Short-Circuit Calculation Methods

Classical calculation

Begin by converting all impedances to “per unit” values. Per unit base values and formulae used are as follows:

S_base =100MVA

V_base =26.4 kV

Let's run through an example calculation to make this discussion a little more tangible. Refer to the one-line diagram in the Figure below with the following input data:

• Utility: 26.4kV, 1,200MVA, X/R=41
• Transformer (T₁): 2MVA, 26.4/4.16kV, DY-G, Z=7%, X/R515
• Motor 1 (M₁): Induction, 4.16kV, 1,000 hp, PF=0.8, efficiency50.8, X"_d= 0.16 pu, X/R=28
• Motor 2 (M₂): Induction, 4.16kV, 49 hp, PF=0.8, efficiency=0.8, X"_d=0.17 pu, X/R=10

Now it's possible to calculate the equivalent Thevenin impedance for a fault at Bus 2 by combining the per unit X and R values to obtain the relative impedances.

Z_Fault=(Z_utility+Z_T1)||Z_Motor1||Z_Motor2=(0.0021+j0.083+0.005+j0.07)||(0.49+j13.8)||(29.8+j298)=0.166+j2.817 pu=2.823ej^86.6

We may now calculate the short-circuit current rms at Bus 2:

The peak duty the breaker is required to close and latch may be evaluated using the following formula, which constitutes a multiplier to the rms current, which was calculated above:
 

Use Table 1, page 1 in ANSI C37.06-1997 Preferred Ratings and Related Required Capabilities to rate new switchgear. It's useful in comparing calculated duty (4,916A and 12,692A) and standard ratings. The Table includes sample values extracted from the ANSI table.

These are the short-circuit current ratings required for our switchgear duty corresponding to a continuous current, for example, 1,200A. No further steps have to be taken, as the table itself, by comparison, provides the required specifications for the equipment to be installed.