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85
High Electric and Magnetic Field Engineering. Cable Engineering
UDC 621.3.022: 621.315.3: 537.311.8 doi: 10.20998/2074-272X.2018.6.08
M.I. Baranov
A CHOICE OF SECTIONS OF ELECTRIC WIRES AND CABLES IN CIRCUITS OF DEVICES OF HIGH-VOLTAGE HIGH-CURRENT IMPULSE TECHNIQUE
Purpose. Implementation of calculation choice of sections of electric wires and cables in circuits of devices of high-voltage high-current impulse technique (HHIT), characterized flowing of pulsed current ip(t) with different amplitude-temporal parameters (ATP). Methodology. Electrophysics bases of technique of high-voltage and high pulsed currents, theoretical bases of the electrical engineering, bases of electrical power engineering, technique of high electric and magnetic fields, and also measuring technique. Results. The results of the developed generalized electrical engineering investigations are resulted in a calculation choice on the condition of thermal resistibility of cable products of boundary permissible sections SCl of the electric uninsulated wires, and also insulated wires and cables with copper (aluminum) cores (shells) with polyvinyl chloride (PVC), rubber (R) and polyethylene (PET) insulation, on which in the circuits of HHIT the axial-flow ofpulsed current ip(t) flows with arbitrary ATP. On the basis of this approach the results of concrete choice of sections SCl are presented for the indicated electric wires (cables) ofpower circuits of HHIT with pulsed current, ATP of which with amplitudes of Imp = (0.1-1000) kA change on an aperiodic law or law of damped sinusoid in nano-, micro- and millisecond temporal ranges. The results of calculation estimation present maximum permissible approximations of SCU ofpulsed current ip(t) of the examined temporal shapes in the indicated electric wires and cables ofpower circuits of HHIT. It is shown that the values of current approximations of SCa for the uninsulated copper (aluminum) wires in the nanosecond temporal range of ATP of pulsed currents ip(t) are about 495 (293) kA/mm2, in the microsecond temporal range - 26 (15) kA/mm2 and in a millisecond temporal range - 543 (320) A/mm2. By a calculation it is set that for the insulated wires (cables) with copper (aluminum) cores (shells) and PET with insulation the indicated current approximation of SCU is approximately: for the nanosecond range - 361 (233) kA/mm2; for the microsecond range -19 (12) kA/mm2; for the millisecond range - 396 (256) A/mm2. Originality. Firstly by a calculation for the concrete temporal shapes of pulses of current ip(t) in the discharge circuits of HHIT, changing in the wide range of the amplitudes Imp on a aperiodic law or law of damped sinusoid, the numeral values of cross-sections SCil and current approximations of SCU are obtained for the uninsulated wires, insulated wires and cables with copper (aluminum) cores (shells) with PVC, R and PET insulation. Practical value. Application in practice of model tests of objects of electrical power engineering, aviation and space-rocket technique on resistibility to direct action of pulsed currents ip(t) with different ATP of natural (currents of lightning) and artificial (discharge currents of HHIT) origin to increase electro-thermal resistibility of the electric uninsulated wires, and also the insulated wires and cables with PVC, R and PET insulation of HHIT widely applied in power circuits. References 13, tables 11, figures 2.
Key words: high-voltage high-current impulse technique, electric wires and cables, calculation choice of boundary permissible sections of wires and cables in the circuit of impulse technique.
Приведены результаты разработанного обобщенного электротехнического подхода к расчетному выбору по условию термической стойкости предельно допустимых сечений SCl электрических неизолированных проводов, а также изолированных проводов и кабелей с поливинилхлоридной (ПВХ), резиновой (Р) и полиэтиленовой (ПЭТ) изоляцией с медными (алюминиевыми) жилами (оболочками), по которым в цепях высоковольтной сильноточной импульсной техники (ВСИТ) протекает аксиальный импульсный ток ip(t) с произвольными амплитудно-временными параметрами (АВП). На основании данного подхода продемонстрированы результаты конкретного выбора сечений SCil для указанных электрических проводов (кабелей) силовых цепей ВСИТ с импульсным током, АВП которого с амплитудами Imp=(0,1-1000) кА изменяются по апериодическому закону или закону затухающей синусоиды в нано-, микро- и миллисекундному временных диапазонах. Представлены результаты расчетной оценки предельно допустимых плотностей SCl импульсного тока ip(t) рассматриваемых временных форм в указанных электрических проводах и кабелях силовых цепей ВСИТ. Полученные результаты будут способствовать повышению электротермической стойкости электрических неизолированных проводов, а также изолированных проводов и кабелей с ПВХ, Р и ПЭ Т изоляцией, широко применяемых в силовых цепях ВСИТ. Библ. 13, табл. 11, рис. 2. Ключевые слова: высоковольтная сильноточная импульсная техника, электрические провода и кабели, расчетный выбор предельно допустимых сечений проводов и кабелей в цепях импульсной техники.
