CN106329455A - Prefabricated-type flexible DC cable terminal stress cone structure - Google Patents

Abstract

The invention provides a prefabricated-type flexible DC cable terminal stress cone structure, and the structure comprises a reinforcing insulation layer, a stress cone semiconducting layer, and a stress cone curve. The stress cone semiconducting layer is disposed on the insulating layer of a DC cable body. The reinforcing insulation layer is disposed on the stress cone semiconducting layer, and the stress cone curve is the lower edge of the stress cone semiconducting layer. On the basis of giving consideration to the impact on the resistivity from the temperature and an electric field, the invention proposes the distribution of an electric field in the insulation of a prefabricated-type flexible DC cable terminal, and provides a theoretical basis for the design of a flexible DC cable connection part. A method for calculating the thickness of the reinforcing insulation layer of the prefabricated-type flexible DC cable terminal is proposed, and guarantees that the interface electric field of the cable insulating layer and the reinforcing insulation layer is within a reasonable range. A reasonable stress cone is designed, thereby solving the phenomenon of centralized potential wires of the flexible DC cable terminal, and guaranteeing that the electric field of the whole stress cone is uniform. The structure meets the requirements of a whole flexible DC cable system for the electrical performances of the terminal, and guarantees the long-time safety and reliability of the flexible DC cable system.

Description

Prefabricated flexible direct current cable terminal stress cone structure

Technical Field

The invention relates to a prefabricated flexible direct current cable terminal stress cone structure.

Background

Flexible direct current transmission has received more and more attention as a new type of power transmission. The flexible direct current cable system is an important component of the flexible direct current power transmission system and comprises a flexible direct current cable body and flexible direct current cable connecting pieces (joints and terminals). The flexible straight cable terminal is a key part of a cable system and is also a link which is easy to break down, so that the flexible straight cable system is restricted from developing to a higher voltage level.

The electric field distribution in the cable stress cone must be taken into account during the cable termination design process. In an ac cable termination, the electric field distribution depends on the dielectric constant of the insulating material, independent of the temperature distribution. In the insulation of a dc cable terminal, the electric field distribution depends on the resistivity distribution, which is related to temperature and electric field, and thus the electric field distribution is more complicated.

At present, no design theory and design method about the flexible straight cable terminal exist, and no structural design is provided based on the direct current electric field distribution. In the existing flexible and straight cable terminal structure design, the alternating current terminal structure design is mostly applied and slightly adjusted, and a specific design theory and a design method are not provided.

Disclosure of Invention

In order to solve the defects in the prior art, the invention provides a prefabricated flexible direct current cable terminal stress cone structure.

In order to solve the technical problem, the invention provides a prefabricated stress cone structure of a flexible direct current cable terminal, which comprises a reinforced insulating layer, a stress cone semi-conducting layer and a stress cone curve, wherein the stress cone semi-conducting layer is arranged on an insulating layer of a direct current cable body, the reinforced insulating layer is arranged on the stress cone semi-conducting layer, the stress cone curve is the lower edge of the stress cone semi-conducting layer, and the calculation method of the stress cone curve comprises the following steps:

step one, calculating the radial electric field intensity E at the position of a stress cone curve y₂(y)；

$E_2\left(y\right)=\frac{{\mathrm{\ρ}}_2\left(y\right)}{2\mathrm{\π}y}\·\frac{U}{R\left(y\right)}$

Where ρ is₂(y) resistivity at the reinforcing insulating layer y, U voltage the reinforcing insulating layer withstands, and R (y) unit resistance from the inner surface of the reinforcing insulating layer to the stress cone curve y;

determining the thickness of the reinforced insulating layer;

radius R of the reinforced insulation layer_sRadial electric field intensity E of₂(Rs) is the maximum working electric field intensity E of the cable insulation layer₀One-half of (1), the expression is as follows:

E₂(R_S)＝0.5E₀

calculating R by combining the expression of the radial electric field intensity at the stress cone curve y and the above expression_sSo as to calculate the thickness delta n ═ R of the reinforced insulating layer_s-R, R is the cable insulation radius;

step three, determining a stress cone curve equation;

axial electric field intensity E of any point on stress cone curve_tRadial electric field E with the spot₂The following relationships exist:

$E_t=E_2\·tan\mathrm{\α}=E_2\·\frac{dy}{dx}$

integrating the above equation to obtainLet E_tIs constant, the radial electric field E₂Expression bring-inAnd obtaining a plurality of groups of coordinates (x, y) by using a numerical solution method to obtain a stress cone curve equation.

