Технологические параметры режима охлаждения полимерной изоляции силовых кабелей
Обоснована методика расчета режима охлаждения силовых кабелей в переходном тепловом режиме. Представлена тепловая схема замещения изолированной токопроводящей жилы. С помощью методов дискретных резистивных схем замещения и узловых потенциалов получено распределение температуры в толще экструдированн...
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| Опубліковано в: : | Електротехніка і електромеханіка |
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| Дата: | 2019 |
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Інститут технічних проблем магнетизму НАН України
2019
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Беспрозванных, А.В. Мирчук, И.А. Кессаев, А.Г. 2019-09-20T14:36:10Z 2019-09-20T14:36:10Z 2019 Технологические параметры режима охлаждения полимерной изоляции силовых кабелей / А.В. Беспрозванных, И.А. Мирчук, А.Г. Кессаев // Електротехніка і електромеханіка. — 2019. — № 3. — С. 44-49. — Бібліогр.: 12 назв. — рос., англ. 2074-272X DOI: https://doi.org/10.20998/2074-272X.2019.3.07 https://nasplib.isofts.kiev.ua/handle/123456789/159021 621.319 Обоснована методика расчета режима охлаждения силовых кабелей в переходном тепловом режиме. Представлена тепловая схема замещения изолированной токопроводящей жилы. С помощью методов дискретных резистивных схем замещения и узловых потенциалов получено распределение температуры в толще экструдированной полиэтиленовой изоляции в разные моменты времени в зависимости от температуры охлаждающей воды. Показано, что длительность переходного процесса, соответствующая достижению одинаковой температуры по всей толщине изоляции, можно рассматривать в качестве критерия при определении технологических параметров охлаждения. Обґрунтовано методику розрахунку режиму охолодження силових кабелів в перехідному тепловому режимі. Представлено теплову схему заміщення ізольованої струмопровідної жили. За допомогою методів дискретних резистивних схем заміщення і вузлових потенціалів отримано розподіл температури в товщі поліетиленової ізоляції в різні моменти часу в залежності від температури води, що охолоджує. Показано, що тривалість перехідного процесу, що відповідає досягненню однакової температури по всій товщині ізоляції, можна розглядати в якості критерію при визначенні технологічних параметрів охолодження. Purpose. The substantiation of the technological parameters of the cooling mode of power cables based on the calculation of the thermal equivalent circuit of a conductive core insulated with polyethylene in transient thermal mode. ru Інститут технічних проблем магнетизму НАН України Електротехніка і електромеханіка Техніка сильних електричних та магнітних полів. Кабельна техніка Технологические параметры режима охлаждения полимерной изоляции силовых кабелей Technological parameters of the cooling mode of polymer insulation of power cables Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Технологические параметры режима охлаждения полимерной изоляции силовых кабелей |
| spellingShingle |
Технологические параметры режима охлаждения полимерной изоляции силовых кабелей Беспрозванных, А.В. Мирчук, И.А. Кессаев, А.Г. Техніка сильних електричних та магнітних полів. Кабельна техніка |
| title_short |
Технологические параметры режима охлаждения полимерной изоляции силовых кабелей |
| title_full |
Технологические параметры режима охлаждения полимерной изоляции силовых кабелей |
| title_fullStr |
Технологические параметры режима охлаждения полимерной изоляции силовых кабелей |
| title_full_unstemmed |
Технологические параметры режима охлаждения полимерной изоляции силовых кабелей |
| title_sort |
технологические параметры режима охлаждения полимерной изоляции силовых кабелей |
| author |
Беспрозванных, А.В. Мирчук, И.А. Кессаев, А.Г. |
| author_facet |
Беспрозванных, А.В. Мирчук, И.А. Кессаев, А.Г. |
| topic |
Техніка сильних електричних та магнітних полів. Кабельна техніка |
| topic_facet |
Техніка сильних електричних та магнітних полів. Кабельна техніка |
| publishDate |
2019 |
| language |
Russian |
| container_title |
Електротехніка і електромеханіка |
| publisher |
Інститут технічних проблем магнетизму НАН України |
| format |
Article |
| title_alt |
Technological parameters of the cooling mode of polymer insulation of power cables |
| description |
Обоснована методика расчета режима охлаждения силовых кабелей в переходном тепловом режиме. Представлена тепловая схема замещения изолированной токопроводящей жилы. С помощью методов дискретных резистивных схем замещения и узловых потенциалов получено распределение температуры в толще экструдированной полиэтиленовой изоляции в разные моменты времени в зависимости от температуры охлаждающей воды. Показано, что длительность переходного процесса, соответствующая достижению одинаковой температуры по всей толщине изоляции, можно рассматривать в качестве критерия при определении технологических параметров охлаждения.
