CC BY
78
High Electric and Magnetic Field Engineering. Cable Engineering
UDC 621.3.022: 621.315.3: 537.311.8 doi: 10.20998/2074-272X.2019.2.06
M.I. Baranov
CALCULATION AND EXPERIMENTAL DETERMINATION OF CRITICAL SECTIONS OF ELECTRIC WIRES AND CABLES IN THE CIRCUITS OF DEVICES OF HIGHVOLTAGE HIGH-CURRENT PULSE TECHNIQUE
Purpose. Implementation of calculation and experimental determinations of critical sections and current densities in electric wires and cables of circuits of devices of high-voltage high-current impulse technique (HHIT), characterized flowing of pulse current ip(t) with different amplitude-temporal parameters (ATPs). Methodology. Electrophysics bases of technique of highvoltage and large pulse currents, theoretical bases of electrical engineering, bases of electrical power energy, technique of high electric and magnetic fields, and also measuring technique. Results. The results of the developed electrical engineering approach are resulted in calculation choice on the condition of electric explosion (EE) in atmospheric air of current-carrying parts of cable-conductor products of critical sections of SCCi of the uninsulated wires, and also the insulated wires and cables with polyvinyl chloride (PVC), rubber (R) and polyethylene (PET) insulation with copper (aluminum) cores (shells) on which in the circuits of HHIT the pulse axial-flow current ip(t) flows with arbitrary ATPs. On the basis of this approach the results of choice of critical sections SCCi are shown for the indicated electric wires (cables) of power circuits of HHIT with pulse current, ATPs of which with amplitudes of Imp=(0.1-1000) kA change on a aperiodic law or law of attenuation of sine wave in nano-, micro- and millisecond temporal ranges. The results of calculation estimation of critical amplitudes of current densities SCCi of -pulses of current ip(t) of the examined temporal shapes are presented in the indicated electric wires and cables of circuits of HHIT. By a calculation way it is set that critical amplitudes of current densities SCCi of pulse current ip(t) for its indicated temporal shapes in the copper (aluminum) cores of the uninsulated wires and insulated wires and cables with copper (aluminum) cores (shells), PVC, R and PET insulation for nanosecond range are numerically 1176 (878) kA/mm2, for the microsecond range 64 (48) kA/mm2 and for the millisecond range 1.29 (0.97) kA/mm2. By the powerful high-voltage generator of current of artificial lightning experimental verification of applicability of the offered calculation relations is executed for the choice of critical sections SCCi and amplitudes of current densities SCCi in wires (cables) at their EE. Originality. First by a calculation way for the specific temporal shapes of pulse currents ip(t) in the discharge circuits of HHIT, changing in nano-, micro- and millisecond temporal ranges with the wide change of the amplitudes Imp on an aperiodic law or law of attenuation of sine wave, the numeral values of critical sections SCCi and amplitudes of current densities SCCi are obtained for the uninsulated wires, insulated wires and cables with copper (aluminum) cores (shells), PVC, R and PET insulation. Practical value. Application of the obtained results is in practice of tests of objects of electrical power energy, aviation and space-rocket technique on resistibility to action of pulse currents ip(t) with different ATPs of natural (currents of the imitated lightning) and artificial (discharge currents of HHIT) origin will be instrumental in the increase of electro-thermal resistibility of the uninsulated wires, and also the insulated wires and cables with PVC, R and PET insulation of HHIT widely applied in power circuits. References 15, tables 7, figures 6. Key words: high-voltage high-current pulse technique, electric wires and cables, calculation choice of critical sections of wires and cables in circuits of pulse technique, experiment.
Hadaui результати розробленого електротехтчиого nidxody до розрахункового вибору за умовою електричного вибуху (ЕВ) струмoпрoвiдних частин кaбельнo-прoвiдникoвoí продукци критичних перерЫв SCCi негзольованих дрoтiв, а також ¿зольованих дрoтiв i кабелв з потвштхлоридною (ПВХ), гумовою (Г) i потетиленовою (ПЕТ) Ьолящею з мiдними (алюмШевими) жилами (оболонками), по яких в колах високовольтно1' сильнoструмнoí iмпульснo'í техшки (ВС1Т) прoтiкae тпульсний акаальний струм ip(t) з довтьними амплтудно-часовими параметрами (АЧП). На niдстaвi цього тдходу прoдемoнстрoвaнi результати вибору критичних перерiзiв SCCi для вказаних електричних дрoтiв (кабетв) силових кт ВС1Тз тпульсним струмом, АЧПякого з амплтудами Imp=(0,1-1000) кА зтнюються по аперюдичному закону або закону затухаючо1' синусо1'ди в нано-, мкро- i мШсекундному часових дiaпaзoнaх. Представлен результати розрахунково1' ощнки критичних амплтуд щтьностей SCCi тпульсш струму ip(t) цих часових форм у вказаних електричних дротах i кабелях кт ВС1Т. Виконана експериментальна перевiркa прaцездaтнoстi запропонованих розрахункових спiввiднoшень для вибору перерiзiв SCCi i щтьностей SCCi струму в дротах (кабелях) при х ЕВ. Отримат результати сприятимуть забезпеченню електрoтермiчнo'í стiйкoстi електричних назольованих дрoтiв, а також iзoльoвaних дрoтiв i кабетв зi ПВХ, Г i ПЕТ Ьолящею, як широко застосовуютьсяу силових колах ВС1Т. Бiбл. 15, табл. 7, рис. 6.