Introduction. One of the challenges in the field of high-voltage high-current impulse technology (HHIT) is a reasonable choice of cross-sections SC of used in it electrical wires and cables. It is known that in wires and cables in the area of HHIT can flow in normal and emergency modes of operation of such equipment pulsed currents ip(t) with different amplitude-temporal parameters (ATP). In this case, the amplitudes Imp of these currents can vary in the range from hundreds of amperes to thousands of kiloamperes, and their duration tp varies from tens of nanoseconds to hundreds of milliseconds [1, 2]. The well-known approach for choosing sections SC of electrical wires (cables) for short-term modes of their operation, used now in traditional industrial electric power engineering, is based on the thermal resistance of
cable-conductor products (CCP) under the conditions of a short circuit (SC) current acting on it with specified ATP [3]. In this case, the thermal resistibility of electrical wires and cables is limited by the maximum permissible short-term temperature 8iS of heating of the parts of wires (cables) at SC. In Table 1, according to the results of [3], the numerical values of the temperature 8iS of heating are given for the main conductive and insulating materials of electrical wires and cables at SC. From the data of Table 1 it can be seen that the value of 8tS should not exceed for used in power electric circuits with current frequency of 50 Hz uninsulated copper and aluminum cores (wires) in SC mode the highest level of 250 °C and 200 °C, and for
© M.I. Baranov
cables (insulated wires) with copper and aluminum cores and PVC (R), PET insulation, respectively, the level of 150 °C and 120 °C [3].
Table 1
The values of the maximum permissible short-term temperature 8ls of heating for the main conductor and insulation materials of wires (cables) of industrial electric power circuits under the action of SC [3]
No. Name of the wire (cable) part °C
1 Tire (core), copper, uninsulated at stresses less 20 N/mm2 250
2 Tire (core), aluminum, uninsulated at stresses less 200
10 N/mm2
3 Cable and insulated wire with copper (aluminum) cores and polyvinyl chloride (PVC) or rubber (R) insulation 150
4 Cable and insulated wire with copper (aluminum) cores and polyethylene (PET) Insulated 120
5 Aluminum part of the steel-aluminum wires of power 200
lines
We point out that in the industrial electric power industry, the long-term permissible temperature 8U of heating the conductive and insulating parts of electrical wires and cables is limited by the conditions for reliable operation of electrical contacts and contact connections or by the conditions of their insulation [3]. In Table 2, according to the data of [3], the well-known numerical values of the heating temperature 8n for the main types of electrical wires and cables used in the field of modern power engineering are given.
Table 2
The values of long-term permissible temperature Qu for the main types of electrical wires (cables) [3]
No. Name of the wire (cable) or the core 0a, °C
1 Wires (cores) uninsulated with any current-carrying tires (parts) 70
2 Cables (wires) with copper (aluminum) tires, PVC, R and PET insulation 65
3 Cables with impregnated cable insulation paper for voltage up to 6 kV 65
4 Cables with impregnated cable insulation paper for voltage up to 35 kV 50
From the data of Table 2 it follows that the maximum long-term permissible temperature 8n of heating for uninsulated wires and cables with PVC, PET and R insulation, which are under current load in industrial electric power circuits, should not exceed respectively the level of 70 °C and 65 °C. Taking into account the data of Table 1, 2, as well as the condition that the wire (cable) before the impulse effect of SC current on it was fully electrically loaded and had temperature 8lh and at SC it heated to temperature 8S, in [3] to select the minimum permissible cross-section Slmin of electrical wire (cable) wire the following calculated ratio is recommended:
Sl min = Bk2 I Ck , (1)
tk
where Bk= | ¿2(t is the Joule (action) integral of the SC
0
current ik(t) with duration tk (a technique of calculation of Bk is presented in [3]), A2-s; Ck is the coefficient (A-s1/2/mm2), whose numerical values are given in Table 3.
