the value of the magnetic induction vector is 0.483 T.