# Substation earthing calculation

## Introduction

Due to the fact that earthing resistance is influenced by many factors, there are no calculation methods, which give 100 % accuracy. There are many mathematical formulas, which are based on experience and theory.

## Objective

To choose proper cross-section of metallic steel tape for earthing of 110/30 kV substation.

## Standard

EN 50522:2010 Earthing of Power Installations Exceeding 1 kV A.C.

## Input data

\begin{equation} I_f = 25 kA \quad t_f = 0,6 s \quad \rho_e = 60 \Omega m \quad D = 77,3 m \end{equation}where:

\(I_k\) - fault current

\(t_k\) - fault time

\(\rho_e\) - soil resistivity, taken from the standard EN 50522:2010 - table J.1 (see below)

\(D\) - diameter of a circle, which area is the same as the lattice earthing

**Soil resistivities for frequencies of alternating currents - range of values, which were frequently measured (table J.1 from EN 50522:2010)**

Type of soil | Soil resistivity \(\rho_e [\Omega m]\) |

Marshy soil | 5 to 40 |

Loam, clay, humus | 20 to 200 |

Sand | 200 to 2 500 |

Gravel | 2 000 to 3 000 |

Weathered rock | mostly below 1 000 |

Sandstone | 2 000 to 3 000 |

Granite | up to 50 000 |

Moraine | up to 30 000 |

## Calculations

Minimum cross-section of earthing conductor on substation can be calculated by:

\begin{equation} A = \dfrac{I}{K} \sqrt{\dfrac{t_f}{ln\dfrac{\Theta_f+\beta}{\Theta_i+\beta}}} \end{equation}where:

\(A\) - cross-section, \(mm^2\)

\(I\) - conductor current, A (RMS value)

\(t_f\) - duration of fault current, s

\(K\) - constant depending on the material of the current-carrying capacity, taken from table D.1 in EN 50522:2010(see below),\(A \cdot \sqrt{s}/mm^2\)

\(\beta\) - reciprocal of the temperature coefficient of resistance of the current-carrying component at 0 \(^\circ C\), EN 50522:2010(see below), \(^\circ C\)

\(O_i\) - initial temperature, values may be taken from IEC 60287-3-1. If no value is laid down in the national tables, 20C as ambient ground temperature at a depth of 1 m should be adopted.

\(O_f\) - final temperature, \(^\circ C\)

**Material constants (table D.1 from EN 50522:2010)**

Material | \(\beta [^\circ C]\) | \(K [A \cdot sqrt{s}/mm^2]\) |

Copper | 234,5 | 226 |

Aluminium | 228 | 148 |

Steel | 202 | 78 |