Harmonic Characterization of Railway Supply Systems · 1 Harmonic Characterization of Railway...
Transcript of Harmonic Characterization of Railway Supply Systems · 1 Harmonic Characterization of Railway...
1
Harmonic Characterization of Railway Supply
Systems
Hugo Miguel Rodrigues Simões
Instituto Superior Técnico
Lisbon, Portugal
Abstract — The introduction of power electronics in the
locomotives’ traction systems contributed to the harmonic
content increase in railway networks. The harmonic
pollution can cause significant voltage fluctuations which
result from resonance excitations. These voltage
fluctuations can activate the protection systems in traction
units or substations. For these reasons, it is necessary to
evaluate voltage harmonics and to model catenaries, to
identify the harmonics’ effect in the network operation.
In this context, a simple railway network is considered as a
case study (a catenary section powered by a substation).
Furthermore, its methodology is used to characterize the
pantograph impedance of a real railway supply network.
Keywords: electrical traction, railway supply network, harmonic
analysis, resonance frequencies.
I. INTRODUCTION
In the second half of the XX century, the interest in railways
structures was small due to the increase of individual transport
use (cars, trucks, airplanes) since, apparently, it wasn’t
possible to achieve the same velocities and versatility.
However with the mass introduction of these transports
society need to make a change, thus returning the railways to
gain importance due to public traffic congestion.
Associated with this railway infrastructure’s development has
been the increasing use of power electronic traction units.
However, there are some aspects to warn because this is a
major source of harmonic content. These harmonics propagate
in the catenary and may excite network resonances [1]. The
resonance excitation can cause problems such as equipment
overheating, interference with communication lines and
command and control systems, operating errors in protection
systems, among others [2].
Therefore there is a need to model the impedance along the
catenary and warn the impedance and resonance frequencies
variability with the rolling stock’s position and the supply
network topology [3]. A precise knowledge of this impedance
allows the proper sizing of filters on traction units or in the
railway structure and the frequency response of the
converter’s control systems [4].
This paper develops an analytical expression of impedance
seen by the rolling stock on a “case study” railway supply
network. Afterwards it’s the study of impedance and
resonance frequencies of the Lisbon North-South’s railways
structure, between Ponte Santana and Águas de Moura.
Finally there is the variability study of infrastructure’s
resonance frequencies when considering the presence of
rolling stock along the catenary and the introduction of a
passive tuned filter in the infrastructure which allows the
reduction of resonance excitations.
II. RAILWAY SUPPLY NETWORK MODELING
The characterization of a railway supply network means to
model the impedance seen by the rolling stock (by its
pantograph) anywhere in the network, commonly named
pantograph impedance. Catenaries (transmission lines) are
seen as a two-port network, expressed in matrix form in (1).
This transmission matrix relates voltages and currents in the
emission point and the receptor point [5].
[
] [
] [
] (1)
The matrix elements are given by:
(2)
(3)
(4)
and define the characteristic impedance and propagation
constant, respectively.
√
(5)
√( )( ) (6)
in which , , e correspond to resistance, inductance,
capacity and conductance per length unit, respectively.
A. Case Study – Definition
It is considered a catenary section fed by a substation (in one
of the terminals) which has an equivalent impedance , a
2
traction unit at position . The catenary has a length and it’s
terminated by impedance in the substation opposite end.
Figure 1 illustrates this configuration and in which is the
pantograph voltage in the traction unit. is considered to
be very high, in other words, the right terminal is open.
CatenarySection withlength l - x
VpCatenary
section with length x
ZSUB ZTER
ZL ZRVp
Substation TerminalTraction Unit
x
l
Figure 1 – Configuration of the railway section in study;
equivalent model; equivalent simplified model.
Since the catenary is terminated by an impedance in one
end and with an impedance in other one, it can be
established the relations (7) and (8).
(7)
(8)
Table 1 presents the necessary data to determine the
pantograph impedance in this simple supply network. These
data were obtained through the company Comboios de
Portugal (CP).
Table 1 – Data used in the case study simulation.
18 6,9 0,18 1,6 13,3
1) Pantograph Impedance
Using the catenary’s transmission matrix, defined in (1), and
the relations (7) and (8) it can be determined the pantograph
impedance (11). This impedance is achieved through a two
impedances parallel: the equivalent impedance seen at the left
side (the substation’s side) and the equivalent impedance
seen at the right side (opposite side of the substation).
( )
( ) (9)
( )
( ) (10)
The matrix elements A, B, C and D have two possible indexes,
L and R, which correspond respectively to the catenary section
of the traction unit’s left side with length ended by the
substation and the catenary section of the traction unit’s right
side with length ended by the impedance .
(11)
Considering the right terminal with a very high impedance and
replacing matrix entries in (9) and (10) by (2) – (4), and
expressions can be simplified in (12) and (13).
(12)
( )
( ) (13)
The pantograph impedance is determined by replacing (12)
and (13) in (11). Note that, for a given supply network
(characterized by , , , , and ), the pantograph
impedance is a function of frequency (by , and ) and
of traction unit’s position (by ).
Knowing that the pantograph depends on the frequency and
the traction unit position in the catenary section, Figure 2
presents the amplitude of this impedance has a function of
these two parameters.
Figure 2 – Pantograph impedance as function of frequency and
traction unit position along the catenary section.
It is observed that the resonance frequency is independent of
the traction unit position. Thus, its value only depends on the
catenary parameters (supply network topology) and the
equivalent impedances on both terminals. A wider range of
frequencies identifies other resonance peaks and verifies that,
whatever the traction unit’s position in the catenary section is,
the resonance frequencies will not change.
2) Resonance Frequencies Estimation
For the resonance frequencies’ direct determination, or its
estimation, expressions (12) and (13) are retaken. The
pantograph impedance is achieved by the parallel of and
. After some mathematical simplification, the result is:
( )
(14)
The resonance frequency matches pantograph impedance’s
maximum, which corresponds to the least denominator of
0
5
10
15
0
2
4
6
0
2
4
6
8
10
x 104
Position [Km]Frequency [kHz]
Impedance Z
P [
Ohm
]
3
(14). This minimum would be zero if there were no losses in
the system. It is considered that the system losses are
negligible to estimate the resonance frequency, as desired.
This approach results in, for the line parameters:
√ (15)
√
(16)
and as resonance condition:
(17)
The resonance condition was obtained considering the
following hypotheses:
The line is ideal (perfect conductors and dielectric);
The substation equivalent impedance, , is purely
inductive.
The second hypothesis is realistic since the substation
impedance is mostly determined by the short-circuit
impedance of the substation transformer. Note that, for the
power transformer used, the resistive component is very small
compared to the inductive (leakage inductance).
Approaching the hyperbolic tangent, in (17), by the first five
terms of its Taylor series expansion and considering the no
losses’ expression, the resonance condition results in (18).
( )
( )
( )
( )
√ ⁄
(18)
It is possible to find a polynomial equation which is a function
of frequency to determine the resonance frequencies
associated to this supply network. Using (15) and (18) and
knowing that , the desired polynomial equation can
be determined.
[( ) √ ] [( )
( )
]
[( )
( )
]
[( )
( )
]
[( )
( )
]
√ ⁄
(19)
Coupled with a variable transformation , expression
(19) allows the resonance frequency direct determination.
Remember that this expression was determined by developing
the first five terms in the Taylor series.
Table 2 shows the resonance frequencies values, considering
the Taylor series expansion of the hyperbolic tangent to the
second, third, fourth and fifth term. This estimated value,
obtained by the direct solution of (19), shows a gradual
approach to the solution found by frequency sweep of
impedance (14). It is conceded a maximum error of 3% in the
polynomial equation solution.
Table 2 - Resonance frequency obtained by direct determination
and sweeping the frequency of the pantograph impedance.
Resonance frequencies determination [kHz]
Direct solution Frequency
sweep of
pantograph
impedance
Up to 2nd
term
Up to 3rd
term
Up to 4th
term
Up to 5th
term
2,93 2,67 2,56 2,51 2,45
Figure 3 graphically shows the pantograph impedance’s
amplitude and argument. It demonstrates the existence of two
resonances with different characteristics, one of which
corresponds to a situation of maximum impedance (in
2,45kHz) and the other to a minimum impedance (in
6,02kHz). In this study, all analyses focus the maximum
impedance situations, which are associated to maximum
catenary voltage.
Figure 3 – Frequency analysis of the pantograph impedance’s
amplitude and argument. It considers the traction unit in the
middle of the catenary.
The analysis focuses on the first resonance peak because,
according to the information obtained, it is the nearest to the
critical harmonic frequencies from the traction units [6].
Figure 4 – Pantograph impedance’s amplitude and argument
obtained when varying the traction unit position.
The zero value found for the impedance argument confirms
that it is a resonance situation. It confirms that the resonance
frequency is equal for any position of the traction unit in the
0 1 2 3 4 5 6 7
100
105
Frequency [kHz]
Impedance Z
P [
Ohm
]
0 1 2 3 4 5 6 7-100
-50
0
50
100
Frequency [kHz]
Arg
um
ent
ZP [
º]
0 2 4 6 8 10 12 14 16 180
5
10x 10
4
Position [Km]
Impedance Z
P [
Ohm
]
0 2 4 6 8 10 12 14 16 18-100
-50
0
50
100
Position [Km]
Arg
um
ent
ZP [
º]
4
catenary section. Accordingly, note the independence of (19),
whose solution is the estimated resonance frequency, from the
traction unit position in the catenary.
B. Sensitivity Analysis of the Resonance Frequencies
The sensitivity analysis of the resonance frequency is made for
two parameters: catenary length and substation’s equivalent
impedance.
These two parameters may change in any supply network and,
therefore, it is important to perform this analysis to measure
the resonance frequency modifications for a given change,
both in the catenary length and the substation equivalent
impedance.
1) Sensitivity to the substation equivalent impedance
Figure 5 shows the resonance frequency values obtained for
different substation inductances. Note that the resonance
frequency is reduced as the substation inductance increases.
Figure 5 – Resonance frequency variation versus substation
inductance variation.
2) Sensitivity to the catenary length
Figure 6 shows the resonance frequency values obtained for
different catenary lengths. Note that the resonance frequency
decreases with the catenary length increasing. As the catenary
length increases, the resonance frequency tends towards a
constant value.
Figure 6 - Resonance frequency variation versus catenary length
variation.
Through Figures 5 and 6 it can be concluded that the first
resonance peak is more sensitive to catenary length changes
than to substation inductance changes.
However, both analyses have a mutual characteristic, the
increase of the catenary length and of the substation
inductance cause a resonance frequency decrease.
III. CHARACTERIZATION OF RAILWAY SUPPLY NETWORK OF
LISBON NORTH-SOUTH LINE: PONTE SANTANA – ÁGUAS DE
MOURA
This section analyzes the railway supply network of Lisbon
North-South line, from Ponte Santana to Águas de Moura. It
focuses the pantograph impedance, seen by the rolling stock,
anywhere in the supply network.
Figure 7 shows the considered network. The catenary is fed by
Fogueteiro’s substation and includes the section between
Ponte Santana and Águas de Moura, beyond Barreiro and
Lagoa de Palha branches in Pinhal Novo.
0 km
Ponte
Santana
17,7 km
Fogueteiro
36.8 km
Pinhal
Novo
49.6 km
Setúbal
65.9 km
Águas
de
Moura
2,1 km
Lagoa da
Palha
15,4 km
Barreiro
SST
2,2 km
Alvito
7,3 km
Pragal
Figure 7 - Current scheme of railway supply network of Lisbon
North-South line (2012).
The analyzed network corresponds to a double track railway
line with the exception of the section Setúbal – Águas de
Moura. It is considered that the catenaries have characteristic
parameters with constant value, which are shown in Table 3
[7].
Table 3 - Electrical parameters of the Lisbon North-South
catenary.
