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# Halbach array generator voltage

The excitation of the magnetic system on the rotor side is due to the Halbach assembly. The Halbach array is a special arrangement of permanent magnets that increases the magnetic field on one side of the assembly while cancelling it to near zero on the other side.

Plane problem of DC magnetics.

Geometry:

Given:
Phase number of turns w = 90,
Coercive force of permanent magnets 730 kA/m,
AC frequency f = 50 Hz
Rotor poles 2p = 4,
Synchronous rotation speed n = 750 rpm.

Calculate the idle generator electromotive force (EMF), display the magnetic field distribution.

Solution
In open circuit condition there is no electric current in the windng, the output voltage is qual to the induced electromotive force.
First in QuickField we measure the flux linkage with half-coils A- and A + as a function rotor angular position. We get this dependency automatically using the LabelMover parametric calculation utility.
We will carry out further calculations using Excel spreadsheets. The electromotive force is calculated as the ratio of the flux linkage increment ΔΦ to the angle increment Δφ:
EMF = -w * dΦ/dt = -w * ΔΦ / (Δt), where
Time increment is related to the angle increment Δφ as: Δt = (Δφ/360) / (n/60).

Result
In LabelMover we set the angle increment to be Δφ = 1 degree. The time required to rotate the rotor by 1 degree is
Δt = (1/360) / (750/60) = 2/9 ms. The total EMF of the phase coil is obtained by summing up EMFs of the individual half-coils.
The amplitude of the fundamental harmonic was calculated in a harmonic analyzer: UA = 19 V.

Magnetic flux density distributon in the permanent-magnet generator • Download simulation files (files may be viewed using any QuickField Edition).