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Application of IEEE 1459-2010 for the power investigation a traction substation transformer secondary voltage

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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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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;
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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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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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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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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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
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
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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... The power part of the dynamic voltage restorer consists of a positive-voltage transformer, a smoothing LC filter, a transistor converter and a capacitor in the constant voltage circuit (Fig. 1). To get an idea of the full power distribution in the power circuit of the dynamic voltage restorer, we will use the wellknown power calculation method [9] in which the full power of the phase: RMS I effective current value. In turn, the square of the total power consists of the square sum of active P, reactive Q and distortion power D: ...
... Accordingly, the power of distortion is determined [9] as follows: ...
... Todorov [20] investigated power components of the secondary buses of a traction substation transformer. Following the order of determination of instantaneous power 979-8-3503-8122-1/24/$31.00 ©2024 IEEE components as regulated by IEEE 1459:2010, using the Fourier transform, power values were calculated for each of the secondary voltage phase, a three-phase transformer, and all three phases together. ...
... A certain rationing of the indicators of the electric energy quality from the calculation methodology standpoint was car ried out based on the materials of studies [1] in the standard [3]. This standard is used to evaluate the electrical power com ponents in complex electrical systems [4], to correct the algo rithms for the operation of power active filters [5] and to deter mine the parameters of power circuit elements a power active filters [6]. Numerically, the power quality indicators are nor malized by the standard [7] for voltage and by the standard [8] for voltage and current. ...
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Purpose. Based on the instantaneous electrical power of a three-phase asymmetric system of sinusoidal periodic current, to determine positive, negative, zero-sequences active and reactive power, as well as invariance power factor. Methodology. In the unbalance case in three-phase electrical system, the electrical energy quality is evaluated by means on voltage and current positive, negative, zero-sequences. At the same time, similar components of active and reactive power have not received practical distribution. But it is precisely in terms of power that electricity is accounted for. The instantaneous power orthogonal components in the time domain are determined using the symmetrical components of voltage and current. Active, reactive powers of positive, negative and zero-sequences are allocated. The result obtained has the property of representativeness, which most of the known results lack. Findings. The three-phase system’s instantaneous power components are analytically determined, including the amplitudes of the oscillating power components. The need to take into account the oscillating instantaneous power components has been proven by means of a graphical interpretation of a special case of the three-phase system mode. As an integral indicator that takes into account the oscillating components of the three-phase system instantaneous power, its root-mean-square value over the repetition period is used. Originality. By calculating the transformer efficiency of the studied model according to the active power positive sequence and the same indicator according to the active power as a whole, it was established, that the component sequence separation affects the results of calculating the generalized indicators, including the power transmission system objects. This can lead to erroneous judgments about the efficiency of the specified facilities functioning. Practical value. The invariance power factor was used to characterize the electrical energy quality level of a three-phase sinusoidal current system in an unbalanced mode.
... При цьому існує ряд складових електричної потужності рекомендованих для спостереження, з урахуванням яких можливо детально розібрати склад електричної потужності мережі [13] - [14]. При роботі з системами моніторингу на основі даних величин, доводиться працювати з великою кількістю даних [15]. ...