In the first step, the resistivity rho of the insulating layer y is enhanced₂The calculation procedure of (y) is as follows:

temperature difference between the reinforcing insulating layer r' and the cable conductor:

${\mathrm{\θ}}_c-{\mathrm{\θ}}_2=({\mathrm{\θ}}_c-{\mathrm{\θ}}_R)+({\mathrm{\θ}}_R-{\mathrm{\θ}}_2)=\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T1}ln\frac{R}{r_c}+\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T2}ln\frac{r^{\′}}{R}$

namely:

in the formula, theta₂To increase the temperature at the outer diameter r' of the insulating layer, θ_RIs the temperature of the outer surface of the cable insulation, theta_cIs the cable conductor temperature, R is the cable insulation radius, ρ_T2To enhance the thermal resistivity of the insulating layer, ρ_T1Is the thermal resistivity, W, of the cable insulation_cLoss of cable conductors; r is_cIs the cable conductor radius;

according to a resistivity formula, increasing the resistivity rho at the position of the insulating layer r₂The expression of (r') is:

${\mathrm{\ρ}}_2\left(r^{\′}\right)=\frac{{\mathrm{\ρ}}_{2,0}{e}^{-a_2{\mathrm{\θ}}_2}}{E_2{\left(r^{\′}\right)}^{{\mathrm{\γ}}_2}}=c_3\frac{r^{\′c_4}}{E_4{\left(r^{\′}\right)}^{{\mathrm{\γ}}_2}}$

wherein,ρ_2,0to enhance the resistivity of the insulating layer; a is₂To enhance the temperature coefficient of resistivity of the insulating layer; gamma ray₂To enhance the resistivity electric field coefficient of the insulating layer; e₂(r ') is the radial electric field strength at the reinforcing insulating layer r ', according to ohm's law:therefore, the temperature of the molten metal is controlled,i current at stress cone curve y; byAnd resistivity p at the reinforcing insulating layer r₂(r') is expressed as:this formula is brought into the resistivity p at the enhanced insulating layer r₂(r') is expressed as:

${\mathrm{\ρ}}_2\left(r^{\′}\right)=c_3{c_7}^{-{\mathrm{\γ}}_2}{r}^{c_4-{\mathrm{\γ}}_2{c}_8}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}$

wherein,

in the first step, the unit resistance r (y) from the inner surface of the enhanced insulating layer to the stress cone curve y is calculated as follows:

$R\left(y\right)=\underset{r_c}{\overset{R}{\∫}}\frac{{\mathrm{\ρ}}_1\left(r\right)}{2\mathrm{\π}r}dr+\underset{R}{\overset{y}{\∫}}\frac{{\mathrm{\ρ}}_2\left(r^{\′}\right)}{2\mathrm{\π}r}{\mathrm{dr}}^{\′}$

wherein the resistivity at the strong insulating layer rResistivity of cable insulation layer r

According to the heat path equation, the following steps are carried out:

${\mathrm{\θ}}_c-{\mathrm{\θ}}_1=\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T1}ln\frac{r}{r_c}$

namely:

according to ohm's law:therefore, the temperature of the molten metal is controlled,i current at stress cone curve y; byAnd resistivity rho at the cable insulation r₁(r) is expressed as:bringing this formula into the resistivity rho at the cable insulation r₁(r) is expressed as:

