Transients in railway environments; Measurements & Modelling ...

Transients in railway environments; Measurements & Modelling 

Authors 

Frans Schoren, BIT TIPS, Singapore 

Erwin Smulders, Holland Railconsult, The Netherlands 

Gert-Jan van Alphen, Holland Railconsult, The Netherlands 

Kees Post, Lambda Engineering BV, The Netherlands 

Contact address: 

Holland Railconsult, PO Box 2855, 3500 GW Utrecht, The Netherlands 

Subject 

The measurements of transients magnetic fields generated by railway systems, 

combined with modelling, both in the time domain as well as in the frequency 

domain. 

Abstract 

Especially in densely populated areas, such as the Netherlands, there is a growing 

demand to integrate railway systems with other infrastructure. A well-balanced EMC 

approach is becoming more and more important. On one side “possible victims” are 

becoming more susceptible with the increase in the bandwidths and frequencies used. 

On the other side, the emission of railway systems can increase with the 

implementation of high-speed lines. The need to reach compatibility between the 

railway system and other electrotechnical systems, both railway related as well as 

those of third parties is paramount. The prediction of the susceptibility of the 

„victims“ is not easy, but can be accomplished, using the relevant immunity standards 

and measurements. It is more complicated to predict the maximum emission of a 

railway system as a whole. 

For the design of grounding systems in railways, 50 Hz considerations play a major 

role. These 50 Hz current distributions and corresponding voltages are reasonably 

well understood and modelling tools are available. However, part of the EMC 

considerations concern higher frequencies due to transients, such as line switching 

and arcing of a pantograph. At the moment there is a large international interest in the 

development of modelling techniques in this area. The majority of the measurements 

and information (e.g. EN 50121-2) available at the moment, is frequency domain 

based and does not supply maximum values to be expected. In an EMC-analysis, a 

time domain based approach, taking maximum values into account, could be more 

useful in the case of transient system behaviour. 

Based on the measured current distribution in the railway system, a model for the 

calculation of transient magnetic fields is presented. The model relies on the Biot- 

Savart relations with time retardation, and is used to predict some worst case values. 

High frequency measurements (both time domain and frequency domain) of currents 

in the track and of transient magnetic field performed in Wiltz, Luxembourg 

(December 1999) are presented. The model has been used to predict some worst case 

values for transient magnetic fields, based on the measured currents. A relatively good 

consistency between the calculated and the measured transient field exists.

Using relatively simple models the worst case high frequency behaviour of railway 

systems is predictable with tolerable accuracy, thus facilitating compatibility studies 

with regard to other systems. This enables the closer integration of the railway system 

with other systems in densely populated areas. 

1 Introduction 

In the extended EMC studies being done for the introduction of the 25 kV, 50 Hz 

power supply system by the Dutch Railways, a lot of attention has been paid to 

grounding in order to reach low voltages both for people and equipment. Many of the 

grounding aspects are focused on the 50 Hz currents (both regular loads and quasi 

steady, a few hundred of milliseconds, short circuit loads), being the prime source for 

possible interference problems and therefore the prime parameters for the 

dimensioning of grounding systems. This grounding system helps to reduce the 

coupling between the different systems and therefore reduces the chance for possible 

disturbances. 

Besides these 50 Hz phenomena, transients are part of the railway environment as 

well. In this paper we present some of the aspects of transients in railway 

environments, encountered in the EMC studies for railways in the Netherlands. Of 

course a grounding system can also perform well with respect to transient phenomena, 

if the particular aspects of these phenomena (such as the small wavelength) are taken 

into account. 

2 Transients 

The subject of “transients” comprises many different type of phenomena, such as the 

switching of a line and the arcing between catenary and pantograph. Common factor 

is that the phenomena do not last long and the frequencies can vary from a few kHz 

(e.g. powering up of a line, see [travelling waves]) to several hundred MHz (due to 

arcing, see e.g. [Shinkansen]). 

