Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application)
This paper deals with using an original and pure electronic method for low-frequency harmonic suppression with wide industrial realization and application, in place of the usually heavy inductive, low-frequency harmonic filters. One of the main applications was made for small land power supply units...
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Інститут кібернетики ім. В.М. Глушкова НАН України
2016
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| Назва видання: | Математичне та комп'ютерне моделювання. Серія: Технічні науки |
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| Цитувати: | Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) / P. Ali Zada, N. Tuncay, B. Ozturk, C. Kivanc, H.A. Mamedov, S.A. Abdullaev // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2016. — Вип. 13. — С. 5-16. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1337232018-06-06T03:03:41Z Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) Ali Zada, P. Tuncay, N. Ozturk, B. Kivanc, C. Mamedov, H.A. Abdullaev, S.A. This paper deals with using an original and pure electronic method for low-frequency harmonic suppression with wide industrial realization and application, in place of the usually heavy inductive, low-frequency harmonic filters. One of the main applications was made for small land power supply units of onboard complexes in ground-based air navigation when preflight ground check-service is made. The transport management at thousands of small provincial airports in the former country is still unfortunate. The same situation is in Northern and central Central Asia, Northern Caucasian and Trans-Caucasian Mountains, oriented to small civil and agricultural services airports, etc. Everywhere the phase and line voltage amplitude unbalance can reach between 10-15% at the settlement’s power tiny transformer or generator and there are thousands and thousands of such local «airports» [1, 6]. This paper has been editing by a native speaker, Ms. Rachel Alcorn — our sincere thanks. У статті розглядається використання оригінального і чисто електронного методу низькочастотного зниження рівня гармонік для широкої промислової реалізації та застосування в якості індуктивних низькочастотних фільтрів гармонік. Одним з основних застосувань методу було здійснено для невеликих блоків живлення бортових комплексів наземного базування повітряної навігації при проведенні передпольотної наземної перевірки та обслуговування. Управління транспортом у великій кількості невеликих провінційних аеропортів проводилося невдало. Та ж ситуація спостерігається в північній і центральній частині Середньої Азії, Північного Кавказу і Закавказьких гір, які орієнтовані на невеликі аеропорти цивільних і сільськогосподарських послуг і т.д. Скрізь в локальних аеропортах дисбаланс фази і амплітуди напруги в лініях може досягати 10-15% при включенні живлення невеликого трансформатора поселення або генератора [1, 6]. Висловлюємо подяку за редагування статті пані Рейчел Алкорн. 2016 Article Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) / P. Ali Zada, N. Tuncay, B. Ozturk, C. Kivanc, H.A. Mamedov, S.A. Abdullaev // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2016. — Вип. 13. — С. 5-16. — Бібліогр.: 22 назв. — англ. 2308-5916 http://dspace.nbuv.gov.ua/handle/123456789/133723 en Математичне та комп'ютерне моделювання. Серія: Технічні науки Інститут кібернетики ім. В.М. Глушкова НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
This paper deals with using an original and pure electronic method for low-frequency harmonic suppression with wide industrial realization and application, in place of the usually heavy inductive, low-frequency harmonic filters. One of the main applications was made for small land power supply units of onboard complexes in ground-based air navigation when preflight ground check-service is made. The transport management at thousands of small provincial airports in the former country is still unfortunate. The same situation is in Northern and central Central Asia, Northern Caucasian and Trans-Caucasian Mountains, oriented to small civil and agricultural services airports, etc. Everywhere the phase and line voltage amplitude unbalance can reach between 10-15% at the settlement’s power tiny transformer or generator and there are thousands and thousands of such local «airports» [1, 6]. This paper has been editing by a native speaker, Ms. Rachel Alcorn — our sincere thanks. |
| format |
Article |
| author |
Ali Zada, P. Tuncay, N. Ozturk, B. Kivanc, C. Mamedov, H.A. Abdullaev, S.A. |
| spellingShingle |
Ali Zada, P. Tuncay, N. Ozturk, B. Kivanc, C. Mamedov, H.A. Abdullaev, S.A. Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) Математичне та комп'ютерне моделювання. Серія: Технічні науки |
