The article presents the methods of determination and analysis of the continuance of harmonics in the supply current of a modern subway vehicle with an asynchronous converter power. Knowledge of the harmonic content of the supply current is a very important part of the study, allowing the vehicle to operate. In order to determine the harmonic voltages and currents, a computer model of the test vehicle and the power supply and subway substations was created. The simulation was created using the SimPowerSystem library, which is part of the Matlab program. The calculation results were compared with the measurement

Popczyk, Marek

Włodarczyk, Jakub

Zając-Domański, Waldemar

Portal Czasopism Naukowych (E-Journals)

*	 Ph.D.	Eng.	Waldemar	Zając-Domański,	M.Sc.	Eng.	Jakub	Włodarczyk,	M.Sc.	Eng.	Marek	Popczyk,	
Department	of	Traction	and	Traffic	Control,	Faculty	of	Electrical	and	Computer	Engineering,	Cracow	
University	of	Technology.
WALDEMAR	ZAJĄC-DOMAŃSKI,	JAKUB	WŁODARCZYK,	MAREK	POPCZYK*
DETERMINATION	OF	HARMONICS	 
IN	CURRENT	OF	THE	POWER	SUPPLY	 
OF	UNDEGROUND	RAILWAY	TRACTION	VEHICLE	
WYZNACZANIE	HARMONICZNYCH	PRĄDU	ZASILANIA	
POJAZDU	TRAKCYJNEGO	METRA
A b s t r a c t
The	article	presents	the	methods	of	determination	and	analysis	of	the	continuance	of	harmonics	
in	 the	 supply	 current	 of	 a	modern	 subway	 vehicle	 with	 an	 asynchronous	 converter	 power.	
Knowledge	of	the	harmonic	content	of	the	supply	current	is	a	very	important	part	of	the	study,	
allowing	 the	 vehicle	 to	 operate.	 In	 order	 to	 determine	 the	 harmonic	 voltages	 and	 currents,	
a	computer	model	of	the	test	vehicle	and	the	power	supply	and	subway	substations	was	created.	
The	simulation	was	created	using	 the	SimPowerSystem	 library,	which	 is	part	of	 the	Matlab	
program.	The	calculation	results	were	compared	with	the	measurement.
Keywords: current harmonics, traction drives, power supply system, SimPowerSystem
S t r e s z c z e n i e
W	artykule	przedstawiono	metody	wyznaczania	i	analizy	przebiegów	harmonicznych	w	prą-
dzie	zasilania	nowoczesnego	pojazdu	metra	z	napędem	przekształtnikowym	asynchronicznym.	
Znajomość	 zawartości	 harmonicznych	 w	 prądzie	 zasilania	 jest	 bardzo	 ważnym	 elementem	
badania	dopuszczającym	pojazd	do	eksploatacji.	W	celu	wyznaczenia	harmonicznych	napięć	
i	prądów	powstał	model	komputerowy	badanego	pojazdu,	sieci	zasilającej	i	podstacji	metra.	Do	
symulacji	została	użyta	biblioteka	SimPowerSystem	będąca	częścią	programu	Matlab.	Wyniki	
obliczeń	porównano	z	pomiarem.
Słowa kluczowe: harmoniczne prądu, napędy trakcyjne, system zasilania, SimPowerSystem
TECHNICAL TRANSACTIONS
ELECTRICAL ENGINEERING
1-E/2016
CZASOPISMO TECHNICZNE
ELEKTROTECHNIKA
DOI: 10.4467/2353737XCT.16.040.5302
178
1. Introduction
The	article	discusses	a	vehicle	power	system.	The	main	circuit	of	a	modern	traction	
vehicle	of	a	subway	railway	was	described,	and	the	parameters	of	replacement	diagrams,	
necessary	 for	 simulation,	 were	 set.	An	 attempt	 was	 made	 to	 compare	 the	 spectra	 of	
harmonics	 in	 the	 supply	 current	 in	 different	 positions	 of	 the	 vehicle	 relative	 to	 the	
substation,	 vehicle	 speed	 and	 propulsion	 torque.	 These	 results	 were	 compared	 to	 the	
normative	limit	values	for	current	supply	harmonics.	It	is	very	important	for	the	electric	
and	electronic	environment	of	the	subway	railway.	The	power	system	is	very	different,	
compared	 to	 the	 conventional	 rail	 system:	 subway	 railway	 traction	 substations	do	not	
