Calculating and measuring fields from power lines

If you know the geometry of the line and the currents (or voltages for electric fields) it is possible to calculate fields quite accurately ( download a tutorial on how to calculate the fields from a three-phase circuit).

Often, it is acceptably accurate to approximate the conductors as infinitely long straight lines and to approximate the currents as exactly balanced (the three currents in the three phases exactly equal).

If necessary, however, you can model the actual sag of the conductors and the actual currents in each conductor (more on unbalanced currents). The results from this exercise are shown here. The red dots are the measured magnetic field, the blue line the calculated magnetic field for the same instant of time. This comparison has been published in a scientific journal - abstract at bottom of this page.

 graph comparing calculated and measured fields

Height above ground

Power-line calculations and measurements are usually performed for 1 m above ground.  This is for a sound scientific reason explained here.

Straight lines and curves

Overhead lines and underground cables are generally pretty straight, and we usually model them as straight lines.  But of course, overhead lines sag between pylons, and sometimes, the conductors of underground cables diverge from each other.  This doesn't usually make a great deal of difference to the fields but we give more detail on the effect of sag and diverging conductors.

If the conductors are straight but only finite in length, they produce less field than the infinite conductors we usually calculate for - but we can calculate how much less quite easily.

Calculating fields for yourself

If you want to calculate fields yourself we provide:

dimensions for some common UK power line designs.

an online calculator for magnetic fields from some common UK power line designs

The abstract of the paper

IEE Proc.-Gener. Transm. Distrib., 142 (September 1995) 481-486
Magnetic fields from transmission lines: comparison of calculations and measurements 

J Swanson

Abstract. An experiment has been performed to compare the calculated and measured magnetic fields produced by a double-circuit 400 kV transmission line. The phase currents were measured in the substation at one end of the line, taking particular care to measure the zero-sequence currents accurately, and the earth-wire current was measured at the span where the experiment was conducted. These currents were used to calculate the magnetic fields, using a number of computer programs based on Ampere’s law. the magnetic field was measured at 22 positions ranging from 100 m on one side of the line to 500 m on the other side. Measured and calculated fields generally agreed well. The largest errors were ±7% ±1 nT. These errors are attributed to a mixture of random errors in the calibration, resolution and synchronisation of the measuring instruments, and systematic errors stemming from the measurement of zero-sequence currents.

See also: