Linear scalar-potential models for permanent-magnet circuits

A scalar-potential equivalent network is developed to represent permanent magnets with linear operating characteristics and their surrounding air regions. The method of allowing for the effect of current in the scalar-potential formulation is explained and demonstrated. The use of the technique is illustrated by means of examples. In the first, the calculation of the leakage factor in a permanent-magnet circuit with an airgap is examined. The influence of magnet permeability on leakage factor and the limitations of a more traditional technique are explained. In the second example, the method for calculating demagnetisation limits is demonstrated for electrical machines with permanent-magnet excitation adjacent to the airgap. The method is applied to the calculation of field flux-density distributions set up by two permanent-magnet rotors, and the results compared with distributions obtained experimentally. Finally, the general `dynamic¿ problem is considered. When reduced to its most basic form, the network is shown to model static and dynamic magnet behaviour in a manner similar to other techniques which assume point operation within the permanent magnet.