CC BY
18
UDC 621.31
doi: 10.20998/2074-272X.2017.5.11
Yu.L. Sayenko, T.K. Baranenko, D.N. Kalyuzhniy
FEATURES OF SELECTION OF CAPACITOR BANKS IN ELECTRIC NETWORKS WITH INTERHARMONIC SOURCES
Purpose. Development of a methodology for selecting capacitor bank parameters designed to compensate for reactive power, if there are sources of interharmonics in the electrical network. Development of a methodology for selecting the parameters of capacitor banks that are part of resonant filters of higher harmonics and interharmonics. Methodology. For the research, we used the decomposition of the non-sinusoidal voltage (current) curve into the sum of the harmonic components with frequencies as multiple of the fundamental frequency - higher harmonics, and not multiple fundamental frequencies - interharmonics. Results. Expressions are obtained for checking the absence of inadmissible overloads of capacitor banks by voltage and current in the presence of voltage (current) in the curve, along with higher harmonics, of the discrete spectrum of interharmonics. When selecting capacitor banks, both for reactive power compensation and for filter-compensating devices, the necessity of constructing the frequency characteristics of the input and mutual resistances of the electrical network for analyzing possible resonant phenomena is confirmed. Originality. The expediency of simplified calculation of the voltage variation at the terminals of the banks of the capacitors of the higher harmonics filters and interharmonics due to the presence of the reactor in the filters is substantiated. Practical value. The use of the proposed approaches will make it possible to resolve a number of issues related to the choice of parameters of capacitor banks in networks with nonlinear loads, including: ensuring reliable operation of capacitor banks when their parameters deviate from their nominal values, as well as deviations in the parameters of the supply network and sources of harmonic distortion; ensuring the absence of resonant phenomena at frequencies of both higher harmonics and interharmonics. References 10.
Key words: capacitor bank, reactive power compensation, filter-compensating device, higher harmonics, interharmonics.
Разработана методика выбора батарей конденсаторов, применяемых как в качестве компенсаторов реактивной мощности при наличии источников интергармоник, так и в составе фильтров высших гармоник и интергармоник. Получены выражения для проверки отсутствия недопустимых перегрузок батарей конденсаторов по напряжению и по току при наличии в кривой напряжения (тока), наряду с высшими гармониками, дискретного спектра интергармоник. Обоснована целесообразность упрощенного учета изменения напряжения на зажимах батарей конденсаторов фильтров высших гармоник и интергармоник за счет наличия реактора в составе фильтров. Использование предложенных подходов позволит комплексно решать ряд вопросов, связанных с выбором параметров батарей конденсаторов в электрических сетях с нелинейными нагрузками. Библ. 10.
Ключевые слова: батарея конденсаторов, компенсация реактивной мощности, фильтро-компенсирующее устройство, высшие гармоники, интергармоники.
Introduction. Rational application of compensating devices in power supply systems allows to reduce power losses in the electric network (EN), to ensure the proper quality of the consumed electricity due to the normalization of voltage levels and, on the whole, allows achieving high technical and economic performance of electrical installations. Thus, the solution of the issues of reactive power compensation (RPC) is one of the aspects of both energy saving in EN and reliability of power supply to industrial enterprises [1-4].
Some of the most commonly used in power supply systems for various purposes of RPC devices are capacitor banks (CB), as they have a number of characteristic advantages: insignificant specific losses of active power, absence of rotating parts, simplicity of installation and operation, relatively low cost, low weight, time of work, the possibility of implementing an individual RPC [5, 6].
However, in modern EN there is a tendency to increase the number and power of nonlinear electric receivers. This is primarily a variety of frequency converters, rectifiers, inverters, DC drives and other semiconductor devices. Sharply varying loads are not only sources of voltage fluctuations, but also harmonic distortions of the current and voltage curves. In the presence of higher harmonics (HG) in the voltage curve, the aging process of the dielectric of capacitors proceeds more intensively than in the case when the capacitors
operate at a sinusoidal voltage. This is explained by the fact that the physicochemical processes in dielectrics, which cause their aging, are significantly accelerated at high frequencies of the electric field. Analogously, the additional heating caused by the current of the HG current is affected. Depending on the frequency characteristics of the power supply systems, the CBs may be in a mode close to the resonance of the currents at the frequency of any of the HG [6-8]. Due to the overloads of the CB, they fail in the HG current. It should be noted that, depending on sources of distortion, a significant spectrum of interharmonics (IG) can be generated along with the HG, which, in accordance with the IEC standard, include harmonic oscillations with frequencies not multiples of the frequency of the supply network [6]. IG have a negative influence on the power supply systems [9]. Thus, the choice of CB parameters for non-sinusoidal modes should consist in preventing resonance modes at both the HG and IG frequencies and ensuring acceptable voltages on the capacitors and their allowable current loading. However, the question of the choice of CB parameters in the presence of IG is insufficiently investigated.
The goal of investigation is the development of a technique for selecting parameters of capacitor banks used both as reactive power compensators in the presence of sources of discrete spectrum of interharmonics, and in the composition of higher and interhamonic filters.