R [Ω/km] L [mH/km] C [nF/km]
Simple Track 0,18 1,6 13,3
Double track 0,09 0,89 26,6
The catenary is modeled as a two-port network, as previously
mentioned, and Fogueteiro’s substation is represented by a
equivalent inductance – which accounts for the short-
circuit inductance of the substation transformer and the
network inductance – and by a 25kV voltage source
, as shown in Figure 8.
Vsub
Lsub
Figure 8 – Equivalent model of Fogueteiro’s substation.
-50 -40 -30 -20 -10 0 10 20 30 40 50-10
-5
0
5
10
15
20
Variation of Lsub
[%]
Variation o
f re
sonance f
requency [
%]
Frequency Sweep
Direct Solution
-80 -60 -40 -20 0 20 40 60 80 100-50
0
50
100
150
200
250
Variation of catenary length [%]
Variation o
f re
sonance f
requency [
%]
Frequency Sweep
Direct Solution
5
Table 4 shows the inductances values considered in the
substation model [7].
Table 4 - Parameters related to the substation representation in
terms of electrical circuits.
L [mH]
6,8
2,7
9,5
For computation purposes, it is considered that the terminals
of North-South line (Ponte Santana and Águas de Moura) and
of Barreiro and Lagoa da Palha branches are open.
A. Methodology
The pantograph impedance is determined by separating the
catenary in four sections and its equivalent model is presented
in Figure 9. The pantograph impedance, along each of the
sections, is determined by the parallel of the left and right side
equivalent impedances seen by the traction unit. This division
is possible because they are homogeneous sections.
Double Track Section
17,7Km
ZTER
Double Track Section
19,1Km
Double Track Section
12,8Km
Single Track Section
16,3Km
ZSUB ZBRANCHES
Fogueteiro Pinhal Novo Setúbal
ZTER
Figure 9 – Railway supply network – equivalent model.
B. Resonance frequencies
The resonance frequencies may suffer some changes if the
supply network topology changes.
This railway structure had different construction and operation
stages until reaching the current topology shown in Figure 7.
Over time there has been a growing network in which the
catenary’s minimum length was 17,7 km, in 1999.
The resonance frequencies may also change depending on the
rolling stock number and location in the supply network.
1) Railway Supply Network Growth
Lisbon North-South supply network has experienced several
changes that modify its electrical topology, and as a result,
may change the pantograph impedance. These changes are a
consequence of the network’s growth and it changes the
resonance frequencies initially defined by the supply network
topology.
The pantograph impedance is calculated while considering the
branches influence and dismissing their existence. Figures 10
and 11 show this impedance in each situation.
Figure 10 – Frequency analysis of the pantograph impedance. It
doesn’t consider the branches influence.
Figure 11 - Frequency analysis of the pantograph impedance. It
is considered the branches influence.
Figure 12 compares the resonance frequencies obtained in
both situations, considering and dismissing the branches
influence.
Figure 12 – Frequency analysis of the pantograph impedance
seen in Fogueteiro.
0
10
20
30
40
50
60
70
0
2
4
6
8
0
1
2
3
4
x 104
Position [Km]Frequency [kHz]
Impedance Z
P [
Ohm
]
0
10
20
30
40
50
60
70
0
2
4
6
8
0
1
2
3
4
x 104
Position [Km]Frequency [kHz]
Impedance Z
P [
Ohm
]
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
0
101
102
103
104
Frequency [kHz]
Impedance Z
P [
Ohm
]
Without branches
With branches
6
The resonance frequencies are determined by the network
topology and, for this reason, it is found that the resonance
frequencies are modified when it counts or disregards the
branches’ existence.
Table 5 summarizes the resonance frequencies associated to
the railway infrastructure in its various stages of construction.
The frequency range considered was from 50Hz to 8000Hz.
Table 5 – Resonance frequencies obtained along the various
stages of the supply network’s construction and operation.
Catenary from
Ponte Santana to:
Fogueteiro
(1999)
5 km to the South of
Fogueteiro (2001)
Resonance
frequencies [Hz]
1900 1800
6600 5100
Catenary from
Ponte Santana to:
Setúbal
(2004)
Águas de
Moura
(2008)
Águas de
Moura +
branches
(2012)
Resonance
frequencies [Hz]
1150 950 800
2250 2050 2050
4300 3200 2600
6500 4750 4000
- 6550 4800
- - 6400
- - 7700
In particular note, in Figure 13, the approximation of the two
lower resonant frequencies defined by the supply network,
over the years. Both resonances get close to the most
significant harmonic frequencies provided by traction units
operation (between 950Hz-1450Hz and 2050Hz-2650Hz).