${\mathrm{\ρ}}_1\left(r\right)=c_1{c_5}^{-{\mathrm{\γ}}_1}{r}^{c_2-{\mathrm{\γ}}_1{c}_6}{I}^{-\frac{{\mathrm{\γ}}_1}{1+{\mathrm{\γ}}_1}}$

the specific resistance r (y) from the inner surface of the enhanced insulating layer to the stress cone curve y is thus obtained by the following expression:

$R\left(y\right)=c_9{I}^{-\frac{{\mathrm{\γ}}_1}{1+{\mathrm{\γ}}_1}}+c_{10}{y}^{c_4-{\mathrm{\γ}}_2{c}_8}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}-c_{11}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}$

the radial electric field intensity E at the stress cone curve y is obtained by combining the expression of the unit resistance R (y) from the inner surface of the enhanced insulating layer to the stress cone curve y and the expression of the resistivity at the strong insulating layer y₂(y) is:

$E_2\left(y\right)=c_{12}{y}^{c_{13}}\frac{1}{c_9{\[\frac{E_2\left(y\right)}{C_7{y}^{c_8}}\]}^{\[{\mathrm{\γ}}_2-\frac{{\mathrm{\γ}}_1(1+{\mathrm{\γ}}_2)}{1+{\mathrm{\γ}}_1}\]}+c_{10}{y}^{c_4-{\mathrm{\γ}}_2{c}_8}-c_{11}}$

the letters referred to in the foregoing calculation represent the following meanings:

θ_cis the cable conductor temperature, theta_RIs the temperature of the outer surface of the cable insulation, theta₁Is the temperature at the outer diameter r of the cable insulation, theta₂To increase the temperature at the outer diameter R' of the insulation, R is the radius of the insulation of the cable, W_cLoss of cable conductors; r is_cIs the cable conductor radius; rho_T2To enhance the thermal resistivity of the insulating layer, ρ_T1Is the thermal resistivity, rho, of the cable insulation_1,0Is the resistivity coefficient, rho, of the cable insulation_2,0To enhance the resistivity coefficient of the insulating layer, a₁Is the temperature coefficient of resistivity of the cable insulation layer, a₂To enhance the temperature coefficient of resistivity, gamma, of the insulating layer₁Is the resistivity field coefficient, gamma, of the cable insulation₂To enhance the resistivity-electric field coefficient of the insulating layer, E₁(r) radial electric field intensity at radius r of the cable insulation layer, E₂(r ') is the radial electric field strength at radius r' of the reinforcing insulation layer;

$c_1={\mathrm{\ρ}}_{1,0}{e}^{-a_1{\mathrm{\θ}}_c}{r_c}^{-a_1{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}}},c_2=a_1{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}},$

$c_3={\mathrm{\ρ}}_{2,0}{e}^{-a_2{\mathrm{\θ}}_c}{\left(\frac{R}{r_c}\right)}^{-a_2{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}}}{R}^{-a_2{\mathrm{\ρ}}_{T2}\frac{w_c}{2\mathrm{\π}}},c_4=a_2{\mathrm{\ρ}}_{T2}\frac{w_c}{2\mathrm{\π}},c_5={\left(\frac{c_1}{2\mathrm{\π}}\right)}^{\frac{1}{1+{\mathrm{\γ}}_1}},$

$c_6=\frac{c_2-1}{1+{\mathrm{\γ}}_1},c_7={\left(\frac{c_3}{2\mathrm{\π}}\right)}^{\frac{1}{1+{\mathrm{\γ}}_2}},c_8=\frac{c_4-1}{1+{\mathrm{\γ}}_2},c_9=\frac{1}{2\mathrm{\π}}{c}_1{c_5}^{-{\mathrm{\γ}}_1}\[\frac{R^{c_2-{\mathrm{\γ}}_1{c}_6}}{c_2-{\mathrm{\γ}}_1{c}_6}-\frac{{r_c}^{c_2-{\mathrm{\γ}}_1{c}_6}}{c_2-{\mathrm{\γ}}_1{c}_6}\],$

