Calculating the magnetic flux density generated by multiple systems of indefinite rectilinear conductors

Purpose

This tool allows you to determine the levels of magnetic flux density dispersed by one or more bundles (or systems) of indefinite rectilinear conductors, all parallel to each other. A model of this type is commonly used to represent power lines, both overhead and underground, as also required by the CEI 211-4 guide Guide to the methods of calculating the electric and magnetic fields generated by power lines and substations, at least for the part relating to two-dimensional models.

The tool is therefore useful for assessing the magnetic field exposure of those who, for work or other reasons, must remain near power lines, in cases where a two-dimensional model allows an accurate result to be obtained. This occurs, in particular, in the presence of overhead and/or underground lines, around which the conductors can be considered parallel to each other and to the ground surface, at least for a sufficiently long section with respect to the distances between the conductors themselves.

General Settings

The application allows you to consider up to 10 conductor bundles, each of which represents, in the most typical case, a three-phase power line; however, the general approach adopted makes the application very flexible, capable of adapting to even very different situations.

Each conductor system is described through the starting data entered in a specific numbered sub-tab, located in the Data Entry tab. This ata consists of the position of the conductors in space (specified by locating the point of intersection of the conductor with the calculation plane) and the values of the intensity and phase of the current on them.

The processing produces, in the Results tab, a summary with the peak value and the distance from the origin of the point at which it is reached, and a table containing the distances from the origin at which a series of significant values are obtained (0.4, 3, 10, and 100 µT).

Two graphs are also displayed, showing respectively the trend of the intensity of the magnetic induction along a segment positioned on the calculation plane and parallel to the ground and the locus of the points where the induction itself reaches a value preset by the user (see following figures, click to enlarge).

Calculating the level of magnetic flux density.

Distribution of points where the induction level reaches the
user-specified value.

Limitations

The basic condition of the model, that is, the validity of a two-dimensional representation of the problem, cannot be considered satisfied in close proximity to pylons or intersections between two or more lines and, in general, in electrical substations.

Definition of the structure of conductor systems

Number of systems

Position of the calculation points along the ground plane

Initial distance

Step m

Number of points

Height above ground m

Slope of ground °

Search field value

Angular step °

Searched value μT

Definition of structures

The tool allows you to define up to 10 conductor systems, that is, overhead or underground power lines, each consisting of 1 to 30 infinite, straight, horizontal, parallel conductors to each other and to the ground.

To place them in space, the relative structure must be absolutely positioned. To do this, you must specify:

the height of the lowest conductor above the ground;
the distance (measured along the ground, which may be inclined) of the foot of the perpendicular duct to the origin of the internal reference system of the structure, from the origin of the absolute reference system (placed at ground level).

The following images show the absolute (in black) and structural (blue) reference systems for flat and inclined terrain (click to enlarge):

Absolute reference system (in black) and structures (blue) for
flat terrain.

Absolute reference system (in black) and structures (blue) for
inclined terrain.

Definition of conductors

Each conductor system is characterized by a structure that documents its geometric characteristics, with reference to the calculation plane (the vertical plane, orthogonal to the direction of the conductors, on which the points where the magnetic field will be calculated are located). We will call the points where the conductors intersect the calculation plane tracks. The structure should be designed as having its own internal orthogonal Cartesian reference system having:

origin at a conventional point on the calculation plane, located vertically at the level of the track of the lowest conductor and horizontally along the axis of the support, in the case of an overhead line, or approximately at the center of the tracks of the conductors, in the case of an underground line;
horizontal X-axis pointing to the right;
vertical Y-axis pointing upward.

The following images show the internal reference system (in blue) for an underground power line, an asymmetrical pylon with three conductors, and a symmetrical pylon with six (click to enlarge):

Definition of the internal reference system (in blue) for a
three-conductor underground line.

Definition of the internal reference system (in blue) for a
three-conductor overhead line.

Definition of the internal reference system (in blue) for a
six-conductor overhead line.

For three voltage values (132 kV, 220 kV, and 380 kV), the user can optionally select one of four predefined structures (single and double circuit, overhead or underground, respectively), chosen as the most impactful in their category from the point of view of the stray magnetic field. Alternatively, the user can define his own custom structure, specifying the number of conductors and, for each of them:

the coordinates of the suspension points, expressed in the structure's internal reference system;
the current value and its phase.

The data relating to one structure can be replicated in another by specifying its progressive number under the heading Replicate these parameters to structure no. ... and pressing the button with the green arrow.

Definition of the calculation points and the field value

Finally, the parameters needed to perform the calculation of magnetic flux density along a segment lying on the calculation plane and parallel to the ground (hereinafter calculation segment) must be specified:

ground slope
initial distance (distance, measured along the ground, of the base of the perpendicular drawn through the starting point of the calculation segment, from the origin - which must be at ground level - of the absolute reference system)
number of points into which to divide the calculation segment
advancement step along the calculation segment
constant height of the calculation segment above the ground

and around the conductors (isohypses at the required induction level):

angular step
magnetic flux density level sought.

The results are displayed in two graphs; some summary data are presented in a table.

Keywords: Calculation, Magnetic flux density, Infinite rectilinear conductors