Ключовi слова: високовольтна сильнострумна iмпульсна техшка, електричш дроти i кабел^ розрахунковий B^ip критичних пеpеpiзiв дроив i кабелiв в колах iмпульсноl техшки, експеримент.
Приведены результаты разработанного электротехнического подхода к расчетному выбору по условию электрического взрыва (ЭВ) токонесущих частей кабельно-проводниковой продукции критических сечений SCCi 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 импульсный аксиальный ток ip(t) с произвольными амплитудно-временными параметрами (АВП). На основании этого подхода продемонстрированы результаты выбора критических сечений SCCi 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 критических амплитуд плотностей SCCi импульсов тока ip(t) рассматриваемых временных форм в указанных электрических проводах и кабелях цепей ВСИТ. Выполнена экспериментальная проверка работоспособности предлагаемых расчетных соотношений для выбора сечений SCCi и плотностей SCCi тока в
© M.I. Baranov
проводах (кабелях) при их ЭВ. Полученные данные будут способствовать обеспечению электротермической стойкости электрических неизолированных проводов, а также проводов и кабелей с ПВХ, Р и ПЭТ изоляцией, широко применяемых в силовых цепях ВСИТ. Библ. 15, табл. 7, рис. 6.
Ключевые слова: высоковольтная сильноточная импульсная техника, электрические провода и кабели, расчетный выбор критических сечений проводов и кабелей в цепях импульсной техники, эксперимент.
Introduction. In practice, when designing, building and operating high-power electrical installations in the field of high-voltage high-current impulse technology (HHIT), specialists need to be able to determine the critical cross sections SCa of electrical wires and cables used in their circuits and containing metal wires (/=1) and shells (/=2). The critical sections Sca of wires (cables) are their cross sections that are not able to withstand the current loads acting on them with one or another amplitude-temporal parameters (ATPs), leading to the appearance of the electric explosion (EE) phenomenon of metal cores (shells) of specified wires and cables and, accordingly, to their failure [1, 2]. Note that the EE phenomenon of current-carrying parts can also be observed in the field of industrial electric power engineering, when wires and cables not reasonably used in power grids are not designed for the flow of high short-circuit (SC) currents through them, reaching at durations of (60-100) ms amplitude values up to (10-100) kA [3]. One of the peculiarities of electrical installations of HHIT, in contrast to electrical installations of industrial electric power engineering, is that pulse currents of various ATPs related to the nano-, micro- and millisecond time ranges can flow through the current-carrying parts of their electrical circuits. In this case, the amplitude values Imp of such pulse currents can reach values that usually vary in the range (0.1-1000) kA [1, 2].
In [4], the author presented a generalized electrical engineering approach that allows for the condition of thermal durability of cable-conductor products (CCP) to carry out an approximate computational choice of the maximum allowable cross sections Sai of uninsulated wires, insulated wires and cables with copper (aluminum) conductors (shells) with polyvinyl chloride (PVC), rubber (R) and polyethylene (PET) insulation, the current-carrying parts of which are influenced in the adiabatic mode by the direct effect of the axial pulse current ip(t), the ATPs of which with amplitudes of 0.1 kA<Imp<1000 kA can vary in nano-, micro- and millisecond time ranges. In this regard, the issues of determining the numerical values of the critical cross sections SCC of electrical wires and cables in relation to the power circuits of HHIT remain relevant in the world and are subject to their decision.
The goal of the paper is to perform the calculation and experimental determination of critical cross sections SCCi and current densities dca in wires and cables of HHIT circuits characterized by the flow of pulse axial currents ip(t) along the current-carrying parts of their CCP with different ATPs.