$c_{10}=\frac{1}{2\mathrm{\π}}\frac{c_3{c_7}^{-{\mathrm{\γ}}_2}}{c_4-{\mathrm{\γ}}_2{c}_8},c_{11}=\frac{1}{2\mathrm{\π}}\frac{c_3{c_7}^{-{\mathrm{\γ}}_2}{R}^{c_4-{\mathrm{\γ}}_2{c}_8}}{c_4-{\mathrm{\γ}}_2{c}_8},c_{12}=\frac{c_3{c_7}^{-{\mathrm{\γ}}_2}U}{2\mathrm{\π}},c_{13}=c_4-{\mathrm{\γ}}_2{c}_8-1.$

the invention achieves the following beneficial technical effects: 1. on the basis of considering the influence of temperature and electric field factors on the resistivity, electric field distribution in the prefabricated flexible and straight cable terminal insulation is provided, and a theoretical basis is provided for the design of a flexible and straight cable connecting piece; 2. the method for calculating the thickness of the reinforced insulating layer of the prefabricated flexible-straight cable terminal is provided, and the electric field of the cable insulating layer-reinforced insulating layer interface is ensured to be in a reasonable range; 3. a reasonable stress cone shape is designed, the phenomenon of potential line concentration of a flexible straight cable terminal is solved, and the electric field of the whole stress cone is ensured to be uniform; 4. the electrical property requirement of the whole flexible straight cable system on the terminal is met, and the long-term safety and reliability of the flexible straight cable system are guaranteed.

Detailed Description

The present invention is further described with reference to the following specific examples, which are only used to more clearly illustrate the technical solutions of the present invention, but not to limit the scope of the present invention.

The invention provides a prefabricated flexible direct current cable terminal stress cone structure, which comprises a reinforced insulating layer, a stress cone semi-conducting layer and a stress cone curve, wherein the stress cone semi-conducting layer is arranged on the direct current cable insulating layer, the reinforced insulating layer is arranged on the stress cone semi-conducting layer, the stress cone curve is the lower edge of the stress cone semi-conducting layer, and the stress cone curve calculation method comprises the following steps:

step one, calculating the radial electric field intensity E at the position of a stress cone curve y₂(y)；

$E_2\left(y\right)=\frac{{\mathrm{\ρ}}_2\left(y\right)}{2\mathrm{\π}y}\·\frac{U}{R\left(y\right)}$

Where ρ is₂(y) resistivity at the reinforcing insulating layer y, U voltage the reinforcing insulating layer withstands, and R (y) unit resistance from the inner surface of the reinforcing insulating layer to the stress cone curve y;

first, the resistivity ρ at the enhancement insulating layer y₂The calculation procedure of (y) is as follows:

temperature difference between the reinforcing insulating layer r' and the cable conductor:

${\mathrm{\θ}}_c-{\mathrm{\θ}}_2=({\mathrm{\θ}}_c-{\mathrm{\θ}}_R)+({\mathrm{\θ}}_R-{\mathrm{\θ}}_2)=\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T1}ln\frac{R}{r_c}+\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T2}ln\frac{r^{\′}}{R}$

namely:

according to a resistivity formula, increasing the resistivity rho at the position of the insulating layer r₂The expression of (r') is:

${\mathrm{\ρ}}_2\left(r^{\′}\right)=\frac{{\mathrm{\ρ}}_{2,0}{e}^{-a_2{\mathrm{\θ}}_2}}{E_2{\left(r^{\′}\right)}^{{\mathrm{\γ}}_2}}=c_3\frac{r^{\′c_4}}{E_4{\left(r^{\′}\right)}^{{\mathrm{\γ}}_2}}$

according to ohm's law:therefore, the temperature of the molten metal is controlled,i current at stress cone curve y; byAnd resistivity p at the reinforcing insulating layer r₂(r') is expressed as:this formula is brought into the resistivity p at the enhanced insulating layer r₂(r') is expressed as:

${\mathrm{\ρ}}_2\left(r^{\′}\right)=c_3{c_7}^{-{\mathrm{\γ}}_2}{r}^{c_4-{\mathrm{\γ}}_2{c}_8}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}$

secondly, the unit resistance R (y) from the inner surface of the enhanced insulating layer to the stress cone curve y is calculated as follows:

