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The magnetic field is a fundamental part of an electrical machine, for establishing the torque and inducing voltages and currents. Then acting as the link between mechanical power and electrical power. This thesis will give a comprehensive study of how magnetism could be modeled. Covering how the magnetic field relates to energy transfer, power flow, and the forces of electrical machines.

An electromagnetic energy transfer is usually described by Poynting’s vector, which has a different formulation than the power flow of electrical engineering. The main difference is that Poynting’s vector localizes the energy flux in the surrounding electromagnetic fields of a current-carrying conductor, instead of inside the conductor itself.

The forces in a machine can be modeled by the field lines of the magnetic flux density. The force density consists of two vector components: the magnetic tension force and the magnetic pressure gradient force. The magnetic tension force acts to straighten curved field lines, based on the curvature of the flux density. The magnetic pressure gradient force acts from areas of high flux to areas of low flux. The force density could describe the forces in a synchronous machine, both for the torque of the load and for the machine’s radial forces between the rotor and the stator.

The force density could also be used to improve the understanding of Maxwell stress tensor,as they are easier to illustrate as vectors, compared to the matrix form within the Maxwell stresstensor. It also expresses the location of the force density, which can improve the use of enclosedvolumes when calculating forces based on the divergence theorem with Maxwell stress tensor.