IEEE Electrification Magazine - September 2016 - 20

rail fasteners, and track slab systems, but they are
demanding on computational power and memory, so
such models cannot be extended easily to entire systems,
including trains. Models assuming homogeneous
structure and soil and using partial differential equations

Insulated
Sleeper Fastener

Running
Rail

may also be adopted, including those that assume the
electrical properties of track layers (longitudinal and insulating resistance), but usually assuming a current source
model for the train. Similarly, local variability and defects
may be introduced by using lumped parameter models or
hybrid models (mixing lumped and distributed circuits),
which can benefit from both approaches.
Limits for stray current phenomena are different,
specified both on the source and the victim side. The EN
50122-2 specifies a maximum of 2.5 mA/m of track current leakage, while the EN 50162 gives a limit of 200 mV
for the impressed potential on concrete installations
(depending on the type of soil and chemicals).

Stray Current
Collector Cable

Examples
Reinforcing
Bars

Induction on Wayside Cables
for 25-kV 50-Hz Systems

Surrounding
Soil

In principle, induction is proportional to the length of parallelism, but, in practice, there may be significant deviations depending on the relative position of victim cables
and return circuit discontinuities. Also, linear proportionFigure 2. The simplified scheme of stray current problems from track
through soil to external victim.
ality with frequency may be violated, especially at system
resonances. This was demonstrated and analyzed for some 2 ×
25-kV, 50-Hz autotransformer lines,
IB
IB
IB
IB
AT IB
IB
IB
considering victim cables of variESS Q
G
D
A AT
M
ous lengths (between about 40 m
36 + 790 38 + 290 39 + 790 41 + 290 42 + 790 44 + 290 45 + 790
and 4 km) (Figures 3 and 4).
42 + 554
As anticipated, equipotential
bonding inside the return circuit,
represented by impedance bonds
8
(IBs), is relevant. The worst case is
Train Locations
not with the vehicle staying among
or close to the victim pairs but
1
when the vehicle is at least one IB
away from the last pair. The resoFigure 3. The victim cables of various lengths and train return-current injection points. Pairs are
numbered from 1 to 8, starting from the longest pair. Train locations are marked by a black
nance observed around 1,800 Hz is
square, impedance bonds are indicated by a vertical dash and IB.
typical of the autotransformer
spacing of many lines and increases the longitudinal voltage above
102
103
the ideally linear relationship by
102
more than an order of magnitude,
101
101
with significant impact on track cir0
100
10
cuits and other devices operating
-1
-1
10
10
around the resonance frequency.
-2
10
10-2
Cable-loading impedance, Z l , is
10-3
10-3
relevant, with larger values bring10-4
ing the cable to an isolated, or float10-5 1
10-4 1
10
102
103
104
10
102
103
104
ing, condition, maximizing the
Frequency (Hz)
Frequency (Hz)
induced voltage. The influence for
(a)
(b)
low Z l = 30 W and high Z l = 1, 200 X
Pair 1
Pair 2
Pair 3
Pair 4
for cables of various lengths from
Pair 5
Pair 6
Pair 7
Pair 8
1-4 km is considered in Figure 5,
showing cables beginning aligned
Figure 4. The normalized induced voltage for 1 A of return current at (a) position D and
(b) position Q.
with IB (position I, similar to the

I E E E E l e c t r i f i c ati o n M agaz ine / SEPTEMBER 2016

44 + 233

44 + 270

43 + 631
4

43 + 231

42 + 332
42 + 555

290
40 + 29

432
41 + 4

Voltage (V)

39 + 850

Buried Steel Pipe

Table of Contents for the Digital Edition of IEEE Electrification Magazine - September 2016