$R\left(y\right)=\underset{r_c}{\overset{R}{\∫}}\frac{{\mathrm{\ρ}}_1\left(r\right)}{2\mathrm{\π}r}dr+\underset{R}{\overset{y}{\∫}}\frac{{\mathrm{\ρ}}_2\left(r^{\′}\right)}{2\mathrm{\π}r}{\mathrm{dr}}^{\′}$

wherein the resistivity at the strong insulating layer rResistivity of cable insulation layer r

According to the heat path equation, the following steps are carried out:

${\mathrm{\θ}}_c-{\mathrm{\θ}}_1=\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T1}ln\frac{r}{r_c}$

namely:

according to ohm's law:therefore, the temperature of the molten metal is controlled,i current at stress cone curve y; byAnd resistivity rho at the cable insulation r₁(r) is expressed as:bringing this formula into the resistivity rho at the cable insulation r₁(r) is expressed as:

${\mathrm{\ρ}}_1\left(r\right)=c_1{c_5}^{-{\mathrm{\γ}}_1}{r}^{c_2-{\mathrm{\γ}}_1{c}_6}{I}^{-\frac{{\mathrm{\γ}}_1}{1+{\mathrm{\γ}}_1}}$

the specific resistance r (y) from the inner surface of the enhanced insulating layer to the stress cone curve y is thus obtained by the following expression:

$R\left(y\right)=c_9{I}^{-\frac{{\mathrm{\γ}}_1}{1+{\mathrm{\γ}}_1}}+c_{10}{y}^{c_4-{\mathrm{\γ}}_2{c}_8}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}-c_{11}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}$

the radial electric field intensity E at the stress cone curve y is obtained by combining the expression of the unit resistance R (y) from the inner surface of the enhanced insulating layer to the stress cone curve y and the expression of the resistivity at the strong insulating layer y₂(y) is:

$E_2\left(y\right)=c_{12}{y}^{c_{13}}\frac{1}{c_9{\[\frac{E_2\left(y\right)}{C_7{y}^{c_8}}\]}^{\[{\mathrm{\γ}}_2-\frac{{\mathrm{\γ}}_1(1+{\mathrm{\γ}}_2)}{1+{\mathrm{\γ}}_1}\]}+c_{10}{y}^{c_4-{\mathrm{\γ}}_2{c}_8}-c_{11}}$

the letters referred to in the foregoing calculation represent the following meanings:

θ_cis the cable conductor temperature, theta_RIs the temperature of the outer surface of the cable insulation, theta₁Is the temperature at the outer diameter r of the cable insulation, theta₂To increase the temperature at the outer diameter R' of the insulation, R is the radius of the insulation of the cable, W_cLoss of cable conductors; r is_cIs the cable conductor radius; rho_T2To enhance the thermal resistivity of the insulating layer, ρ_T1Is the thermal resistivity, rho, of the cable insulation_1,0Is the resistivity coefficient, rho, of the cable insulation_2,0To enhance the resistivity coefficient of the insulating layer, a₁Is the temperature coefficient of resistivity of the cable insulation layer, a₂To enhance the temperature coefficient of resistivity, gamma, of the insulating layer₁Is the resistivity field coefficient, gamma, of the cable insulation₂To enhance the resistivity-electric field coefficient of the insulating layer, E₁(r) radial electric field intensity at radius r of the cable insulation layer, E₂(r ') is the radial electric field strength at radius r' of the reinforcing insulation layer;

$c_1={\mathrm{\ρ}}_{1,0}{e}^{-a_1{\mathrm{\θ}}_c}{r_c}^{-a_1{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}}},c_2=a_1{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}},$

$c_3={\mathrm{\ρ}}_{2,0}{e}^{-a_2{\mathrm{\θ}}_c}{\left(\frac{R}{r_c}\right)}^{-a_2{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}}}{R}^{-a_2{\mathrm{\ρ}}_{T2}\frac{w_c}{2\mathrm{\π}}},c_4=a_2{\mathrm{\ρ}}_{T2}\frac{w_c}{2\mathrm{\π}},c_5={\left(\frac{c_1}{2\mathrm{\π}}\right)}^{\frac{1}{1+{\mathrm{\γ}}_1}},$

