Symmetrical short circuits on saturated alternators

IN ORDER to solve the problem of a 3-phase short circuit on the terminals of a saturated machine, one generally starts by writing the differential equation for each winding either on the stator or on the rotor. Any of these differential equations is of the form e=pψ—ir. The solution of these equations under the specified initial conditions gives the solution to the problem. However, the difficulty in their solution arises from their nonlinearity. Here there are two kinds of nonlinearity. The first is due to the change of the coupling coefficients between the different windings due to the rotation of the rotor. This nonlinearity could be removed by using the transform to direct and quadrature components as used by R. H. Park.¹ The second kind of nonlinearity is due to the saturation in the magnetic circuit, and it could be dealt with by separating the solution into a free transient that meets linear conditions and a particular solution that meets saturated conditions and could be obtained using Reinhold Rüdenberg´s method by analysis² with the initial current being obtained by the principle of conservation of flux linkage.³ The differential equations of the stator winding transformed to direct and quadrature components as given by Mr. Park¹ are