# 3-Phase Short Circuit¶

First, declare an array of zeros of size equal to the number of nodes in the circuit.

Then for single bus failure, compute the short circuit current at the selected bus and assign that value in the position of the array .

Then, compute the voltage increment for all the circuit nodes as:

Finally, define the voltage at all the nodes as:

## Multiple bus failures¶

For all bus in selected buses , . This, along with the equations for and above, and for non-selected buses, gives the equation:

in which is added to the diagonals of .

Short circuit currents can now be computed through the equation for above. Note that the single bus short circuit current computation above follows if has only one bus.

**Variables:**

- : Array of fault currents at the system nodes.
- : Subarray of such that all entries for non-selected buses are removed.
- : Array of system voltages prior to the failure. This is obtained from the power flow study.
- : Subarray of such that all entries for non-selected buses are removed.
- : Impedance of the failure itself. This is a given value, although you can set it to zero if you don’t know.
- : Impedance of the failures of selected buses .
- : system impedance matrix. Obtained as the inverse of the complete system admittance matrix.
- : submatrix of such that all rows and columns for non-selected buses are removed.