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, 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}

Magnitudes:

  • \textbf{I}: Array of fault currents at the system nodes.
  • \textbf{V}_{pre-failure}: Array of system voltages prior to the failure. This is obtained from the power flow study.
  • 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}: system impedance matrix. Obtained as the inverse of the complete system admittance matrix.