1. Problem definition. Consider the widely used uninsulated copper and aluminum wires in HHIT power circuits, as well as insulated wires and cables with copper (aluminum) inner conductors and outer shells (reverse conductors) with specific electrical conductivity y0i of their nonmagnetic material, which usually have PVC, R and PET insulation [1-3]. It is assumed that in the round
solid or split copper (aluminum) conductors (shells) of the above wires and cables of the HHIT electrical circuits pulse currents ip(t) flow in their longitudinal direction, the ATPs of which correspond to nano-, micro- or millisecond time ranges with amplitudes Imp varying in the range from 100 A to 1000 kA. We assume that the wires and cables under consideration are placed in the surrounding air environment, the temperature of which corresponds to room temperature and equal to 80 = 20 °C [2]. We suppose that the preliminary current load of the current-carrying parts of the CCP of power circuits of HHIT is absent. Therefore, the initial temperature 0Ci (before the affect of the pulse current ip(t) on the CCP) of the core (shell) material of the wire (cable) will be equal to the ambient air temperature 00. We use the assumption that the pulse axial current ip(t) is almost uniformly distributed over the cross section SCi of the core and shell (screen) of the wire (cable). At the same time, we remember that the penetration depth Ai~[6tm/(^M0y0i)]12 in the quasi-stationary mode, where ,M0=4rc-10-7 H/m is the magnetic constant [2], of the azimuthal magnetic field pulse with time tm corresponding to its amplitude, for example, for an aperiodic microsecond current pulse of artificial lightning of the temporal shape t/tp=10 ^s/350 ^s (tm~1.6Tp16 ^s) [5], where t, tp are the front duration and the duration of the current pulse at the level of its half-decay, in the studied non-ferromagnetic materials of the core (shell) of the wire (cable) is for copper approximately 0.65 mm, but for aluminum is 0.82 mm [4]. These numerical values A,- are often commensurate with the actual radii of the cores and the thicknesses of the shells of the wires (cables) under consideration, in which the EE phenomenon of the current-carrying parts of the CCP may be observed. For millisecond axial current pulses ip(t), the accepted assumption about the uniform nature of its radial distribution in the studied conductors (shells) of wires and cables becomes even more legitimate. Thus, for example, for an aperiodic millisecond pulse of a long-term C- component of artificial lightning current of the temporal shape r/rp= = 7 ms/160 ms (tm~ 11 ms), the considered penetration depth Ai for copper is about 17 mm, and for aluminum is 22 mm. We use the condition of adiabatic nature of the electrothermal processes taking place at durations of pulsed current ip(t) of no more than 1000 ms in the materials of the cores (shells) of the CCP under study, at which the influence of heat transfer from the surfaces of their current-carrying parts having the current temperature 8c/>80 as well as the thermal conductivity of layers of their conductive materials of the core (shell) and insulation on Joule heating of the current-carrying parts of the CCP are neglected.
It is required by calculation in an approximate form to determine the critical sections SCCi of current-carrying parts for uninsulated copper (aluminum) wires, as well as for insulated wires and cables with copper (aluminum)
cores (shells), PVC, R and PET insulation, used in HHIT circuits and influenced by direct effect of axial pulse current ip(t) of various amplitudes Imp, varying in nano-, micro- and millisecond time ranges. In addition, it is necessary to experimentally verify the operability of the obtained relations for the approximate calculation of the critical sections SCa of wires (cables) and critical densities dca of the pulse current ip(t) in them on the operating electrical installations of HHlT.
2. Electrical engineering approach to the calculation selection of the critical sections SCCi and current densities SCa in electrical wires and cables of HHIT circuits. For critical cross sections SCCi of conductive cores (shells) of the considered non- and insulated with PVC, R and PET insulation electrical wires and cables in HHIT circuits with pulse axial current ip(t) of arbitrary ATPs from the equation of their heat balance at the adiabatic Joule heating of current-carrying parts of the CCP the following calculated relation follows [1]:
Cik, (1)
ip (t) = kp2Impi exp(-&) sin(®t),
(4)
SCCi = ( Jca )1/2/ D
where JCiA = j ip (t)dt - the integral of the action of the
o
pulse current ip(t) with the duration of its flow tp in the CCP and given ATPs, A2-s; Dak = (J«)1'2, A-s1/2/m2; Jak is the critical value of the current integral for the material of the current-carrying cores (shells) of the studied electric wires and cables of the HHIT circuits, A2-s/m4.
In Table 1 at 0o=2O °C known numerical values are given for such basic characteristics of copper and aluminum cores (shells) of the studied wires (cables) of the HHIT power circuits as y0i and Jak.