With respect to EMC, the main interests in the EMC standards are not as much in one 

typical pulse shape (considered in the time domain), but more in the overall envelop 

of the phenomena (in the frequency domain). This is also summarised in the railway 

emission limits, such as described in [EN50121]. In frequency domain measurements 

one has to include sufficient (e.g. arcing) phenomena in order to make sure that the 

full spectrum is covered (especially with broadband measurements with 

corresponding high sweep times). Therefore in this paper we approach the phenomena 

in the time domain, in order to look for the maximum values. 

Two main concerns with respect to transients are: 

1. the magnitude of the electromagnetic fields emitted from the source (the radiated 

disturbance) and 

2. how these EM fields would couple into cables, connected to signaling and 

telecommunication equipment. This second concern will be covered in a future 

publication. 

Based on a simple model we have made a prediction of the order of magnitude of the 

magnetic inductance, given the currents in the track. With some practical 

measurements, a check on the predictions has been performed. At the end of 2000 and 

the first quarter of 2001 additional measurements have been performed as part of a

major design verification study. At the moment analyses are still being made, thus the 

results from these measurements could not be incorporated in this publication. 

In the calculations presented below we have been looking for expected maximum 

values to appear in practice, in order to be able to use these maximum values in the 

judgement of EMC of systems in a transient (railway) environment. If worst case 

considerations are already satisfying EMC requirements, no further detailed analysis 

would be necessary. 

For the second concern, from EM fields to coupled (disturbance) voltages in cables, 

one can make use of the work performed by [Vance]. In this paper however, we will 

concentrate on the first step. 

3 Currents 

3.1 Predicted peak currents 

Since [EN50121] emission limits are not a maximum level (but rather the 80/80 

value), some equipment owners are interested to know real maximum levels. In order 

to predict maximum field strengths, one has to know the maximum currents, which 

are the source for those fields. By treating the railway line as a transmission line, one 

can estimate the wave impedance of the line and in combination with the supply 

voltage a current wave amplitude can be estimated. For the impedance of the 

transmission line we use the following approach. 

For the capacitance of line above a flat plate: 

2 l 

C 

0 with l = length, h = height and r is the radius of the conductor 

ln 2 h 

r 

For the inductance of a line above a flat plate; 

0l 

L ln 2h 

with the same l, h and r values 

2 r 

For the wave impedance: 

ln 2 h 

0 

Z r 

0 

2 

0 

Now introducing some rough figures for a railway line; h = 5,5 m, r = 0,1 m, Z 0 can 

be estimated to be 282 Ohm. In a 25 kV system, with a step voltage of 25 kV * 2 = 

35 kV, that leads to peak currents of 125 A. Note that these current values can only be 

measured in practice, if the switching phenomena happens on or near the top value of 

the voltage. 

3.2 Measurement set up 

In search of the maximum transient phenomena, measurements have been performed 

in Luxembourg. The measurement results have not been published yet, but the 

measurement systems are described in [railway measurements]. The measurement set 

up is shown in figure 1 and figure 2. One set up concerns the time domain 

measurements of track current and magnetic field and the other concerns the 

frequency domain measurements of magnetic and electromagnetic fields. The 

measured electromagnetic fields in the frequency domain are not used in this paper.

NOTE: these measurements were not performed to support the modelling presented in 

this paper. The model was set up at a later stage to find a theoretical back-up for the 

measurement results. Therefore distances may not always be ideally chosen and some 

conversion factors had to be used. 

Figure 1 Measurement set up for time domain currents and magnetic fields 

Figure 2 Measurement set up for frequency domain magnetic fields

The actual current sensors and magnetic field sensor (both for horizontal and vertical 

field component) are shown in figure 3 and figure 4. 

Figure 3 Current sensors (time domain) 

Figure 4 Magnetic field sensor (time domain)

The bandwidths of the measurement systems are as follows: 

- current sensors; 10Hz-1.6MHz, 

- magnetic field sensor: 10Hz-1.8MHz. 

All data have been digitised and stored. 

3.3 Measured currents 

Figures 5, 6 and 7 show three of the measured currents in the track, during switching 

activities. Due to the measurement set-up, the load is very close to the measurement 

position and therefore the current measured will likely be the whole return current. No 

distribution towards earth wires or reduction via potential stray current has occurred at 

this point. This may not be the case in general, stray currents of up to 40% of the load 

have been found to appear in practise, see [EB]. 