have	filters,	there	is	the	so-called	third	rail,	there	are	short	distances	between	stops	and	
there	is	heavy	traffic.
2. Discussion of the main circuit of a modern subway car
In	modern	 traction	 vehicles,	 the	main	 elements	 of	 any	 vehicle	 powered	 by	 a	 direct	
current	 network	 are	 traction	 converters	 (current	 inverters),	 asynchronous	 squirrel	 cage	
motors,	braking	resistors	and	the	input	filter.	The	current	received	from	the	pantograph	of	
the	vehicle	is	transmitted	to	the	main	switch	protected	against	both	overvoltage	(spark	gap)	
and	overload	(fuse	and	overcurrent	relay).	The	next	element	in	the	vehicle	is	the	LC	filter	
composed	of	the	inductive	element	L	and	the	capacitance	element	C.	It	plays	an	important	
role:	it	blocks	signals	within	a	certain	frequency	range	or	allows	them	to	pass,	and	compacts	
defined	harmonics.	 It	 is	an	 input	circuit	of	 the	 inverter	acting	as	a	 traction	converter.	 In	
order	 to	 transform	 the	 current	 received	 by	 the	 pantograph	 of	 the	 traction	 line,	 traction	
inverters	are	used.	In	most	applications	in	modern	subway	vehicles,	inverters	are	used	to	
power	 the	 traction	motors.	Motors	 and	 their	 rotational	 speed	 are	 formed	by	 an	 inverter	
using	a	scalar	adjustment	of	 the	output	voltage	frequency,	by	changing	 the	shape	of	 the	
amplitude	and	frequency	of	the	basic	three-phase	harmonic	voltage	wave	produced	by	the	
inverter.	In	order	to	precisely	control	the	torque	of	the	motor	in	the	inverter	drive,	vector-
based	control	is	used,	based	on	the	spatial	vectors	representing	voltage,	magnetic	fluxes,	
motor	currents.	These	vectors	are	rotating	vectors	in	the	variable	complex	plane.	Modern	
traction	 inverters	 are	 built	 in	 the	 IGBT	 technology	 (Insulated	Gate	Bipolar	Transistor),	
insulated	gate	 transistors	 are	 characterised	by	high	power,	 high	breakdown	voltage	 and	
high	speed	switching.	Control	of	IGBT	consists	in	changing	the	potential	of	the	insulated	
gate.	The	traction	inverter,	depending	on	the	type	of	vehicle	and	power	system,	can	feed	
each	 traction	motor	 independently	 or	 as	 a	 group	 of	 four	motors,	 for	 example.	The	first	
solution	allows	for	the	optimal	use	of	traction	properties.	It	has	an	independent	string	of	
power	supply	for	each	traction	motor	(independent	power	and	control).	The	calculations	
were	performed	for	the	data	in	Table	1.
179
Ta b l e 	 1
Number	of	engines 16
Type	of	traction	motors 1TB2006-0GA02	power	160	[kW]
Continuous	power 2240	[kW]
Supply	voltage 750	[V]	DC/	third	rail
Type	of	converter	drive
Supply	voltage
SITRAC	G	750	D	570/800M	IGBT	
from	300	[VDC]	to	950	[VDC]
Main	inverters
The	output	frequency	from	0	to	200	[Hz]	Rated	input	current	
of	600	[A]	Output	voltage	three-phase	3×570	[V]	AC	
Fig.	1.	Diagram	of	the	main	circuit	of	a	modern	subway	car
3. Designated parameters of the replacement system
Each	element	of	 the	diagram	of	 the	 replacement	system	requires	 the	calculation	of	 its	
parameters	for	a	precise	image.
3.1.	The	determined	parameters	of	replacement	system	
Replacement	reactance	of	XGPZ	source	determined	by	the	formula	(1):	
 X
U
SGPZ Z
=
∗ [ ]1 1
2. Ω   (1)
180
where:
XGPZ	 –		 reactance	of	the	main	point	of	the	power	supply,	
U	 –	 rated	voltage	in	[V],
SZ –	 short-circuit	power	GPZ	at	the	rails	of	the	power	supply	[VA],
for	the	following	data	
we	obtain:
XGPZ –		 2.0625	[Ω]
U –		 15	[kV]
SZ		 –	 120	[MVA]
L50 –	 6.568	[mH]
3.2.	Resistance	and	inductance	of	power	cables	
For	cable	line	of	NHKXS	type	3×	(1×240	mm2)	with	a	length	of	1.000	[m],	we	obtain:
RP –	 0.0786	[Ω]
LP –	 0.265	[mH]
