# A CHOICE OF SECTIONS OF ELECTRIC WIRES AND CABLES IN CIRCUITS OF DEVICES OF HIGH-VOLTAGE HIGH-CURRENT IMPULSE TECHNIQUE.

UDC 621.3.022: 621.315.3: 537.311.8Introduction. One of the challenges in the field of high-voltage high-current impulse technology (HHIT) is a reasonable choice of cross-sections [S.sub.C] 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 [i.sub.p](t) with different amplitude-temporal parameters (ATP). In this case, the amplitudes [I.sub.mp] of these currents can vary in the range from hundreds of amperes to thousands of kiloamperes, and their duration [t.sub.p] 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 [[theta].sub.lS] 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 [[theta].sub.lS] 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 [[theta].sub.lS] 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 [degrees]C and 200 [degrees]C, and for cables (insulated wires) with copper and aluminum cores and PVC (R), PET insulation, respectively, the level of 150 [degrees]C and 120 [degrees]C [3].

We point out that in the industrial electric power industry, the long-term permissible temperature [[theta].sub.ll] 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 [[theta].sub.ll] for the main types of electrical wires and cables used in the field of modern power engineering are given.

From the data of Table 2 it follows that the maximum long-term permissible temperature [[theta].sub.ll] 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 [degrees]C and 65 [degrees]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 [[theta].sub.ll] and at SC it heated to temperature [[theta].sub.lS], in [3] to select the minimum permissible cross-section [S.sub.lmin] of electrical wire (cable) wire the following calculated ratio is recommended:

[S.sub.lmin] = [B.sup.1/2.sub.k] / [C.sub.k], (1)

where [mathematical expression not reproducible] is the Joule (action) integral of the SC current [i.sub.k](t) with duration [t.sub.k] (a technique of calculation of [B.sub.k] is presented in [3]), [A.sup.2] x s; [C.sub.k] is the coefficient (A x [s.sup.1/2]/[mm.sup.2]), whose numerical values are given in Table 3.

Taking into account the fact that ATP of pulsed currents [i.sub.p](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 [S.sub.C] of electrical wires (cables) in the HHIT circuits is essentially impossible technical way. In this regard, an approximate calculation of sections [S.sub.C] of electrical wires and cables of HHIT for various ATPs of the pulsed current [i.sub.p](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 [i.sub.p](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 [i.sub.p](t) flow, ATPs of which correspond to nano-, micro- or millisecond time ranges with amplitudes [I.sub.mp], 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 [[theta].sub.0] = 20 [degrees]C. We use the assumption that in the first approximation the pulsed current [i.sub.p](t) is almost uniformly distributed over the cross-section [S.sub.ci] 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 [[tau].sub.f]/[[tau].sub.p] = 10 [micro]s/350 [[micro]s ([[tau].sub.f], [[tau].sub.p] are, respectively, the front duration at the level (0.1-0.9) [I.sub.mp] and the current pulse duration at the level of 0.5 [I.sub.mp]) the penetration depth [[delta].sub.i] 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 [[DELTA].sub.i] in practice can be commensurate with the real radii of the core and the wall thickness of the wire (cable) shell. For current pulses [i.sub.p](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 [i.sub.p](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 [[theta].sub.Ci[greater than or equal to][theta].sub.0] 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 [i.sub.p](t) is limited by their maximum permissible short-term heating temperature [[theta].sub.CiS], 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 [[theta].sub.CiS] corresponds to the maximum permissible short-term temperature [[theta].sub.CiS] 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 [[theta].sub.CiS] will be approximately 250 [degrees]C (200 [degrees]C), for their insulated wires (cables) with copper and aluminum cores (shells) and PVC (R) insulation [[theta].sub.CiS] [approximately equal to] 150 [degrees]C, and for their CCP with the indicated conductors (shells) and PET insulation [[theta].sub.CiS][approximately equal to] 120 [degrees]C. It is required by calculation in an approximate form to determine the boundary permissible cross-sections [S.sub.Cil] 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 [i.sub.p](t) of various amplitudes [I.sub.mp] in the nano-, micro- and millisecond time ranges.