Table 1
Thermophysical characteristics of the material of the considered cores (shells) of electrical wires and cables of power circuits of HHIT before exposure to them of pulse axial current ip(t) (at 6»0=20 °C) [2]
Material of the core (shell) of the wire (cable) Numerical value of the characteristic
Y,,, 107 (O-m)-1 Jak, 1017 A2-s-m-4
Copper 5.81 1.95
Aluminum 3.61 1.09
As for the calculation determination in (1) of the integral of action JCA of the pulse axial current ip(t) with arbitrary ATPs, for the case of its change over time t according to the aperiodic law of the form [1]
ip (t) = kp1lmp [exp(-a1) - exp(-«2i)], (2)
where ai~0.76/xp, a2~2.37/zf are the shape coefficients of the aperiodic current pulse with given ATPs, flowing in the HHIT; kpi=[(ai/a2)m - (ai/a2)"]-1 is the normalization factor; m=ai/(a2-ai); n=a2/(a2-ai), the calculation expression for the integral of action JCiA of the current pulse ip(t) flowing in the HHIT power circuit takes the following approximate analytical form [4, 6]:
JCiA * k2p1llp[o.658Tp -0.633rf ]. (3)
In case of a change in time t of the current pulse ip(t), acting on the materials of the wire (cable) of the HHIT, according to the law of a damped sinusoid of the form [1]
where d=Ap/Tp is the current attenuation coefficient; m=2n/Tp is the current frequency; Tp is the current oscillation period; Ap=ln(Imp1/Imp3) is the logarithmic decrement of pulse current oscillations with the first Imp1 and the third Imp3 amplitudes in the HHIT circuit; kp2=[exp(-Ap/2n-arcctgAp/2n)sin(arcctgAp/2n)]-1 is the normalizing coefficient for the damped sinusoidal current, then the approximate calculation expression for the integral of action JCiA of the pulse axial current ip(t) flowing in the HHIT power circuit takes the following simplified analytical form [4]:
JCiA * kp2IIP1[TP (4Ap)-1 - ApTp (4A2p + 16n2)-1]. (5)
Knowing from normative documents or experimental data the numerical values of the quantities Imp, Tf, tp, Ap, Tp and taking into account the estimates of the values of the normalizing coefficients kp1 and kp2 by (2)-(4) for the two temporal shapes, the changes in the pulse current ip(t), we can in an approximate form (with an error of no more than 10%) calculate the critical cross sections SCCi of current-carrying cores (shells) of wires and cables used in electrical power circuits of HHIT. Having found the numerical values of the cross sections SCCi, taking into account the accepted assumptions, the critical amplitudes of the densities 8CCi of the pulse current ip(t) of a given temporal shape in electrical wires and cables of HHIT circuits can be determined as a first approximation from the relation dCCl~Impl/SCCi.
3. Calculation determination of critical cross-sections SCCi and current densities SCa in electrical wires (cables) for nanosecond current pulses in HHIT circuits. Let us consider the case when an aperiodic current pulse of temporal shape r/rp=5 ns/200 ns flows through copper (aluminum) cores (shells) of the HHIT, which was used at the time to simulate an electromagnetic pulse (EMP) of a high-altitude nuclear explosion and test of various objects of military and civilian use for resistibility to the damaging effects of the indicated EMP [4, 7, 8]. From (2), we find that for this calculation case, the shape coefficients ax and a2 of the used current pulse ip(t) take the following numerical values: ai~3.8-106 s-1; a2~4.7-108 s-1. In this case, the normalizing coefficient kp\ is approximately equal to kpi~1.049. In Table 2, taking into account (3) for a specific set of values of the current amplitude Imp, the numerical values of the integral of action JCiA are given for the aperiodic nanosecond current pulse of the temporal shape tJtp=5 ns/200 ns flowing through the current-carrying copper and aluminum parts of the studied wires and cables [4, 9].
Knowing the numerical values of the integral of action of the current JCiA (see Table 2) and the integral of current JCik (see Table 1), the critical sections SCCi of the considered electrical wires (cables) can be determined relatively easily from (1). Table 3 shows the calculated by (1) numerical values of the critical sections SCCi for uninsulated wires with copper (aluminum) cores and insulated wires (cables) with copper (aluminum) cores (shells), PVC, R and PET insulation, experiencing the effect of aperiodic nanosecond current pulse of the temporal shape tJtp=5 ns/200 ns.
r
Table 2
Numerical values of the integral of action JCA for a nanosecond
aperiodic current pulse of the temporal shape 5 ns/200 ns, flowing in the current-carrying parts of the considered CCP [4]
Amplitude value Imp= Impl of the current pulse of the temporal shape 5 ns/200 ns, kA Value of the integral of action JCAA of the current pulse 5 ns/200 ns, A2-s
1 0.141
10 14.13
30 1.27-102
50 3.53102
70 6.92-102
100 1.41103
200 5.65103
500 3.53104
1000 1.41105
Table 3
Numerical values of the critical sections SCCi for wires (cables)
with copper (aluminum) cores (shells) in the HHIT power circuits with a nanosecond current pulse of 5 ns/200 ns, whose amplitude varies from 10 kA to 500 kA
Type of insulation in the wire (cable) of the HHIT power circuit Material of the core (shell) of the wire (cable) Value of the section SCCi, mm2
Amplitude Imp of the pulse current 5 ns/200 ns, kA
10 50 100 500
Without insulation, PVC, R and PET insulation Copper 0.008 0.042 0.085 0.425
Aluminum 0.011 0.057 0.114 0.569
Table 4 shows the numerical values of the integral of action JCA calculated by (5) for a microsecond current pulse varying in time t according to the law of a damped sinusoid of the form (4) [12].