Table 3
The values of the coefficient Ck for the main types of electrical wires and cables of industrial electric power circuits under the action of SC [3]
No. Name of the wire (cable) and the core Ck, A-s1/2/mm2
1 Wires (cores), copper, uninsulated 170
2 Wires (cores), aluminum, uninsulated 90
3 Cables (insulated wires) with PVC and R insulation and copper cores 120
4 Cables (insulated wires) with PVC and R insulation and aluminum cores 75
5 Cables (insulated wires) with PET insulation and copper cores 103
6 Cables (insulated wires) with PET insulation and aluminum cores 65
Taking into account the fact that ATP of pulsed currents ip(t), used in the field of HHIT, usually do not correspond to ATP of SC current in industrial electric network, application of (1) and data of Table 3 for the calculation determination of sections SC of electrical wires (cables) in the HHIT circuits is essentially impossible technical way. In this regard, an approximate calculation of sections sC of electrical wires and cables of HHIT for various ATPs of the pulsed current ip(t) flowing through them is an actual applied scientific and technical problem.
The goal of the paper is performing a calculation selection of sections sC of electrical wires and cables in circuits of HHIT devices, characterized by the flow of pulsed current ip(t) with various ATPs.
1. Problem definition. We consider the widely used in electric circuits of HHIT uninsulated copper and aluminum wires, as well as insulated wires and cables with copper (aluminum) inner cores and outer shells, having PVC, R and PET insulation [1, 2]. It is assumed that in the round solid or split copper (aluminum) cores and shells of these wires and cables of HHIT electric circuits in their longitudinal direction pulsed currents ip(t) flow, ATPs of which correspond to nano-, micro- or millisecond time ranges with amplitudes Imp, varying in a wide range from 0.1 kA to 1 MA. We believe that the wires and cables under investigation are placed in the surrounding air environment, the temperature of which is 80=20 °C. We use the assumption that in the first approximation the pulsed current ip(t) is almost uniformly distributed over the cross-section SCi of the core (i=1) and the shell (i=2) of the wire (cable). One of the rationales of this assumption is that, for example, for a current pulse of a short lightning discharge of the temporal shape t/tp=10 ^s/350 ^s (tf, tp are, respectively, the front duration at the level (0.1-0.9) Imp and the current pulse duration at the level of 0.5 Imp) the penetration depth ai of the azimuthal magnetic field of the specified artificial lightning current into the studied non-ferromagnetic materials of the wire (cable) is approximately 0.65 mm for copper and 0.82 mm for aluminum [4]. These numerical values of A,-
in practice can be commensurate with the real radii of the core and the wall thickness of the wire (cable) shell. For current pulses ip(t), related to the millisecond time range (as for SC currents in circuits of power facilities), the use of such an assumption in the calculation of the cross-sections Sa of wires (cables) becomes even more legitimate. Let us take advantage of the adiabatic nature of pulsed current ip(t) with a duration of no more than 1000 ms in the materials of the cores (shells) of the considered CCP of electrothermal processes, under which the influence of heat transfer from the surfaces of their current-carrying parts having the current temperature 8Cl>80 and thermal conductivity of their materials and insulation on Joule heating of the current-carrying parts of the cores (shells) of wires (cables) is neglected. We believe that the thermal resistivity of wires (cables) of electric circuits of HHIT when exposed to a pulsed current ip(t) is limited by their maximum permissible short-term heating temperature 8CS, depending on the degree of reduction of the mechanical strength of the core (shell) material and the thermal conditions of operation conditions of the CCP insulation in the mode of its short-term heating by a current pulse of nano-, micro- or millisecond duration, flowing through their current-carrying parts. As in [4], we assume that the value of temperature 8CiS corresponds to the maximum permissible short-term temperature 8iS of heating wires and cables by SC currents of industrial frequency (see Table 1) known from [3]. Then, in accordance with the data of Table 1, for uninsulated copper (aluminum) wires of circuits of HHIT, the value of 0as will be approximately 250 °C (200 °C), for their insulated wires (cables) with copper and aluminum cores (shells) and PVC (R) insulation 8cs=150 °C, and for their CCP with the indicated conductors (shells) and PET insulation 8CS~120 °C. It is required by calculation in an approximate form to determine the boundary permissible cross-sections SCl of current-carrying parts for uninsulated copper (aluminum) wires, as well as for insulated wires and cables with copper (aluminum) cores (shells) and PVC (R), PET insulation, used in HHIT circuits and experiencing a direct axial pulsed current ip(t) of various amplitudes Imp in the nano-, micro- and millisecond time ranges.
