Download compensation for non-active current components at mains supply

XXIV Symposium
Electromagnetic Phenomena in Nonlinear Circuits
June 28 - July 1, 2016 Helsinki, FINLAND
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COMPENSATION FOR NON-ACTIVE CURRENT COMPONENTS
AT MAINS SUPPLY VOLTAGE UNBALANCE
Atef S. Al-Mashakbeh*, Mykhaylo Zagirnyak, Andrii Kalinov and Mariia Maliakova
*
Tafila Technical University, Electrical Engineering Department,
P.O. Box 179, Tafila, 66110, Jordan, e-mail: [email protected]
Kremenchuk Mykhailo Ostrohradskyi National University,
Institute of Electromechanics, Electric Machines and Apparatus Department
Pershotravneva str. 20, Kremenchuk, 39600, Ukraine, e-mail: [email protected]
Abstract - Analytical research of compensation for nonactive current
components in a three-phase three-wire power-supply system has
been carried out with the use of cross-vector theory of instantaneous
power in frequency domain. The obtained results allowed us to
propose a method of improvement the compensation for non-active
current components under supply voltage unbalance by means of the
use of mains supply voltage signals balancing block. The results of
numerical modeling of the processes of compensation for non-active
current components under the conditions of supply voltage
unbalance have revealed the advantages of the proposed method in
comparison with the classical one.
I. INTRODUCTION
It is commonly known, that in most cases the real load of
power-supply systems is characterized by both nonlinearity of
its characteristics and unsymmetry of its parameters by
phases. This leads to appearance of higher harmonics in
current and voltage signals and also to amplitude and angle
unsymmetry of voltages and currents in the system. This
means that in load currents the non-active components
appears. In accordance with works [1-2] the active current is
only a main harmonic component of the current signal, and it
has sinusoidal waveform and flows co-phased with the mains
voltage. All the rest components of load current, conditioned
by unsymmetrical load, are non-active. The flow of nonactive current components in power-supply systems leads to
increase the losses in transformers, power lines, capacitors of
reactive power compensators, etc. To compensate these
currents the power active filters (APF) are used [1, 3, 5-6].
However, in the author’s opinion [1], the use of p-q theory of
instantaneous power (IP) for calculation of APF compensation
currents in the system with non-sinusoidal and unbalanced
supply voltage is doubtful. It can be explained by the fact that
interpretation of power components according to p-q IP theory,
as well as of other theories, does not answer the question: what is
the reason of non-sinusoidality and unbalance – the load or the
mains. It is shown in paper [1] that APF operation on the basis of
p-q IP theory at distorted mains voltages may cause still bigger
distortions of current signals.
The purpose of the paper is the improvement of methods of
compensation for non-active current components under the
conditions of unbalance of supply voltage in order to increase the
efficiency of operation of power-supply system.
II. MATERIAL AND RESULTS OF THE RESEARCH
A. Research of compensation processes in an analytical form in
frequency domain
Processes of compensation for nonactive current components
in a three-phase three-wire system, caused by amplitude
unbalance of loads current, are considered in frequency domain
in an analytical form. In this case it was assumed that there is no
currents influence on mains voltage distortion, i.e. power of the
power-supply system is unlimited. Output orthogonal cosine and
sine components of current in three-phase three-wire mains were
3
1
I1 m ; I A b1 = − I1m ;
4
4
1
1
3
= ε B I1m ; I C a1 = −
εC I1m ; I C b1 = − εC I1m ,
2
4
4
presented in frequency domain: I A a1 =
I B a1 = 0 ; I B b1
where ε B , εC – coefficients of amplitude unbalance of phase
В and phase С, respectively; shear angle of the first harmonic
component of current ϕ I 1 = −30 el. deg. Numerical values of
coefficients of unbalance were taken ε B = 0.8 , εC = 1.2 ,
respectively.
