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2020 IEEE KhPI Week on Advanced Technology (KhPIWeek)
199
Application of IEEE 1459-2010 for the power
investigation a traction substation transformer
secondary voltage
Oleh Todorov
Institute of electromechanics, energy saving
and automatic control systems
Kremenchuk Myhailo Ostrohradskyi
National University
Kremenchuk, Ukraine
ORCID 0000-0001-5703-6790
Olexii Bialobrzheskyi
Institute of electromechanics, energy saving
and automatic control systems
Kremenchuk Myhailo Ostrohradskyi
National University
Kremenchuk, Ukraine
ORCID 0000-0003-1669-4580
Sulym Andrii
State Enterprise
'Ukrainian Scientific
Railway Car Building
Research Institute'
Kremenchuk, Ukraine.
ORCID 0000-0001-8144-8971
Abstract — Today, with a steady increase in the number of
consumers in which semiconductor converters are available, the
nonlinear distortions value in electricity is increasing. Assessment
of the electricity quality in traction networks is a problem related
to the complexity of energy processes mathematical formalization
in unballanced and non-sinusoid terms. Therefore, there is a need
to find a calculation method with simple implementation and high
informativeness indicators. The purpose is in the power
components investigation of the secondary busbars a traction
substation transformer, using the standard of IEEE 1459 - 2010.
Guided by order of determining the instantaneous power
components, regulated by standard IEEE 1459-2010, using the
Fourier transform, the power values for each of the secondary
voltage phases a three-phase transformer and the three phases as
a whole were calculated. It is established that during the
calculation as indicators reflecting of unballanced three-phase
transformer mode, is use only fundamental harmonic components.
This does not take into account the transition effect of pair
harmonics and multiples of three harmonics, respectively, on the
negative and zero sequences. It is noted, that the reactive power is
calculated only by the fundamental harmonic. The higher
harmonics reactive power is not included in recommended for
definition. The results can be used in electrical energy control and
metering systems, as motivating, to take steps to maintain of
electricity quality required level at the metering point.
Keywords — traction substation transformer, power, voltage,
current, phase, fundamental harmonic, non-sinusoidal, unbalanced
I. INTRODUCTION
Considering the interconnectedness value of electricity
generation, transmission, distribution and consumption
processes, given the complexity and branching a power supply
system, the issue of improving energy metering is very important.
The increase of electricity use in transport leads to growth at the
such consumers share. There is a significant pace in the country
electrification of both the magistral railways and the industrial
enterprise railways. The transport unit is a locomotive, is
powered by a DC or AC contact network and is a single-phase
load. The connection point of this load to the contact network is
always changing, as is the power consumption mode.
Complicating this process, the semiconductor converters
widespread use in locomotives traction complex. In addition,
with the implementation of AC contact network, use a specific
connection of transformers on secondary voltage side.
In the electric power analysis, the importance to reactive
power is given, which in turn is a compound indicator, in its
determination accuracy [1]. Researchers [1], as a several methods
comparison result of reactive power determination, note
significant differences of the final results. With the best method
of reactive power calculation for traction systems power losses,
authors is noted the calculation method proposed by S. Fryze.
And as an reactive power used indicator [2], the usual calculation
of cos(φ) is not enough, and it is better to use tg(φ), since with a
slight change in the power factor from 0,95 to 0,96 the coefficient
tg(φ) can change from 0,36 to 0,30. To combat with low power
factor, developing semiconductor converters control system,
which are provide reactive power low level [3], but use of its
determination traditional order.
Today in Ukraine widely used indicators and their normal and
maximum permissible norms are regulated by the standard
GOST 13109-97, while an important parameter as current is not
taking into account. As noted in [4], neglecting the permissible
deviation values leads to a number of problems, one of which is
the DC systems values determination. In general in situations
with low voltage distortionsand sufficiently current large
distortions in the conversion process, the conclusion leads, that
the standard main task is not so much the electricity improvement
as the technical selection under electricity distortions. Study [4]
authors note, that taking into account such value as the current
total harmonic distortion is necessary in the electricity quality
determining.
To improve the traction substations work quality, it is also
necessary to take into account the unbalance influence, that
occurs already during the electricity transmission from traction
substation to main grid. As a studies result [5] the reliability of
using the harmonic ratio coefficient was determined, by which it
is possible to determine the unbalance degree for a DC traction
network transformer. In addition it is noted, that the main
network unbalance affects the redistribution of power between
phases [6].
