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Three phase transformer losses
Three phase transformer losses
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 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.
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 |
* Reference: http://en.wikipedia.org/wiki/Transformer
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