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Laminated iron core losses

Problem type:
Plane problem of AC magnetics.

Geometry:
three phase transformer

All length units are in millimeters

Given:
Core I permeability μ1 - nonlinear*
Core E permeability μ2 - nonlinear*
Core material density ρ = 7650 kg/m3,
Frequency f = 400 Hz.
Winding1 no-load current 16.5 mA,
Winding1 number of turns 324.
Winding1 conductor cross-section 0.19 mm2
Winding1 average turn length 111 mm.

Task:
Calculate the core losses in the no-load mode of transformer.

Solution:
In no load mode the secondary winding is in open circuit state. There is current only in the primary winding. The primary winding is modelled as multi-turn winding - the average current density is specified.

Core is laminated, zero conductivity is specified. Core losses are calculated using Bertotti equation:
pv = kh·f·Bm2 + kc·f2·Bm2 + ke·(f·Bm)3/2
Coefficients kh, kc, ke are calculated as a result of the curve fitting using free utility Core loss coefficients calculator.

Results:
Core E magnetic loss is 0.87 W.
Core I magnetic loss is 0.12 W.
Flux density distribution in the core:

laminated core magnetic loss

* Reference: Core loss and magnetization curves are provided by Arnold Magnetics.

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