To analyze the energy installation or system mode are use
methods based on instantaneous power spectral analysis [7]. This
approach allows the instantaneous power use as a certain criterion
for the electrical engineering complex controllability [8]. Some
researchers pay close attention to the distortions, which
accompany the energy transfer process and to some extent on
/20/$31.00 ©2020 IEEE
978-1-6654-0501-0
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2020 IEEE KhPI Week on Advanced Technology (KhPIWeek)
200
energy conversion process affect [9]. Studies are perform using
current and voltage signals Fourier analysis.
The different approaches analysis to the traction networks
indicators estimation creates a problem related to the complexity
of energy processes mathematical formalization in unbalanced
and non-sinusoidal terms. Therefore, there is a need to find a
calculation method with simple implementation and high
informativeness of indicators.
The purpose is in the power components investigation of the
secondary busbars a traction substation transformer, using the
standard of IEEE 1459 - 2010.
II. STATEMENT OF BASIC MATERIAL
A. Traction network section construction and transformer
mode parameters measurement
Investigation object is the three-phase transformer TDN-
16000/110/10kV secondary voltage buses (Fig. 1.) of alternating
current traction substation. Transformer primary winding is
connected to the 110kV switchgear, with phases
, ,
ABC
to
which currents correspond
, ,
A B C
I I I
. The 10 kV secondary
winding is connected to a three-wire traction network with an a
phase as a zero wire and two load phases b and c.
Consumers in the contact network are single phase industrial
autonomous electric locomotive OPE1A, on which the ODCE-
8000/10 traction transformer is installed. The regulation of
locomotive movement mode is provided by the RSB-6000
rectifier unit. Changing the number of locomotives railroad haul,
the movement schedule, loading and unloading of dumpers cause
a traction substation loading schedule are complicated. The
controlled rectifiers operation of RSB installation leads to non-
sinusoidal current and voltage distortion of transformer
secondary winding busbars. The use a transformer Δ secondary
winding circuit may, in turn, partially compensate asymmetry,
but not entirely. Current and voltage measurements were made
using a Fluke 434 electric energy quality monitoring device.
Current and voltage waveforms is shown for a time certain
amount in Figure 2.
Fig. 1. Transformer connection circuit 110/10 kV
Fig. 2. Transformer operating mode time diagram: a) current, b) voltage
When choosing the power components calculating method,
given the complexity of accurately determining a reactive power
and distortion power, the calculation procedure according to
IEEE 1459 – 2010 is selected [10]. To date, this standard has
comprehensively addressed the distortions power defining issue,
as well as proposing the basic power values that should be guided
in three-phase networks analysis.
B. Measurements results analysis on the transformer
secondary voltage busbar a traction substation.
The power components calculation is performed on currents
and voltages basis, which are represented by Fourier series in
the form
( )
( ) ( )
( )
0
1
0
1
( ) sin
cos sin ,
n n
N
n n
n
N
a b
n
ft A A n t
A A n t A n t
=
=
=+ + =
= + +
ω ϕ
ω ω
where
n
– harmonic number;
N
– harmonics maximum
number;
0
A
– constant component of voltage or current;
n
A
–
n-th harmonic amplitude;
ω
– angular frequency;
п
ϕ
– n-th
harmonic phase shift;
n
a
A
– n-th harmonic cosine component
amplitude;
n
b
A
– n-th harmonic sine component amplitude.
Constant component
0
A
, the cosine
n
a
A
and the sine
n
b
A
components for n harmonics are determined in a known
manner:
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2020 IEEE KhPI Week on Advanced Technology (KhPIWeek)
201
0
0
1
( ) ;
T
A f t dt
T
=
0
0
2
( ) cos( ) ;
2
( )sin( ) ,
n
n
T
a
T
b
A f t n t dt
T
Af t
п t dt
T
=
=
ω
ω
where
T
– period duration;
( )
f t
– voltage or current function.