Обґрунтовано методику розрахунку режиму охолодження силових кабелів в перехідному тепловому режимі. Представлено теплову схему заміщення ізольованої струмопровідної жили. За допомогою методів дискретних резистивних схем заміщення і вузлових потенціалів отримано розподіл температури в товщі поліетиленової ізоляції в різні моменти часу в залежності від температури води, що охолоджує. Показано, що тривалість перехідного процесу, що відповідає досягненню однакової температури по всій товщині ізоляції, можна розглядати в якості критерію при визначенні технологічних параметрів охолодження.
Purpose. The substantiation of the technological parameters of the cooling mode of power cables based on the calculation of the thermal equivalent circuit of a conductive core insulated with polyethylene in transient thermal mode.
|
| issn |
2074-272X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/159021 |
| citation_txt |
Технологические параметры режима охлаждения полимерной изоляции силовых кабелей / А.В. Беспрозванных, И.А. Мирчук, А.Г. Кессаев // Електротехніка і електромеханіка. — 2019. — № 3. — С. 44-49. — Бібліогр.: 12 назв. — рос., англ. |
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44 ISSN 2074-272X. Electrical Engineering & Electromechanics. 2019. no.3
© G.V. Bezprozvannych, I.A. Mirchuk, A.G. Kyessayev
UDC 621.319 doi: 10.20998/2074-272X.2019.3.07
G.V. Bezprozvannych, I.A. Mirchuk, A.G. Kyessayev
TECHNOLOGICAL PARAMETERS OF THE COOLING MODE OF POLYMER
INSULATION OF POWER CABLES
Introduction. The cooling mode of polymer insulation after application to the extruder is one of the main factors determining
cable performance. Theoretically, it is ideal to cool the insulation when the temperature of the cooling medium is equal to the
melting point of the insulation material: in this case, the probability of formation of voids in the insulation is less. The cooling
process is usually not subject to stringent requirements, since most insulating materials allow for quite sharp cooling. The
exception is polyethylene, which requires gradual cooling. When the insulation is cooled in a cooling bath, the temperature
decrease starts from the surface. In this regard, the cooling of the insulation of polyethylene is carried out in steps to a
temperature at which the cooled extruded insulation will not be deformed or damaged on the receiving drum. Polyethylene is
characterized by a large value of thermal expansion coefficient, the maximum value of which is in the temperature range
(90-125) C. As a result, there is an uneven reduction in the volume of the upper and inner insulation layers, especially for
cables with a considerable insulation thickness. The rapid cooling of polyethylene leads to the formation of cracks, air
inclusions both between the insulation and the conductive core, and in the layers located near the core. Purpose. The
substantiation of the technological parameters of the cooling mode of power cables based on the calculation of the thermal
equivalent circuit of a conductive core insulated with polyethylene in transient thermal mode. Methodology. The calculation of
the temperature distribution in the thickness of extruded polyethylene insulation at different points in time, depending on the
temperature of the cooling water, is made by the method of electrothermal analogies. There is a transition from the thermal
equivalent circuit of power cables to the equivalent circuit of the discrete resistive equivalent circuit method, which is
calculated using the nodal potential method. As a result of solving a three-diagonal system of linear algebraic equations by
sweeping and finding at each discretization step (time step) thermal power fluxes in the branches of the thermal equivalent
circuit, the temperature in the thermal capacitances determines the temperature in each insulation layer. Practical value. The
duration of the transition process, corresponding to the achievement of the same temperature throughout the thickness of the
insulation, can be considered as a criterion in determining the length of the cooling bath sections depending on the extrusion
(reception) rate. References 12, figures 6.
