Slot embedded conductor

QuickField simulation example

This is an example of the slot embedded conductor simulation, performed with QuickField software. A solid copper conductor embedded in the slot of an electric machine carries a current I at a frequency f.

Problem Type
Plane-parallel problem of AC magnetics.

Geometry

Given
Conductivity of copper σ = 58,005,000 S/m;
Current in the conductor I = 1 A;
Frequency f = 45 Hz.

Task
Determine current distribution within the conductor and complex impedance of the conductor.

Solution
We assume that the steel slot is infinitely permeable and may be replaced with a Neumann boundary condition (zero tangential field). We also assume that the flux is contained within the slot, so we can put a Dirichlet boundary condition (A=const) along the top of the slot.

The complex impedance per unit length of the conductor can be obtained from the equation Z = V / I, where V is a voltage drop per unit length.

Results
Current density in slot embedded conductor:

Impedance Z = 0.000175 + j0.000471 Ohm/m

*Reference: A. Konrad, Integrodifferential Finite Element Formulation of Two-Dimensional Steady-State Skin Effect Problems, IEEE Trans. Magnetics, Vol MAG-18, No. 1, January 1982.

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