How to Calculate/Find the Rating of Transformer in kVA (Single Phase and Three Phase)?

Calculate & Find the Rating of Single Phase & Three Phase Transformers in kVA

We know that, Transformer always rated in kVA.  Below are the two simple formulas to find the rating of Single phase and Three phase Transformers.

Find Rating of Single Phase Transformer

Rating of Single Phase Transformer:

P = V x I.

Rating of a single phase transformer in kVA

kVA= (V x I) / 1000

Rating of a Three Phase Transformer

Rating of a Three Phase Transformer:

P = √3. V x I

Rating of a Three phase transformer in kVA

kVA = (√3. V x I) /1000

But Wait, A question is raised here… Look at the General nameplate rating of a 100kVAtransformer.

Did you notice something????Anyway, I don’t care what is your answer 😉  but lets me try to explain.

Here is the rating of Transformer is 100kVA.

But Primary Voltages or High Voltages (H.V) is 11000 V = 11kV.

And Primary Current on High Voltage side is 5.25 Amperes.

Also Secondary voltages or Low Voltages (L.V) is 415 Volts

And Secondary Current (Current on Low voltages side) is 139.1 Amperes.

In simple words,

Transformer rating in kVA = 100 kVA

Primary Voltages = 11000 = 11kV

Primary Current = 5.25 ASecondary Voltages = 415V

Secondary Current = 139.1 Amperes.

Now calculate for the rating of transformer according to

P=V x I (Primary voltage x primary current)

P = 11000V x 5.25A = 57,750 VA = 57.75kVA

Or P = V x I (Secondary voltages x Secondary Current)

P= 415V x 139.1A = 57,726 VA = 57.72kVA

Once again, we noticed that the rating of Transformer (on Nameplate) is 100kVA but according to calculation…it comes about 57kVA…

The difference comes due to ignorance of that we used single phase formula instead of three phase formula.

Now try with this formula P = √3 x V x I

P=√3 Vx I (Primary voltage x primary current)

P =√3 x 11000V x 5.25A = 1.732 x 11000V x 5.25A = 100,025 VA = 100kVA

Or P = √3 x V x I (Secondary voltages x Secondary Current)

P= √3 x 415V x 139.1A = 1.732 x 415V x 139.1A= 99,985 VA = 99.98kVA

Consider the (next) following example.

Voltage (Line to line) = 208 V.

Current (Line Current) = 139 A

Now rating of the three phase transformer

P =  √3 x V x I

P = √3 x 208 x 139A = 1.732 x 208 x 139

P = 50077 VA = 50kVA