3.3.	Replacement	parameters	for	a	triple-coil	transformer	
Replacement	parameters	for	the	transformer	were	calculated	for	the	data	from	Table	2.
T a b l e 	 2
COILS
I II III
Rated	voltage	in	[kV]	Un 15.75 0.665 0.665
Losses	in	copper	APcu	in	[kW] 19 19 19
Short	circuit	voltage	for	each	pair	of	coils:
AUZI-II	=12	[%]
AUZI-III	=12	[%]
AUZII-III=	12	[%]
Idling	current	in	[%]	Io 0.36
Losses	in	iron	APfe	in[	kW] 3.6
Rated	power	for	all	coils	[kVA]	Sn 2400
The	following	results	were	obtained	from	the	calculations:
•  Resistance	of	coils	GNY:	0.155	[Ω],
•  Inductance	of	coils	GNY:	0.02	[H],
•  Resistance	of	lateral	branch:	813.165	[Ω],
•  Inductance	of	lateral	branch:	32.695	[H],
•  Resistance	of	coil	DNA:	3.685×10–4		[Ω],
181
•  Inductance	of	coils	DNA:	1.173×10–5	[H],
•  Resistance	of	coil	DNY:	1.106×10–3	[Ω],
•  Inductance	of	coils	DNY:	1.173×10–4	[H].
Fig.	2.	Replacement	diagram	of	a	triple-coil	transformer
3.4.	Set	of	diodes
A	set	of	diodes	consists	of	two	6	pulse	rectifier	bridges,	connected	in	parallel;	by	using	
two	transformers	with	different	internal	connections,	phase	angles	of	voltages	supplying	the	
bridges	are	shifted	from	each	other	by	an	angle	n/6,	so	that	we	incidentally	obtain	a	12	pulse	
rectifier.	The	diagram	of	the	set	of	diodes	is	shown	in	Figure	3.
Fig.	3.	Diagram	of	12-pulse	set	of	diodes
182
3.5.	Traction	Network	Model
It	was	assumed	that	the	network	between	the	substation	and	the	vehicle	will	be	represented	
by	one	four-pole	with	the	parameters	based	on	the	assumed	distance	between	objects.	Based	
on	the	data	and	calculations,	the	following	parameters	of	the	subway	traction	network	model	
were	obtained	(Table	3).
T a b l e 	 3
Parameters of the traction network model
Assumptions Unit	parameters	of	the	network
Third	rail	traction	line	type	with	section	6601	mm2
Double	track	line	with	tracks	isolated	from	each	other	
Rail	paths	type	S49
Power	supply	cable	with	section	2×625	mm2
Resistance	Rsm =	31.4	mΩ/km	
Inductance	Lsm =	0.695	mH/km	
Capacity	Csm =	2.6	nF/km
4. Simulation of power and control system in SimPowerSystem
Calculated	or	assumed	parameters	were	used	to	build	a	complete	replacement	system	of	
the	vehicle	 together	with	its	power	system.	This	system	was	created	in	SimPowerSystem,	
which	 is	 Simulink	 library	 version	 7.3.	 SimPowerSystem	 provides	 ready-made	 electrical	
components	 and	 power	 electronics	 (sources,	 converters,	motors,	 etc.).	This	 simplifies	 the	
creation	of	the	system,	as	there	is	no	need	to	create	a	mathematical	model	of	the	motor	or	
inverter	 etc.,	 and	 the	very	 structure	of	 the	 system	consists	of	 an	 appropriate	 combination	
of	blocks	and	application	parameters	the	item	requested	by	the	program.	However,	a	direct	
connection	between	the	elements	is	possible	only	within	the	library.
SimPowerSystem	 also	 has	 in	 its	 library	 blocks	 responsible	 for	 the	 display	 of	 the	
measured	signals,	such	as	the	Scope	block,	which	corresponds	to	the	virtual	oscilloscope	
and	allows	a	real-time	preview	and	recording	of	the	measured	signal.	A	great	advantage	
of	SimPowerSystem	libraries	are	embedded	signal	analysis	tools,	including	FFT	analysis,	
and	a	 tool	 for	determining	 the	 impedance	of	 a	 component	 as	 a	 function	of	 frequency.	
These	tools	were	used	to	calculate	the	characteristic	of	the	impedance	of	the	input	filter	of	
the	vehicle	as	a	function	of	frequency,	as	well	as	to	determine	the	harmonics	in	the	input	
current	 of	 the	 vehicle	 in	 this	 article.	During	 simulation,	 the	 SimPowerSystem	 library	
