3-Phase Short Circuit¶

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

$\textbf{I} = \{0, 0, 0, 0, ..., 0\}$

Then for single bus failure, compute the short circuit current at the selected bus $i$ and assign that value in the $i^{th}$ position of the array $\textbf{I}$ .

$\textbf{I}_i = - \frac{\textbf{V}_{pre-failure, i}}{\textbf{Z}_{i, i} + z_f}$

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

$\Delta \textbf{V} = \textbf{Z} \times \textbf{I}$

Finally, define the voltage at all the nodes as:

$\textbf{V}_{post-failure} = \textbf{V}_{pre-failure} + \Delta \textbf{V}$

Multiple bus failures¶

For all bus $i$ in selected buses $B$ , $\textbf{V}_{post-failure, i} = -\textbf{z}_{f,i} \textbf{I}_i$ . This, along with the equations for $\Delta \textbf{V}$ and $\textbf{V}_{post-failure}$ above, and $\textbf{I}_i = 0$ for non-selected buses, gives the equation:

$\textbf{V}_{pre-failure, B} = -(\textbf{Z}_B + \textbf{z}_{f,B}) \times \textbf{I}_B$

in which $\textbf{z}_{f, B}$ is added to the diagonals of $\textbf{Z}_B$ .

Short circuit currents $\textbf{I}_B$ can now be computed through the equation for $\textbf{V}_{pre-failure, B}$ above. Note that the single bus short circuit current computation above follows if $B$ has only one bus.

Variables:

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