2. A generalized approach to the choice of sections SCii of electrical wires (cables) in the field of HHIT. For the boundary permissible cross-sections SCil of the current-carrying cores (shells) of the considered electric wires and cables with axial pulsed current ip(t) of arbitrary ATPs, the following approximate calculated dependence [5] follows from the equation of their heat balance in the adiabatic mode:
SCil - (JCiA)1/2/Cl
(2)
F
where JCiA = ji2p(t)dt is the action integral of the pulsed
current ip(t) with duration tp and given ATPs,
Ap-s;
Ci = (Jcis - Jc«)1/2, A-s1/2/m2; Jas, Jcii are, respectively, the current integrals for the current-carrying cores (shells) of the studied electric wires and cables of the HHIT power circuits, the maximum permissible short-term and long-term heating temperatures of the material of which
„1/2/^2.
correspond to 8iS (see Table 1) and 8U (see Table 2) values, A2-s/m4.
To find the numerical values of the JCS and JCU current integrals included in (2), the following analytical expressions can be used [2, 5]:
JaiS = Y0iP0i lnk-Aw(0S -00) +1]; (3)
Jail = YmPm ln[%A); (0i -00) +1], (4) where y0i, c0i, fi0i are, respectively, the specific electrical conductivity, the specific volume heat capacity and the thermal coefficient of specific electrical conductivity of the core (shell) material of the wire (cable) of the HHIT electrical circuit under study before they are subjected to a pulsed current ip(t) with arbitrary ATPs.
Table 4 presents numerical values of y0i, c0i and fi0i at temperature 80=20 °C [2, 6].
Table 4
The main thermophysical characteristics of the material of the current-carrying cores (shells) of electric uninsulated wires and insulated wires as well as cables of power circuits of HHIT at 80=20 °C [2, 6]
Material of the core (shell) of the wire (cable) Values yoi, 107-(Q-m)-1 Values c0i, 106-J/(m3-°C) Values p0i, 10-9-m3/J
Copper 5.81 3.92 1.31
Aluminum 3.61 2.70 2.14
As for the calculation definition in (2) of the integral of action JCA of the pulsed current ip(t) with arbitrary ATPs, for the case of its change over time t according to the aperiodic law of the form
ip (t) = kp1lmp [exp(-«1i) - exp(-«2?)], (5)
where a1~0.76/rp, a2~2.37/Tf are, respectively, the shape coefficients of the aperiodic current pulse with given ATPs flowing in the electric circuit of the HHIT; kp1=[(a1/a2)m - (a1/a2)"]-1 is the normalization factor; m=a1/(a2-a1); n=a2/(a2-a1); the calculated expression for the integral of action JCA of the current pulse ip(t) flowing in the HHIT circuit takes the following convenient analytical form [7]:
(6)
J
CiA
■ khip[o.658rp -0.633rf
XpV p "U'UJJi f
where t, tp are respectively, the durations of the front and the half-fall of the current pulse ip(t).