Key words: cooling mode, polyethylene insulation, thermal equivalent circuit, discrete resistive equivalent circuit method,
transient mode, nodal potentials method, system of linear algebraic equations, cooling bath length.
Обґрунтовано методику розрахунку режиму охолодження силових кабелів в перехідному тепловому режимі.
Представлено теплову схему заміщення ізольованої струмопровідної жили. За допомогою методів дискретних
резистивних схем заміщення і вузлових потенціалів отримано розподіл температури в товщі поліетиленової ізоляції
в різні моменти часу в залежності від температури води, що охолоджує. Показано, що тривалість перехідного
процесу, що відповідає досягненню однакової температури по всій товщині ізоляції, можна розглядати в якості
критерію при визначенні технологічних параметрів охолодження. Бібл. 12, рис. 7.
Ключові слова: режим охолодження, поліетиленова ізоляція, теплова схема заміщення, метод дискретних резистивних
схем заміщення, несталий режим, метод вузлових потенціалів, система лінійних алгебраїчних рівнянь, довжина
ванни охолодження.
Обоснована методика расчета режима охлаждения силовых кабелей в переходном тепловом режиме. Представлена
тепловая схема замещения изолированной токопроводящей жилы. С помощью методов дискретных резистивных
схем замещения и узловых потенциалов получено распределение температуры в толще экструдированной
полиэтиленовой изоляции в разные моменты времени в зависимости от температуры охлаждающей воды. Показано,
что длительность переходного процесса, соответствующая достижению одинаковой температуры по всей толщине
изоляции, можно рассматривать в качестве критерия при определении технологических параметров охлаждения.
Библ. 12, рис. 7.
Ключевые слова: режим охлаждения, полиэтиленовая изоляция, тепловая схема замещения, метод дискретных
резистивных схем замещения, неустановившийся режим, метод узловых потенциалов, система линейных
алгебраических уравнений, длина ванны охлаждения.
Introduction. The cooling mode of polymer
insulation after application in the extruder is one of the
main factors determining cable performance.
Theoretically, the cooling of the insulation is ideal at the
temperature of the cooling medium equal to the melting
point of the insulation material: in this case, the
probability of formation of voids in the insulation is less
[1-3]. In the process of cooling, heat from the surface of
the insulation is removed with the help of air or water of
lower temperature. The cooling process is mainly subject
to the laws of convective heat transfer, and, here forced
convection is usually observed due to the continuous axial
movement of the workpiece during the technological
process. The process of temperature change over the
thickness of the insulation or shell, that is, inside a solid,
occurs according to the laws of heat conduction.
The cooling process is usually not subject to
stringent requirements, since most insulating materials
allow for quite sharp cooling. The exception is
polyethylene, which requires gradual cooling. When the
insulation is cooled in a cooling bath, the temperature
decrease starts from the surface. In this regard, the
cooling of insulation of polyethylene is carried out
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2019. no.3 45
stepwise to a temperature at which the cooled extruded
insulation will not be deformed or damaged on the
receiving drum [2, 3]. At cable companies, extruded
coating is cooled to temperatures (40…50) С to comply
with safety requirements [4].
The length of the cooling bath depends on the speed
of extrusion, the diameter of the core (or cable) and the
thickness of the insulation (shell). The length of the bath
for cooling insulation based on crystalline polymers is
longer than for cooling insulation of amorphous polymers,
since the crystallization process is exothermic [2, 3].
The rewinding speed depends on the diameter of the
extruded cables. So, for telephone cables, the conductor
diameter of which does not exceed 1 mm, the reception
speed is one of the highest and reaches 1200 m/min. As
the diameter of the core increases, the reception speed
decreases and for power cables it is about (6-30) m/min.
At cooling of polyethylene insulation, speed is limited by
the length of the cooling bath.