The calculated and measured fields shown later in this paper, are related to these 3 

measured currents. 

1 Switch on of the line circuit breaker 

Figure 5 Measured current 1 in the rails during switching (switch on) 

In figure 5 one can see some clipping at the upper peaks. Most likely the signal is 

symmetrically and achieves peak values of about 120A. Main frequency components 

appear to be about 230kHz and 400kHz.



In figure 6 there is no clipping, the amplitude is just slightly lower, but the main 

frequency component is around 200kHz, although some higher frequency content is 

present as well. 

3 Switch on of the line circuit breaker. 


The pulse shape in figure 7 is a bit different, amplitude is about similar and the main 

frequency components in the order of 200kHz.

3.4 Simulation currents 

In order to calculate the fields as a result of the current in the track, we make use of 

some real track currents, which have been presented in the previous paragraph. Some 

simulation currents will be derived from the measured currents, in order to be used in 

the model to calculate the magnetic inductance. For the first approach only 1 main 

frequency component will be used as the basis for the simulation current (no curve 

fitting has been applied). The three respective simulation currents are presented in 

figures 8, 9 and 10. 


Figure 8 Simulated current 1 in the rails during switching (switch on) 


Figure 9 Simulated current 2 in the rails during switching (switch on)


Figure 10 Simulated current 3 in the rails during switching (switch on) 

4 Magnetic fields 

4.1 Model for calculating transient magnetic fields 

For the purpose here only a two conductor model is considered. The cross section 

geometry of the two currents in the railway conductors (for simplicity reduced to only 

catenary and rails) is shown in figure 11. 

Figure 11 Geometric configuration for the current and the observation point P 

For an infinite long line current of low frequency one can use the Biot-Savart formula 

to calculate the magnetic inductance at a certain distance d. E.g. for the vertical and 

horizontal components of the magnetic inductance that would be as follows (in which 

B (in T) is calculated as 

I 

B 

0 

H and H ): 

2 r

Table 1, Calculated magnetic inductance (µT) 

Current B y (peak) B x (peak) d: 4.5 

10 -0.10 -0.38 h1: 3.58 

50 -0.52 -1.88 h2: -1.92 

100 -1.04 -3.77 

110 -1.14 -4.15 

120 -1.25 -4.52 

125 -1.30 -4.71 

The distances (d, h1, h2) are derived from the Luxembourg measurement set-up. 

In case the frequency under consideration is no longer low, but e.g. some transient 

phenomena is involved, the same Biot-Savart approach can still be applied, however 

retardation should be added, see figure 12, which shows a top view (note forward and 

return current are on top of each other). For a definition of low frequency, we propose 

the following consideration: 

The magnetic field of an infinitely long conductor (when using a Biot-Savart 

approach) is mainly caused by the contribution of the line elements in the direct 

vicinity of the observer. If this portion of length of the complete line is in the order of 

magnitude of the phenomena, which are studied, then time retardation becomes 

necessary. For the contribution of a piece between z=–A and z= +A of the infinite line 

in the z-direction formula (1) can be found: 

H 

Ie 

sgn z 

2 

partial 

e and 

with A r 

(1) 

2 2 

2 

4 r 

2 r 

1 

1 

r 

z 

2 

A 

A 

I 

1 

1 

r 

A 

2 

Using formula (1) we can find the frequency limit, where retardation becomes 

necessary: 

f r 

(2) 

c 

r 

2 

2r 

2 

1 

c 

fraction of wavelength 

speed of light 

with : 

fraction of total magnetic field 

distance of observer 

When we use formula (2) with the following data: =0.25 (quarter wavelength) 

=0.95 (95 % of the field in observation point) and r=5m (distance) and c=3 x 10 8 m/s 

we find f r = 2.5 MHz. For instance for a distance of 60 m we find f r = 210 kHz.

Figure 12 Retardation principle 

When retardation has to be applied, the current has to be considered place dependent. 