In the case of a change in time t of the acting on the materials of the wire (cable) of the HHIT pulsed current ip(t) according to the law of a damped sinusoid of the form
ip (t) - kppIipi exp(-St) sin(®t), (7)
where d=Ap/Tp is the current attenuation coefficient; œ=2n/Tp is the circular frequency of the current oscillations; Tp is the period of the current oscillations; Ap=ln(Iip1/Iip3) is the logarithmic decrement of pulsed current oscillations with the first Iip1 and the third Iip3 amplitudes in the HHIT circuit; kp2 = [exp(-Jp/2n-arcctgJp/2n)-sin(arcctgJp/2n)]-1 is the normalization factor for damped sinusoidal current; the calculated expression for the integral of action JCiA of the current pulse ip(t) flowing in the HHIT circuit takes
the following sim
JCiA ~ kp2Iipi
île analytical form [5]:
Tp (4 A p )-1 - A pTp (4Ap +16^2)-1]. (8)
r
From (4) it can be seen that at 0n=00=20 °C (wires and cables are de-energized) the value of the current integral JCll=0, which will lead by (2) to a decrease in the cross-section SCil.
Knowing from normative documents or experimental data the numerical values of Imp, t, tp, Ap, Tp, taking into account the estimates of the values of the normalizing coefficients kp1 and kp2 by (2)-(8) for the specified temporal shapes of the pulsed current ip(t), we can be calculate in the approximate form (with an error of up to 5 %), the boundary permissible cross-sections SCil of the conductive wires (shells) of wires and cables used in the electric circuits of HHIT. Finding the values of the SCil sections, taking into account the accepted assumptions, the maximum permissible pulsed current densities of the pulsed current ip(t) of one or another shape in electrical wires (cables) of the HHIT circuits can be determined in the first approximation from the dependence like
8Cil~Imp/SCi l.
3. The choice of cross-sections SCil of electrical wires (cables) for nanosecond current pulses in the field of HHIT. First, we will focus on the selection of the SCil sections of the wires (cables) under consideration, along copper (aluminum) cores (shells) under the conditions Jcll=0 or Jcl#0, the axial aperiodic current pulse of the time shape r/rp=5 ns/200 ns flows [8]. Note that at one time this nanosecond current pulse ip(t) of both polarities was used when imitating in HHIT discharge circuits with the necessary air field-formation systems and, accordingly, in their working air volumes with powerful electromagnetic pulse (EMP) dimensions of the high-altitude nuclear explosion (HNE) [9, 10]. From (5) we find that for this calculation case, the form coefficients a1 and a2 of the current pulse ip(t) take the following numerical values: a1~3.8-106 cs-1; a2~4.7-108 s-1. Here, for this current pulse, the normalizing coefficient kp1 is approximately equal to kp1~1.049. Table 5 presents by (6) the numerical values of the action integral JCA for a series of values of the amplitude Imp of the considered powerful nanosecond current pulse of the time shape 5 ns/200 ns used in testing military and civilian objects for resistibility to EMP of HNE [9, 10].
Table 5
The values of the integral of action JCiA for nanosecond aperiodic current pulse of the shape 5 ns/200 ns
The value of the amplitude Imp of the current pulse of the shape 5 ns/200 ns, kA The value of the integral of action JCAof the current pulse 5 ns/200 ns, A2-s
1 0.141
10 14.13
30 1.27-102
50 3.53-102
70 6.92-102
100 1.41103
200 5.65-103
500 3.53-104
1000 1.41105
with copper (aluminum) cores (shells) with PVC, R and PET insulation for the cases of their preliminary current load (Ja#0) or full de-energizing (Jcii=0).
Comparison of data of Table 3, 6 indicates that the numerical values of the coefficients Ck h Cl for the considered wires and cables in the case when JCl#0 and the value of this integral of the current is determined from (4) differ from 3 to 8 %. In the case when JCll=0 (the case traditional for HHIT), these differences increase and range from 9 to 26 %. In Table 7 based on (2) and calculated data of Table 5, 6 at JCll=0 (wires and cables in the HHIT power circuit are without prior current load) the results of the selection of the boundary permissible cross-sections SCil for the wires (cables) in the HHIT circuits under study, along which a powerful nanosecond current pulse of the time shape of 5 ns/200 ns with amplitude Imp equal to 10, 50, 100, and 500 kA are presented.