From the data of Table 3 it follows that the estimated critical amplitudes of the densities dCC=Imp/SCCi of a nanosecond current pulse of temporal shape 5 ns/200 ns for both uninsulated wires and wires and cables with copper (aluminum) cores (shells) and PVC, R and PET insulation are, respectively, approximately 1176 kA/mm2 and 878 kA/mm2.
4. Calculation determination of critical cross-sections SCa and current densities dca in electrical wires (cables) for microsecond current pulses in HHIT circuits. Figure 1 shows a typical oscillogram of a pulsed A- component of an artificial lightning current formed in a high-current discharge circuit of a high-voltage lightning current generator (LCG) for testing objects of aeronautical and rocket technology on lightning resistibility in accordance with US regulations [10, 11]. It can be seen that this component of current pulses ip(t) of a lightning simulated under laboratory conditions in time t varies according to the law of damped sinusoid. Let us make the choice of critical sections SCCi and densities 8ca of current in current-carrying cores (shells) of wires and cables for the discharge circuit of the LCG in relation to current pulse ip(t) of lightning shown in Fig. 1.
From the experimental data presented in Fig. 1, we obtain that for the used in approximate calculations of critical cross sections SCCi a large exponentially decaying sinusoidal pulse current, the decrement of its oscillations is equal to Ap=ln(Impi/Imp3)=2.505. From (4) for this type of current pulse, we find that the coefficient &p2=1.731.
Fig. 1. Typical oscillogram of a microsecond pulsed A- component of an artificial lightning current flowing in a highvoltage discharge circuit of a high-voltage LCG (Imp1=-207 kA;
Imp3~-16.9 kA; 7^185 ^s; vertical scale - 56.3 kA/division; horizontal scale - 50 ^s/division) [12]
Using (1) and summarized in Table 4 the results of the calculation of the integral of action JCiA of the pulse current ip(t) of the form (4), we find the critical sections SCCi for the wires (cables) under study in the HHIT power circuits, in which the microsecond current pulse of the form (4) with the ATPs corresponding to the experimental data characteristic of Fig. 1 flows. Table 5 presents the results of such a computational determination of the critical sections SCCi for the wires and cables under consideration, which are widely used in HHIT discharge power circuits [1, 2, 12].
Table 4
Values of the integral of action JCiA for current pulse ip(t), changing in the microsecond time range according to the law of damped sinusoid of the form (4)
Value of the first amplitude Imp1 of a damped sinusoidal current pulse, kA Value of the integral of action JCiA of the current pulse of the form (4), A2-s
10 4.77-103
30 4.29-104
50 1.19105
70 2.34-105
100 4.77-105
207 2.05-106
300 4.29-106
500 11.92106
700 23.4-106
1000 47,7-106
From the presented in Table 5 calculated data, it follows that the estimated critical amplitudes of the densities ôCCl~Imp1/SCCi of the microsecond current pulse ip(t) with ATPs corresponding to the experimental data of Fig. 1, both for uninsulated wires and wires (cables) with copper and aluminum cores (shells), PVC, R and PET insulation are numerically, respectively, about 64 kA/mm2 and 48 kA/mm2.
Table 5
Numerical values of critical sections SCCi for wires (cables) with
copper (aluminum) cores (shells) in HHIT circuits with a microsecond current pulse of the form (4), the first amplitude of which Imp1 varies from 30 kA to 207 kA
Type of insulation in the wire (cable) of the HHIT power circuit Material of the core (shell) of the wire (cable) Value of the section SCCi, mm2
The first amplitude Imp1 of the current pulse of the form (4), kA
30 50 100 207
Without insulation, PVC, R and PET insulation Copper 0.469 0.781 1.564 3.243
Aluminum 0.627 1.045 2.092 4.337
CH1 SO.OrnVfyj
Fig. 2. Typical oscillogram of a millisecond long-term C- component of the current of artificial lightning flowing in the discharge circuit of a high-power high-voltage LCG (Imp~-835 A; t—7 ms; ^-160 ms; vertical scale - 282 A/division; horizontal scale - 100 ms/division) [12]
From (2) at tj-7 ms and xp-160 ms, we find that a1-4.75 s1 and a2-3.38T02 s-1. Then the normalization
coefficient kp1 takes a numerical value equal to about kp1~1.077. Using (3) and varying the amplitude value Imp, one can calculate the numerical values of the integral of action JCiA for the millisecond current pulse ip(t) used. Table 6 shows the numerical values of JCiA for a series of amplitudes Imp of the current pulse ip(t) of temporal shape 7 ms/160 ms.