2000 2002 2004 2006 2008 2010 20120
1000
2000
3000
4000
5000
6000
7000
8000
Year
Fre
quency [
Hz]
1st resonance
2nd resonance
2650Hz
2050Hz
1450Hz
950Hz
Figure 13 - Comparison between the two lower resonance
frequencies, over the years.
2) Rolling stock distribution along the catenary
The rolling stock presence on a railway supply network also
affects the resonance frequencies initially defined by its
topology. From an electrical point of view, it represents the
introduction of equivalent impedance in the network at the
point where the traction unit is located. In other words, there is
a change in the supply network topology.
It is considered a distribution of rolling stock in which there
were excitations of resonances and overvoltage flowing in the
catenary. Figure 14 shows the distribution of rolling stock.
0km
Ponte
Santana
17,7km
Fogueteiro
36.8km
Pinhal
Novo
49.6km
Setúbal
65.9km
Águas
de
Moura
2,1km
Lagoa da
Palha
15,4km
Barreiro
SST
2,2 km
Alvito
7,3km
Pragal
1 unidade motora
2 unidades motoras
12,3km 19km 22km 32,5km 38,5km 41,4km 46,4km59,4km 65,9km
Figure 14 – Railway supply network scheme with the rolling
stock distribution in the overvoltage situation.
At the overvoltage instant, the pantograph impedance seen in
Fogueteiro is shown in Figure 15 and 16 being, respectively,
ignored and considered the branches existence.
Figure 15 – Frequency analysis of the pantograph impedance
seen in Fogueteiro. Disregards the branches influence.
Figure 16 - Frequency analysis of the pantograph impedance seen
in Fogueteiro. Considers the branches influence.
0 500 1000 1500 2000 2500 3000 3500 4000 4500 500010
-1
100
101
102
103
104
Impedance [
Ohm
]
Frequency [Hz]
With rolling stock
Without rolling stock
0 500 1000 1500 2000 2500 3000 3500 4000 4500 500010
-1
100
101
102
103
104
Impedance [
Ohm
]
Frequency [Hz]
With rolling stock
Without rolling stock
7
It is found that, in any of these situations, the resonance
frequencies increase with the rolling stock presence in the
supply network.
It is also noted that critical changes occur primarily in the first
two resonance frequencies, approaching these to the critical
harmonic frequencies from the traction units (around 1200Hz
and 2400Hz) [7].
C. Use of a passive tuned filter in the railway supply
network: preliminary analysis
In order to eliminate the resonance excitation, it is explored
the possibility of using a passive LC series filter in the supply
network or in the rolling stock. The aim is to warn the main
problems associated with the use of a filter.
The filter is tuned to 1200Hz and the filter’s parameters
dimensioned for this cutoff frequency are presented in Table
6.
Table 6 – Sized L and C parameters of the tuned filter.
17,59 1
1) Positioning the filter
It’s important to warn the filter location since it also affects
the resonance frequencies defined by the supply network.
Thus, it is determined the pantograph impedance observed in
Fogueteiro for various locations of the filter: in Fogueteiro, in
Pinhal Novo, at the beginning and at the end of the catenary.
These results were determined considering the current railway
supply network (Figure 7).
Figure 17 – Frequency analysis of the pantograph impedance in
Fogueteiro. Comparison of the results with and without the filter
located at Fogueteiro.
Figure 18 – Frequency analysis of the pantograph impedance in
Fogueteiro. Comparison of the results with and without the filter
located at Pinhal Novo.
Figure 19 – Frequency analysis of the pantograph impedance in
Fogueteiro. Comparison of the results with and without the filter
located at the beginning of the catenary.
Figure 20 – Frequency analysis of the pantograph impedance in
Fogueteiro. Comparison of impedance results with and without
the filter located at the end of the catenary.