For the vertical component of the magnetic inductance the equation becomes: 

By( t) 

A 

10 6 ( 4 ) 

l2 

l1 

d 1 d 

s 2 d 2 s 2 d 2 

h1 2 d 2 percentage 

d 

h2 2 d 2 I1 s t 

s 2 d 2 

where A is the current amplitude, d is the distance between the track and the 

observation point P, h1 and h2 are the heights of the conductors (see figure 11) and c 

is the speed of the wave, I1 (x,t) describes the current function in the space-time 

domain and s is the integration variable. The percentage variable is introduced to be 

able to do calculations for situations where the return current may not be exactly equal 

to the forward current, due to current in the soil. Here we concentrate on the vertical 

component, since the available measurements provide vertical component data only. 

We do not have to integrate from – to + over the current path, since the 

contribution of the far away conductors to the inductance in point P is negligible. The 

integration interval, from l1 till l2, will have to be related to the time duration of the 

current pulse and the propagation speed. 

In case: 

- we use a characteristic currents, as shown in figures 8, 9 and 10 as input 

current for a simple 2 conductor model, as indicated in figure 11, and 

- we use the retardation principle, as indicated in figure 12, 

we can calculate a corresponding magnetic inductance. 

In order to compare the calculated fields with the measured one, we use the 

parameters of the measured situation in Luxembourg. The parameters would be d = 

4.5m, H1 = 3.58m and H2 = -1.92m. The length over which the integration takes 

place is from –1000m to +1000m from the observation point (using Biot-Savart 

equations). Further it is assumed that I2 = 100% of I1, meaning that none of the 

current runs return via the soil but all remain in the above ground conductors. 

Note that the return current (I2) is drawn above the forward current in figure 11, but 

this is just for definition purposes, the actual position is below I1. 

c 

ds

4. 2 Calculated magnetic fields 

The calculated vertical magnetic inductances, based on the simulated rail currents are 

shown in figures 13, 14 and 15. 


Figure 13 Calculated magnetic inductance 1 during switching (switch on) 


Figure 14 Calculated magnetic inductance 2 during switching (switch on)


Figure 15 Calculated magnetic inductance 3 during switching (switch on) 

4.3 Measured Magnetic Fields (time domain) 

To compare the calculation of the magnetic inductance due to the transient currents 

with the measured values, we present the measured magnetic inductance at that 

particular position. It shows the vertical component of the magnetic inductance, 

measured at the same cross section where the track current was measured. Again three 

samples (figures 16, 17 and 18). 


Figure 16 Measured magnetic inductance 1 during switching (switch on)


Figure 17 Measured magnetic inductance 2 during switching (switch on) 


Figure 18 Measured magnetic inductance 3 during switching (switch on)

4.4 Measured Magnetic Fields (frequency domain) 

During the switching events, a spectrum analyser has been measuring simultaneously 

(but over a longer time period). This antenna was set up at a distance to the - current 

measurement of 15.5m and the measuring bandwidth was larger as well (9kHz- 

30MHz), see figure 19. 

Figure 19 Measured spectrum magnetic field in frequency domain 

Maximum values appear to be in the range of 80-85dB V/m. Note that the measured 

value depends on the used measurement bandwidth. The calculated spectrum of 

measured magnetic inductance 1 is shown in figure 20. 

Figure 20 Calculated spectrum of measured time domain field

Maximum values here are in the order of 100-105dB V/m, but these values where 

measured at 4.5m distance. A conversion from dB A/m to dB V/m has been 

performed by inserting the 51.5dB value. Note that the bandwidth of the time domain 

measurement chain is limited to 1.8MHz and the resolution of the stored data also 

limit the reliable frequency content, therefore a full comparison is impossible. The 

main result however, remains that the time domain analysis shows slightly higher 

values than the frequency domain measurements (even when corrected for the 

difference in distance (correction according to [EN50121]); about 13-19dB gives 93- 

104dB V/m for the frequency domain measurements). This is likely to be due to the 

measurement principle; time domain focuses on 1 event and frequency domain 

sweeps over the measurement range (in a maximum hold acquisition mode) and may 

“miss” certain peak values. Although in this particular case the difference is not that 

big. 