Existing methods for calculation of the cooling
modes of extruded insulation allow one to calculate the
cable rewinding speed at a known cooling bath length or
the bath length at a given rewinding speed [5, 6] without
taking into account the temperature distribution over the
entire insulation thickness in transient thermal mode.
Problem definition. Technological parameters of
the cooling mode affect the internal structure of the
polymer: the lower the cooling rate, the higher the content
of the crystalline phase in the polymer insulation. At rapid
cooling, relaxation processes do not have time to
complete, a violation of the internal morphological
structure occurs, leading to the formation of a non-
equilibrium structure of polymer insulation with a
predominance of the amorphous phase [1-3]. The
quantitative ratio of the crystalline and amorphous phases
ultimately determines the thermal, mechanical and
electrical characteristics of extruded insulation.
At sharp cooling, it is also possible the formation of
internal voids in the thickness of extruded insulation. This
process is most likely to occur when cooling
polyethylene, in which the volume of the melt at
temperature of 200 С is practically 25% higher than at
20 С: a sharp change in volume occurs near its melting
point [7]. Polyethylene is characterized by a large value of
thermal expansion coefficient, the maximum value of
which is in the temperature range (90-125) С. As a
result, there is an uneven reduction in the volume of the
upper and inner insulation layers, especially for cables
with a considerable insulation thickness. The sharp
cooling of polyethylene leads to the formation of cracks,
air inclusions both between the insulation and the
conductive core, and in the layers located near the core.
Thus, in [5] the degree of cable cooling is
determined at a given temperature at the inlet to the bath
and the temperature of the cooling water during
convective heat exchange between the surface of the
insulation and cooling water [8].
For power cables, it is important to obtain the
temperature field distribution over the thickness of
extruded polyethylene insulation, which is determined by
the thermal conductivity of polyethylene insulation,
taking into account the temperature of heating of the
conducing core and the temperature of the cooling water.
The goal of the paper is the justification of the
technological parameters of the cooling mode of power
cables based on the calculation of the thermal equivalent
circuit of a conductive core insulated with polyethylene in
transient thermal mode.
Thermal equivalent circuit of extruded insulated
core in transient thermal mode. In the general case, the
calculation of the temperature field over the thickness of
the insulation when it is cooled is reduced to the
specification of single-valued conditions: geometric
conditions that characterize the shape and dimensions of
the extruded conductive core; physical conditions
characterizing thermal conductivity, heat capacity, density
of the core, insulation and cooling medium, respectively;
initial conditions characterizing the temperature
distribution at the initial moment of time (at t = 0);
boundary conditions characterizing the interaction of the
extruded insulation under consideration with the
environment [9].
To calculate the temperature distribution in the
thickness of extruded polyethylene insulation at different
times, depending on the cooling water temperature, we
use the method of electrothermal analogies [9]. There is a
complete analogy between the thermal and electrical
equivalent circuits, which allows using the well-known
methods of the theory of electrical circuits to calculate
thermal circuits. The analogue of the potential in the
thermal equivalent circuit is the temperature (T), and the
analogue of the current is the heat flux (P) per unit length
of insulation along its axis (per unit length of cable).
The thermal equivalent circuit of insulation of power
cables (Fig. 1) is calculated using the method of discrete
resistive equivalent circuits [9]. For this, thermal
quantities will be replaced by their electrical counterparts.
Then we calculate the thermal circuit and determine the
desired temperature [9].
The thermal substitution circuit (Fig. 1) reflects: the
heat capacity of the core Cg; the temperature-dependent
(non-linear) thermal resistances Rt and thermal
capacitances Ct of each insulation layer (from 1 to M), the
thermal resistance of heat transfer Rtо from the surface of
the wire insulation, as well as the effect of the source of
heating of the wire to the medium temperature Tw.
Tw
RtoRt 1 2 3 ... M
Cg Ct
Fig. 1. Thermal substitution circuit of the extruded
insulated core in transient thermal mode
To calculate the temperature field in the process of
cooling of a moving insulated conductive core, we take
the following assumptions:
1) an insulated core is considered symmetric about
its axis;
2) the core moves at a constant speed;
46 ISSN 2074-272X. Electrical Engineering & Electromechanics. 2019. no.3
3) the core material and insulation is isotropic;
4) changes in the size of the wire caused by
shrinkage of the insulation are not take into account;
5) the heat transfer along the conductive core is
neglected;
6) the internal sources of heat released during the
phase transition of the polymer during cooling of the
insulation are not take into account;
7) each element has constant electrical and physical
characteristics in its volume.