$c_6=\frac{c_2-1}{1+{\mathrm{\γ}}_1},c_7={\left(\frac{c_3}{2\mathrm{\π}}\right)}^{\frac{1}{1+{\mathrm{\γ}}_2}},c_8=\frac{c_4-1}{1+{\mathrm{\γ}}_2},c_9=\frac{1}{2\mathrm{\π}}{c}_1{c_5}^{-{\mathrm{\γ}}_1}\[\frac{R^{c_2-{\mathrm{\γ}}_1{c}_6}}{c_2-{\mathrm{\γ}}_1{c}_6}-\frac{{r_c}^{c_2-{\mathrm{\γ}}_1{c}_6}}{c_2-{\mathrm{\γ}}_1{c}_6}\],$

$c_{10}=\frac{1}{2\mathrm{\π}}\frac{c_3{c_7}^{-{\mathrm{\γ}}_2}}{c_4-{\mathrm{\γ}}_2{c}_8},c_{11}=\frac{1}{2\mathrm{\π}}\frac{c_3{c_7}^{-{\mathrm{\γ}}_2}{R}^{c_4-{\mathrm{\γ}}_2{c}_8}}{c_4-{\mathrm{\γ}}_2{c}_8},c_{12}=\frac{c_3{c_7}^{-{\mathrm{\γ}}_2}U}{2\mathrm{\π}},c_{13}=c_4-{\mathrm{\γ}}_2{c}_8-1.$

determining the thickness of the reinforced insulating layer;

radius R of the reinforced insulation layer_sRadial electric field intensity E of₂(Rs) is the maximum working electric field intensity E of the cable insulation layer₀One-half of (1), the expression is as follows:

E₂(R_S)＝0.5E₀

calculating R by combining the expression of the radial electric field intensity at the stress cone curve y and the above expression_sSo as to calculate the thickness delta n ═ R of the reinforced insulating layer_s-R, R is the cable insulation radius;

step three, determining a stress cone curve equation;

axial electric field intensity E of any point on stress cone curve_tRadial electric field E with the spot₂The following relationships exist:

$E_t=E_2\·tan\mathrm{\α}=E_2\·\frac{dy}{dx}$

integrating the above equation to obtainLet E_tIs constant, the radial electric field E₂Expression bring-inAnd obtaining a plurality of groups of coordinates (x, y) by using a numerical solution method to obtain a stress cone curve equation.

Example one

A prefabricated flexible straight cable terminal with rated voltage of +/-320 kV is adopted.

First, radial electric field intensity E at stress cone curve y₂(y) calculation of

For a +/-320 kV prefabricated flexible straight cable terminal, U is 320 kV; rho_1,0＝ρ_2,0＝10¹⁶Ω.m；a₁＝0.06℃^-1，a₂＝0.05℃^-1；θ_c＝90℃，w_c＝68W；ρ_T1＝3.5K.m/W，ρ_T2＝3.3K.m/W；r_c＝26.5mm，R＝50.5mm；γ₁＝2.2，γ₂The data is brought to the radial electric field strength E at the stress cone curve y, 1.69₂(y) the calculation formula:

$E=\frac{7.29\×{10}^{14}\×y^{0.29}}{1.27\×{10}^7\×{\left(\frac{E}{2.28\×{10}^9\×y^{0.29}}\right)}^{-0.16}+1.76\×{10}^9\×y^{1.29}-3.67\×{10}^7}$

secondly, the thickness of the insulating layer is enhanced

The insulation thickness R of the flexible straight cable body is 24mm, and the maximum electric field E is₀18kV/mm, then E (R)_s)＝9kV/mm。

Taking E (R) to leave enough safety margin_s) R is obtained by substituting formula as above under 7kV/mm_S71.5mm, the reinforced insulation thickness Deltan R can be obtained_S-R＝21mm。