2. A generalized approach to the choice of sections [S.sub.Cil] of electrical wires (cables) in the field of HHIT. For the boundary permissible cross-sections [S.sub.Cil] of the current-carrying cores (shells) of the considered electric wires and cables with axial pulsed current [i.sub.p](t) of arbitrary ATPs, the following approximate calculated dependence [5] follows from the equation of their heat balance in the adiabatic mode:

[S.sub.Cil] = [([J.sub.CiA]).sup.1/2]/[C.sub.l], (2)

where [mathematical expression not reproducible] is the action integral of the pulsed current [i.sub.p](t) with duration [t.sub.p] and given ATPs, [A.sup.2] x s; [C.sub.l] = ([J.sub.CIS] - [J.sub.Cll], [A x s.sup. 1/2][m.sup.2]; [J.sub.CIS] - [J.sub.Cll] 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 correspond to [[theta].sub.ls] (see Table 1) and [[theta].sub.ll] (see Table 2) values, [A.sup.2] x s/[m.sup.4].

To find the numerical values of the [J.sub.ClS] and [J.sub.Cll] current integrals included in (2), the following analytical expressions can be used [2, 5]:

[mathematical expression not reproducible] (3)

[mathematical expression not reproducible], (4)

where [[gamma].sub.0i], [c.sub.0i], [[beta].sub.0i] 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 [i.sub.p](t) with arbitrary ATPs.

Table 4 presents numerical values of [[gamma].sub.0i], [c.sub.0i], [[beta].sub.0i] temperature [[theta].sub.0i] = 20 [degrees]C [2, 6].

As for the calculation definition in (2) of the integral of action [J.sub.CiA] of the pulsed current [i.sub.p](t) with arbitrary ATPs, for the case of its change over time t according to the aperiodic law of the form

[mathematical expression not reproducible], (5)

where [[alpha].sub.1] [approximately equal to] 0.76/[t.sub.p], [[alpha].sub.2] = 2.37/[t.sub.f] are, respectively, the shape coefficients of the aperiodic current pulse with given ATPs flowing in the electric circuit of the HHIT; [k.sub.p1] = [([[alpha].sub.1]/ [[alpha].sub.2]).sup.m] - ([[alpha].sub.1]/ [[alpha].sub.2]).sup.n-1] is the normalization factor; m = [[alpha].sub.1]/([[alpha].sub.2]/ [[alpha].sub.1]); n = [[alpha].sub.2]/([[alpha].sub.2]/ [[alpha].sub.1]); the calculated expression for the integral of action [J.sub.CiA ]of the current pulse [i.sub.p](t) flowing in the HHIT circuit takes the following convenient analytical form [7]:

[mathematical expression not reproducible] (6)

where [[tau].sub.f], [[tau].sub.p] are respectively, the durations of the front and the half-fall of the current pulse [i.sub.p](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 [i.sub.p](t) according to the law of a damped sinusoid of the form

[mathematical expression not reproducible], (7)

where [delta] = [[DELTA].sub.p]/[T.sub.p] is the current attenuation coefficient; w=2[pi]/[T.sub.p] is the circular frequency of the current oscillations; [T.sub.p] is the period of the current oscillations; [[DELTA].sub.p] = ln([I.sub.mp1]/[I.sub.mp3]) is the logarithmic decrement of pulsed current oscillations with the first [I.sub.mp1] and the third [I.sub.mp3] amplitudes in the HHIT circuit; [k.sub.p2] = [exp(-[DELTA]p/2[pi]-arcctg[I.sub.mp3]/2n)-sin(arcctg[[DELTA].sub.p/2[pi])].sup.-1] is the normalization factor for damped sinusoidal current; the calculated expression for the integral of action [J.sub.CiA] of the current pulse [i.sub.p](t) flowing in the HHIT circuit takes the following simple analytical form [5]:

[mathematical expression not reproducible]. (8)

From (4) it can be seen that at [[theta].sub.ll] = [[theta].sub.0] = 20 [degrees]C (wires and cables are de-energized) the value of the current integral [J.sub.Cll]=0, which will lead by (2) to a decrease in the cross-section [S.sub.Cil].