| author_facet |
Ali Zada, P. Tuncay, N. Ozturk, B. Kivanc, C. Mamedov, H.A. Abdullaev, S.A. |
| author_sort |
Ali Zada, P. |
| title |
Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) |
| title_short |
Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) |
| title_full |
Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) |
| title_fullStr |
Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) |
| title_full_unstemmed |
Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) |
| title_sort |
parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (mathematical model, study and industrial application) |
| publisher |
Інститут кібернетики ім. В.М. Глушкова НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/133723 |
| citation_txt |
Parametrical method of low-frequency harmonics suppression in rectifier’s output voltage under supply voltage unbalances (Mathematical model, study and industrial application) / P. Ali Zada, N. Tuncay, B. Ozturk, C. Kivanc, H.A. Mamedov, S.A. Abdullaev // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2016. — Вип. 13. — С. 5-16. — Бібліогр.: 22 назв. — англ. |
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Математичне та комп'ютерне моделювання. Серія: Технічні науки |
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Серія: Технічні науки. Випуск 13
5
P. Ali Zada*, Prof. Dr.,
N. Tuncay*, Prof. Dr.,
B. Ozturk*, Asst. Prof.,
C. Kivanc*, Res. Asst.,
H. A. Mamedov**, D-r of Tech. Sciences, Prof.,
S. A. Abdullaev**
*OKAN University, Istanbul, Turke,
**Azerbaijan Technical University, Baku, Azerbaijan
PARAMETRICAL METHOD OF LOW-FREQUENCY HARMONICS
SUPPRESSION IN RECTIFIER’S OUTPUT VOLTAGE UNDER
SUPPLY VOLTAGE UNBALANCES (MATHEMATICAL MODEL,
STUDY AND INDUSTRIAL APPLICATION)
This paper deals with using an original and pure electronic
method for low-frequency harmonic suppression with wide indus-
trial realization and application, in place of the usually heavy in-
ductive, low-frequency harmonic filters. One of the main applica-
tions was made for small land power supply units of onboard com-
plexes in ground-based air navigation when preflight ground
check-service is made. The transport management at thousands of
small provincial airports in the former country is still unfortunate.
The same situation is in Northern and central Central Asia, North-
ern Caucasian and Trans-Caucasian Mountains, oriented to small
civil and agricultural services airports, etc. Everywhere the phase
and line voltage amplitude unbalance can reach between 10-15% at
the settlement’s power tiny transformer or generator and there are
thousands and thousands of such local «airports» [1, 6]. This paper
has been editing by a native speaker, Ms. Rachel Alcorn — our
sincere thanks.
Key words: noise, adaptive methods, telemetry canals.
Introduction. Voltage disturbance is the most common type of
power quality (PQ) degradation phenomenon [11–13]. Among the various
types of voltage disturbances, voltage variation and unbalance occur fre-
quently because of different regular switching loads in the supply network
[14–15]. The presence of nonlinear loads across the power system network
also degrades the PQ. Thereby, slight changes in the convertors voltage or
load make the operating parameters change. Applying varying voltages (or
their angles), or simultaneous variation of both of them to a three-phase
bridge AC-DC convertor can cause the variation of side-operating parame-
ters. In this case, it is necessary to study the operating performance under
variable conditions. This paper presents the performance analysis of a
three-phase bridge AC-DC convertor system for voltage variations using
an experimental case study. In order to study the performance variations of
© P. Ali Zada, N. Tuncay, B. Ozturk, C. Kivanc, H. A. Mamedov, S. A. Abdullaev, 2016
Математичне та комп’ютерне моделювання
6
a three-phase AC-DC convertor system for voltage variations. Voltage
unbalance has been interpreted and expressed mathematically as a voltage
unbalance factor (VUF) in a number of ways [16]. The VUF as expressed
by the IEC (International Electro technical Commission) is
VUF = (VN / VP) * 100 %
where VN and VP are magnitudes of negative and positive sequence voltage
components.
As discussed, there will be infinite possibilities of voltage combina-
tions that will satisfy a VUF. This can be reduced to a unique case by con-
sidering the complex nature of the sequence components which is the
complex voltage unbalance factor (CVUF) defined as the ratio of the nega-
tive sequence voltage phasor to the positive sequence voltage phasor, and
it is expressed as CVUF = KV ے V, where KV is the ratio of magnitudes nega-
tive sequence voltage to the positive sequence voltage and V = (N –P) is the
phase angle by which the negative sequence component leads the positive
sequence component.
