Modeling Earth Networks by Equivalent Electric Circuits. Theory

Today, the electrification of industrial, commercial and domestic buildings for functional or energy efficiency purposes is increasingly leading to problems of electromagnetic compatibility. Earthing systems are essential for maintaining equipotentiality in buildings, whatever the operating conditions. They help protect people and property against insulation faults and external hazards such as lightning.

On the other hand, they have never been dimensioned with regard to the propagation of conducted disturbances in the [10 kHz-30 MHz] band generated inside the building by power electronics converters, which are increasingly present in new buildings.

The design of earth networks is generally based on empirical dimensioning. These are either simplistic or, on the contrary, are based on cumbersome numerical modelling and are therefore not very usable. Moreover, the existence of disturbances occupying increasingly wide frequency bands calls for models that take this parameter into account. For new buildings, equipotentiality of wiring must be ensured over a wide frequency range. This aspect has received little attention to date.

The aim of this article is to propose models in the form of equivalent electrical circuits of ground network components (piles, grids, conductive plates, wire cabling, etc.). These will be introduced into a 0D simulator (electrical circuit simulator), which can integrate sources of disturbance such as power electronic converters, lightning and the various components of the distribution network, such as surge arresters or other protection devices, distribution transformers, loads, etc., as long as their "circuit" models are available. The advantages of this modeling technique are numerous:

• easy business approach thanks to the handling of discrete components and very fast access to the calculation of global quantities ;

• understanding and analysis of physical phenomena, mastery of the predominant parameters, retained link with the geometry of the grounding and distribution network;

• sizing and optimization made easy thanks to a semi-analytical approach ;

• close development with the electromagnetic PEEC method, which is today the leading method for calculating wiring devices in electrical engineering and power electronics, etc.

This first article proposes an original modeling method based on the analytical resolution of Poisson's equation, with the aim of obtaining a model in the form of an equivalent electrical circuit of a conductor-earth assembly. New analytical formulations have been developed. Initially adapted to basic geometries, they...