After this impedance analysis it is possible to select the best
location of the filter, among those considered, for the removal
of the resonance frequencies, defined by the supply network,
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-1
100
101
102
103
104
Frequency [kHz]
Impedance [
Ohm
]
Without LC filter
With LC filter
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
0
101
102
103
104
Frequency [kHz]
Impedance [
Ohm
]
With LC filter
Without LC filter
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
0
101
102
103
104
Frequency [kHz]
Impedance [
Ohm
]
With LC filter
Without LC filter
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
0
101
102
103
104
Frequency [kHz]
Impedance [
Ohm
]
With LC filter
Without LC filter
8
from near the critical frequencies provided by traction units
operation.
Table 7 gathers the resonance frequencies obtained for
different locations of the tuned filter. Note that the results
obtained and the choice of the favorable position also depend
on the filter parameters sizing. The frequency range was
limited to 5000Hz.
Table 7 – Comparison between the resonance frequencies
obtained for the different locations of the filter.
Location of the
tuned filter
At the beginning of
the catenary
(0 Km)
Fogueteiro
(17,7 Km)
Resonance
frequencies [Hz]
650 750
950 1150
2450 2250
2850 2600
4100 4000
4900 4850
Location of the
tuned filter
Pinhal Novo
(36,8 Km)
At the end of the
catenary
(65,9 Km)
Resonance
frequencies [Hz]
600 500
1550 1150
2050 2150
2650 4100
4000 >5000
4800 -
It appears that the best position, among the ones analyzed, for
the filter installation is the beginning of the catenary. There is
no resonance between about 1000Hz and 2500Hz, and this is
the frequency range in which the harmonic content of the
traction units fits the most.
2) Operating the filter at the fundamental frequency
There are some issues that must be cautioned when choosing
the filter position to install which relate to its impedance at the
fundamental frequency (50Hz).
It was found that the LC series passive filter has a capacitive
character much more pronounced the lower the inductance
value , at the fundamental frequency.
The filter parameters can be modified while maintaining the
cutoff frequency at 1200Hz. Thus, with a new parameters
sizing, the supply network topology changes resulting in new
resonance frequencies. In other words, the best location for the
filter may be different from the previous one.
It is considered a new passive tuned filter, located at the
beginning of the catenary, whose parameters are shown in
Table 8.
Table 8 – New L and C parameters of the tuned filter.
175,9 100
Figure 21 shows the pantograph impedance seen in
Fogueteiro. It compares the resonance frequencies obtained
with both passive tuned filters.
Figure 21 – Frequency analysis of the pantograph impedance
seen in Fogueteiro. Comparison of impedance results with the LC
filter and the L’C’ filter.
With the new filter the first resonance occurs at 100Hz while
the second and third resonances almost don’t change. Both
filters cause, as expected, a significant decrease in the
infrastructure’s impedance in Fogueteiro near the cutoff
frequency.
3) Rolling stock equipped with tuned filter
The introduction of a tuned filter in the rolling stock has the
advantage of requiring smaller filters and costs overall.
However, it may require a more technical solution and
difficult to implement if it is found that changes in the traction
unit location (and in the filters), also changes the resonance
frequencies defined by the supply network topology.
D. Frequency analysis of the railway supply network with a
tuned filter and a certain rolling stock distribution
Considering the presence of the first tuned filter and the
distribution of rolling stock at the overvoltage instant, it is
determined the pantograph impedance anywhere in the supply
network. This impedance is presented in Figure 22.
Figure 22 – Frequency analysis of the pantograph impedance.
Considers a tuned filter at the beginning of the catenary and the
rolling stock distribution at the overvoltage instant.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
0
101
102
103
104
Frequência [kHz]
Impedância
Zp [
Ohm
]
Com filtro LC
Com filtro L'C'
0
10
20
30
40
50
60
70
0
1
2
3
4
5
0
0.5
1
1.5
2
x 104
Position [Km]Frequency [kHz]
Impedance [
Ohm
]
9
Figure 23 presents the pantograph impedance seen in
Fogueteiro comparing three situations from no filter and
rolling stock until the introduction of the filter and the rolling
stock in the infrastructure. It is considered the actual network
topology shown in Figure 5.