Knowing from normative documents or experimental data the numerical values of [I.sub.mp], [t.sub.f], [t.sub.p], [DELTA].sub.p], Tp, taking into account the estimates of the values of the normalizing coefficients [k.sub.p1] and [k.sub.p2] 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 [S.sub.Cil] of the conductive wires (shells) of wires and cables used in the electric circuits of HHIT. Finding the values of the [S.sub.Cil] sections, taking into account the accepted assumptions, the maximum permissible pulsed current densities of the pulsed current [i.sub.p](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 [[delta].sub.Cil] [approximately equal to] [I.sub.Imp] [S.sub.Cil].

3. The choice of cross-sections [S.sub.Cil] of electrical wires (cables) for nanosecond current pulses in the field of HHIT. First, we will focus on the selection of the [S.sub.Cil] sections of the wires (cables) under consideration, along copper (aluminum) cores (shells) under the conditions [J.sub.Cll] = 0 or [J.sub.Cll] # 0, the axial aperiodic current pulse of the time shape [t.sub.p]/[t.sub.p] = 5 ns/200 ns flows [8]. Note that at one time this nanosecond current pulse [i.sub.p](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 [[alpha].sub.1] and [[alpha].sub.2] of the current pulse [i.sub.p](t) take the following numerical values: [[alpha].sub.1] [approximately equal to]3.8 x [10.sup.6] [cs.sup.-f]; [[alpha].sub.2] [approximately equal to] 4.7 x [10.sup.8] [s.sup.-1]. Here, for this current pulse, the normalizing coefficient [k.sub.p1] is approximately equal to [k.sub.p1] [approximately equal to] 1.049. Table 5 presents by (6) the numerical values of the action integral [J.sub.CiA] for a series of values of the amplitude [I.sub.mp] 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 6 shows the calculated by (2) the numerical values of the coefficient [C.sub.l] for uninsulated wires with copper (aluminum) cores and insulated wires (cables) with copper (aluminum) cores (shells) with PVC, R and PET insulation for the cases of their preliminary current load ([J.sub.Cll]#0) or full de-energizing ([J.sub.Cll]=0).

Comparison of data of Table 3, 6 indicates that the numerical values of the coefficients [C.sub.k] u [C.sub.l] for the considered wires and cables in the case when [J.sub.Cll] [not equal to] 0 and the value of this integral of the current is determined from (4) differ from 3 to 8 %. In the case when JC =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 [J.sub.Cll]=0 (wires and cables in the HHIT power circuit are without prior current load) the results of the selection of the boundary permissible crosssections SCi 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 [I.sub.mp] equal to 10, 50, 100, and 500 kA are presented.

From the data of Table 7 it follows that the estimated maximum allowable density [[delta].sub.Cil] [approximately equal to] [I.sub.mp]][S.sub.Cil] of a nanosecond current pulse of the shape 5 ns/200 ns for uninsulated wires with copper and aluminum cores is approximately 495 kA/[mm.sup.2] and 293 kA/[mm.sup.2], and for cables with copper (aluminum) cores (shells) and PET insulation 361 (233) KA/[mm.sup.2].

4. The choice of cross-sections [S.sub.Cil] 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 [i.sub.p](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 [S.sub.Cil] of wires and cables for the discharge circuit of the LCG applicable to a given current pulse [i.sub.p](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 [S.sub.Cil], [[DELTA].sub.p] = ln([I.sub.mp1]/[I.sub.mp3]) = 2.505. Then by (7) for this current the coefficient [k.sub.p2] = 1.731. Table 8 shows the numerical values of the integral of action [J.sub.CiA] calculated by (8) for a given microsecond current pulse [13], changing according to the law of a damped sinusoid.

