Faults - Scenario 4

This post demonstrates how to estimate the kiloAmpere Interrupting Capacity (kAIC) rating of the first circuit breaker at the secondary side of a transformer using the Infinite Bus Method. The method assumes infinite supply from the primary side with negligible line impedances.

Below is a modified version of Example D13 (Available Short Circuit Current) in Appendix D of the 2017 Philippine Electrical Code (PEC).

SITUATION

Two adjacent buildings are supplied by two different distribution transformers.

One transformer is single-phase rated 100kVA, 230V with 2.5% impedance. The other is three-phase rated 100kVA, 230V line-to-line and also has 2.5% impedance.

What minimum kAIC ratings are needed for the first circuit breakers down the line of each transformer to safely interrupt the maximum symmetrical fault currents?

ANALYSIS

1.) SINGLE-PHASE TRANSFORMER LOAD-SIDE SUB-CIRCUIT

Base Power, 1ph: S,base = 100kVA
Base Voltage, 1ph: V,base = 230V
Impedance, given: Z = 2.5%

1.1.) Base current, 1ph:

i,base = S,base / V,base
i,base = 100kVA /  230V
i,base = 434.78261 A

1.2.) Short-circuit current, per-unit:

V,pu = 1 pu
i,pu = (V,pu / %Z) * 100
i,pu = (1 / 2.5) * 100
i,pu = 40 pu

1.3.) Short-circuit current, 1ph:

i,sc = i,pu * i,base
i,sc = 40 * 434.78261 A
i,sc = 17,391.304 Amps
i,sc = 17.391 kiloAmps

1.4.) CB minimum interrupting capacity:

1-phase circuit breaker >= 18 kAIC

2.) THREE-PHASE TRANSFORMER LOAD-SIDE SUB-CIRCUIT

Base Power, 3ph: S,base = 100kVA
Base Voltage, LL: V,base = 230V
Impedance, given: Z = 2.5%

2.1.) Base current, 1L:

i,1ph = i,1L (assuming Y-config)
i,1L = i,base

i,base = S,base / (sqrt(3) * V,base)
i,base = 100kVA /  (sqrt(3) * 230V)
i,base = 251.02186 A

2.2.) Short-circuit current, per-unit:

V,pu = 1 pu
i,pu = (V,pu / %Z) * 100
i,pu = (1 / 2.5) * 100
i,pu = 40 pu

2.3.) Short-circuit current, 1L:

i,sc = i,pu * i,base
i,sc = 40 * 251.02186 A
i,sc = 10,040.874 Amps
i,sc = 10.041 kiloAmps

2.4.) CB minimum interrupting capacity:

3-phase circuit breaker >= 11 kAIC

CONCLUSIONS

The 1-phase circuit breaker needs a kAIC rating of at least 18 kiloAmps, while the 3-phase circuit breaker needs a kAIC rating of at least 11 kiloAmps.

For the same power and voltage ratings, three-phase breakers usually have lower interrupting capacities because the currents are distributed over three lines, while currents on single-phase breakers are concentrated on one line.