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Three phase transformer losses

three phase transformer losses, transformer loss FEA finite element analysis, core loss calculation, copper loss calculation

Unbalanced load is connected to the three phase transformer.

Problem type:
Plane problem of AC magnetics.

Geometry:

Given:
Core permeability μ = 1000,
Core mass density ρ = 7650 kg/m³,
Core losses C_m = 1.5 W/kg (at f=50 Hz and B=1.5 T),
Copper conductivity g=56e6 S/m,
Primary winding Y: 6.25 mm² x 2560 turns,
Secondary winding Δ: 16 mm² x 150 turns,
Frequency f=50 Hz.

Task:
Calculate magnetic and electric losses in the three phase transformer.

Solution:
Winding (copper) losses volume density:
p_e = j² / g [W/m³].
Steinmetz equation to calculate core (steel) losses volume density:
p_m = C_m · (f/50)^α · (B/1.5)^β · ρ [W/m³],
where α = 1, β = 2, B - average flux density in the core (peak value).

Results:
Average flux density in the core (peak value): B = √0.746 · √2 = 1.22 T.
Power losses in the core p_m = 1.5 · (50/50)¹ · (1.22/1.5)² · 7650 = 7.59 kW/m³.

Winding (copper) losses volume density
p_e = (I/S)² / g:

* Reference: http://en.wikipedia.org/wiki/Transformer

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