Harmonics amplitudes
n
A
and their phase shift
п
ϕ
are
related to the orthogonal components amplitudes:
2 2
; arctan .
n
nn
n
b
n a b п
a
A
A A A A
= + =
ϕ
Harmonic amplitude calculation results, currents and
voltages for the case under study are shown in Figure 3. The
current load distribution by the first harmonic (Fig. 3 a) by the
phases is uneven. What causes an voltage unbalance (Fig.3.b)
by the basic harmonic. In relation to the first harmonic
amplitude, current harmonics amplitudes are much larger as
opposed to the voltages.
Fig. 3. Harmonic amplitude distribution (discrete spectrum): a) current, b)
voltage
In future, analysis is performed for all three phases for
certain unification purpose, we will use indexing of the phase
Ф, assuming that it assumes values А, В, С. Phase сurrent and
voltage will be considered further by separating of fundamental
(first) harmonic from others in the form:
1 1 0
1 1 0
1
1
1
1
() ( ) ( )
sin( ) cos( ) ;
( ) ( ) ( )
sin( ) cos( ) ,
h h
h h
ФФ Фh
Фm Фu Фm Фm Фu
h
Ф Ф Фh
Фm Фi Фm Фm Фi
h
u t u t u t
U t U U h t
i t i t i t
I t I I h t
≠
≠
= + =
=+ + + −
= + =
=+ + + −
ω ϕ ω ϕ
ω ϕ ω ϕ
where 2,3, 4
h N
=
K – harmonic number;
Ф
– phase
, ,
ABC
;
0
Фm
U – voltage constant component;
h
Фm
U – h-th harmonic
voltage amplitude;
h
Фu
ϕ
– h-th harmonic voltage phase shift;
0
Фm
І
– current constant component;
h
Фm
І
– h-th harmonic
current amplitude;
h
Фі
ϕ
– h-th harmonic current phase shift.
Standard [6] architecture is based on the power indicators
analysis, which can be represented in the diagrams form Fig. 4.
Fig. 4. Powers distribution diagram IEEE 1459-2010: a - three-phase circuit for
phases, b - three-phase circuit as a whole.
Parameters such as active power (P) and nonactive power (N)
are basic. In both scheme, we can distinguish the common
fragments of the apparent power (
S
) distribution by the
fundamental apparent power (
1
S
) nonfundamental apparent
power (
N
S
). In both cases, the power due to the higher harmonics
is divided by the current distortion power (
I
D
), the voltage
distortion power (
U
D
) and the harmonic apparent power (
H
S
).
Which in turn is distributed in both cases by the harmonic active
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2020 IEEE KhPI Week on Advanced Technology (KhPIWeek)
202
power (
H
P
) and the harmonic distortion power (
H
D
). It should
be noted that the reactive power of the nonfundamental
harmonics is not used in this distribution.
Due to the presence of asymmetry (unbalance) in three-phase
networks, the diagrams left branches on Figure 4 a and b is differ.
Unlike in (Fig. 4 a), in (Fig. 4 b) the fundamental apparent power
is additionally divided by the fundamental positive-sequence
apparent power (
1
S
+
) and the fundamental unbalanced power (
1
U
S
).
Consider the power components distribution order for each
phase separately (Fig. 4a). Apparent power:
2 2 2 2
1
N
S UI P N S S
= = + = + ,
where
U
- voltage RMS value;
І
- current RMS value, which
are defined as follows:
2 2
0 0
1 1
( ) ; ( )
T T
U u t dt I i t dt
T T
= =
In turn, the fundamental apparent power:
2 2
1 1 1
S P Q
= + ,
is determined by the respective active and reactive power:
1 1 1 1 1 1
1 1
cos( ); sin( )
m m m m
P U I Q U I
= =
θ θ
,
where
1
m
U
– voltage fundamental harmonic RMS value;
1
m
I
–
current fundamental harmonic RMS value;
1
θ
– difference of
voltage and current fundamental harmonic phase shift
1 1 1
u i
= −
θ ϕ ϕ
.
Nonfundamental apparent power
2 2 2
N I U H
S D D S
= + +
In this expression, the first two components depend on the
total harmonic distortion of voltage (
U
THD
), of current (
I
THD
) and are defined as follows:
1 1
;
Uh І h
THD U U THD
І І
= = .
Accordingly, the distortions power caused by
nonfundamental harmonics of voltage and current are calculated
as:
1 1
;
U U I I
D S THD D S THD
= = .
