DC railways and the magnetic fields they produce—the geomagnetic context

Abstract

DC electric railways produce magnetic fields, not only from the intended traction currents, but also from unintended earth-leakage currents; these fields, particularly those from the leakage currents, are becoming an increasing problem for geomagneticians. This paper introduces the relevant properties of DC-railway tractionpower circuits, and the various ways in which earth-leakage currents are produced, and discusses models of how these leakage currents vary along the track and with train position. It describes the geometry of the resultant magnetic fields, and gives the formal algebra for calculating the magnetic field when these leakage currents are known, but also suggests some simple approximations that could be used when the current distribution is not known in detail. This paper also summarises previous relevant papers.

Modelling the magnetic field caused by a dc-electrified railway with linearly changing leakage currents

“…It should be emphasised that the formulas are exact including somewhat complicated algebraic manipulations. This is, however, justifiably criticised by Frank Lowes in his impressive and significant paper (Lowes, 2009) because the geometry and the physical interpretations are obscured by the algebra. On the other hand, since exact closed-form solutions exist that are easy to handle in computer calculations, they are worth being used in numerical modelling of the magnetic fields in question.…”

“…It should be noted that we neglect the track extensions beyond the substation and beyond the train (at x < 0 and x > L). This assumption includes an approximation (see Lowes, 2009). However, to be consistent and comparable with the study presented by Pirjola et al (2007), the assumption of neglecting the extensions is also made in this paper.…”

“…Similarly to Georgescu et al (2002) and by Pirjola et al (2007), we assume that the current, which leaks into the ground everywhere along the track between the train and the substation, returns to the system at the substation. Thus, the situation considered in this paper corresponds to figure 3(b) of Lowes (2009), i.e. the leakage current is zero at the substation and increases linearly reaching its maximum at the train.…”

“…the leakage current density per unit length (= j) is the same at each infinitesimal section [x, x + dx] between the substation (x = 0) and the train (x = L). On page viii of Lowes (2009), the constantleakage approximation is called "a completely unrealistic situation". Lowes proves this statement by careful investigations of the track-to-soil voltages and the associated leakage currents in different cases.…”

“…Consequently, advance calculations and estimations of expected magnetic fields at geomagnetic observatories due to possible dc equipment and devices being in the planning stage are very important. Problematic magnetic fields are created especially by dc-electrified railways (e.g., Yanagihara, 1977;Georgescu et al, 2002;Pirjola et al, 2007;Lowes, 2009; and references therein). There are historical examples of the need to close a geomagnetic observatory and move it to a more distant location because a dc-electrified railway or tramway makes the operation impossible (e.g.…”