© Yu.L. Sayenko, T.K. Baranenko, D.N. Kalyuzhniy
Statement of the main material. The technical conditions for the operation of the CB provide for limiting the excess of voltage and current above nominal values by certain values of cu and c (in fractions of nominal values). So, according to international standards, capacitors must withstand the increased voltage of the network, which operates for a certain period of time. For example, the EN-60831-1/2 Standard specifies the requirements according to which at the industrial frequency the capacitor must withstand a voltage of 1.1Unom up to 8 hours per day. In addition, the capacitors must be designed for continuous operation at current not exceeding 1.3Inom. Thus, the values of cu and c are 1.1 and 1.3, respectively.
Then, if there are HG in the voltage curve a condition of absence of unacceptable overload of the CB by voltage [6] :
U,
CB
+IU
n=2
nCB
Un
■< Cu
(1)
nom,CB
where UCB is the voltage at the terminals of the CB at the industrial frequency (main harmonic voltage), in calculations it is allowed to use the nominal voltage of the CB Unom cb as Ucb; n is the number of the harmonic component; UnCB is the voltage of the n-th harmonic on capacitors.
The condition for excluding unacceptable overload of the CB by current:
CB
+ I i2cb
n=2
In
< c,
(2)
lnom,CB
where ICB is the current of the industrial frequency in the CB (main harmonic current), as in the case of voltage, it is allowed in the calculations to use the rated current Inom,CB as ICB; InCB is the current of the n-th harmonic flowing through CB.
If the discrete spectrum of the IG is present in the current and voltage curves, conditions (1) and (2) take the following form:
U,
CB
+ IU2
k=1 vk ^
VkCB
U
■< Cu
(3)
nom,CB
I V
'CB • VkCB k=1 Vk ^
< C ,
For the practical application of the condition for the absence of unacceptable overloads of the CB by voltage and current, in the presence of a discrete spectrum of the IG along with the HG, it is advisable to reduce it to the following:
1+-
1
N
Unom,CB k=1 Vk ^
I UVcCB
< Cu
1+
1
N
I1,2
VkCB
< C,
(5)
(6)
I
2nom,CB k=1 vk ^
there N is the number of last harmonic taken into account.
In expressions (5) and (6), the number N should be determined by the frequency range, where the harmonics have the most significant amplitudes. In the general case, the values of N and vN will depend on the source of the IG.
Considering that the excess voltage at the terminals of the CB is allowed up to a value of cu (not more than 8 hours every 24 hours), and the permissible current overload to the value c,=1.3; It is more convenient to transform (5) and (6) to the following form:
N
Unom,CB ^ 2-2 IUVkCB
1 k=1
Vk
N
Inom,CB ^ 12 I IVkCB •
\ k=1
1 Vk ^
(7)
(8)
Verification of the absence of resonant modes during the operation of the CB connected to a network with non-sinusoidal sources can be performed by analyzing the frequency characteristics of the corresponding EN. Frequency characteristics of EN can be obtained both experimentally and by calculation. The method for calculating the resonant modes in EN involves the construction of a circuit for replacing the network under consideration, determining the parameters of the replacement circuit at harmonic frequencies and calculating the frequency characteristics of the input and mutual resistances (or conductances) of network nodes at harmonic frequencies [10].
On the basis of the obtained replacement scheme, a matrix of nodal conductivities of the EN at the frequency of the n-th harmonic is formed:
Y = 1yn
I ' (4)
nom,CB
where k is the number of the harmonic component of the voltage and current curves, respectively; vk is the relative frequency of the k-th harmonic component (the value of vk at some k can coincide with the relative HG frequency n); Uv CB is the voltage of the vk-th harmonic on
capacitors; IVkCB is the current of the vk-th harmonic flowing through CB.
Y11n Y21n
Y12n Y22n
Y
J1mn Y
12mn
Y
-1- mmM
(9)
'm1n Jm2n
Each of the diagonal elements of this matrix corresponds to a specific node of the system and is equal to the sum of the conductivities of all branches directly connected to this node. The off-diagonal elements are equal to the conductivities of the corresponding branches connecting the given pair of nodes taken with the minus sign. In the absence of such branches, the off-diagonal element is assumed to be zero.
The input resistance of the EN on the side of the node with the number i at the frequency of the n-th harmonic can be found as [10]
A
7 _ ^lln
Z"n _ D
(10)
where Dn is the determinant of the matrix of nodal conductances (9) at the frequency of the n-th harmonic; Aiin is the algebraic complement of the determinant Dn.
Mutual (transfer) resistance of the i-th and j-th nodes of the EN at the frequency of the n-th harmonic is
7 _-
A
ijn
Dn
(11)
where Aijn is the algebraic complement of the determinant
Dn.
Algebraic complements Aiin and Aijn can be found as
(12)
A _ D •
iin iin
v2 - r
Since all elements of the filter circuit have active resistance (terminals of capacitors, reactors, bus bars, cables, etc.), then taking into account the active
resistance, the voltage change coefficient is determined by the expression [6]
v2tgq)r
(16)
tg V
p -1)2
+1
Ajn = (-1)'+jDjn , (13)
where Diin is the minor obtained from the determinant Dn deleting the i-th row and the i-th column; Dijn is the the minor obtained from the determinant Dn deleting the i-th row and the j-th column.