Similarly determined, the harmonic apparent power, due to
nonfundamental harmonics of current and voltage
1
H U I
S S THD THD
= .
Harmonic active power
0 0
1
cos( )
h h h
Hm m m m
h
P U I U I
≠
= +
θ
,
where
h
m
U
– nonfundamental harmonic voltage RMS value;
h
m
I
– nonfundamental harmonic current RMS value;
h
θ
–
voltage and current nonfundamental harmonics difference
phase shift
h h h
u i
= −
θ ϕ ϕ
. As a result, the harmonic distortion
power is determined by the current and voltage nonfundamental
harmonics
2 2
H H H
D S P
= − .
For the case under consideration, the powers calculation
results for each phase are summarized in Table I.
Generalized indicators defining for a three-phase system as a
whole raises some difficulties. Thus there is a need to use the
Fortescue transformation. This transformation is complexly
linked to the instantaneous power determining process and its
performance [11].
TABLE I. CALCULATIONRECOMMEND RESULTS OF PHASE VALUES,
SYSTEMS WITH NON-SINUSOIDSL CURRENT AND VOLTAGE
Value Phase
A B C
,
S MVA
0,594 0,356 0,83
1,
S MVA
0,594 0,396 0,83
,
N
S MVA
0,295 0,189 0,292
,
H
S kVA
12,198 12,036 19,338
,
P MW
-0,042 0,319 0,508
1
,
P MW
-0,042 0,319 0,507
,
H
P kW
0,665 0,475 -0,003
,
N Mvar
0,592 0,157 0,657
1,
Q Mvar
-0,592 -0,158 -0,657
,
I
D Mvar
0,291 0,183 0,264
,
U
D Mvar
0,122 0,046 0,122
,
H
D kvar
12,179 12,027 19,388
PF
-0,07 0,897 0,611
1
PF
-0,071 0,896 0,611
1
N
S S
0,497 0,533 0,351
Consider the power components distribution order for a three-
phase scheme [9] (Fig. 4b). Effective apparent power
2 2 2 2
1
3
e e e e eN
S U I P N S S
= = + = +
where
e
U
– effective voltage;
e
І
– effective current, which are
in turn defined by expressions.
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203
Effective voltage
2 2 2 2 2 2
11 1
2 2
1
1
( )
3
,
e AB BC CA ABh BCh CAh
e eh
U U U U U U U
U U
= + + + + + =
= +
where
1 1 1
, ,
AB BC CA
U U U
– fundamental harmonic linear voltage
RMS value; , ,
ABh BCh CAh
U U U – nonfundamental harmonic
linear voltage RMS value;
1
e
U
– fundamental effective voltage;
eh
U
– nonfundamental effective voltage.
Effective current:
2 2 2 2 2 2 2 2
1 1 1 1
0.577 ( ) ,
e A B C Ah Bh Ch e eh
I I I I I I I I I
= + + + + + = +
where
1 1 1
, ,
A B C
I I I
– fundamental harmonic currents RMS
value;
, ,
Ah Bh Ch
I I I
– nonfundamental harmonic currents RMS
value;
1
e
I
– fundamental effective current;
eh
I
–
nonfundamental effective current.
Fundamental effective apparent power:
2 2
1 1 1 1 1
3
e e e U
S U I S S
+
== + .
The first of which – fundamental positive-sequence
apparent power, determined accordingly fundamental positive-
sequence active (
1
P
+
) and reactive (
1
Q
+
) powers:
2 2
1 1 1
S P Q
+ + +
= + .
To determine fundamental positive-sequence active and
reactive power, it is necessary to determine the voltage and
current positive-sequence RMS values:
1 1
1 1
0
1
cos( )
9
T
Am Au
U U t
T
+
= − +
ω ϕ
1 1 1 1
2
1 1
2 4
cos cos ;
3 3
Bm Bu Cm Cu
U t U t dt
+ − + + − +
π π
ω ϕ ω ϕ
1 1
1 1
0
1
cos( )
9
T
Am Ai
I I t
T
+
= − +
ω ϕ
1 1 1 1
2
1 1
2 4
cos cos
3 3
Bm Bi Cm Ci
I t I t dt
⋅ ⋅
+ − + + − +
π π
ω ϕ ω ϕ
.
