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Main > Application > Sample problems

Three phase transformer losses

Unbalanced load is connected to the three phase transformer.

Problem type:
Plane problem of AC magnetics.

Geometry:

three phase transformer

three phase transformer circuit

Given:
Core permeability μ = 1000,
Core mass density ρ = 7650 kg/m3,
Core losses Cm = 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:
pe = j2 / g [W/m3].
Steinmetz equation to calculate core (steel) losses volume density:
pm = Cm · (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 pm = 1.5 · (50/50)1 · (1.22/1.5)2 · 7650 = 7.59 kW/m3.

three phase transformer losses

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

Windinng name

Conductor cross section, S

Phase current (RMS), I

Joule heat losses, pe

A1

6.25 mm2

19 A

165 kW/m3

B1

6.25 mm2

13.4 A

82 kW/m3

C1

6.25 mm2

9.4 A

40 kW/m3

A2

16 mm2

45.7 A

146 kW/m3

B2

16 mm2

35.3 A

87 kW/m3

C2

16 mm2

23.2 A

38 kW/m3

three phase transformer currents

Download Download simulation files transformer_losses.zip.

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View movie Watch online on YouTube.

References:
http://en.wikipedia.org/wiki/Transformer