Table 6
Numerical values of the integral of action JCiA for a current pulse ip(t) varying in a HHIT circuit in the millisecond time range according to the law of the form (2)
5. Calculation determination of critical cross-sections SCCi and current densities SCa in electrical wires (cables) for millisecond current pulses in HHIT circuits. Figure 2 shows a typical oscillogram of a long-term C- component of the artificial lightning current generated under laboratory conditions according to the requirements of [10] in the LCG discharge circuit for the purpose of experimentally determining the lightning resistibility of aerospace objects under direct lightning conditions. From the data in Fig. 2 it can be seen that the aperiodic current pulse ip(t) of the artificial lightning of negative polarity of this component of the total current of a thunderstorm discharge varies in the millisecond time range. Its amplitude Imp at tm-11 ms is approximately 835 A. At the same time, the duration of the front of the test current pulse is about Tf-7 ms, and its duration at the level of 0.5Imp is xp-160 ms. In addition, from the data in Fig. 2 it follows that the total duration of the flow of the used component of the current pulse ip(t) of artificial lightning in the discharge circuit of a high-voltage LCG reaches a value of about 1000 ms. On the basis of the proposed electrical engineering approach, we perform the determination of the critical sections Sca of wires (cables) for the LCG discharge circuit involved in the formation of the specified current pulse ip(t).
Amplitude value Imp=Impi of an unipolar millisecond aperiodic current pulse 7 ms/160 ms, A Value of the integral of action JCiA of a millisecond current pulse 7 ms/160 ms, A2-s
100 1.17103
200 4.68T03
300 1.05T04
400 1.87T04
500 2.92-104
700 5.73T04
835 8.15104
900 0.95T05
1000 1.17105
Then, taking into account the data of Table 6, according to (1) in the accepted approximation, one can find the critical sections SCCi for uninsulated and insulated wires and cables with copper (aluminum) cores (shells), PVC, R and PET insulation, which are affected by an axial millisecond aperiodic current pulse ip(t), ATPs which correspond to the data in Fig. 2. Table 7 shows the calculated numerical values of the critical sections SCCi for the indicated wires (cables) with a millisecond aperiodic current pulse ip(t) of the temporal shape 7 ms/160 ms, found as described above. Based on the relation of the form SCCl-Imp/SCCi, the data of Table 7 allows us to estimate the numerical values of critical densities dCCi in wires (cables), along which a millisecond aperiodic current pulse ip(t) of a temporary shape of 7 ms/160 ms with an amplitude of Imp, varying in a wide range from 100 A to 1000 A, flows in the longitudinal direction.
Table 7
Numerical values of the critical sections SCCi for uninsulated wires and insulated wires (cables) with copper (aluminum) cores (shells), PVC, R and PET insulation in HHIT circuits that are affected by a millisecond current pulse of temporal shape of 7 ms/160 ms varies from 100 A to 1000 A
Type of insulation in the wire (cable) of the HHIT power circuit Material of the core (shell) of the wire (cable) Value of the section Sca, mm2
Amplitude Imp of the current pulse 7 ms/160 ms, A
100 500 835 1000
Without insulation, PVC, R and PET insulation Copper 0.077 0.387 0.647 0.775
Aluminum 0.103 0.518 0.865 1.036
From the presented in Table 7 quantitative data, it follows that the estimated critical amplitudes of the densities dCC—Imp/SCCi of a millisecond aperiodic current pulse ip(t) of the shape 7 ms/160 ms with ATPs
corresponding to the oscillogram in Fig. 2, for uninsulated wires with copper and aluminum cores, as well as wires (cables) with copper and aluminum cores (shells) having PVC, R and PET insulation, are approximately equal to 1.29 kA/mm2 and 0.97 kA/mm2, respectively.
6. Results of experimental verification of the calculation relations for the determination of the critical sections SCCi and the current densities SCCi in the wires (cables) of the HHIT circuits. This functional test of the critical sections SCCi of wires (cables) recommended for calculation determination by the relation (1) and the critical amplitudes of the pulse current densities ip(t) in their cores (shells) calculated by relation dCC—Imp/SCCi we carry out using a powerful high-current high-voltage LCG [13] which simulates the normalized by [10] ATPs of the pulsed A- components of the artificial lightning current (see Fig. 1) and is equipped with verified by the state metrological service appropriate measuring equipment [15]. To do this, we first realize on the specified generator the effect of this lightning current component with ATPs normalized by requirements [10] (7mp1~-205 kA; I,^--16.9 kA; Tp-200 ^s; Ap~ln(/mp1//mp3)~2.495; 4-38 ^s; Jcm-2.17-106 A2-s) previously obtained at the load equivalent (cable brand PK 75-17-31 with a copper core of section of 10.2 mm2), on the test sample (TS) with length of 0.55 m wire of grade nB-2.5 with PVC insulation and a cross-section of a split copper core equal to SC1-2.5 mm2. According to the above initial data for ATPs of the used damped sinusoidal current pulse of the microsecond range and (1), the critical section for the tested copper wire is approximately equal to SCC1-3.34 mm2. At |Impi205 kA, this critical section corresponds to the critical amplitude of the density of this current pulse, which is numerically equal to ¿CC1-61.4 kA/mm2. It is seen that SC1<SCC1. In this regard, it was possible to conclude before the planned experiment that the tested wire, when exposed to its copper core with cross section SC1-2.5 mm2 of the pulsed A - component of the lightning current with normalized ATPs, should undergo the EE and fail. Indeed, this conclusion was confirmed by the corresponding electrophysical experiment carried out on the indicated high-current LCG under the conditions of the highvoltage laboratory, the results of which applied to the nature of the abrupt change in time t due to the EE of the copper core with section SC1-2.5 mm2 of the tested wire of grade nB-2.5 with PVC insulation PVC insulation of the original current pulse ip(t) are presented in Fig. 3.