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Мета роботи. Застосування статистичного аналізу на об’ємні вибірки даних параметрів споживання електричної енергії, для зменшення обсягу даних про потужності вузла мережі, які зберігатимуться. Методи дослідження. Використання методів статистичної обробки даних, в системі графічного програмування LabVIEW. Отримані результати. Електрична енергія є одним з видів енергії обсяги генерування, транспортування, розподілу та використання якої постійно зростають. На всіх зазначених етапах відбувається контроль параметрів швидкості зміни електричної енергії – потужності. Потужність характеризується певними параметрами що підлягають безперервному моніторингу. Зміна потужності в умовах промислових підприємств має складний характер з певними стохастичними складовими. Необхідність фіксації детальної інформації викликає зростання обсягу даних, які підлягають зберіганню. Як наслідок, виникає завдання обробки даних про обсяги електричної енергії та параметри електричної потужності зі зменшенням обсягу даних та збереженням інформативності. Ґрунтуючись на статистичній концепції нормального розподілу, в середовищі графічного програмування побудовано підсистему обробки даних на інтервалах вибірки активної та реактивної потужностей секції низької напруги знижуючої підстанції. З використанням показників характеристики нормального розподілу активної та реактивної потужностей, виконано аналіз їх напівдобових вибірок. Виділені інтервали на яких суттєво розрізняються показники нормального розподілу, що дозволило сформувати висновки про наявність режимів наближених до холостого ходу. Наукова новизна. Встановлено, що через складність охоплення великих проміжків часу за умови фіксації даних про параметри електричної потужності, виникає дилема щодо обсягу результуючої інформації та її деталізації, для уникнення втрат інформації запропоновано процедуру, що базується на законі нормального розподілу вибірки даних, та в тривалих процесах знижує обсяг результуючих даних, які підлягають зберіганню, з можливістю фіксації суттєвих відхилень за показниками ексцесу та асиметрії відповідної вибірки. Практична цінність. Застосовуючи в системі моніторингу при довгостроковому спостереженні за параметрами електричної потужності запропонований метод можливо значно зменшити кількість даних під час передачі основної інформації, рівня потужності та діапазону коливань, а також, за необхідності, використати додаткову інформацію про зміни в інтервалах спостереження, виражені через ексцес та асиметрію.
Conference Paper
The cable line is one of the main elements in the power transmission system, but due to the cable lines considerable length, monitoring the line condition and tracking its damage is a complex process. In practice, methods quite a variety are used to monitor the line condition, through monitoring the change in current and voltage in high-voltage cable lines with long distances, and control parameters using equivalent circuits. Study object is a short cable line, 6 km long, with a connected source of 6 kV, in a network with a non-linear load. Given its short-length, the overall changes in voltage and current will not have significant deviations between the input and output of the cable line. The main observation is carried out in the high frequencies area at a 2500 Hz frequency with the expectation of evident deviations in the current and voltage caused by the influence a non-linear load. By conducting two experiments, a line without damage and a line with damaged insulation, a number of deviations in the pulses change over time were revealed. The most evident deviations occur in the current, which is expressed due to a change in the main pulses amplitude and the significant appearance low-amplitude fluctuations between damaged phases under the influence of opposite-phase pulses.
Article
Purposes The purpose of this paper is to identify on the instantaneous electrical power basis of a nonsinusoidal periodic current three-phase asymmetric system, active and reactive positive, negative and zero sequence powers, taking into account higher harmonics. The main power theories, including those embodied in the IEEE 1459 standard, do not allow to evaluate some of power components. Design/methodology/approach A well-known fact is that the three-phase AC system total power with the symmetry of currents and voltages is constant. It corresponds to the electrical energy transfer process in a DC system. In this case, the electrical energy transmission can be taken as high quality. It has been established that the components of active and reactive powers are because of the product of current and voltage of unidirectional sequences. The orthogonal components of the oscillating power are because of the product of the voltage and current components of different sequences, with the exception of the zero sequence. Findings For an unbalanced nonsinusoidal mode of a three-phase system, the components of instantaneous power were defined, corresponding to the active and reactive positive and negative and zero sequences powers with the selection of the fundamental and higher harmonics. The active and reactive powers of sequences were divided into two categories – consumed and generated. Originality/value It is proposed to use the ratio of “interfere” power RMS value to the total power RMS value to assess the instantaneous power distortion.
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The development of electric power industry is accompanied by an increase in the number of consumers subjected to loads with nonlinear characteristics. The arising problem of the distortion of electrical energy that takes place when the mentioned consumers are in operation is partially solved by using means of improving the quality of electrical energy. The increase in the share of small generating plants that are placed in the nodes of consumers exacerbates the interaction of non-linear loads, forming additional parallel streams of electrical energy. Distorted electrical power is not an indication to account. Existing views on distorting power are amenable to criticism. In the well-known works, the proposals for the assessment of power using the quadratic norm and the quadratic norms of its components have been grounded. For the analysis of processes of formation the components of electrical power, a diagram of the simplest circuit containing a series-connected source of electromotive force, resistors and a diode is considered; also, the circuit was conditionally separated into a source and a consumer. The analysis of the power formation of each circuit element is performed with the use of the expression of current and voltage, as periodic functions represented by the trigonometric form of Fourier series. The power components are separated with the use of the known interaction of harmonic components of current and voltage of different orders. For the circuit elements, the power components formed by current and voltage harmonics of the same order are selected as well as power components formed by current and voltage harmonics of different orders, in which, in their turn, the power components are selected that have the same order as the first ones. The power formed by the action of the latter group is proposed to be attributed to the distorting power and to account its action by the corresponding quadratic norm. A numerical calculation has been performed with a use of the specified power component distribution. Time diagrams illustrate the process of interaction of the power components, which–in the case of the diode–leads to no change in power over time.