At frequencies corresponding to the frequencies of the resonances of the currents, the values of the input and mutual resistances of the nodes will tend to infinity (if the active resistances are neglected). At resonances of currents, a relatively small harmonic current, whose frequency coincides with the resonance frequency, causes considerable stresses at the network nodes (due to large input and mutual resistances of the nodes). This leads to the flow of significant currents in the branches of the network and the overload of the CB.
Due to the fact that changes in the EN occur in the frequency characteristics of the input and mutual resistances caused by changes in the resistance of the mains power, the capacities and modes of the connected loads, and possible switchings in the circuit, it is necessary to take into account these factors and determine possible ranges of changes in the resonance frequencies.
The approach taken to the choice of CB parameters used for RPC is also valid for the selection of the CB that are part of the filter-compensating devices (FCD) used to reduce the voltage nonsinusoidal and, at the same time, the RPC.
The presence of the reactor in the composition of the filter changes the voltage at the terminals of the CB by a value that depends on the frequency of the filter setting v [6],
UCB = avU en, (14)
where Uen is the linear (phase) voltage of the electric network; av is the voltage change coefficient.
Without account of the active resistance of the filter circuit
(15)
where tgpr = xJR; xr is the filter reactor's resistance depending from the resonant condition; Rf is the total active resistance of the filter circuit.
The ratio xJRf is the Q of the contour. Thus, we can write tgq>r = Q. For the FCD of the HG Q>10 [10], according to the investigations carried out for the FCD IG, especially installed in the low-frequency band, the inequality Q>10 is also satisfied.
Calculations have shown that the determination of the coefficient av from expression (15) gives an error in the direction of increase, in comparison with the coefficient av determined by the expression (16), by not more than 1 % at Q=10, with the exception of the range 0.55 < v < 0.7. In the indicated range, the maximum error for v = 0.7 is 1.9 %. As the quality factor increases, the error decreases significantly. So, for example, even at Q=20, the error of calculating av from expression (15) for all frequencies entering the possible zones of the FCD IG unit is less than 1 %.
Thus, when choosing the nominal voltage of the CB of the IG filters, the coefficient av should be determined in accordance with (15). In this case, a slight overestimation of the rated voltage is possible, which is preferable from the point of view of reliable operation of the CB filters when they are detuned.
Taking into account the expressions (5) and (14), the condition for the absence of an unacceptable overload of the CB of the FCD tuned to the frequency v, by voltage:
22
avku +-
1
N
u
■lu
2
VkCB
< Cu _ 1.1.
(17)
nom,CB k_1 Vk *1
rge ku _
Ue
Unom,CB
The CB current ICB is proportional to the voltage on
the bank UCB, therefore we can write [10]
CBavkU.
ICB _ In
(18)
Substituting (18) into (6), after the transformations, we obtain the condition for the absence of an unacceptable overload of the CB of the FCD by current:
2; 2 , avku +-
1
N
I2
112
VkCB
< cl _ 1.3.
(19)
' nom,CB k_1 Vk *1
Conclusions. When choosing capacitor banks for both reactive power compensation and filter-compensating devices, it is necessary to build the frequency characteristics of the input and mutual resistances of the electrical network for analyzing possible resonant phenomena, both in the node with the source of the interharmonics, and in all other nodes of the network. When building frequency characteristics, it is necessary to take into account the active resistances of the elements of the electrical network, which have
a_
2
v
a significant effect on the impedance at resonance of currents.
When choosing the parameters of the filter capacitor banks, a complex solution of a whole range of issues is necessary including ensuring their reliable operation when the parameters of both the filters themselves and the power supply network are disturbed, sources of harmonic distortion from nominal ones; the absence of resonant phenomena at the frequencies of both higher harmonics and interharmonics. The solution of these questions requires: calculation of the spectral composition of the currents of the sources of higher harmonics and interharmonics, rational selection of the zone(s) for the installation of the filter-compensating device, as accurate as possible calculation of the actual frequency of the filter adjustment and the possible range of its deviations.
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Received 19.08.2017
Yu.L. Sayenko1, Doctor of Technical Science, Professor, T.K. Baranenko1, Candidate of Technical Science, Associate Professor,
D.N. Kalyuzhniy2, Candidate of Technical Science, Associate Professor,
1 Pryazovskyi State Technical University,
7, Universytets'ka Str., Mariupol, 87500, Ukraine, phone +380 629 446551,
e-mail: [email protected], [email protected]
2 O.M. Beketov National University of Urban Economy in Kharkiv,
12, Revolution Str., Kharkiv, 61002, Ukraine,
phone +380 57 7073117,
e-mail: [email protected]
How to cite this article:
Sayenko Yu.L., Baranenko T.K., Kalyuzhniy D.N. Features of selection of capacitor banks in electric networks with interharmonic sources. Electrical engineering & electromechanics, 2017, no.5, pp. 67-70. doi: 10.20998/2074-272X.2017.5.11.