For most AC-DC convertor systems, it is quite difficult to measure
the individual phase voltages, as the neutral point is often not externally
available. Since all calculations are computed on a per-phase basis, to cal-
culate the voltage unbalance factor (KV), a definite relationship must exist
between the magnitudes of the KV computed using line and phase voltage
values. Voltage variations and unbalance can be classified into balanced
over voltage (BOV), balanced under voltage (BUV), unbalanced over
voltage (UBOV), unbalanced under voltage (UBUV) and unbalanced
equal voltage (UBEV); and by making use of the upper limit of voltage
variations, the ambiguity among voltage combinations that lead to the cal-
culation of CVUF can be greatly reduced.
This paper deals with an original and pure electronic method with its
wide industrial realization and application for suppression rectifier’s low-
frequency harmonics due to the different types of the voltage unbalances
mentioned above.
Body. The transportation management at thousands of small provincial
airports is still unfortunate in Northern and central Siberia oil fields service,
Ural, Turkey, Central Asia, Northern Caucasian and Transcaucasia Mountains,
oriented to small airports or of distant agricultural services, etc.
Their converters often are fed through the weak three-phase airfield
network, or from the settlement’s autonomous diesel generator with a lim-
ited power supply. Besides, there are some random-fluctuation regimes
that lead to a rising asymmetry (unbalance) of phases and lines’ voltage
amplitudes in the feeding network.
The generally recognized upper limit for running any motor or gen-
erator with unbalanced voltages is usually around 5% — Table 1, (10%
Серія: Технічні науки. Випуск 13
7
[10]). However, the allowable nameplate power of an electrical machine
must be de-rated according to the following table for voltage unbalances
1% and greater [9] (extrapolated from the curve www.epri.com: «Power
Plant Electrical Reference Series», Volume 6 Motors):
Table 1
Motors output as a function of unbalance in the supplied voltage
Voltage Unbalance Output De-Rating
1% 98%
2% 96%
3% 92%
4% 85%
5% 76%
Fig. 1. Motors output as a function of unbalance in the supplied voltage
Phase voltage unbalance should be less than one percent for proper
motor operation. If any three phase unit (a motor, rectifier, transformer
etc) must be operated with a phase unbalance of greater than one percent,
then the unit should be de-rated according to the presented table. A unit
should not be operated at all where phase unbalance is greater than five
percent. (http://cipco.apogee.net/mnd/mspupha.asp).
From the other point of view, it is known that under such voltage un-
balance conditions (even up to 10%, for distant wilderness places) the low-
frequency harmonic components appear in the rectifier load voltage and
current output spectrums. They penetrate into the onboard network electri-
cal motors or electronic devices, dramatically decreasing their output
power and this may cause a reason for auto-oscillations or other undesir-
able processes [1–9, 11] only because of ineffective filtering of their low-
frequency harmonics. In addition, these harmonics may become a source
of interference for the airport’s other ground service apparatuses.
Математичне та комп’ютерне моделювання
8
Therefore, the problem of low-frequency harmonic suppression is
very important, but the practical realization of low frequency filters (in
particularly the inductive ones) clashes with the problem of the mobile
rectifier’s overall mass and dimensions, a converter’s stability under cer-
tain conditions, its efficiency and other difficulties.
There are many well-known ways to improve the filtration efficiency
of a thyristor voltage rectifier (TVR). One of these ways is the transition to
multi-pulse rectifiers (3, 6, 12, 18, 24, etc.). The pulse frequency of such
rectifiers is equal to f * N, where N is the pulses-number of the rectified
voltage (3, 6, 12, 18, 24, etc.) and f is the frequency of the supply voltage.
When the asymmetry of phase voltage amplitude has taken place, the influ-
ence of low frequency harmonic components are increased significantly in
these rectifiers — usually by frequency 2f Hz pulsations appear in the recti-
fier’s output voltage — about 10% of its maximum value (proportional to
the level of the phase or line voltage amplitude unbalance). These pulsations
can make the spectrum of output voltage harmonics even worse than the
spectrum of 2- or 3- pulse rectifiers. The application of passive or resonant
filters results in a considerable increase of the mobile rectifier’s weight and
size. Moreover as the onboard apparatuses work with sharply variable loads,
there are output voltage fluctuations and possible voltage surge and over-
loads in these rectifier filters. Therefore, the passive and resonant filters are
rarely applied for suppressing and smoothing the low-frequency harmonics
in the ground service thyristor voltage rectifiers at small airports.
This paper outlines an untraditional [2, 3, 8], but a pure electronic
approach to the suppression of low-frequency harmonics without the use
of any additional low-pass filters with heavy inductors or big capacitors.
