Calculation of Voltage Drop

How to calculate voltage drop for power cable?

 

Solution:-

 We have two types of power supply: -

 1.    Single Phase

2.    Three phase

Firstly we calculate on single phase supply:-

Vdp = (2 X Ic X (Rcos ᶿ + Xsinᶿ ) X L) / (1000 X Vs)

Where

Vdp = Voltage Drop (%)

Ic = Operating Current of Circuit (A)

R = Power Cable Resistance (Ohm/km)

Cos ᶿ = Power Factor

X = Conductor inductive reactance (Ohm/km)

ᶿ = Phase angle of load

L = Power Cable Length (m)

Vs = Voltage Supply (V)

 

Here

Lo = Ic / Vs

 

Where

Lo = Load of Circuit (W)

 

 Therefore

Vdp = (2 X L X (Rcos ᶿ + Xsinᶿ ) X L) / 1000XVs

 

Use 1000 for convert ohm/km to ohm/m.

Power Factor Calculation:-

Cos ᶿ = Lo / (I X V)

 

Where

Lo = Load of Circuit (W)

I = Current (A)

V = voltage (V)

 

Let we assumed that

Cos ᶿ = Lo / (I X V) = 1

Xsinᶿ = Negligible

 

Therefore

Vdp = (2 X Lo X R X L) / 1000 X Vs

 

Now we calculate on Three phase supply:-

Vdp = (1.732 X Ic X (Rcos ᶿ + Xsinᶿ ) X L) / (1000 X Vs)

 

OR

 Vdp = (1.732 X Lo X (Rcos ᶿ + Xsinᶿ) X L) / 1000 X Vs

 

After consider assumptions then:-

 

Vdp = (1.732 X Ic X R X L) / (1000 X Vs)

 

OR

 

Vdp = (1.732 X Lo X R X L) / 1000 X Vs

 

Note: - used multiply by 100 for converting %.

 

Example:-1

Voltage Drop = ?

Operating Current of Circuit = 24.05 A

Power Cable Resistance = 1.47 Ohm/km

Power Cable Length = 56

Voltage Supply = 240V

 

Solution:-

We know that 240V voltage for single phase, then we have formula:-

 

Vdp = (2 X Ic X R X L) / (1000 X Vs)

 

Now put the value:-

Vdp = (2 X 24.05 X 1.47 X 56) / (1000 X 240)

Vdp = 3959.592 / 240000

Vdp = 0.0164983

Vdp (%) = 0.0164983 X 100

Vdp (%) = 1.65

Example:-2

Voltage Drop = 1.25%

Operating Current of Circuit = 22.26 A

Power Cable Resistance = ?

Power Cable Length = 72 m

Voltage Supply = 240V

 

Solution:-

We have equation for solution of calculate voltage drop:-

Vdp = (2 X Ic X R X L) / (1000 X Vs)

Putting all value in this formula:-

(1.25 / 100) = (2 X 22.26 X R X 72) / (1000 X 240)

0.0125 = (3205.44 X R) / 240000

0.0125 X 240000 = (3205.44 X R)

3000 = 3205.44 X R

R = 3000 / 3205.44

R = 0.936 Ohm/m

Now we selected just less resistance cable.

And we have 0.93 Ohm/m cable resistance, so we selected this cable.