Nonlinear Theory of Salient Pole Machines

The partial differential equation for the vector potential of salient-pole heteropolar machines is established by considering nonlinearities of the iron and current density fields. The nonlinear equation, similar to Poisson´s equation, is transformed into a partial difference equation to find the magnetic induction at discrete points in the cross section of the heteropolar machine. Alternating relaxation methods are used to obtain numerical solutions. The relaxation procedure is accelerated considerably by a new method of adjusting the vector potential between successive iterations. The method is used to find the no-load characteristic and the no-load air-gap flux distributions of a medium-sized 8-pole salient-pole alternator. Calculated voltages and test results show good agreement.