Thirdly, determining a stress cone curve equation

The calculated coordinates (x, y) of a plurality of groups on the stress cone curve of the +/-320 kV prefabricated flexible and straight cable terminal are respectively as follows: (0,50.5), (11.9,51.5), (23.4,52.5), (34.5,53.5), (45.2,54.5), (55.6,55.5), (65.6,56.5), (75.4,57.5), (84.9,58.5), (94.1,59.5), (103.1,60.5), (111.8,61.5), (120.3,62.5), (128.6,63.5), (136.7,64.5), (144.6,65.5), (152.3,66.5), (159.9,67.5), (167.3,68.5), (174.6,69.5), (181.7,70.5), (188.7,71.5) finally a stress cone shape is obtained.

Example 2

A prefabricated flexible straight cable terminal with rated voltage of +/-200 kV is adopted.

First, radial electric field intensity E at stress cone curve y₂(y) calculation of

For a +/-200 kV prefabricated flexible straight cable terminal, U is 200 kV; rho_1,0＝ρ_2,0＝10¹⁶Ω.m；a₁＝0.06℃^-1，a₂＝0.05℃^-1；θ_c＝90℃，w_c＝66W；ρ_T1＝3.5K.m/W，ρ_T2＝3.3K.m/W；r_c＝20.4mm，R＝36.4mm；γ₁＝2.2，γ₂The data is brought to the radial electric field strength E at the stress cone curve y, 1.69₂(y) the calculation formula:

$E=\frac{5.63\×{10}^{14}\×y^{0.27}}{8.47\×{10}^6\×{\left(\frac{E}{2.81\×{10}^9\×y^{0.27}}\right)}^{-0.16}+2.21\×{10}^9\×y^{1.27}-3.26\×{10}^7}$

secondly, the thickness of the insulating layer is enhanced

The insulation thickness R of the flexible straight cable body is 15mm, and the maximum electric field E is₀20kV/mm, then E (R)_s)＝10kV/mm。

Taking E (R) to leave enough safety margin_s) R may be obtained by substituting formula (22) at 7kV/mm_S46.4mm, the reinforced insulation thickness Deltan R can be obtained_S-R＝10mm。

Thirdly, determining a stress cone curve equation

A plurality of groups of coordinates (x, y) on the stress cone curve of the +/-200 kV prefabricated flexible and straight cable terminal can be obtained through calculation, and the coordinates are respectively as follows: (0,36.4), (12.2,37.4), (23.7,38.4), (34.6,39.4), (44.9,40.4), (54.7,41.4), (64,42.4), (72.9,43.4), (81.4,44.4), (89.6,45.4), (97.6,46.4) finally a stress cone shape is obtained.

The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (3)

1. Flexible direct current cable terminal stress cone structure of prefabricated formula, its characterized in that: the stress cone semi-conductive layer is arranged on an insulating layer of a direct current cable body, the reinforced insulating layer is arranged on the stress cone semi-conductive layer, the stress cone curve is the lower edge of the stress cone semi-conductive layer, and the stress cone curve calculation method comprises the following steps:

step one, calculating the radial electric field intensity E at the position of a stress cone curve y₂(y)；

$E_2\left(y\right)=\frac{{\mathrm{\ρ}}_2\left(y\right)}{2\mathrm{\π}y}\·\frac{U}{R\left(y\right)}$

Where ρ is₂(y) resistivity at the reinforcing insulating layer y, U voltage the reinforcing insulating layer withstands, and R (y) unit resistance from the inner surface of the reinforcing insulating layer to the stress cone curve y;

determining the thickness of the reinforced insulating layer;

radius R of the reinforced insulation layer_sRadial electric field intensity E of₂(Rs) is the maximum working electric field intensity E of the cable insulation layer₀One-half of (1), the expression is as follows:

E₂(R_S)＝0.5E₀

calculating R by combining the expression of the radial electric field intensity at the stress cone curve y and the above expression_sSo as to calculate the thickness delta n ═ R of the reinforced insulating layer_s-R, R is the cable insulation radius;

step three, determining a stress cone curve equation;

axial electric field intensity E of any point on stress cone curve_tRadial electric field E with the spot₂The following relationships exist:

$E_t=E_2\·tan\mathrm{\α}=E_2\·\frac{dy}{dx}$

integrating the above equation to obtainLet E_tIs constant, the radial electric field E₂Expression bring-inAnd obtaining a plurality of groups of coordinates (x, y) by using a numerical solution method to obtain a stress cone curve equation.