5 Comparisons 

For comparison the calculated minimum and maximum values (all values in T) are 

compared to the measured values in the following table (note; the number of decimals 

suggest more accuracy than actually achieved). 

Table 2, comparison between measured and calculated values 

Current Measured 

Minimum 

Measured 

Maximum 

Calculated 


Calculated 

Maximum 

Calculated 

Without* 

1 -1.12 0.96 -0.63 0.72 1.25 

2 -0.57 0.73 -0.61 0.49 1.04 

3 -0.86 1.27 -0.66 0.67 1.1 

* calculated without the retardation 

From the table we conclude that the calculated values are within a factor of 2 (6dB) of 

the measured values. However, this is also true for the non-retarded calculation, which 

tends to produce values on the high side. 

One aspect should not be forgotten here; as indicated retardation starts to play a role 

from a certain frequency range upwards. In this particular case the measured values 

are still on the lower end of the frequency range (200-400kHz) such that retardation 

may not improve the model results. As indicated earlier, for a short distance from the 

current, we expect retardation to be required for frequencies over 2.5MHz. 

Another point to be considered is the distance of the measuring point towards the 

currents. Since for larger distances away from the current path, the length of the line 

over which the current will contribute to the field value at the observation point P will 

increase, the frequency (at which the effects of retardation become visible) will drop. 

Though not yet significant, this can be seen in the following table, in which for 

simulated current number 2 the observation point P is set at 30m from the track. Note: 

we have no measured data in the Luxembourg series for this situation. 

Table 3, calculations for a larger distance (30m) 

Current Measured 


Measured 

maximum 

Calculated 


Calculated 

Maximum 

Calculated 

without* 

2 n.a. n.a. -3.2 * 10 -3 2.6 * 10 -3 7 * 10 -3 

* calculated without the retardation

6 Conclusion 

With a relatively simple model, which incorporates retardation, the order of 

magnitude of the magnetic inductance due to a transient current can be calculated. 

Based on measurements performed in a railway system in Luxembourg, we estimate 

that with this model fields can be calculated within a factor of 2 of the actual values. 

Further evaluation, based on new measurement data gathered during a 4 months 

measurement period in the new 25kV system of the Havenspoorlijn in the 

Netherlands, can be used to check the validity of this approach for establishing 

maximum magnetic inductance values near transient currents. 

In addition, a translation from these fields to disturbance voltages in cables (based on 

[Vance] approach), will be a useful tool to address EMC questions of railway lines 

near offices or industrial type of installations. This however, will be dealt with in a 

future publication.

7 Acknowledgments 

The paper is based on work performed for Rob Dirven of High Speed Line South 

Organisation (HSL-Zuid organisatie) in the Netherlands. We would like to thank also 

the kind co-operation of Jeannot Fürpass, Guy Müller and Jules Majeres of the 

Chemin de Fer Luxembourgeois (CFL) during the measurements in Luxembourg. 

8 References 

[EB] 

[EN50121] 

[railway measurements] 

[travelling waves] 

[Shinkansen] 

[Vance] 

Alphen van G., H. Smulders, “Messungen im 

Autotransformernetz der CFL und Überprüfung mit 

SimspoG”, Elektrische Bahnen 98 (2000) 7, pp. 242-248. 

2000. 

CENELEC, EN50121, Railway applications, 

Electromagnetic compatibility, September 2000. 

Smulders H., R. de Graaff, M. Janssen, G. van Alphen, 

“Measurement Systems for AC Power Supply Systems”, 

RTS Railway Traction Systems Conference, Capri, Italy, 

Proc. II, pp. 139-159, May 15-17, 2001. 

Math Bollen, On travelling waves based protection of highvoltage 

networks, PhD thesis, Eindhoven university of 

technology, 1989 

Takehiko Kawamura, Yoshishige Yoshida, Radio 

disturbance wave due to high-speed electric vehicles, QR 

of RTRI, vol 33, no 3, August 1992. 

E.F. Vance, Coupling to shielded cables, Wileyinterscience 

publication, USA, 1978.

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