Determine the phase shift, currents and voltages of the
positive sequence
1 1
1
1 1
1 1 1 1
1 1 1 1
cos( )
arctan sin( )
2 4
cos cos
3 3
;
2 4
sin sin
3 3
Am Au
u
Am Au
Bm Bu Cm Cu
Bm Bu Cm Cu
U
U
U U
U U
++
=+
+ + + +
+ + + +
ϕ
ϕϕ
π π
ϕ ϕ
π π
ϕ ϕ
1 1
1
1 1
1 1 1 1
1 1 1 1
cos( )
arctan sin( )
2 4
cos cos
3 3
.
2 4
sin sin
3 3
Am Ai
i
Am Ai
Bm Bi Cm Ci
Bm Bi Cm Ci
I
I
I I
I I
++
=+
+ + + +
+ + + +
ϕ
ϕϕ
π π
ϕ ϕ
π π
ϕ ϕ
and their difference
1 1
1
.
u i
+ + +
= −
θ ϕ ϕ
Then the active and reactive power of the positive-sequence:
(
)
(
)
1 1 1 1 1 1 1 1
cos ; sinP U I Q U I
+ + + + + + + +
= =
θ θ
.
As a result, determined the fundamental harmonic
unbalanced power:
2 2
1 1 1
U
S S S
+
= − .
Current effective distortion power in three-phase circle:
1 1 1 1
3 .
eI eh e e eh e e eU
D U I S U U S THD
= = =
Voltage effective distortion power in three-phase circle:
1 1 1 1
3 .
eU e eh e eh e e eI
D U I S I I S THD
= = =
Effective harmonic power:
1
3 .
eH eh eh e eU eI
S I U S THD THD
= =
As a result, the effective nonfundamental effective apparent
power:
2 2 2 2 2
1
eN e e eI eU eH
S S S D D S
= − = + +
Separately allocate harmonic active power:
( )
0 0
1
cos( )
h h h
H Фh Фm Фm Фm Фm Ф
Ф Ф h
P P U I U I
≠
= = +
θ
.
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2020 IEEE KhPI Week on Advanced Technology (KhPIWeek)
204
Due to this, the harmonic distortion power determined:
2 2
eH eH H
D S P
= + .
Additionally, power factor are determined
e
P
PF
S
= ,
and fundamental positive-sequence power factor
1
1
1
P
PF
S
+
+
+
= .
The calculation results for the case under study are listed in
Table II.
TABLE II. RESULTS OF RECOMMEND VALUES FOR THREE PHASE
SYSTEMS WITH NON-SINUSOIDAL CURRENT AND VOLTAGE
Combined Fundamental power Nonfundamental
power
1,93
e
S MVA
=
1
1,889
e
S MVA
=
11,63
S MVA
+=
10,954
U
S MVA
=
0,395
eN
S MVA
=
0,023
eН
S MVA
=
0, 786
P MW
= 10,795
P MW
+=
1,137
Н
P kW
=
1,762
N Mvar
= 11, 423
Q Mvar
+=−
0,377
eI
D Mvar
=
0,116
eU
D Mvar
=
0,023
eН
D Mvar
=
0, 407
PF = 1
0, 488
PF +=
1
1
0,586
U
S
S+=
1
0,209
eN
e
S
S=
III. CONCLUTIONS
Using the definition power components standard IEEE 1459
- 2010 for the analysis of energy processes on the traction
substation transformer secondary voltage busbar, opens the way
for a mode thorough analysis. Rational use of indicators for
each phases separately and indicators for three phases together.
It is established that the reactive power is calculated only by
basic harmonic. The higher harmonics reactive power is not
included in the indicators recommended for determination.
Defined for the mode, which is being analyzed, that phase
A nonactive power in significantly exceeds the active power, at
the expense fundamental reactive power. This causes a power
factor close to zero.
It is established that only indicators by fundamental
harmonics are used in the calculation of indicators showing the
unbalance of the three-phase transformer mode. This does not
take into account the effect of the pair harmonics and harmonics
of multiple three transition, respectively, in the negative and
zero sequences.
From the obtained results it follows, that most of the power
is reactive power, as evidenced by the 0.407 power factor and
there is a large level 0.586 of unbalance. The additional load
formed by harmonics is a significant 0.209.
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