Figure 23 – Frequency analysis of the pantograph impedance
seen in Fogueteiro. Comparison of impedance results: without
filter and rolling stock; with filter and without rolling stock; with
filter and rolling stock.
Note that, with the filter introduction, the first resonance gives
rise to two resonances centered on the previous one. These
two resonances are maintained when the rolling stock
distribution is included in the supply network with the filter.
Also with the filter existence, the second resonance changes
significantly from 2050Hz to 2450Hz.
IV. CONCLUSIONS
The pantograph impedance determination had a simple
principle: for a given location of the traction unit, the
impedance seen by it is given by the parallel of the equivalent
impedance of the left and the right side of the traction unit.
With the theoretical development made for the case study, it
was found that resonance frequencies only depend on the
supply network topology. In other words, the resonances in a
supply network are equal for any traction unit position in that
network. Accordingly the same was found with the supply
network’s computer simulation.
The railway supply network of Lisbon North-South line’s
analysis had the main focus on studying the changes observed
in their resonance frequencies and how they change when it is
considered to be a certain rolling stock distribution in the
supply network and a tuned filter at the beginning of the
catenary. Over the years, there have been changes in
resonance frequencies defined by the supply network because
its topology has been changing. According to the distribution
of rolling stock that was studied, their presence causes an
increase in the resonance frequencies.
Within a preliminary analysis, one possible solution to nullify
the resonance excitation is the inclusion of a filter tuned to
1200Hz and located in the supply network. It is necessary to
warn the dimensioning of filter parameters and also its
location in the catenary because these variables affect the
resonance frequencies defined by the supply network. The best
position for the filter, among the studied locations, is the
beginning of the catenary because it allows the resonance
displacement outside the range 1000Hz – 2500Hz which
incorporates most of the harmonic content from traction units.
Therefore, the installation of the filter at the beginning of the
catenary is a viable solution, only for the analyzed rolling
stock distribution, because it is not guaranteed that the filter
fulfills its purpose if the distribution changes.
REFERENCES
[1] Joachim Holtz, Heinz-Jürgen Klein, “The Propagation of
Harmonic Currents Generated by Inverter-Fed Locomotives in
the Distributed Overhead Supply System”, IEEE Transactions
on Power Electronics, Vol. 4, No. 2, pp 168-174, April 1989.
[2] H. Lee, C. Lee, G. Jang, Sae-hyuk Kwon, “Harmonic
Analysis of the Korean High-Speed Railway Using the Eight-
Port Representation Model”, IEEE Transactions on Power
Delivery, Vol. 21, No. 2, pp 979-986, April 2006.
[3] M. Fracchia, A. Mariscotti, P. Pozzobon; “Track and
Traction Line Impedance Expressions for Deterministic and
Probabilistic Voltage Distortion Analysis”, IEEE Int. Conf.
Harmonics and Quality of Power, pp. 589-594, October 2000.
[4] A. Mariscotti; P. Pozzobon; “Synthesis of Line Impedance
Expressions for Railway Traction Systems”, IEEE
Transactions on Vehicular Technology, Vol. 52, No. 2, pp.
420-430, March 2003.
[5] J. A. Brandão Faria, “Electromagnetic Foundations of
Electrical Engineering”, Editora Wiley & Sons, UK, pp. 335-
355, August 2008.
[6] Rui Santo et al, “Relatório de Ensaio – Medição da
característica eléctrica – Sector Sul alimentado pela
Subestação do Fogueteiro – UQE3500 (Fertagus)”, REFER
EP, December 2011.
[7] A. Dente, J. Santana, P. Branco, T. Correia de Barros,
“Sobretensões no Circuito Intermédio de CC de Alimentação
dos Conversores de Tracção dos Alfa Pendulares (CPA
4000)”, IST, Setembro 2011.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
0
101
102
103
104
Frequency [kHz]
Impedance [
Ohm
]
Without LC filter and rolling stock
With LC filter and without rolling stock
With LC filter and rolling stock