Jumaeva D.J., Toirov O.Z., Sulaymonova Z., Uralova F.
ANALYSIS OF HEAT PROCESSES OF CONNECTED POLYETYLINE INSULATED CABLE LINES *
Аннотация:
the article deals with the analysis of thermal processes of connected cable lines with polyethylene insulation in the cable industry
Ключевые слова:
insulation, cable, polymer, polyethylene, analysis, calculation
УДК 621.315
Jumaeva D.J.
Doctor of Technical Sciences, Professor, Institute of General and Inorganic
Chemistry Laboratory of Colloid Chemistry and Industrial Ecology
(Uzbekistan, Tashkent)
Toirov O.Z.
Doctor of Technical Sciences, Professor, Head of Department
"Electrical Machines" Tashkent State Technical University
(Uzbekistan, Tashkent)
Sulaymonova Z.
Master Student of the Department "Electrical Machines"
Tashkent State Technical University
(Uzbekistan, Tashkent)
Uralova F.
Master Student of the Department "Electrical Machines"
Tashkent State Technical University
(Uzbekistan, Tashkent)
ANALYSIS OF HEAT PROCESSES
OF CONNECTED POLYETYLINE INSULATED CABLE LINES
Abstract: the article deals with the analysis of thermal processes of connected cable lines with polyethylene insulation in the cable industry.
Keywords: insulation, cable, polymer, polyethylene, analysis, calculation.
When determining the design of cable lines, the choice of dimensions and material of insulation is made, for which electrical and thermal calculations are made.
The analysis of thermal processes in cable lines is designed to determine the maximum -permitted cable load current, the value of which is limited to the maximum operating temperature of polyethylene insulation in the normal mode. The maximum allowable current is directly affected by the method of deposition, cooling conditions (natural and forced-forced), thermal load conditions (stationary, transient, cyclic and emergency) [1-4]. There are no normative documents for long-term allowable currents for cable lines with a capacity of 35 kV and above, which are determined by thermal calculation for each -special cable. It is provided in lower voltage classes, but for non-standard cases it requires filling and explanation.
A simulation model of thermal processes of cable lines with polyethylene insulation in stationary mode with natural cooling has been developed. Ten minutes after the cable lines are switched on under load, it enters stationary mode, in which the switching mode continues. When using cable lines with BPE insulation, the heat sources are as follows: core and screen as well as light heating main insulation and shell cable lines are available.
When the cable lines are switched on under load, the amount of heat generated is greater than the amount of heat released Qajr> Qolin, the cable lines heat up, but the heat removal gradually increases and Qajr = Qolin is set to stationary mode.
Fig.1. The temperature difference depends on the heating time
An important indicator in modeling is the temperature difference between the core and the environment: Δt = tя-t0 (1)
Here tliv- living temperature, tа – ambient temperature.
In this case, the heating of the cable when turned on under load at any time is given by the described exponential law and takes the following form:
Δtх=Δtmах (1-еt/Т) (2)
Here Δtmах - maximum temperature difference; t - heating time; Т- the time constant of heating the cable, where Δtх=0,633 Δtmах
The heating of cable lines during cooling is also exponentially time dependent:
Δtх=Δtmахеt/Т (3)
The thermal processes that take place in cable lines can be described by dividing them into heat sources, the largest of which is the core:
(4)
Here Рt1= specific thermal resistance of the electrical insulation of the cable; r is the flow radius from the core surface to the insulation surface (4) combining the expression:
(5)
Result, (5) then the temperature difference is obtained from the core depending on a single heat source:
(6)
for the concentric layer of any thermal insulation resistance of the sign this expression (6) takes the following form:
t1-t2= Δt=Q1*T1 (7)
(7) the "heat" law of the expression flow. The temperature difference is equal to the product of the heat flow and the heat resistance [1].
There are several heat sources in cable lines, so the principle of superposition of sources to connect them is applied under the influence of limiting the continuous allowable current in the core.
A computer simulation of thermal processes with a single source from the core was performed to determine the long-term allowable flow as a starting point for the analysis of thermal processes and for the convenience of subsequent calculations.
Fig.2. Equivalent thermal circuit of a single-core cable laid on the ground. ¬Heat resistance: T1 - basic insulation; T2 - screen; T3 - shells; T4 is the transition from the heated surface of the cable to the environment (ground)
From the scheme of heat equivalent the equation of the law of "heat" of flow is formed:
t1-t2=Δt=Qж⸱Т1+ Qж⸱Т2+ Qж⸱Т3+ Qж⸱Т4 (8)
Where t1 is the maximum allowable temperature of the cable core; t0 - ambient temperature; T = T1 + T2 + T3 + T4 is the total thermal resistance of the cable. When laying power cables, the soil temperature (at the level of cable laying) is obtained: t0 = 15°C for summer, t0 = 0°C for winter. When laying the cable in the air, the average annual ambient temperature t0 = 25°C is obtained if there is no special data on the annual change of its laying temperature. [2].
Heat flux from a conducting core:
Qж=I2⸱R (9)
Here I - the maximum temperature allowed in the current in the conductor core; t1; R- electrical resistance of the conductor at room temperature t1; Permissible current in the maximum core [1]:
(10)
The heat sources in the cable line are: conductive core Qj, electrical main insulation Qgi shell Qo, metal screen Qe, semiconductor screen Qpe - the losses in the dielectric are distributed over the entire volume of insulation so the heat flow through the layers at different distances from the center of the cable is not the same. Part of the heat flux (Qd) must be calculated by -integration.
