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.
Plane-parallel problem of AC magnetics.
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=56 MS/m,
Primary winding Y: 6.25 mm² x 2560 turns,
Secondary winding Δ: 16 mm² x 150 turns,
Frequency f=50 Hz.
Calculate magnetic and electric losses in the three phase transformer.
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).
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:
|Winding 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