Transformers have two major components that drive losses: the core and the coils. The typical core is an assembly of laminated steel, and core losses are mostly related to magnetizing (energizing) the core.
Core losses are roughly constant from no-load to full-load when feeding linear loads. They represent a continuous cost, 24 hours/day, for the 25-year or more life of the transformer.
Formulas in spreadsheet
- HV Full load current = VA / (1.732 · Volt)
- LV Full load current = VA / (1.732 · Volt)
- HV Side I2R losses = I²R · 1.5
- LV Side I²R losses = I²R · 0.5 · 3
- Total I² R lossses at Amb. temp = Hv losses + Lv losses
- Total Stray losses at Amb. temp = Measured losses – I²R losses
- I²R lossses at 75° C temp = ((225 + 75) · losses) / (225 + Amb. temp) .
- Stray losses at 75° C temp=((225 + Amb. temp)(Stray losses at Amb. temp)) / 300
- Total Full load losses at 75° C = I²R losses at 75° C + Stray losses at 75° C
- Total Impedance at amb. temp = (Imp. voltage · 1.732) / Full load current
- Total Resistance at amb. temp = I²R losses / I²
- Total Reactance (X) = SQRT (Impedance² – Resistance²)
- Resistance at 75° C = (300 · resistance at amb ) / (225 + Amb. temp)
- Impedance at 75° C = SQRT (R² at 75° C + X²)
- Percentage Impedance = (Z at 75° C · I · 100)/V1
- Percentage Resistance = ( R 75° C · I · 100)/V1
- Percentage Reactance = (X · I · 100) / V
- Regulation at Unity P.F. = (%R cosø + %Xsinø)
- Regulation at 0.8 P.F. = (%R cosø + %Xsinø) + 1/200(%R sinø – %Xcosø)2
Efficiency at Unity P.F
- At 125 % of Transformer Loading = (kVA · 1.25 · 100)/((kVA · 1.25)+(I²R losses · 1.25²)+(No Load Losses))
Efficiency at 0.8 P.F
- At 125 % of Transformer Loading = (kVA · 1.25 · P.F. · 100)/((kVA · P.F. · 1.25)+(I²R losses · 1.25²)+(No Load Losses))
Contribution to transformer losses
Load level varies widely, with some installations running very heavily loaded and others more lightly loaded.
This difference substantially impacts actual losses incurred. Unfortunately, there is a small body of field data available, driven by the factors such as a lack of awareness of the cost of the losses, and the cost of gathering detailed data from a reasonable number of individual transformers.
Since there are a wide variety of transformers on the market serving different purposes, and available from different manufacturers, actual losses incurred in the field will vary substantially from installation to installation.
|Software:||Spreadsheet for Transformer Losses Calculation|
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