There is a rapidly growing interest in these so-called parametric methods
for suppressing harmonics in the rectified voltage. They are simple for techni-
cal realization and efficient in practice. For the effective work on the paramet-
ric methods, it is necessary to find and technically understand the connection
between the asymmetry characterizing main parameters and the level of the
generated-additionally low-frequency harmonics.
Theoretically the rectifier semiconductor valve system can be de-
scribed by the nonlinear, non-homogeneous (dissimilar) differential equa-
tions with periodically and discretely changing coefficients and perturbing
functions by changing their amplitude and frequency:
11* 1 12* 2 1 * 1 11* 1 12* 2 1 *
21* 1 22* 2 2 * 2 21* 1 22* 2 2 *
1* 1 2* 2 * 1* 1 2* 2 *
, ,
, ,
,
n n n n
n n n n
n n nn n n n n nn
a y a y a y f t b y b y b y
a y a y a y f t b y b y b y
a y a y a y f t b y b y b
,ny
(1)
or in matrix form [A].s[Y] = F(t, ω) + [B]·[Y].
Серія: Технічні науки. Випуск 13
9
The equations (1) are the generalized mathematical model of the
semiconductor valve converter in which the models of a semiconductor
valve and its control system are taken into consideration. Thus, this model
allows us to investigate the semiconductor valve converters at any interval
of the discreteness. However, its application for analyzing the harmonic
composition of the rectified voltage takes a lot of time to calculate, as it is
necessary to determine the conditions of the valves at each interval of the
discreteness that is bound with the joint decision of the control system and
electromagnetic process equations in the converter itself
T T
B BA Z Ai A E , (2)
where T — the matrix transposition symbol; A, ZB and EB — the matrix of
the connections, resistances and electromotive forces branches matrixes; and
i — the connection current matrix in accordance with the graph of the dia-
gram. The problem is simplified considerably if the angle of bias show-
ing the switching point’s bias in asymmetric modes is brought relative to the
switching points of the symmetric modes (fig. 2) in the model. In this case it
isn’t necessary to conduct the work to find the switch-on/off moments of the
valves at each interval of the discreteness or to solve the equation in full
volume, but it may limit the mathematical model of the rectifier describing
the voltage envelope. In this case, the equation of the mathematical model,
for example, bridge thyristor rectifier for the continuous current mode can be
written in the following way: : 60I ib I electric degrees from
natural switching points. Thus, the non-symmetrical three-phase voltages
can be written in the following way:
1 1
2 2
3 3
sin / 6 ;
sin / 2 ;
sin 5 / 6 ,
u t U t
u t U t
u t U t
(3)
where U1m = 1, U2m > U1m, U3m = U1m. Then the equations of the output
voltage envelope in the interval of the discreteness λ = 2π / m, correspond-
ing to the symmetric mode taking into account Δαib for the asymmetric
modes, will be the following:
1 3 2
1 1 2 1
1
/ /
,
0 /
r b
r b
u t u t u t
u t u t
(4.1)
2 1 2
1 2 1 3 2
1 1 2
/ /
,
/ /
r b
r b
u t u t u t
u t u t
(4.2)
Математичне та комп’ютерне моделювання
10
3 1 3
2 3 2 3 3
2 2 3
/ /
,
/ /
r b
r b
u t u t u t
u t u t
(4.3)
4 2 3
3 4 2 1 4
3 3 4
/ /
,
/ /
r b
r b
u t u t u t
u t u t
(4.4)
5 2 1
4 5 3 1 5
4 4 5
/ /
,
/ /
r b
r b
u t u t u t
u t u t
(4.5)
6 3 1
5 6 3 2 6
5 5 6
/ /
.
/ /
r b
r b
u t u t u t
u t u t
(4.6)
The advantages of these equations (4.1–4.6) are that both r and
ib enter in each interval of the discreteness. On the one hand, r de-
fines the degree of asymmetry of the output voltage curve; on the other
hand, it defines the asymmetry of the control angles which appear.
Additionally, the equations (2) follow the idea that by means of
r changing at each interval of the discreteness, this may compensate for
the influence of ib and fix the same values of r at the intervals when
the low-frequency pulse components will be:
130 sin120 sin120 .ib i iarcctg U U (5)
Thus, the equation (2) makes us think that if it may be receiving the
information about current value of ib in each interval of the discrete-
ness, then by means of bringing the correction in the control angles, it may
influence the output voltage spectrum structure as far as possible.
