# Peak Short-Circuit Current¶

## Current Calculation¶

The peak short-circuit current is calculated as:

$\begin{split}\begin{bmatrix} i_{p, 1} \\ \vdots \\ i_{p, n} \\ \end{bmatrix} = \sqrt{2} \left( \begin{bmatrix} \kappa_{1} \\ \vdots \\ \kappa_{1} \\ \end{bmatrix} \begin{bmatrix} \underline{I}''_{kI, 1} \\ \vdots \\ \underline{I}''_{kI, n} \\ \end{bmatrix} + \begin{bmatrix} \underline{I}''_{kII, 1} \\ \vdots \\ \underline{I}''_{kII, n} \\ \end{bmatrix} \right)\end{split}$

where $$\kappa$$ is the peak factor.

## Peak Factor $$\kappa$$¶

In radial networks, $$\kappa$$ is given as:

$\kappa = 1.02 + 0.98 e^{-{3}{R/X}}$

where $$R/X$$ is the R/X ratio of the equivalent short-circuit impedance $$Z_k$$ at the fault location.

In meshed networks, the standard defines three possibilities for the calculation of $$\kappa$$:

• Method A: Uniform Ratio R/X

• Method B: R/X ratio at short-circuit location

• Method C: Equivalent frequency

The user can chose between Methods B and C when running a short circuit calculation. Method C yields the most accurate results according to the standard and is therefore the default option. Method A is only suited for estimated manual calculations with low accuracy and therefore not implemented in pandapower.

Method C: Equivalent frequency

For method C, the same formula for $$\kappa$$ is used as for radial grids. The R/X value that is inserter is however not the

Method B: R/X Ratio at short-circuit location

For method B, $$\kappa$$ is given as:

$\kappa = [1.02 + 0.98 e^{-{3}{R/X}}] \cdot 1.15$

while being limited with $$\kappa_{min} < \kappa < \kappa_{max}$$ depending on the voltage level:

Voltage Level

$$\kappa_{min}$$

$$\kappa_{max}$$

< 1 kV

1.0

1.8

> 1 kV

2.0