# Thermal Short-Circuit Current¶

## Current Calculation¶

The equivalent thermal current is calculated as:

$\begin{split}\begin{bmatrix} \underline{I}_{th, 1} \\ \vdots \\ \underline{I}_{th, n} \\ \end{bmatrix} = \begin{bmatrix} \sqrt{m_1 + n_1} \\ \vdots \\ \sqrt{m_n + n_n} \\ \end{bmatrix} \begin{bmatrix} \underline{I}''_{k, 1} \\ \vdots \\ \underline{I}''_{k, n} \\ \end{bmatrix}\end{split}$

where m and n represent the dc and ac part of the thermal load.

## Correction Factors m and n¶

For short-circuit currents far from synchronous generators, the factors are given as:

$n = 1 m = \frac{1}{2 \cdot f \cdot T_k \cdot ln(\kappa - 1)} [e^{4 \cdot f \cdot T_k \cdot ln(\kappa - 1)} - 1]$

where $$\kappa$$ is the peak factor defined here and $$T_k$$ is the duration of the short-circuit current that can be defined as a parameter when running the short-circuit calculation.