Using the calculated data for the coefficient [C.sub.]l, given in Table 6, (2) and summarized in Table 8 the results of determining the integral of action [J.sub.CiA], we find the boundary permissible cross-sections [S.sub.Cil] 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 [J.sub.Cll]=0, the results of such a determination of the boundary permissible cross-sections of [S.sub.Cil] 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 [[delta].sub.Cil] [approximately equal to] [I.sub.mp1]/[S.sub.Cil] of the microsecond pulsed current [i.sub.p](t) with the ATP corresponding to the data in Fig. 1, for uninsulated wires with copper and aluminum cores is approximately 26 kA/[mm.sup.2] and 15 kA/[mm.sup.2], and for cables with copper (aluminum) cores (shells) and PET insulation 19 (12) KA/[mm.sup.2].

5. The choice of cross-sections SCil 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 [i.sub.p](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 [t.sub.mp] [approximately equal to] 11 ms, is about 835 A. At the same time, the duration of the front of the test current pulse is approximately [[tau].sub.f] [approximately equal to] 7 ms, and its duration at the level of 0.5 [I.sub.mp] is [[tau].sub.p] [approximately equal to] 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 [S.sub.Cil] of wires (cables) for a discharge circuit of the LCG involved in generating the specified current pulse [i.sub.p](t).

From (5) at [[tau].sub.f] [approximately equal to] 7 ms and [[tau].sub.p] [approximately equal to] 160 ms, we find that [[alpha].sub.1] [approximately equal to] 4.75 [s.sup.-1] and [a.sub.2] [approximately equal to] 338 x [10.sup.2] [s.sup.-1]. Then the normalizing coefficient [k.sub.p1] takes a numerical value of approximately [k.sub.p1] [approximately equal to] 1.077. Using (5) and varying the value of the current amplitude [I.sub.mp], it is possible to calculate the numerical indices of the integral of action [J.sub.CiA] for the considered millisecond current pulse [i.sub.p](t). Table 10 shows the numerical values of [J.sub.CiA] for a number of amplitudes of [I.sub.mp] of a given pulse current [i.sub.p] (t).

Further, assuming that [J.sub.Cll] = 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.sub.l], summarized in Table 6. Taking into account these numerical values of [C.sub.l] and the data of Table 10, according to (2), in the accepted approximation, it is possible to find the boundary permissible cross-sections [S.sub.Cil] 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 [i.sub.p](t), which ATPs correspond to the data of Fig. 2. Table 11 shows the numerical values of the boundary permissible cross-sections [S.sub.Cil] for the indicated wires (cables) with a millisecond aperiodic current pulse [i.sub.p](t), found in the manner described above. Based on the ratio of the form [[delta].sub.Cil] [approximately equal to][I.sub.mp]/[S.sub.Cil], the data of Table 11 allow us to estimate the numerical values of the maximum permissible densities [[delta].sub.Cil] in wires (cables), through which a millisecond aperiodic current pulse [i.sub.p](t) with amplitude [I.sub.mp,] varying in the range (100-1000) A, flows in the longitudinal direction.

From the data of Table 11 it follows that the estimated maximum permissible density [[delta].sub.Cil] of the millisecond aperiodic current pulse [i.sub.p](t) with the ATPs corresponding to the data in Fig. 2, for uninsulated wires with copper and aluminum conductors is approximately 543 A/[mm.sup.2] and 320 A/[mm.sup.2], and for cables with copper (aluminum) cores (shells) and PET insulation 396 (256) A/[mm.sup.2].

The results of experimental studies in discharge circuits of HHIT with pulsed currents [i.sub.p](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 [S.sub.Cil] 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 [S.sub.Cil] 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 [i.sub.p](t), ATPs of which with different amplitudes [I.sub.mp] can vary in nano-, micro- and millisecond time ranges.

