Accurate kVA Transformer Sizing for Single-Phase & Three-Phase Systems

How to Calculate the Rating of Single Phase & Three Phase Transformers in kVA

We know that a transformer is always rated in kVA. Below are the two simple formulas which can be used to find and calculate the rating of Single Phase and Three Phase Transformers.

In any case, both the voltage and currents should be form an individual side either primary or secondary respectively ( e.g. Primary voltage x primary current or secondary voltage x secondary current). To property size a transformer for a required home appliance, you should select the supply voltage and secondary load current in amperes.

Sizing a Single Phase Transformer

Rating of Single Phase Transformer:

P = V x I

Where:

• V = Primary or Secondary Voltage
• I = Primary or Secondary Current
• P = Power of transformer in VA (Volt-Amps)

Rating of a single phase transformer in kVA

kVA= (V x I) / 1000

Example:

Suppose a 1-phase transformer having the secondary voltage and current of 240V and 62.5A respectively. Calculate the size of the  single-phase transformer.

Solution:

• Secondary Voltage: 240V
• Load Current: 62.5A

Transformer Rating = P = V x I

Putting the values:

P = 240V x 62.5A

P = 15000 VA = 15 kVA

Sizing a Three Phase Transformer

Rating of a Three Phase Transformer:

P = √3 x V x I

Where:

• V = Primary or Secondary Voltage
• I = Primary or Secondary Current
• √3 = 1.732
• P = Power of transformer in VA (Volt-Amps)

Rating of a Three phase transformer in kVA

kVA = (√3 x V x I) / 1000

Example:

A 3-phase transformer having the primary voltage and current of 7200V and 4A respectively. Calculate the size of the three phase transformer.

Solution:

• Primary Voltage: 7200V
• Primary Current: 4A

Transformer Rating = P = √3 x V x I

Putting the values:

P = 1.732 x 7200V x 4A

P = 49,881 VA ≈ 50 kVA

Transformer Rating in kVA Calculator

The following calculator will calculate the rating of the transformer in kVA, Primary or secondary voltage and current respectively. Just enter any two values and click on calculate to find the desired value.

Now, look at the General nameplate rating of a 100kVA transformer.

The nameplate clearly shows the rating of transformer is 100 kVA.

The primary voltages or high voltages (HV) is 11000 V = 11kV.

And the primary current on the high voltage (HV) side is 5.25 Amperes.

Also secondary voltage or low voltages (LV) is 415 Volts

And secondary current (load current on low voltages (LV) side) is 139.1 Amperes.

In simple words,

• Transformer rating in kVA = 100 kVA
• Primary Voltages = 11000 = 11kV
• Primary Current = 5.25 A
• Secondary 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

As you noticed, the rating of the transformer (on the nameplate) is 100 kVA but according to the calculation, the calculated value is  57kVA.

Well, The difference comes due to ignorance of the fact that we used a single phase formula instead of three phase formula. It means it is a three phase transformer and we will use the associated formula for it. 

Let’s clear it using the three phase transformer rating formula.

P = √3 x V x I

P = √3 V x 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 ≈ 100kVA

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

That’s it. Now you know how to properly size a three phase and single phase transformer with suitable rating in VA or kVA for home appliances or any other load applications.

The following table shows the dry transformer data of standard kVA rating, Voltage and Current rating for both single phase and three phase transformers.

Single Phase Transformer				Three Phase Transformer
KVA Rating	Amperes			KVA Rating	Amperes
	120V	240V	600V		120V	240V	480V	600V
0.75	6.25	3.13	1.25	3	8.33	7.22	3.61	2.89
1	8.33	4.17	1.67	9	25	21.7	10.8	8.66
1.5	12.5	6.25	2.5	15	41.6	36.1	18	14.4
2	16.7	8.33	3.33	20	55.5	48.1	24.1	19.2
3	25	12.5	5	25	69.4	60.1	30.1	24.1
5	41.6	20.8	8.33	30	83.3	72.2	36.1	28.9
7.5	62.5	31.3	12.5	37.5	104	90.2	45.1	36.1
10	83.3	41.7	16.7	45	125	108	54.1	43.3
15	125	62.5	25	75	208	180	90.2	72.2
25	208	104	41.7	100	278	241	120	96.2
37.5	313	156	62.5	112.5	312	271	135	108
50	417	208	83.3	150	416	361	180	144
75	625	313	125	225	625	541	271	217
100	833	417	167	300	833	722	361	289
167	1392	696	278	500	1388	1203	601	481
250	2083	1042	417	750	2082	1804	902	722

Here is the table in the image format if you need to download as a reference.

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