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Laminated iron core losses

# Laminated iron core losses

**Problem type:**

Plane problem of AC magnetics.

**Geometry:**

All length units are in millimeters

**Given:**

Core I permeability μ1 - nonlinear*

Core E permeability μ2 - nonlinear*

Core material density ρ = 7650 kg/m^{3},

Frequency *f* = 400 Hz.

Winding1 no-load current 16.5 mA,

Winding1 number of turns 324.

Winding1 conductor cross-section 0.19 mm^{2}

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:

*p*_{v} = *k*_{h}·*f*·*B*_{m}^{2} + *k*_{c}·*f*^{2}·*B*_{m}^{2} + *k*_{e}·(*f*·*B*_{m})^{3/2}

Coefficients *k*_{h}, *k*_{c}, *k*_{e} 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:

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

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