Per Unit Representation of Transformer

PER UNIT REPRESENTATION OF TRANSFORMER

Two winding transformer has primary and secondary winding. Therefore the p.u impedance deserves particular attention.

(a) The approximate equivalent circuit of a two winding transformer with impedance referred to low voltage (primary) side.

Equivalent circuit of a single phase transformer referred to LV side shown in Figure 1.21.

(b) The approximate equivalent circuit with impedance referred to high voltage (secondary) side.

The equivalent circuit of a single phase transformer referred to HV side shown in Figure 1.22.

Mutual impedance in pu between lines of different voltage level

Let us consider two three phase lines of different voltage levels with mutual reactance X_m present shown in Figure 1.23.

Transformer always rated in KVA. Below are the two simple formulas to find the rating of Single Phase and Three Phase Transformers.

Rating of a Single Phase Transformer in KVA

kVA = (V x 1)/1000

Rating of a Three Phase Transformer

Rating of a Three Phase Transformer:

P= √3 V x 1

Rating of a Three Phase transformer in KVA

kVA = (√3 V x 1)/1000

Here is the rating of Transformer is 1000 kVA.

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

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 A

Secondary Voltages = 415V

Secondary Current = 139.1 Amperes

Now calculate for the rating of transformer according to

P = V x 1 (Primary voltage x Primary current)

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

or P = V x 1 (Secondary voltages x Secondary current)

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

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

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 1

P = √3 V x 1 (Primary voltage x Primary current)

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

VA = 100 kVA

Or P = √3 x V x 1 (Secondary voltages x Secondary current)

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

VA = 99.98 kVA

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 1

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

P = 50077 VA = 50 kVA

Transformer rating is expressed in kVA, not in kW. Rating of a transformer or any electrical machine reflects its load carrying capability without overheating. Temperature rise (major threat to insulation) arises due to internal loss within the machine.

There are two type of losses in a transformer;

i. Copper Losses.

ii. Iron Losses or Core Losses or Insulation Losses.

Copper Losses (I²R) are variable losses which depends on Current passing through transformer windings while Iron Losses or Core Losses or Insulation Losses depends on voltage.

So the transformer is designed for rated voltage (iron loss) and rated current (copper loss). We can't predict the power factor while designing the machine, because power factor depends upon the load which varies time to time.

When a manufacturer makes a transformer, UPS etc., they have no idea of the type of load that will be used and consequently they can only rate the device according to its maximum current output that the conductors can safely carry (at unity Power Factor) and the insulation rating of the conductors (voltage and temperature).