Analytical expressions of variable components of
instantaneous active and reactive power and their
root-mean-square (RMS) values were obtained:


(1)
P2rms = 1 / 4 U1m I1m 1 + εB2 + εC 2 −εC εB −εC −εB   ;






Q2rms = 3 / 4  U1 m I1 m 1 + ε B 2 + εC 2 − εC ε B − εC − ε B   . (2)




Compensation currents in frequency domain were
calculated according to cross-vector theory:
I A b1 = − (1 / 4 ) I1m ;
I A a1 = − 3 / 12 I1m −2 + ε B + εC  ;
(
=(
I B a1 =
I C a1
(
)
)
3 / 24 ) I
3 / 24 I1m 1 + ε B + εC  ;
1m
I B b1 = (1 / 8 ) I1m 3ε B − 1 − εC  ;
1 + ε B − 5εC  ; I C b1 = (1 / 8 ) I1m 1 + ε B − εC  .
Correctness of the obtained orthogonal components of
compensating current is confirmed by the fact that provided
ε B = εC = 1 expressions of variable components of
instantaneous active and reactive power and their RMS values
P2rms , Q2rms acquire zero values. The analysis performed in an
analytical form made it possible to come to the conclusion that
compensation for non-active current components is possible
without taking into account the unbalanced components of
supply voltage in the algorithm of generation of compensation
currents.
B. Mathematical modeling of compensation system operation
To confirm the results of analytical research a mathematical
model of a section of power-supply mains was created. It
consists of balanced/unbalanced linear load, active-inductive
resistances of the mains, blocks of currents and voltages
measurement, APF, APF control system, separation block (SB),
as well as voltage signal balancing block (VSBB).
VSBB (Fig. 1) is meant for balancing of supply voltage
signals before their feed to APF control system. Amplitude
values of voltage in every phase were determined in VSBB by
means of Fourier transform (FT) (Fig. 1, block I).
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135
power at the mains active resistances ∆P efficiency η of the
supply mains.
TABLE I
INDICES OF APF OPERATION AT UNBALANCED SUPPLY VOLTAGE AND
BALANCED LOAD
Fig. 1. Supply mains VSBB
The obtained numerical values were added up and then
averaged (Fig. 1, block II). Coefficients KA, KB, KC were
determined by division of the obtained values by initial
amplitude (Fig. 1, block III). These coefficients are necessary to
balance voltage amplitudes in every phase (Fig. 1, block IV).
After that a voltage signal without components caused by voltage
unbalance was fed to the system of compensator control.
Unbalanced supply voltage – balanced load. During research
of compensator operation under the conditions of supply voltage
unbalance the amplitude unbalance was introduced into phase А
by the value of coefficient ε A = 0.885 (Fig. 2, I). This value of
amplitude undalance corresponds to voltage reciprocal sequence
coefficient K 2U = 4 %, which is twice as big as the boundary
value in accordance with European Standard EN 50160 [4]. In
such a system unbalance of supply voltage causes current
unbalance at the supply terminal (Fig. 2, I).
iA(t),
iB(t),
iC(t),
A
400
I
III
II
200
0
0.02
0.04
0.06
0.08
0.1
0.12 0.14
0.16 0.18
0.2
t, c
200
400
600
Fig. 2. Mains currents before (I) and after (II) connection of a classical
compensator, and also after connection of compensator with VSBB and SB (III)
In this case the work of classical compensator
(Fig. 2, II) was characterized by decrease of voltage unbalance
coefficient ( K 2U =1.76 %), but considerable total harmonic
distortion (THD) of current with THDI = 9 % was observed
(Fig. 2, II). It is caused by the fact that a voltage signal distorted
(THDU = 11 %) due to incorrect operation of APF control system
under the conditions of supply voltage unbalance was fed to
compensator control system.
SB described in papers [5-6] was proposed to be used for
correct APF operation under the conditions of harmonic
distortions of supply voltage. Transfer to frequency domain was
performed and voltage harmonic composition was determined at
the point of APF connection in SB with the use of FT. After that
supply voltage harmonic components caused by mains distortions
were determined with the use of the analysis of the sign of
corresponding frequency component of active power. These
voltage components were removed and did not participate in
generation of signal at the transfer to the time domain. The
obtained signals were fed to APF control system [5-6]. The
following parameters were calculated for quantitative
assessment of compensation (TABLE I): THDI and THDU,
voltage drop at the mains resistances ∆U, reactive power
constant component Q, coefficients of unbalance of current and
voltage of reciprocal sequence K 2I and K 2U , respectively, loss
Param. ∆U, THDU, THDI,
Q,
Mode
V
var
%
%
Before comp. 27.84
0
0
1.22·105
After comp.