The way of practically carrying out the given algorithm consists of
the following steps. First, the crossing point of the phase voltage across
zero and natural switching point in each interval of the discreteness is
measured, and then the control angle correction in the same interval ac-
cording to received results is formulized.
The block diagram of the implemented method and voltage diagrams
show the efficiency of the correction as presented in fig. 2 and fig. 3a, 3b,
respectively.
Серія: Технічні науки. Випуск 13
11
Fig. 2. The block diagram of the realized method
S1 — the First Synchronizer to synchronize the work of the Converter of the
Slot to the Voltage (CSV) in each interval of the discreteness; S2 — the Sec-
ond Synchronizer interrupting the work of CSV in the natural switching points
(when equal to the line voltages). The time-slot between the synchronous
pulses S1 and S2 is proportional to the measured voltage. In the capacity of
CSV usually a Saw-Tooth Oscillator (STO) is used, the start of which is syn-
chronized with S1 while the ending is synchronized with S2.
CSV output voltage is sent to the input of the Selection and Storage De-
vice (SSD). The pulses with the output of S1 simultaneously enter the control-
ling input of SSD after each interval of the discreteness. These pulses allow
the instantaneous value of the voltage corresponding to the ending of the in-
terval between the moments of the synchronous pulses S1 and S2 in SSD to be
recorded. The voltage kUc enters one of the Adder’s (A) inputs with the SSD
output, another input, the controlling voltage Ucnt, is presented.
There is algebraic summation Ucnt and kUc in the Adder and its sum
U Ucnt – kUc enters the Comparator block (C) with the adder’s output.
The Comparator block sets the corrected control angle, gives the signal
throw Impulse Distributor (ID) and Impulse Former (IF) for switching the
Rectifier’s Thyristor (RT) off at the proper instant of the current period.
Next period (in 60 el. degrees) the process is repeated and corrected signal
feeds the next value etc.
Thus, in one period 6 correcting signals are formed which set corrected
control angles accordingly. The value of correcting signal (voltage) Uc is de-
fined in each synchronizing time period in the following way:
as c ibt , the amplitude dependence and t are changing linearly,
then cU tg t , where φ — is the tilt angle of the CSV output voltage (saw-
tooth voltage in our case). In one turn, 2 1s st t t is the time interval be-
tween two synchronous signals from S2 and S1. And ts1 can be decomposed
into two components, one of which is constant and corresponds to the sym-
metric mode ts1h, but another changes depending on the asymmetry of the sup-
ply voltages — Δts1. Therefore: 1 1 1s s h st t t and after substituting this
expression into the equation Uc the following expression was received
Математичне та комп’ютерне моделювання
12
2 1 1 ,c s s h s ch cU tg t t tg t U U (6)
where Uch — the constant component, which corresponds to the symmetric
mode.
Fig. 3. Correction efficiency shown in the voltage diagrams
It may be compensated with entering a bias voltage in the control
voltage Ucnt in the adder A. ΔUc is the variable component of the correc-
tion voltage which is proportional to the supply voltage phase increment of
the amplitude changing. Thus, it can be considered as proportionality
U ≡ ΔU. The coefficient k is defined as the ratio ic ib , where
Δαic — the angle increment in asymmetry. The system provides the full
compensation of the switching moments changing (the control angles),
that is, the constancy of the control angle in linearly scanning voltages of
CSV and equal increasing speed of this voltages ( 1k ) the method al-
lows changing k in any intervals to promote better correction and therefore
better the smoothing of the output voltage.
The worst nonsymmetrical feeding case happens when phases A and
C are 12% lower than phase B. The results of comparing the converter
Серія: Технічні науки. Випуск 13
13
output DC voltage spectrogram for the two cases — with and without the
application of the electronic method mentioned above of low-frequency
harmonic suppression in output DC voltage — are presented in Table 2.