From the data in Fig. 3 it follows that the EE in the discharge circuit of the specified LCG of the copper core with cross section SC1-2.5 mm2 of grade nB-2.5 wire with PVC insulation causes a sharp deformation of the current pulse ip(t) flowing through it compared to its original shape (see Fig. 1). From the oscillogram in Fig. 3 it follows that the experimental value of the critical amplitude of the density 8ca of the microsecond current pulse ip(t) in the conducted electrophysical experiment is approximately dCC1-Imp/SCC1-205 kA/3.34 mm2-61.4 kA/mm2. Compared with the calculated value of the critical amplitude density 8ca used in the experiment the damped sinusoidal current pulse ip(t) which equals to ^CC1 -Imp/SCC1-205 kA/3.34 mm2-61.4 kA/mm2, the
obtained experimental value of the critical current density 8CC1 differs from it by about 8 %.
CHI 5.Q0V M 5Q.QJUS CH1\-1,00V
Fig. 3. Oscillogram of the pulsed A- component of the artificial
lightning current, deformed by the EE process in the LCG discharge circuit of a split copper core with SC1—2.5 mm2 section of the tested TS of grade nB-2,5 wire, 0.55 m long with PVC insulation (Imp1—-166.7 kA; ¿CC1=|Imp1|/SC1=66.7 kA/mm2; vertical scale - 56.3 kA/division; horizontal scale -50 ^s/division) [1, 14]
Figure 4 shows a general view of a desktop of a high-voltage high-current LCG, on which a tested on electrothermal resistibility to the action of pulsed A-component of an artificial lightning current with ATPs normalized by [10, 11] (Imp1--205 kA; Imp3--16.9 kA; Tp-200 ^s; tm-38 ^s; Ap-ln(Imp1/Imps)-2.495; JCiA-2.17-106 A2-s) TS of the radio frequency cable brand PK 75-4-11 with length of 0.55 m with solid copper core with section SC =0.407 mm2 and copper braid with section SC2=2.44 mm2 is fixed prior to exposure on it of the specified microsecond pulse current ip(t). The inner copper core and the outer copper shell-braid at the edges of this cable were connected in parallel and connected together to the discharge circuit of a high-current highvoltage LCG [14].
Fig. 4. General view of the desktop of the LCG with 0.55 m length rigidly fixed on its massive aluminum electrodes the tested radio frequency cable brand PK 75-4-11 with a solid copper core with section SC1=0.407 mm2 and a copper shell-braid with section SC2=2.44 mm2 prior to the impact on it of the
pulsed A- component of the artificial lightning current with normalized ATPs (the core and the shell-braid at the ends of this cable were connected to the high-current discharge circuit of the LCG in parallel) [1, 14]
Figure 5 shows an oscillogram of the pulsed A-component of the artificial lightning current used in the experiment deformed by the EE of the copper current-carrying parts of the tested TS of the radio frequency
cable of the PK 75-4-11 brand with a total cross section of the core and braid, equal to (5,c1+^'c2)~2.85 mm2.
CURSOR
::::::
;
! ; ; *
v"
:
::::::
;
CH1 5.00V
Type
Source
m:ii
Delta 16.1V
Cursor 1 0.00V
Cursor 2 -16.1V
CH1 \ -1.00V
M 50.0JUS
Fig. 5. Oscillogram of a pulsed A- component of an artificial lightning current deformed by EE in a discharge circuit of a LCG of a solid copper core with SC1=0.407 mm2 section and a copper braid with SC2=2.44 mm2 section of a tested TS of a 0.55 m
in length radio frequency cable PK 75-4-11 brand with PET insulation (Imp1=-184.7 kA; ¿ca=Imp1|/(Sc1+Sc2)-64.8 kA/mm2; vertical scale - 56.3 kA/division; horizontal scale -50 ^s/division) [1, 14]
Figure 6 shows the external view of the LCG desktop immediately after the impact of the specified current pulse ip(t) on the tested in its high-current discharge circuit TS of the cable of the brand PK 75-4-11 with PET insulation and full cross section of its copper current-carrying parts (SC1+SC2)-2.85 mm2. Due to the phenomenon of the EE of its solid copper core and hollow copper shell-braid, which occurred in the TS of the cable, sublimation of its copper current-carrying parts occurred with the destruction of the belt and protective PET insulation of the test cable sample. Insulating and metal elements of the LCG were subjected to active metallization with brown-red copper vapor (see Fig. 6). On this desktop in the EE zone of the tested TS of the cable, there is the presence of small melted and charred fragments of its protective PET insulation.