Table 6
The values of the coefficient Cl values for uninsulated wires, insulated wires (cables) with copper (aluminum) cores (shells) in HHIT circuits with nano-, micro- and millisecond current pulses
Insulation type in the wire (cable) of the HHIT power circuit Material of the core (shell) of the wire (cable) Values of Cl, 108 A-s1/2/m2
Jcii=0 Jaé0
Without insulation Copper 1.860 1.563
Aluminum 1.096 0.880
PVC, R Copper 1.506 1.160
Aluminum 0.972 0.745
PET Copper 1.355 0.957
Aluminum 0.877 0.616
Table 7
The values of the boundary permissible cross-sections SCl for wires (cables) with copper (aluminum) cores (shells) in HHIC circuits with a nanosecond current pulse of the shape 5 ns/200 ns, the amplitude of which varies in a wide range from 10 kA to 500 kA
Insulation type in the wire (cable) of the HHIT power circuit Material of the core (shell) of the wire (cable) Values of the cross-section Sai, mm2
Amplitude Imp of the current pulse 5 ns/200 ns, kA
10 50 100 500
Without insulation Copper 0.020 0.101 0.202 1.010
Aluminum 0.034 0.171 0.342 1.714
PVC, R Copper 0.025 0.125 0.250 1.250
Aluminum 0.039 0.193 0.386 1.933
PET Copper 0.028 0.138 0.278 1.386
Aluminum 0.043 0.214 0.428 2.142
Table 6 shows the calculated by (2) the numerical values of the coefficient Cl for uninsulated wires with copper (aluminum) cores and insulated wires (cables)
From the data of Table 7 it follows that the estimated maximum allowable density Ôcil~lmp/Sca of a nanosecond current pulse of the shape 5 ns/200 ns for uninsulated wires with copper and aluminum cores is approximately 495 kA/mm2 and 293 kA/mm2, and for cables with copper (aluminum) cores (shells) and PET insulation 361 (233) KA/mm2.
4. The choice of cross-sections SCil of electrical wires (cables) for microsecond current pulses in the field of HHIT. Fig. 1 shows a typical oscillogram of a
pulsed A- component of an artificial lightning current reproduced in the discharge circuit of a powerful lightning current generator (LCG) for testing aeronautical and rocket-space technology objects for lightning resistibility in accordance with the requirements of US SAE ARP 5412: 2013 [11] and SAE ARP 5416: 2013 [12]. It can be seen that the indicated component of the pulsed current ip(t) of the lightning simulated under laboratory conditions in time t varies according to the damped sinusoid law. We make the choice of cross-sections SCii of wires and cables for the discharge circuit of the LCG applicable to a given current pulse ip(t).
From the experimental data presented in Fig. 1, we find that for the bipolar oscillatory current pulse used in the calculations of the cross-sections SCi , Ap=ln(Impi/Imp3)=2.505. Then by (7) for this current the coefficient Ap2=1.731. Table 8 shows the numerical values of the integral of action JCA calculated by (8) for a given microsecond current pulse [13], changing according to the law of a damped sinusoid.
CH1 5.00VEU MSO.Ojus
Fig. 1. A typical oscillogram of a microsecond pulsed A- component of an artificial lightning current flowing in a discharge circuit of a high-voltage LCG (Impi~ -207 kA;
=185 ^s; vertical scale 56.3 kA/division; horizontal scale 50 ^s/division) [13]
Imp3~ - 16.9 kA; Tp
Table 8
The values of the integral of action JCA for current pulse ip(t), changing in the microsecond time range according to the law of damped sinusoid of the form (7)
The value of the first amplitude Impi of the damped sinusoidal current pulse, kA The value of the integral of action JCiA of the current pulse of the form (7), A2-s
10 4.77T03
30 4.29-104
50 1.19105
70 2.34T05
100 4.77-105
207 2.05T06
300 4.29-106
500 11.92106
700 23.4T06
1000 47.7-106
Using the calculated data for the coefficient C , given in Table 6, (2) and summarized in Table 8 the results of determining the integral of action JCiA, we find
the boundary permissible cross-sections SCi for the wires (cables) under study in HHIT circuits, in which a microsecond current pulse of the form (7) flows with ATPs corresponding to the data typical of Fig. 1. In Table 9 at JC =0, the results of such a determination of the boundary permissible cross-sections of SCi for the wires and cables under consideration used in the discharge circuits of HHIT are presented.
