Introduction

Transformer voltage drop is important to know since it is one of the factors that affect the performance of an electrical system where it is installed. Obviously high voltage drop in transformer could lead into low voltage at the load side of the system.

Formula

Single Phase Transformer: Vd = I (R cos theta + X sin theta)
Three Phase Transformer: Vd =  sqrt(3) x I (R cos theta + X theta)

where:

Vd = voltage drop
R = Resistance
X = Reactance
theta = power factor angle

Example 1 (Single Phase Transformer)

Find the voltage drop of the single phase transformer supplying a 50 HP motor with a power factor of 0.70. The transformer has manufacturer rating given below.
• voltage rating = 12.7KV /  230V
•  KVA rating = 100 KVA
• % R =  2.24 %
• % X = 3.34 %
Solution:

In this case the resistance and reactance of the transformer is given in its percentage form, therefore we need to determine the actual value of these quantities. In determinin23g the actual values we need to use the following formula,

R actual = 10 (%R) (KV secondary) ^2
KVA transformer

R actual = 10 (2.24%) (0.23 KV) ^ 2     >> use 230 V secondary as base voltage
100 KVA

R actual = 0.01185 ohms >> value of the actual resistance

X actual  = 10 (%X) (KV secondary) ^ 2
100 KVA

X actual = 10 (3.44%) (0.23 KV) ^2 >> use 230 V secondary as base voltage
100 KVA

X actual = 0.0182 ohms >> value of the actual reactance

Determine the value of the current

P = 50 HP x  746 W = 37,300 watts
HP

I = P / VL * pf

I = 37, 300 Watts / 230 V * 0.7
I = 231 Amperes

cos theta = 0.7
sin theta = 0.7

Vd = I (R cos theta + X sin theta)
Vd = 231 A x [ (0.01185)( 0.7) + (0.0182) (0.7) ]

Vd = 4.85 Volts or

%Vd = (4.85 V) x 100 = 2.11 %
230 Volts Base

Example 2 (Three Phase Transformer)

Find the voltage drop of the three phase transformer supplying a 100 KVA load with a power factor of 0.80. The transformer has manufacturer rating given below.
• voltage rating = 12.7KV /  230V
•  KVA rating = 150 KVA
• % R =  1.08 %
• % X = 1.63 %
Solution:
The process is still the same above but we differ only in the final calculation of the current since the value that we can get is to be multiplied with sqrt(3) or 1.73.

R actual = 10 (%R) (KV secondary) ^2
KVA transformer

R actual = 10 (1.08%) (0.23 KV) ^ 2     >> use 230 V secondary as base voltage
100 KVA

R actual = 0.0031 ohms >> value of the actual resistance

X actual  = 10 (%X) (KV secondary) ^ 2
100 KVA

X actual = 10 (1.63%) (0.23 KV) ^2 >> use 230 V secondary as base voltage
100 KVA

X actual = 0.0047 ohms >> value of the actual reactance

Determine the value of the current

I = S / (1.73 x VL)
I = 100,000 VA / (1.73 x 230)
I = 251 Amperes

cos theta = 0.8
sin theta = 0. 6

Vd = 1.73 x I (R cos theta + X sin theta)
Vd = 1.73 x 251 A x [ (0.0031)( 0.8) + (0.0047) (0.6) ]

Vd = 2.30 Volts or

%Vd = (2.30 V) x 100 = 1.0 %
230 Volts Base