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

[email protected]

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


19,1Km


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


Impedance Z

P [

Ohm

]

0

10

20

30

40

50

60

70

0

2

4

6

8

0

1

2

3

4

x 104


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.


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.



located at Pinhal Novo.



located at the beginning of the catenary.


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.


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


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.


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

harmonic characterization of railway supply systems · 1 harmonic characterization of railway...

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