From the presented in Table 9 the calculated data, it follows that the estimated maximum allowable density SCipImp\/SCij of the microsecond pulsed current ip(t) with the ATP corresponding to the data in Fig. 1, for uninsulated wires with copper and aluminum cores is approximately 26 kA/mm2 and 15 kA/mm2, and for cables with copper (aluminum) cores (shells) and PET insulation 19 (12) KA/mm2.
Table 9
The values of the boundary permissible Sal cross-sections for wires (cables) with copper (aluminum) cores (shells) in HHIT circuits with a microsecond current pulse of the form (7), the first amplitude Imp1 of which varies in a wide range from 30 kA to 207 kA
Insulation type in the wire (cable) of the HHIT power circuit Material of the core (shell) of the wire (cable) The values of the cross-section SCil, mm2
The first amplitude Imp1 of the current pulse of the form (7), kA
30 50 100 207
Without insulation Copper 1.113 1.854 3.713 7.698
Aluminum 1.889 3.147 6.301 13.06
PVC, R Copper 1.375 2.290 4.586 9.507
Aluminum 2.131 3.549 7.105 14.73
PET Copper 1.528 2.546 5.097 10.57
Aluminum 2.362 3.933 7.875 16.32
5. The choice of cross-sections SCii of electrical wires (cables) for millisecond current pulses in the field of HHIT. Fig. 2 shows a typical oscillogram of a long-term C-component of the artificial lightning current generated according to the requirements of [11, 12] in the discharge circuit of the LCG for the purpose of the experimental determination of lightning resistibility of aerospace equipment objects in flight conditions in air. It can be seen that the aperiodic current pulse ip(t) of the negative polarity of this component in the composition of the total artificial lightning discharge current varies in a millisecond time range. Its amplitude Imp which corresponds to the time tmp~ 11 ms, is about 835 A. At the same time, the duration of the front of the test current pulse is approximately Tf ~7 ms, and its duration at the level of 0.5 Imp is tp ~ 160 ms. According to the requirements of [11, 12], the total duration of the flow of the specified component of the current pulse of artificial lightning in the conductors of the discharge circuit of a powerful high-voltage LCG reaches about 1000 ms. On the basis of the proposed electrical engineering approach, we perform the choice of cross-sections SCi of wires (cables) for a discharge circuit of the LCG involved in generating the specified current pulse ip(t).
CH1 SO.OmVEy M 100ms CH1 \ -40,0mV
Fig. 2. A typical oscillogram of a millisecond long-term C- component of an artificial lightning current flowing in a discharge circuit of a powerful high-voltage LCG (Imp~ -835 A; Tf -7 ms; Tp-160 ms; vertical scale 282 A/division; horizontal scale 100 ms/division) [13]
Table 10
Values of the integral of action JCA for unipolar current pulse ip(t), varying in millisecond time range by aperiodic low
The values of the amplitude Imp of the unipolar millisecond aperiodic current pulse 7 ms/160 ms, A The values of the integral of action JCA of the millisecond current pulse 7 ms/160 ms, A2-s
100 1.17103
200 4.68-103
300 1.05T04
500 2.92-104
700 5.73T04
835 8.15T04
1000 1.17105
numerical values of the maximum permissible densities dCil in wires (cables), through which a millisecond aperiodic current pulse ip(t) with amplitude Imp, varying in the range (100-1000) A, flows in the longitudinal direction.
Table 11
The values of boundary allowable cross-sections SCil for uninsulated wires and insulated wires (cables) with copper (aluminum) cores (shells) in HHIT circuits with a millisecond aperiodic current pulse of 7 ms/160 ms, amplitude Imp of which varies in the range from 100 A to 1000 A
-160 ms, we find that Then the normalizing
From (5) at Tf -7 ms and a1-4.75 s-1 and a2-338-102 s-1 coefficient kp1 takes a numerical value of approximately kp1-1.077. Using (5) and varying the value of the current amplitude Imp, it is possible to calculate the numerical indices of the integral of action JCiA for the considered millisecond current pulse ip(t). Table 10 shows the numerical values of JCiA for a number of amplitudes of Imp of a given pulse current ip(t).