Fig. 4. Nonsymmetrical feeding of the converter
(A and C phases are 10% lower): the DC output voltage spectrograms
Table 2
Voltage unbalances influence on low harmonic amplitudes (mainly 100 Hz)
Unbalance Case 10% 100Hz 200Hz 300Hz 400Hz 500Hz 600Hz
1. The method is not applied 9.2% 1.9% 3.9% 3.9% 1.8% 0.22%
2. The method is applied 0.85% 1.7% 0.41% 0.62% 0.21% 0.43%
Output de-rating (times) 1/2 10.82↓ 1.11↓ 9.5↓ 6.3↓ 8.6↓ 0.51↑
Not wanting to overburden the paper with comments to the other un-
balance cases (5% and 7.5%) DC output voltage spectrogram’s photo re-
sults, it is best to confine the final remarks about these two cases: the per-
centage of 100Hz harmonic and output de-rating (times) are 1.27% (3.61)
for 5%, and 2.53% (7.2) for 7.5% unbalance cases, respectively. All these
results confirm the efficiency of the method proposed and allow us to re-
ject the use of the usually heavy inductive low-frequency-harmonic filters.
Математичне та комп’ютерне моделювання
14
The thorough studies of the DC converter model, [7] and laboratory
experiments have shown (table 2) the sensitivity and the almost linear pro-
portionality between the phase-, voltage-amplitude unbalances and the low
harmonic of the converter output voltage (100Hz amplitudes before and
after applying the method). The other harmonics up to 600Hz are not too
sensitive to the applied voltage unbalance and are usually suppressed by
little traditional RLC filters.
Conclusion. The ground power supplies must completely correspond
to the characteristics of the onboard power supplies during the ground ser-
vice and maintenance of aircrafts’ onboard complexes. If low-frequency
harmonics appear in the output of the ground power supplies, it means that
there is an amplitude asymmetry of the feeding voltages and their suppres-
sion is bound with well-known difficulties. Therefore, it is important to
solve this question. This paper presented the simple mathematical model
of the m-phase rectifier and its output voltage curves taking into account
the real instant value of asymmetry in each interval of the discreteness. In
addition, the description of the correction arrangement way is given, which
allows the rectifier output voltage smoothing considerably increasing or, in
other words, the ability of suppressing the converter’s low-frequency volt-
age harmonics. It simultaneously raises the speed of the control system
and the possibility of forming the necessary rectifier output characteristics.
Acknowledgments. In memory of Prof., Dr. Sc. Abdullaev A.A.
(Azerbaijan Technical University). The authors wish to thank the indi-
viduals who supported and provided real practical help in workshops, on
the field and in the lab study, and developed several pilot projects of the
converter: from the Azerbaijan Electrical Engineering Technology Insti-
tute (Azelectrotechprom), colleagues from OKAN University (Turkey)
and to all who have shared their comments, corrections and suggestions
during several meetings and conferences. The authors gratefully acknowl-
edge the contributions of the native speaker Ms. Rachel Alcorn, (Queen
Margaret University, Edinburgh, Scotland) for the work to read and edit
English content the original version of this document).
References:
1. Abdulaev A. A. Modulation in Rectifiers with a Control System of Synchro-
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Rectifier’s Control Method, Publ. In BI. — 1990. — No. 37.
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No 1644317 Rectifier’s Control Device, Publ. in BI. — 1991. — No 15.
4. Kulizade K. N., Ali-zade P. G., Kuliev A. C., Cascade Converter for Electric
Drive Motors, PATENT AC SU 543118. — 1974/1976.
Серія: Технічні науки. Випуск 13
15
5. Ali-Zada P. H., Kuliyev H. M., Thyristor Converter, (Priority from 27 Jan.
1998) PATENT. — 2000 0207 01.11.2000, Azerbaijan.
6. Abdulaev A. A. Ground Power Supplies for Servicing the Onboard Complexes /
A. A. Abdulaev, S. A. Abdullaev, N. A. Aliev, E. B. Abbasov // The first Eurasian
Symposium on Space Science and Technologies, Turkey. — 1993.
7. Ustun O. Multifunctional Electrodynamic Model of Electric Drive and Motors
/ O. Ustun, P. G. Ali-Zade // The IV Electromechanical Symposium, Bursa,
Dec.17-21, 1997, TURKEY.
8. Ali-Zade P. H. Ground Airport Power Supplies for Servicing the Onboard
Complexes / P. H. Ali-Zade, H. A. Mamedov, S. A. Abdullaev, V. S. Allah-
verdiev // Creating The Future, 3rd FAE International Symposium
Gemikonağı, 25-26 Nov, 2004. — Cyprus. — P. 497–500
9. Power Plant Electrical Reference Series, Volume 6: Motors. — Access mode:
www.epri.com.