Given the initial values of the temperature at the exit
of extruded polyethylene insulation from the
vulcanization chamber at time t = 0, namely: of a heated
conductor, insulation (the temperature of which is the
same throughout the thickness and on the surface),
cooling water, it is possible to obtain the temperature
distribution across the insulation thickness at different
points in time.
The calculation technique. From the thermal
equivalent circuit (Fig. 1), we turn to the equivalent
circuit of the discrete resistive equivalent circuit (DREC)
method (Fig. 2) [10], in accordance with which
capacitances are represented by sources of EMF Есg, Есt
and resistors Rсg, Rсt. The EMF sources «remember» the
temperatures on the capacitances at the previous (k–1)th
time («old» temperature). Finding a «new» temperature at
the current k-th instant of time in time interval h is
defined as
1 kk TP
C
h
T . (1)
Tw
RtoRt 1 2 3 ... M
Rcg
Ecg
Rct
Ect
Fig. 2. Discrete resistive equivalent circuit of extruded insulated
core in transient thermal mode
The calculation of the DREC is performed by the
method of nodal potentials [9, 10]. The system of linear
algebraic equations (SLAE) of the method of nodal
potentials for the case of M nodes (the number of layers
along the insulation thickness) has the form [9]
M
M
M
M
MMMMMM
MMMMMM
M
M
M
M
M
J
J
J
J
J
J
J
GGGGG
GGGGG
GGGGG
GGGGG
GGGGG
GGGGG
GGGGG
1
5
4
3
2
1
1
5
4
3
2
1
4321
,14,13,12,11,1
554535251
444434241
334333231
224232221
114131211
......
...
...
..................
...
...
...
...
...
,(2)
where J1 – JM are the nodal «currents» (heat flow):
J1 – JM–1=0;
to
c
M R
T
J ;
tctcgt RRRR
G
111
11
is
the nodal conductivity of the first node (the sum of the
conductivities of the branches converging at the first
node);
tctt RRR
G
111
22 is the nodal conductivity of
the second node;
;...;;; 22)1)(1(225522442233 GGGGGGGG MM
toctt
MM RRR
G
111
;
tR
G
1
12 is the mutual
conductivity between the 1st and the 2nd nodes (taken
with a minus sign the total conductivity between the 1st
and the 2nd nodes); 12453423 ... GGGG ;
0... 1151413 MGGGG .
As a result of solution of the three-diagonal SLAE
(2) by the method of sweeping and finding at each
discretization step (time interval) thermal power fluxes in
the branches of the thermal equivalent circuit, the
temperatures in the thermal capacitances, the temperature
is determined in each insulation layer. The order of the
resolving system of linear algebraic equations is
determined by the product of the number of nodes and the
number of discretization steps.
The influence of technological modes of cooling
and design parameters of cables on the temperature
distribution across the thickness of extruded
polyethylene insulation. The calculation of the
temperature distribution over the thickness of the
insulation is carried out with given thermal characteristics
(thermal conductivity λ, specific heat capacity c, density
ρ): for copper conductor λg = 200 W/(m·K); cg = 420
J/(kg·K); ρg = 8300 kg/m3 [11, 12].
For polyethylene: the density is assumed to be
ρd = 940 kg /m3; the dependences of the thermal
conductivity and specific heat capacity on temperature are
given as approximating functions [1, 7]:
d = 0,35 W/(m·K) at T 120 С;
d = 0,41 – 0,001T at T < 120 С;
cd = 3150 J/(kg·K) at T 115 С;
cd = 3750 – 4,78T at T < 115 С;
Thermophysical characteristics of cooling water
required for the calculation of thermal resistance Rto: λw =
= 0,24 W/(m·K); cw = 5000 J/(kg·K); ρw = 1000 kg/m3 [5].