Insulation type in the wire (cable) of the HHIT power circuit Material of the core (shell) of the wire (cable) The value of the cross-section SCil,mm2
Amplitude Imp of the current pulse 7 ms/160 ms, A
100 500 835 1000
Without insulation Copper 0.184 0.919 1.535 1.839
Aluminum 0.312 1.559 2.605 3.121
PVC, R Copper 0.227 1.135 1.896 2.271
Aluminum 0.352 1.758 2.937 3.519
PET Copper 0.252 1.261 2.107 2.524
Aluminum 0.390 1.948 3.255 3.900
Further, assuming that JCu=0 (the wires and cables in the discharge circuit of HHIT are previously de-energized), we use the results of an approximate calculation of the coefficient C h summarized in Table 6. Taking into account these numerical values of C and the data of Table 10, according to (2), in the accepted approximation, it is possible to find the boundary permissible cross-sections SCi for uninsulated and insulated wires and cables with copper (aluminum) cores (shells) with PVC, R and PET insulation, which are subjected to an axial millisecond aperiodic current pulse ip(t), which ATPs correspond to the data of Fig. 2. Table 11 shows the numerical values of the boundary permissible cross-sections SCi for the indicated wires (cables) with a millisecond aperiodic current pulse ip(t), found in the manner described above. Based on the ratio of the form 8Cu-ImJSCii, the data of Table 11 allow us to estimate the
From the data of Table 11 it follows that the estimated maximum permissible density dCil of the millisecond aperiodic current pulse ip(t) with the ATPs corresponding to the data in Fig. 2, for uninsulated wires with copper and aluminum conductors is approximately 543 A/mm2 and 320 A/mm2, and for cables with copper (aluminum) cores (shells) and PET insulation 396 (256) A/mm2.
The results of experimental studies in discharge circuits of HHIT with pulsed currents ip(t) of micro- and millisecond duration of electrothermal resistibility of prototypes of uninsulated wires, insulated wires and cables with copper cores (shells) with PVC and PET insulation, presented by the author in [5, 13] , confirm the validity of the basic calculation data on the choice of the cross-sections SCi presented in Table 9, 11.
Conclusions.
1. The presented generalized electrical engineering approach allows, according to the condition of thermal resistibility of CCP, to carry out an approximate calculation choice of boundary permissible cross-sections SCi of uninsulated wires, insulated wires and cables with copper (aluminum) cores (shells) with PVC, R and PET insulation, the current-carrying parts of which are affected axial current pulse ip(t), ATPs of which with different amplitudes Imp can vary in nano-, micro- and millisecond time ranges.
2. Using the examples of the change in time t of the pulsed current ip(t) flowing through the specified wires (cables) according to aperiodic law or the damped sinusoid law, the possibilities of the proposed electrical engineering approach to the specific choice of the boundary permissible cross-sections SCi for the considered types of uninsulated wires, insulated wires and cables widely used in the discharge circuits of HHIT are demonstrated.
3. It is shown that, in the first approximation, the maximum permissible densities da—Imp/Sai of the
considered temporal shapes of pulsed current p(t) in copper (aluminum) cores of non-insulated wires for the nanosecond range are numerically about 495 (293) kA/mm2, for the microsecond range 26 (15) kA/mm2 and for the millisecond range 543 (320) A/mm2. For insulated wires (cables) with copper (aluminum) cores (shells) and PET insulation, the numerical values of the maximum permissible densities dCa of the considered pulsed currents ip(t) for the nanosecond range are about 361 (233) A/mm2, for the microsecond range 19 (12) kA/mm2 and for the millisecond range 396 (256) A/mm2.
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Received 07.08.2018
M.I. Baranov, Doctor of Technical Science, Professor, Scientific-&-Research Planning-&-Design Institute «Molniya», National Technical University «Kharkiv Polytechnic Institute», 47, Shevchenko Str., Kharkiv, 61013, Ukraine, phone +380 57 7076841, e-mail: baranovmi@kpi.kharkov.ua
How to cite this article:
Baranov M.I. A choice of sections of electric wires and cables in circuits of devices of high-voltage high-current impulse technique. Electrical engineering & electromechanics, 2018, no.6, pp. 56-62. doi: 10.20998/2074-272X.2018.6.08.