10. 10. ПОТ РМ-016-2001, Inter branch rules on a labor safety (rules) at opera-
tions of electro-installations. PEEP and PUE, (п.6.6 Tab. 6 the Appendix 1,
PEEP). Access mode: http://www.enerkomp.ru/documents/need.html
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ferent Voltage Unbalance Conditions Using Simulation and Experimental Re-
sults / A. Jalilian, R. Roshanfekr // Taylor & Francis, Inc., Electric Power
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IEEE Trans. Power Del. — 2006. — Vol. 21, № 1. — P. 322–329.
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to 1996 (in Norwegian) EFI, Trondheim, Norway, EFI TR A4460.
Математичне та комп’ютерне моделювання
16
22. SIMPOW, Power System Simulation and Analysis Software User Manual //
ver. (ABB) 10.1.093, STRI, Ludvika, Sweden, 2003.
У статті розглядається використання оригінального і чисто елек-
тронного методу низькочастотного зниження рівня гармонік для
широкої промислової реалізації та застосування в якості індуктив-
них низькочастотних фільтрів гармонік. Одним з основних застосу-
вань методу було здійснено для невеликих блоків живлення борто-
вих комплексів наземного базування повітряної навігації при прове-
денні передпольотної наземної перевірки та обслуговування. Управ-
ління транспортом у великій кількості невеликих провінційних ае-
ропортів проводилося невдало. Та ж ситуація спостерігається в пів-
нічній і центральній частині Середньої Азії, Північного Кавказу і
Закавказьких гір, які орієнтовані на невеликі аеропорти цивільних і
сільськогосподарських послуг і т.д. Скрізь в локальних аеропортах
дисбаланс фази і амплітуди напруги в лініях може досягати 10-15%
при включенні живлення невеликого трансформатора поселення або
генератора [1, 6]. Висловлюємо подяку за редагування статті пані
Рейчел Алкорн.
Ключові слова: шум, адаптивні методи, телеметричний канал
зв’язку.
Отримано: 20.04.2016
УДК 519.6
М. В. Артюх,
О. М. Литвин, д-р. фіз.-мат. наук, професор
Українська інженерно-педагогічна академія, м. Харків
ЗАСТОСУВАННЯ ДИВІДІРІАЛЬНОГО
ТА МУЛЬТИГРАЛЬНОГО ЧИСЛЕНЬ В ДОСЛІДЖЕННІ
ЕКОНОМІКИ СІЛЬСЬКОГО ГОСПОДАРСТВА УКРАЇНИ
У статті наведено основні поняття дивідіріального та му-
льтигрального числень, розглянуто виробничу функцію зі
змінними коефіцієнтами еластичності. Розроблено математич-
ні моделі виробничих функцій для дослідження економіки
сільського господарства України.
Ключові слова: дивідіріальне числення, мультигральне
числення, виробнича функція, коефіцієнт еластичності, ВВП
сільського господарства, основні засоби, оборотні активи.
Вступ. Застосування економіко — математичного моделювання
відіграє велику роль при дослідженні й прогнозуванні економічних
систем різного рівня. Оскільки на результат виробництва має вплив
© М. В. Артюх, О. М. Литвин, 2016
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>>
<<
/AllowImageBreaks true
/AllowTableBreaks true
/ExpandPage false
/HonorBaseURL true
/HonorRolloverEffect false
/IgnoreHTMLPageBreaks false
/IncludeHeaderFooter false
/MarginOffset [
0
0
0
0
]
/MetadataAuthor ()
/MetadataKeywords ()
/MetadataSubject ()
/MetadataTitle ()
/MetricPageSize [
0
0
]
/MetricUnit /inch
/MobileCompatible 0
/Namespace [
(Adobe)
(GoLive)
(8.0)
]
/OpenZoomToHTMLFontSize false
/PageOrientation /Portrait
/RemoveBackground false
/ShrinkContent true
/TreatColorsAs /MainMonitorColors
/UseEmbeddedProfiles false
/UseHTMLTitleAsMetadata true
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/BleedOffset [
0
0
0
0
]
/ConvertColors /ConvertToRGB
/DestinationProfileName (sRGB IEC61966-2.1)
/DestinationProfileSelector /UseName
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements true
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MarksOffset 6
/MarksWeight 0.250000
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PageMarksFile /RomanDefault
/PreserveEditing true
/UntaggedCMYKHandling /UseDocumentProfile
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [600 600]
/PageSize [419.528 595.276]
>> setpagedevice
|