The calculations are performed for initial insulation
temperature of 200 C at time t = 0 when extruded
polyethylene insulation exits the vulcanization chamber.
1. The influence of the temperature of the cooling
medium on the temperature distribution. Figure 3
shows the dynamics of the temporal variation of the
temperature distribution in polyethylene insulation 2 mm
thick (i is the layer number in the thickness of the
insulation, measured from the core), depending on the
cooling water temperature. The temperature of the water
in the cooling bath is respectively:
• 30 С (Fig. 3,a, curve 1 in Fig. 3,d);
• 60 С (Fig. 3,b, curve 2 in Fig. 3,d);
• 90 С (Fig. 3,c, curve 3 in Fig. 3,d).
The calculation results are obtained for a conductive
copper core heated to 90 С with cross section of 95 mm2.
As the calculations show (compare Fig. 3,c and Fig. 4),
heating the core to 90 С reduces the probability of
formation of air cavities near the core, provides a more
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2019. no.3 47
uniform temperature distribution across the insulation
thickness during the same transient time and improves
adhesion of the polymer melt to the metal conductor.
0 20 40 60 80 100
40
60
80
100
120
140
160
180
T, o
C
i
Tw = 30
o
C t= 1 c
2
3
100 c100 s
t = 1 s
а
0 20 40 60 80 100
60
80
100
120
140
160
180
T, o C Tw =60
o
C t = 1 c
2
3
100 c
i
100 s
t = 1 s
b
0 20 40 60 80 100
90
100
110
120
130
140
150
160
170
180
190
2
t= 1 c
3
100 c
i
Tw = 90
o
C
T,
o
C
100 s
t = 1 s
c
t, s
d
Fig. 3. The effect of cooling water temperature on
temporal distribution dynamics of temperature through the
thickness of polyethylene insulation
At cooling water temperature of 30 С, the most
sharp cooling of the insulation is observed (compare
curve 1 with curve 3 in Fig. 3,d). The decrease in
temperature starts from the surface of the insulation (see
Fig. 3, layer i = 100 at t = 1 s). The surface layer, cooling
over time t = 5 s, tends to reduce its volume, while the
internal ones, which are not yet cooled, impede this
reduction. In this case, the surface layer hardens under the
action of radial pressure and is in a stretched state with
frozen internal stresses. Upon subsequent cooling of the
inner layers, their volume is reduced, but this occurs
under conditions when the outer layers have already
hardened. Volume reduction may occur unevenly, and at
the most mechanically weak points, i.e. where insulation
is last cooled.
0 20 40 60 80 100
60
80
100
120
140
160
180
i
T, oC Tw=90 o C
C
oTg=50
t=1 c
2
3
100 c
100 s
t = 1 s
Fig. 4. Dynamics of temperature distribution over the thickness
of the insulation at the temperature of the core equal to 50 С
The probability of formation of bubbles and voids in
the core, the temperature of which is higher in comparison
with the outer layers of insulation, increases significantly.
The time required to complete the transient thermal
process in the first section of the cooling bath with water
temperature of 90 С (see Fig. 3,c, curve 3 in Fig. 3,d,
curve 1 in Fig. 5) is about 100 s.
t, s
Fig. 5. Temporal diagram of the temperature distribution across
the thickness of the polyethylene insulation with step cooling in
a three-section bath
During this time, over the entire thickness of the
insulation, practically the same temperature is established,
equal to the cooling water temperature of 90 С, which
reduces the probability of formation of cavities and the
concentrations of thermomechanical stresses in the
thickness of the polyethylene insulation.
48 ISSN 2074-272X. Electrical Engineering & Electromechanics. 2019. no.3
The transient time can be considered as a criterion to
substantiate the relationship between the length L1 (m) of
the first section of the cooling bath and the reception
speed v (m/s). For the case considered, the L1/v value is
100 s. At a rewind speed of v = 0,2 m/s = 12 m/min, the
length of the first section should be equal to 20 m. The
length of the bath can be reduced at least twice with that
same reception speed: at such a length, the temperature
difference between the inner and outer layers of insulation
does not exceed 10 С (see Fig. 5, curve 1).