31.4
11
9
100
After comp.
24.25 0.2 0.005
-85
with VSBB
and SB
η,
∆P,
W
1.965·104
1.386·104
%
92.45
94.69
, K 2I ,
%
%
3.98 3.98
4.1 1.76
1.383·104
97.72
4.25 0.176
K 2U
Unbalanced supply voltage-unbalanced load. In this case
unbalance was introduced into phase А of supply voltage by the
value of coefficient ε A = 0.885 and into load of phase С with
level 10 % of the value of its active resistance. In this case the level
of unbalance by coefficient of voltage reciprocal sequence K 2U
made 4.03 %. In this case the same characteristics of APF
operation as in the previous case were observed (TABLE II) –
compensator with VSBB and SB enbled decrease of load current
unbalance level to K 2 I = 0.17 % and maintain THDI and
THDU at a practically zero level.
TABLE II
INDICES OF APF OPERATION AT UNBALANCED SUPPLY VOLTAGE AND
UNBALANCED LOAD
Param. ∆U, THDU, THDI,
Q,
∆P,
Mode
V
%
%
var
W
Before comp. 27.25
0
0
–1.18·105
1.9·104
After comp.
27.2
7.3
7.35
450
1.3621·104
After comp.
24.15 0.002 0.005
–93.5
1.35·104
with VSBB
and SB
η,
%
92.05
94.7
, K 2I ,
%
%
4.03 4.87
4.15 1.72
94.72
4.32
K 2U
0.17
III. CONCLUSIONS
Use of the developed method with balancing and separation of
supply voltage harmonics, as compared with the classical system
of compensation, makes it possible to decrease the level of
unbalance of current signals with reciprocal sequence coefficient
by 1.3..1.5 %, reduce power line losses ∆P by 0.5..0.7 %, the
value of reactive power after compensation Q by 15..23 %,
voltage drop at the mains resistances ∆U by 0.5..23 %, improve
the system efficiency by 0.3..2.5 %, achieve practically zero
value of coefficient of current sinusoidality distortion THDI.
REFERENCES
[1] Czarnecki L.S., Samuel S. Pearce, “CPC-based comparison of
compensation goals in systems with nonsinusoidal voltages and
currents”, International School on Nonsinusoidal Currents and
Compensation, Łagow, Poland pp. 27-36, 2010.
[2] Peng F.Z., Tolbert L.M., Zhaoming Qian “Definition and compensation
of non-active current in power systems”, Power Electronics Specialists
Conference, 2002. pesc 02. 2002 IEEE 33rd Annual, Vol. 4, 23–27 June
2002, Cairns, Qld, pp. 1779–1784, 2002.
[3] Akagi H., Kanazawa Y., Nabai A., “Generalized theory of the
instantaneous reactive power in three-phase circuits”, Proceeding of Int.
Power Electronic Conference, pp. 1375–1386, 1983.
[4] European standard EN 50160 “Voltage characteristics of electricity
supplied by public distribution systems”, CENELEC TC 8X, 2006.
[5] Zagirnyak M., Maliakova M., Kalinov A., “Analysis of operation of
power components compensation systems at harmonic distortions of
mains supply voltage”, Proceedings 2015 ACEMP–OPTIM–
Electromotion 2015 Joint Conference, 02–04 September, Side, Turkey,
978-1-4763-7239-8/15 IEEE, pp. 355–362, 2015.
[6] Zagirnyak M., Maliakova M., Kalinov A., “Compensation of higher
current harmonics at harmonic distortions of mains supply voltage”,
Proceedings 2015 16th international conference on computational
problems of electrical engineering (CPEE), 02–05 September, Lviv,
Ukraine, IEEE Catalog Number CFP15A10-PRT, ISBN 978-617-607803-6, pp. 245–248, 2015.
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Proceedings of EPNC 2016, June 28 - July 1, 2016 Helsinki, FINLAND