may	use	one	of	three	methods	of	the	system	solutions:	continuous,	discrete,	phase,	and	
also	of	the	algorithm	of	ideal	commutation,	which	improves	the	efficiency	and	reduces	
the	 simulation	 time	 for	 the	 systems	with	elements	of	a	high	switching	 frequency.	The	
continuous	method	has	a	high	accuracy	by	changing	the	size	of	the	sampling	step,	and	
it	is	used	to	capture	the	dynamics	of	the	system.	The	discreet	method	allows	to	control	
the	accuracy	of	the	simulation	by	selecting	the	time	step.	In	the	simulation	of	the	vehicle	
and	the	network,	the	method	used	was	the	discreet	method	with	integration	step	equal	to	
Ts	=	10	[ps].
183
Fig.	4.	The	full	diagram	of	the	circuit	system	built	in	Simulink:	green	indicates	the	power	system	
along	with	the	power	line,	light	brown	indicates	rectifier	transformers,	and	blue	indicates	rectifiers
Fig.	5.	Diagram	of	the	control	system	of	traction	motor	of	the	vehicle,	built	in	Simulink,	orange	indi-
cates	an	inverter,	blue	indicates	a	pulse	generator,	and	red	indicates	blocks	of	traction	motors,	green	
indicates	the	measurement	of	various	parameters	with	‘Scope’	blocks
184
5. Charts obtained from the simulation
Fig.	6.	Starting	from	top	to	bottom,	the	continuance	as	a	function	of	time,	the	Uab	voltage	of	ASM	
motor,	the	phase	currents	Ia,	Ib,	Ic	of	ASM	motor,	the	angular	velocity	omega	of	ASM	motor,	 
Te	torque	of	ASM	motor	for	a	vehicle	speed	of	20	km/h
Fig.	7.	From	the	top:	charts	of	voltage	on	a	substation	with	a	resistant	type	of	current	load	 
Iobc	=	1000	[A]	and	harmonics	occurring	at	this	voltage
185
Fig.	8.	From	the	top:	charts	of	voltage	of	the	power	supply	of	the	vehicle	versus	time	and	harmonics	
spectrum	for	a	speed	of	20	km/h
Fig.	9.	From	the	top:	charts	of	the	input	current	Idc	of	the	inverter	versus	time	of	the	power	supply	of	
the	vehicle	and	harmonics	spectrum	for	a	speed	of	20	km/h
186
6. Charts obtained from actual measurements of the drive of the subway vehicle
Fig.	10.	From	the	top:	charts	of	voltage	of	the	power	supply	of	the	vehicle	versus	time	and	harmonics	
spectrum	for	a	speed	of	20	km/h
Fig.	11.	From	the	top:	chart	of	the	input	current	Idc	of	the	inverter	versus	time	of	the	power	supply	of	
the	vehicle	and	harmonics	spectrum	for	a	speed	of	20	km/h
187
7. Conclusions
The	 article	 presents	 the	method	 of	 calculation	 of	 the	 harmonics	 in	 the	 power	 supply	
system	 of	 the	 subway	 railway	 vehicle.	 The	model	 of	 the	 vehicle,	 the	 power	 system	 and	
traction	substation	was	built	in	Simulink	and	can	be	used	to	determine	the	current	harmonics	
in	order	 to	evaluate	and	allow	the	vehicles	 to	operate.	Due	to	 the	exact	calculation	of	 the	
exemplary	parameters	of	the	system,	the	model	accurately	reflects	the	phenomena	occurring	
during	the	cooperation	of	the	vehicle	with	a	substation	and	makes	the	absolute	error	A	low	–	
about	2%	.The	results	of	the	calculations	show	the	dominant	role	of	harmonics	coming	from	
substations	 because	 substations	 operate	 without	 filters.	 There	 are	 also	 present	 harmonics	
resulting	from	the	operation	of	the	inverter	and	there	may	occur	harmonics,	which	are	a	result	
of	the	phenomenon	of	the	“avalanche	of	harmonics”.
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Determination of harmonics in current of the power supply of undeground railway traction vehicle

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Determination of harmonics in current of the power supply of undeground railway traction vehicle

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