Fig. 6. External view of the desktop of the LCG after the EE of
the current-carrying parts of the tested in its high-current discharge circuit TS of 0.55 m long of the RF cable of the PK 75-4-11 brand with PET insulation and connected in the gap of the discharge circuit of a high-voltage generator with total cross section of its copper core and copper braid equals to (SCi+SC2)=2.85 mm2 (/„^=-184.7 kA; dca~Vmpi|/(^ci+^c2)~64.8 kA/mm2) [1, 14]
Due to the fact that for the tested cable of brand PK 75-4-11, the following inequality is fulfilled (SC1+SC2)<SCCi, its current-carrying copper parts together with PVC insulation were destroyed by the apparent in the carried out experiment the EE of the solid round core and hollow braid-shell of the selected size of the CCP. At the calculated by (1) value of a critical section for this type of cable, equal to SCCi-3.34 mm2, the calculated critical amplitude of the density dca of the used in the experiment a microsecond current pulse ip(t) for it was numerically dCC—ImpISCC—61.4 kA/mm. From the oscillogram in Fig. 5 it follows that the experimental value of the critical density amplitude 8ca of the specified current pulse ip(t) is numerically equal in module to ¿cc,-Imp/(Sc1+Sc2)-64.8 kA/mm2. It can be seen that the obtained experimental value for the value of the critical amplitude of the density 8CCi of a current pulse of microsecond duration in the cable under study differs from its corresponding calculated value by no more than 6%. Thus, experimental studies for a microsecond current pulse ip(t) performed on a high-current high-voltage LCG have confirmed the performance of the proposed calculation relations for determining the critical sections SCCi and critical amplitudes of current densities dCCi for the specified time range in the current-carrying parts of the wires and cables of HHIT power circuits.
Conclusions. 1. The proposed electrical engineering approach allows for the condition of EE in atmospheric air of the current-carrying parts of the CCP to carry out an approximate calculation of the critical cross sections SCCi and amplitudes of current densities 8CCi for uninsulated wires with copper (aluminum) cores, as well as for insulated wires and cables with copper (aluminum) cores (shells) with PVC, R and PET insulation, through which the pulse current ip(t) flows, the ATPs of which varies in the nano-, micro- and millisecond time ranges.
2. On the basis of the obtained approximate calculated relations, specific capabilities of the proposed electrical engineering approach for selecting critical cross sections Sca and amplitudes of current densities dCCi in the indicated wires and cables of HHIT power circuits, in current-carrying parts of which large pulse currents ip(t) varying in time t according to aperiodic law or damped sinusoid law with the first current amplitude Imp1, are demonstrated.
3. It has been determined by calculation that the critical amplitudes of densities SCCl-Imp1/SCCi of pulse current ip(t) for its considered temporal shapes in copper (aluminum) cores of uninsulated wires and insulated wires and cables with copper (aluminum) cores (shells), PVC, R and PET insulation for the nanosecond time range are numerically approximately 1176 (878) kA/mm2, for the microsecond time range 64 (48) kA/mm2, and for the millisecond time range 1.29 (0.97) kA/mm2.
4. Experiments carried out using high-current highvoltage LCG with regard to the effect on the current-carrying parts of the nB-2,5 grade wire with PVC insulation and the cable of the PK 75-4-11 grade with PET insulation of a microsecond damped sinusoidal current pulse of artificial lightning with normalized ATPs in accordance with the requirements of acting the field of lightning protection of aerospace technology objects of
the USA SAE ARP 5412: 2013 document confirmed the performance of the recommended calculation relations for determining the critical sections SCa and amplitudes of current densities 8CCi in indicated wires and cables of the HHIT circuits.
5. The results obtained for the critical cross sections SCCi and current densities 8CCi can also be used in the practice of implementation in the atmospheric air with the help of HHIT electrical installations of the EE phenomena of uninsulated thin metal conductors (wires) used in a number of modern applied electrophysical technologies.
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Received 12.11.2018
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. Calculation and experimental determination of critical sections of electric wires and cables in the circuits of devices of high-voltage high-current pulse technique. Electrical engineering & electromechanics, 2019, no.2, pp. 3946. doi: 10.20998/2074-272X.2019.2.06.