The insulation in the second and the third sections is
cooled by water, the temperature of which is equal to
50 С and 20 С, respectively, in significantly less time
(compare curve 1 and curves 2, 3 in Fig. 5). The length of
the second section L2 is 10 m, of the third (to ensure the
insulation temperature of about 40 С) is L3 = 4 m. Thus,
the total length of the three-section cooling bath will be
30 m. Such cooling mode parameters provide less
probability of formation of voids, air inclusions and
cracks in the thickness of the insulation. The results
obtained are consistent with the data given in [1, 5].
2. The influence of cable design parameters on
the temperature distribution across the thickness of
extruded polyethylene insulation. The effect of the
diameter of the conductive core on the temperature
distribution across the insulation thickness at different
points in time is shown in Fig. 6.
t = 1 s
2 s
Fig. 6. The influence of the conductive core cross section on the
temperature distribution across the thickness of the polyethylene
insulation
The insulation thickness in both cases is 2 mm.
Curve 1 corresponds to the cross section of a copper core
of 95 mm2, curve 2 – of 240 mm2. At the initial cooling
moment, for internal insulation layers located near the
core of a larger cross section, the temperature is lower
compared to the temperature distribution for insulation
with a core of a smaller cross section. The difference is
further leveled, which allows using a bath of the same
length for cooling.
Increasing the thickness of the insulation leads to an
increase in the time of the transient thermal process, and
hence the length of the first cooling section (Fig. 7). To
maintain the same length of the first section of the cooling
bath when cooling cables with a greater insulation
thickness, it is necessary to reduce the reception rate
accordingly.
Figure 7 shows the effect of the number of layers on
the temperature distribution: M = 100 (Fig. 7,a), M = 300
(Fig. 7,b). The core cross section is 95 mm2, the insulation
thickness is 6 mm. An increase in the number of layers
along the insulation thickness improves the calculation
accuracy by 8 %.
t = 1 s
300 s
a
1 s
300 s
b
Fig. 7. The influence of the number of layers on the temperature
distribution over the thickness of the insulation
Conclusions.
A technique is developed for calculation of the
technological parameters of the cooling mode of power
cables. The technique is based on the calculation of the
thermal equivalent circuit of a conductive core insulated
with polyethylene in transient thermal mode, taking into
account the dependence on temperature of thermal
resistance and heat capacity using methods of discrete
resistive equivalent circuits and nodal potentials.
The duration of the transient, corresponding to
achieving the same temperature throughout total thickness
of the insulation of power cables of different designs, is
substantiated. It is shown that the duration of the transient
can be considered as a criterion in determining the length
of the sections of the cooling bath, depending on the rate
of extrusion (reception).
The influence of the diameter of the conducting core
and the thickness of the polyethylene insulation on the
cooling mode of the power cables is established.
The proposed technique can be applied to select
technological cooling modes for other types of cables, for
example, symmetric, radio frequency and optical cables.
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Received 11.03.2019
G.V. Bezprozvannych1, Doctor of Technical Science, Professor,
I.A. Mirchuk2, Postgraduate Student,
A.G. Kyessayev1 , Candidate of Technical Science,
1 National Technical University «Kharkiv Polytechnic Institute»,
2, Kyrpychova Str., Kharkiv, 61002, Ukraine,
тел/phone +38 057 7076010,
e-mail: bezprozvannych@kpi.kharkov.ua
2 Private Joint Stock Company «Ukraine Scientific-Research
Institute of Cable Industry»,
2-P, Promychlennaya Str., Berdyansk, Zaporozhye Region,
71101, Ukraine,
тел/phone +38 066 8288554,
e-mail: garik710@ukr.net
How to cite this article:
Bezprozvannych G.V., Mirchuk I.A., Kyessayev A.G. Technological parameters of the cooling mode of polymer
insulation of power cables. Electrical engineering & electromechanics, 2019, no.3, pp. 44-49. doi: 10.20998/2074-
272X.2019.3.07.
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