Unsymmetric Two-Phase Current

Initial Short-Circuit Current

The two-phase initial short-circuit current is calculated in the same way the three-phase current is calculated, only with a source voltage of \(c \cdot \sqrt{2} \cdot V_N\) instead of \(\frac{c \cdot V_N}{\sqrt{3}}\):

\[\begin{split}\begin{bmatrix} \underline{I}''_{k2, 1} \\ \vdots \\ \underline{I}''_{k2, m} \\ \end{bmatrix} = \begin{bmatrix} \frac{c_1 \cdot \sqrt{2} \cdot V_{N, 1}}{Z_{11} + Z_{fault}} \\ \vdots \\ \frac{c_n \cdot \sqrt{2} \cdot V_{N, n}}{Z_{nn} + Z_{fault}} \end{bmatrix}\end{split}\]

Peak Short-Circuit Current

The peak short-circuit current is calculated as:

\[\begin{split}\begin{bmatrix} i_{p2, 1} \\ \vdots \\ i_{p2, n} \\ \end{bmatrix} = \sqrt{2} \begin{bmatrix} \kappa_{1} \\ \vdots \\ \kappa_{1} \\ \end{bmatrix} \begin{bmatrix} \underline{I}''_{k2, 1} \\ \vdots \\ \underline{I}''_{k2, n} \\ \end{bmatrix}\end{split}\]

where the factor \(\kappa\) is calculated for each bus as defined here.

Thermal Short-Circuit Current

The equivalent

\[\begin{split}\begin{bmatrix} \underline{I}_{th2, 1} \\ \vdots \\ \underline{I}_{th2, n} \\ \end{bmatrix} = \begin{bmatrix} \sqrt{m_1 + n_1} \\ \vdots \\ \sqrt{m_n + n_n} \\ \end{bmatrix} \begin{bmatrix} \underline{I}''_{k2, 1} \\ \vdots \\ \underline{I}''_{k2, n} \\ \end{bmatrix}\end{split}\]

where the factors m and n are calculated for each bus as defined here.