2. Using the examples of the change in time t of the pulsed current [i.sub.p](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 [S.sub.Cil] 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 [[delta].sub.Cil] [approximately equal to][S.sub.Cil] of the considered temporal shapes of pulsed current [sup.p](t) in copper (aluminum) cores of non-insulated wires for the nanosecond range are numerically about 495 (293) kA/[mm.sup.2], for the microsecond range 26 (15) kA/[mm.sup.2] and for the millisecond range 543 (320) A/[mm.sup.2]. For insulated wires (cables) with copper (aluminum) cores (shells) and PET insulation, the numerical values of the maximum permissible densities [[delta].sub.Cil] of the considered pulsed currents [i.sub.p](t) for the nanosecond range are about 361 (233) A/[mm.sup.2], for the microsecond range 19 (12) kA/[mm.sup.2] and for the millisecond range 396 (256) A/[mm.sup.2].

doi: 10.20998/2074-272X.2018.6.08

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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

Caption: 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 ([I.sub.mp1] [approximately equal to] -207 kA; [I.sub.mp3] [approximately equal to] - 16.9 kA; [T.sub.p] [approximately equal to] 185 [micro]s; vertical scale 56.3 kA/division; horizontal scale 50 [micro]s/division) [13]

Caption: 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 ([I.sub.mp] [approximately equal to] -835 A; [[tau].sub.f] [approximately equal to]-7 ms; [[tau].sub.p] = d60 ms; vertical scale 282 A/division; horizontal scale 100 ms/division) [13]

