A factory substation, constructed in the 60s, still in active service is supplied at 11,000v, through an underground cable of 0.06 sq.in. section 7 miles from a substation containing 2 ---- 33,000/11,000v transformers each 2,500 kVA + 5% reactance. The short circuit kVA on the 33,000 busbars is 250,000 kVA. What is the value of the short circuit at the factory substation?
Assuming a 5,000 kVA base, it is first necessary to find the equivalent reactance reactance of the supply system-----
5,000 x 100/React. % of supply system = 250.000kVA
React. of supply system = 5,000 x 100/250,000 = 2%
Each transformer on 5,000 kVA base has 5 x 5,000/2500 % reactance = 10%
2 in parallel give -------------------------------------------------------------------------------5%
As the resistance of the line will be comparable with its reactance, both should be taken into account.
Reactance of 0.06 sq.in. cable = 0.1682 ohms per mile.
Resistance of 0.06 sq.in. cable = 0.7184 ohms per mile.
Current equivalent to 5,000 kVA at 10,000v = 262 amps.
Voltage reactance drop = 262 x 0.1682 x 7= 308v
Voltage resistance drop = 262 x 0.7184 x 7 = 1,320v
Phase voltage =11,000/√3 = 6,350v
% Reactance drop = 308/6350 x 100 =4.85%
% Resistance drop = 1320x 100/6350 = 20.8%
Totalling up Resistance Reactance
Supply system ---- 2.00%
Transformers ---- 5.00%
Cable 20.8% 4.85%
-----------------------------------------------
20.8% 11.85%
% impedance = √20.8sq + 11.85sq √432 + 140
= √572 = 23.9%
Short circuit = 5,000 x 100/23.9kVA = 20,900 kVA
Regards, UKPN.