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.