Transformer Losses
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.
These losses, also known as no-load losses, are present all the time the transformer is powered on – regardless of whether there is any load or not.
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 |
| Version: | 10.06.2013  |
| Developer: | Jignesh Parmar |
| Size: | 36 Kb |
| Price: | Free |
| Download: | Right here | Video Courses | Membership | Download Updates |
How can I calculate no load losses and load losses of power trafo when I have total losses of trafo available only?
Great work, keep it up ^_^
On this formula: Total Stray losses at Amb. temp = Measured losses – I²R losses, if I measured V= 384, I= 20 and W= 1015, for a 24MVA, 231200V (on tap 1), how do I relate the measured power into the equivalent input power which I can use in the formula?
The spreadsheet for transformer losses calculations is a good work
how do find out the value of resistance in hv and lv side
please review cell H33, i think efficiency should not be highest at 125%
Dear all,
How can I get the value 1.5 in ” HV Side I2R losses = I²R · 1.5″ and 0.5*3 in
” LV Side I²R losses = I²R · 0.5 · 3″ .
Thank you in advanced.
Dear all,
What are the values 1.5 in HV and 0.5*0.3 and LV ?
HV Side I2R losses = I²R · 1.5
LV Side I²R losses = I²R · 0.5 · 3
Thank you in advanced.
IEC60076-1, Clause 10.2 specified that: “The resistance of each winding, the terminals between which it is measured”.
It means in short-circuit test to get resistance values, they will measure the resistance between two transformer terminals (A-B, B-C & C-A).
HV – Delta Connection: Rwinding = Rmeasured x 1.5
[Because they measured terminal – terminal while 1Rwinding // (Rwinding + Rwinding)]
LV – Star connection: Rwinding = Rmeasured x 0.5
[Because they measured terminal – terminal while Rwinding + Rwinding]
HV – Delta connection: Current through winding Iw = I/sqrt(3)
LV – Star connection: Current through winding Iw = I
So now we calculate the copper loss (resistance loss): 3 windings so that we have to multiple with 3
HV – Delta connection: 3 x Iw x Iw x Rw = 3 x I/sqrt(3) x I/sqrt(3) x R x 1.5 = I x I x R x 1.5
LV – Star connection: 3x Iw x Iw x Rw = 3x I x I x R x 0.5 = I x I x 0.5 x 3
Dear sir,
For finding i^2R losses on hv side =I^2R.1.5
What does 1.5 means
Dear Venjateswar,
Did you find any answer for this question ?
Best regards,
Hello!
what is V1 and V for the percentage impedance and reactance?
Thanks!
The V1 is the voltage that, applied to the HV side of the Tx whose voltage rating is V, shall circulate the rated current on the LV side of the Tx with it’s terminal short circuited. This voltage is expressed as a %age.
Z%=(V1/V)*100.
Is the measured loss a physically measured value? Is there a way of estimating this number based on the transformer size?
Edvard / Jignesh
well done gents this is practical and useful I like it!.
Here is a suggestion for you ready reckoner spread sheets for estimating:
overhead power lines e.g. 415V AC distance covered number of bends and calculate the number of posts, cross arms, insulators, conductor sizes, tension, weight of the conductors….
same for 22kV or 33kv or underground with approximate schedules of rates so I can enter local steel costs ideal pole spacing typical sag heights….
can you provide spreadsheet for transformer losses calculation of 1000kva
Can’t you use this spreadsheet? Just edit field rated power in kVA.
How can we convert this losses to thermal losses?
They are thermal origin. Find out more here:
https://electrical-engineering-portal.com/transformer-heat-copper-and-iron-losses
EEP provides much more information about any given electrical article which is guide line for technical people.
Thank you Ahmad!