Article
Full-text available
Purpose: Determination of the analytical interrelation of Clarke and Fortescue transformation for an asymmetric sinusoidal system of currents of a three-phase four-wire network. Methodology: To find the way for the use of the direct, reverse and zero sequences as components of the power circulating in the intersection of the four-wire current line, a problem is set to determine the interrelation of Clarke (a-b-0) and Fortescue (1-2-0) transformations. An analysis of the order of calculation of the direct, reverse and zero sequences components is carried out for the general case and for every separate phase. Comparison of Clarke transformation for separate sequences is performed using Euler formulae in an exponential form. Analytical relations determining the components of the current and voltage of direct and reverse sequences in domain a-b-0 are obtained. The said relations are used as the basis for instantaneous power decomposition in the use of p-q theory. The performed numerical calculation of current and voltage components, as well as power according top-q theory, confirms the obtained analytical results. Findings: Interrelation of direct and reverse sequence conversion of voltages (currents) in domain 1-2-0 (Fortescue transformation) with voltages (currents) in domain a-b-0 (Clarke transformation) is analytically substantiated, which makes it possible to separate in the latter the components caused by the action of direct and reverse sequences. originality: Analytical determination of direct, reverse sequence components in domain a-b is proposed to use these components during calculation of instantaneous power according to p-q theory for four-wire lines. Practical value: The obtained results present a part of the analysis of electric power components in electrical four-wire networks with asymmetric parameters of the mode and they can be developed for networks with nonsinusoidal voltages and currents.
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A comparative characteristic of different concepts and expressions for determination of reactive power in the circuits with non-sinusoidal electric values has been given. For the first Ukrainian electric locomotives of DE1 type with the system of DC electric traction, the values of reactive power after Budeany, Fryze, and also the differential, integral and generalized reactive powers have been determined. Some measures on reducing its consumption by the DC electric rolling stock have been suggested.
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A power approach to estimation of electromechanical complexes controllability using instantaneous power method has been offered. It has been determined that power controllability characterizes the quality of energy conversion processes in the system, reflects manifestation of nonlinear properties of the object. A mathematical procedure for determination of power losses for the whole power channel of electromechanical complex power conversion has been developed. It has been shown that formation of balance equations of separate instantaneous power components underlies the estimation of electromechanical complexes power controllability.
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The instantaneous power component analysis of energy conversion processes in all the elements of electromechanical complex power channel has been performed. It has been established that effective power is a quality measure for power processes in the system. An index of electromechanical complex power channel capacity has been offered. It has been proved that instantaneous power component, reflecting energy exchange processes in the system, causes decrease of the object power channel capacity.
Characteristics of electric power under uncertainty, Engineering
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Y. I Gorelov, "Characteristics of electric power under uncertainty, Engineering", Tula 2016 pp.46-55
The quality of electricity use in electrical traction systems
  • V G Sychenko
  • D A Bosiy
V. G. Sychenko and D. A. Bosiy, "The quality of electricity use in electrical traction systems", Modern technologies. System analysis. Modeling №4, Irkutsk, 2015, pp. 143 -149
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  • D R Zemskyi
D. A. Bosiy and D. R. Zemskyi, "Balance of electric energy of traction substation of direct current at different levels of voltage asymmetry of external power supply system", Easten-European Journal of Enerprise Technologies, Kharkiv, 2014, pp.52 -57.
Indicators of electrical energy quality in the direct current electric traction system
  • V A Petrov
V. A. Petrov, "Indicators of electrical energy quality in the direct current electric traction system", Visnyk DNURT, Dnipro, 2010, pp. 180 -183