Table 1 The values of the maximum permissible short-term temperature [[theta].sub.lS] 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 [[theta].sub.IS] [degrees]C 1 Tire (core), copper, uninsulated at stresses 250 less 20 N/[mm.sup.2] 2 Tire (core), aluminum, uninsulated at 200 stresses less 10 N/[mm.sup.2] 3 Cable and insulated wire with copper (aluminum) cores and polyvinyl chloride (PVC) 150 or rubber (R) insulation 4 Cable and insulated wire with copper 120 (aluminum) cores and polyethylene (PET) Insulated 5 Aluminum part of the steel-aluminum wires of 200 power lines Table 2 The values of long-term permissible temperature [[theta].sub.ll] for the main types of electrical wires (cables) [3] [[theta].sub.II] No. Name of the wire (cable) or the core [degrees]C 1 Wires (cores) uninsulated with any current- 70 carrying tires (parts) 2 Cables (wires) with copper (aluminum) tires, 65 PVC, R and PET insulation 3 Cables with impregnated cable insulation 65 paper for voltage up to 6 kV 4 Cables with impregnated cable insulation 50 paper for voltage up to 35 kV Table 3 The values of the coefficient [C.sub.k] 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 [C.sub.k], A x [s.sup.1/2]/ [mm.sup.2] 1 Wires (cores), copper, uninsulated 170 2 Wires (cores), aluminum, uninsulated 90 3 Cables (insulated wires) with PVC 120 and R insulation and copper cores 4 Cables (insulated wires) with PVC 75 and R insulation and aluminum cores 5 Cables (insulated wires) with PET 103 insulation and copper cores 6 Cables (insulated wires) with PET 65 insulation and aluminum cores 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 [[theta].sub.0] =20 [degrees]C [2, 6] Material of the Values Values core (shell) of [[gamma].sub.01]. [c.sub.0i]. the wire [10.sup.7] x [10.sup.6] x J/ (cable) ([OMEGA] x ([m.sup.3] x m).sup.-1] [degrees] C Copper 5.81 3.92 Aluminum 3.61 2.70 Material of the Values core (shell) of [[beta].sub.0i]. the wire [10.sup.9] x (cable) ([m.sup.3] /J Copper 1.31 Aluminum 2.14 Table 5 The values of the integral of action [J.sub.CiA] for nanosecond a periodic current pulse of the shape 5 ns/200 ns The value of the The value of the amplitude Imp of the integral of action current pulse of the [J.sub.Cil]of the shape 5 ns/200 ns, current pulse 5 ns/ kA 200 ns, [A.sup.2] x s 1 0.141 10 14.13 30 1.27 x [10.sup.2] 50 3.53 x [10.sup.2] 70 6.92 x [10.sup.2] 100 1.41 x [10.sup.3] 200 5.65 x [10.sup.3] 500 3.53 x [10.sup.4] 1000 1.41 x [10.sup.5] Table 6 The values of the coefficient [C.sub.l] values for uninsulated wires, insulated wires (cables) with copper (aluminum) cores (shells) in HHIT circuits with nano-, micro- and millisecond current pulses Insulation type Material of the Values of [C.sub.l] in the wire core (shell) of [10.sup.8] A x (cable) of the the wire [s.sup.1/2]/[m.sup.2] HHIT power (cable) [J.sub.Cll] [J.sub.Cll] circuit = 0 not equal to] 0 Without Copper 1.860 1.563 insulation 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 [S.sub.Cil] 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 Material of the Values of the cross-section in the wire core (shell) of [S.sub.cil], [mm.sup.2] (cable) of the the wire HHIT power (cable) Amplitude Imp of the circuit current pulse 5 ns/200 ns, kA 10 50 100 500 Without Copper 0.020 0.101 0.202 1.010 insulation 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 8 The values of the integral of action [J.sub.CiA] for current pulse [i.sub.p](t), changing in the microsecond time range according to the law of damped sinusoid of the form (7) The value of the The value of the first amlitude integral of action [I.sup.mp1] of the [J.sub.CiA] of the damped sinusoida current pulse of the current pulse, kA form (7), [A.sup.2]xs 10 4.77 x [10.sup.3] 30 4.29 x [10.sup.4] 50 1.19 x [10.sup.5] 70 2.34 x 10.sup.5] 100 4.77- x [10.sup.5] 207 2.05 x [10.sup.6] 300 4.29 x [10.sup.6] 500 11.92 x [10.sup.6] 700 23.4 x [10.sup.6] 1000 47.7 x [10.sup.6] Table 9 The values of the boundary permissible [S.sub.Cil] 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 [I.sub.mp1] of which varies in a wide range from 30 kA to 207 kA Insulation type The values of the cross- in the wire Material of the section [S.sub.Cil] [mm.sup.2] (cable) of the core (shell) of The first amplitude [I.sub.mp1] of HHIT power the wire the current pulse of the form circuit (cable) (7), kA 30 50 100 207 Without Copper 1.113 1.854 3.713 7.698 insulation 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 Table 10 Values of the integral of action [J.sub.CiA] for unipolar current pulse [i.sub.p](t), varying in millisecond time range by aperiodic low The values of the The values of the amplitude [I.sub.m]p integral of action of the unipolar [J.sub.CiA] of the millisecond millisecond current aperiodic current pulse 7 ms-160 ms, pulse 7 ms/160 ms, A [A.sup.2]-s 100 1.17 x [10.sup.3] 200 4.68 x [10.sup.3] 300 1.05 x [10.sup.4] 500 2.92 x [10.sup.4] 700 5.73 x [10.sup.4] 835 8.15 x [10.sup.4] 1000 1.17 x [10.sup.5] Table 11 The values of boundary allowable cross-sections [S.sub.Cil] 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 [I.sub.mp] of which varies in the range from 100 A to 1000 A Insulation type The value of the cross- in the wire Material of the section [S.sub.Cil] [mm.sup.2] (cable)of the core (shell) of HHIT power the wire (cable) Amplitude [I.sub.mp] of the circuit current pulse 7 ms/160 ms, A 100 500 835 1000 Without Copper 0.184 0.919 1.535 1.839 insulation 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

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Author: | Baranov, M.I. |
---|---|

Publication: | Electrical Engineering & Electromechanics |

Article Type: | Report |

Date: | Jun 1, 2018 |

Words: | 6402 |

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