Analytical Calculation of the Magnetic Field of a Synchronous Machine with an Uneven Air Gap

Abstract: A method of conformal mapping of the uneven air gap of a salient-pole synchronous machine onto a circular ring has been proposed. It is based on the representation of the variable-width ring in the complex z plane as a set of segments of two nonconcentric circles of which adjacent pairs are shifted relative to each other by the pole pitch. The magnetic field in the circular ring of the complex t plane can be found as a solution to the first boundary-value problem with known scalar magnetic potentials at the boundaries, which are known to be invariant under conformal transformations. The magnetic inductions in the variable-width ring in the z plane are found by multiplying the induction values found in a circular ring of the t plane by the absolute value of the derivative (Formula presented.) known from the described problem. The calculation scheme was verified in the application to the geometry of the Sayano-Shushensky hydroelectric generator using the MATHCAD program. © 2022, Allerton Press, Inc.