Fig.3. Equivalent thermal circuit of a single-core cable laid on the ground with all heat sources
The heat flux from the core and screen is determined by the following expressions: Qj=I2jR, Qэ=I2эR=a1Qj it is difficult to calculate the heat flux from the screen of cable lines under operating conditions, so in the future mathematical model there is a coefficient representing the ratio of heat flux. The heat flux from the core is taken from the screen: a1=Qe/Qj, Although cable lines, which also apply to the heat flow from the shell, are not significant, it should be taken into account because the shell is statistically the most damaged cable line element. The heat flux from the losses in the main insulation is expressed as follows: Qги=СU2фωtgδ here C is the cable power per kilometer; Uф- phase voltage; ω=2πf, here f- frequency of the electric field; tgδ- dielectric loss tangent [3].
Given the above, the equation is based on Om's law of heat (Fig.3):
(11)
The heat balance equation (11) for insulated cable lines then allows to determine the heating of the main insulating elements of the cable lines. The thermal resistance of the main insulation can be calculated from the following expression:
(12)
Here pt1 - specific heat resistance of insulation; r1 - radius on the surface of the core or screen across the core; r2 - radius along the surface of the electrical insulation.
Thermal resistance of the cable to the ground from the heated surface:
(13)
here pt2 - the specific thermal resistance of the cable to the ground from the heated surface; L - cable laying depth: rh from the center of the cable is the outer radius of the cable rh
The thermal resistance when laying the cable in the air is calculated by the expression:
(14)
Here pt3 - the specific thermal resistance of the transition from the heated surface of the cable to the ambient air; dh - the outer diameter of the cable.
The specific heat resistance [4] values of the materials are given in Table 1.
Table 1. Specific heat resistance of materials used
for insulation and protective coatings
|
Raw materials |
pt, K⸱m/ВТ |
|
Insulation materials: |
|
|
Polyethylene |
3,5 |
|
Polyvinyl chloride |
5,0-6,0 |
|
Insulating rubber |
5,0 |
|
Butyl rubber based rubber |
5,0 |
|
Ethylene propylene rubber |
3,5-5,0 |
|
Protective coating materials: |
|
|
Polyvinyl chloride |
5,0-6,0 |
|
Polyethylene |
3,5 |
|
Polychloroprene |
5,5 |
|
Conductor materials: |
|
|
Concrete |
1,0 |
|
Fibra |
4,8 |
|
Asbestos cement |
2,0 |
|
Polyvinyl chloride |
7,0 |
|
Polyethylene |
3,5 |
Several cables are laid in the pit. Cables with backup and load up to 50% do not affect the others, but if each has a load, if it exceeds 50%, then the maximum allowable current should be multiplied by the correction factors (Table 2) [5-6].
To protect against mechanical damage in hard places, the cells on the concrete blocks where the cables are laid will be like 2x2, 2x3. To pull the cable into the block, the hole in the block cell is slightly larger than the outer diameter so the surface of the cable and the block in the hole in the cell remain a thin layer of air with high heat resistance.
Table 2. Load coefficients for cables laid in trenches
|
n |
1 |
2 |
3 |
4 |
5 |
6 |
|
I = 100 mm |
1,0 |
0,90 |
0,85 |
0,80 |
0,78 |
0,75 |
|
I = 300 mm |
1,0 |
0,93 |
0,90 |
0,87 |
0,86 |
0,85 |
n - the number of cables in the trench; I - the distance between the cables in the light.
In this case, the other cables heat each other. Due to this and the deteriorated heat dissipation, depending on the location of the cell with the cable, the load on it can be reduced by 20-25%. Correction factors presented in the form of reference data are used to account for the long-term allowable flow decrease due to the presence of an air layer in the block cell [7].
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Kargin V.A. Encyclopedia of polymers, vol. 1 - 3, ch. ed., M., 1977
Volynsky A.L. How to mix polymers // Nature- 2014. - No. 3.- P. 44−52
Tager A.A. Physical chemistry of polymers, M.: Nauchny Mir, 2007.Manufacturers of power cables for medium and high voltage with XLPE insulation in Russia and CIS countries // Cable-news. 2007. No. 9.
Olimjon Toirov, Kamoliddin Alimkhodjaev, Akhror Pardaboev Analysis and ways of reducing electricity losses in the electric power systems of industrial enterprises, SUSE-2021, E3S Web of Conferences 288, 01085 (2021) https://doi.org/10.1051/e3sconf/202128801085
Toirov O.Z., Shatursunov Sh.Sh., Akberdiev M.A. Increasing the efficiency of the liquid fuel combustion chamber of the wire annealing furnace due to the adjustable electric drive // Международный научный журнал “Вестник науки”. 2022. №5 (50). Т. 4. ISSN 2712-8849.
Номер журнала Вестник науки №5 (50) том 4
Ссылка для цитирования:
Jumaeva D.J., Toirov O.Z., Sulaymonova Z., Uralova F. ANALYSIS OF HEAT PROCESSES OF CONNECTED POLYETYLINE INSULATED CABLE LINES // Вестник науки №5 (50) том 4. С. 273 - 280. 2022 г. ISSN 2712-8849 // Электронный ресурс: https://www.вестник-науки.рф/article/5674 (дата обращения: 24.04.2024 г.)
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