2. The prefabricated flexible direct current cable termination stress cone structure of claim 1, wherein: in the first step, the resistivity rho of the insulating layer y is enhanced₂The calculation procedure of (y) is as follows:

temperature difference between the reinforcing insulating layer r' and the cable conductor:

${\mathrm{\θ}}_c-{\mathrm{\θ}}_2=({\mathrm{\θ}}_c-{\mathrm{\θ}}_R)+({\mathrm{\θ}}_R-{\mathrm{\θ}}_2)=\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T1}ln\frac{R}{r_c}+\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T2}ln\frac{r^{\′}}{R}$

namely:

in the formula, theta₂To increase the temperature at the outer diameter r' of the insulating layer, θ_RIs the temperature of the outer surface of the cable insulation, theta_cIs the cable conductor temperature, R is the cable insulation radius, ρ_T2To enhance the thermal resistivity of the insulating layer, ρ_T1Is the thermal resistivity, W, of the cable insulation_cLoss of cable conductors; r is_cIs the cable conductor radius;

according to a resistivity formula, increasing the resistivity rho at the position of the insulating layer r₂The expression of (r') is:

${\mathrm{\ρ}}_2\left(r^{\′}\right)=\frac{{\mathrm{\ρ}}_{2,0}{e}^{-a_2{\mathrm{\θ}}_2}}{E_2{\left(r^{\′}\right)}^{{\mathrm{\γ}}_2}}=c_3\frac{r^{\′c_4}}{E_2{\left(r^{\′}\right)}^{{\mathrm{\γ}}_2}}$

wherein, ρ_2,0to enhance the resistivity of the insulating layer; a is₂To enhance the temperature coefficient of resistivity of the insulating layer; gamma ray₂To enhance the resistivity electric field coefficient of the insulating layer; e₂(r ') is the radial electric field strength at the reinforcing insulating layer r ', according to ohm's law:therefore, the temperature of the molten metal is controlled,i current at stress cone curve y; byAnd resistivity p at the reinforcing insulating layer r₂(r') is expressed as:this formula is brought into the resistivity p at the enhanced insulating layer r₂(r') is expressed as:

${\mathrm{\ρ}}_2\left(r^{\′}\right)=c_3{c_7}^{-{\mathrm{\γ}}_2}{r}^{c_4-{\mathrm{\γ}}_2{c}_8}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}$

wherein,

3. the prefabricated flexible direct current cable termination stress cone structure of claim 1, wherein: in the first step, the unit resistance r (y) from the inner surface of the enhanced insulating layer to the stress cone curve y is calculated as follows:

$R\left(y\right)=\underset{r_c}{\overset{R}{\∫}}\frac{{\mathrm{\ρ}}_1\left(r\right)}{2\mathrm{\π}r}dr+\underset{R}{\overset{y}{\∫}}\frac{{\mathrm{\ρ}}_2\left(r^{\′}\right)}{2\mathrm{\π}r}{\mathrm{dr}}^{\′}$

wherein the resistivity at the strong insulating layer rResistivity of cable insulation layer r

According to the heat path equation, the following steps are carried out:

${\mathrm{\θ}}_c-{\mathrm{\θ}}_1=\frac{W_c}{2\mathrm{\π}}{\mathrm{\ρ}}_{T1}ln\frac{r}{r_c}$

namely:

according to ohm's law:therefore, the temperature of the molten metal is controlled,i current at stress cone curve y; byAnd resistivity rho at the cable insulation r₁(r) is expressed as:bringing this formula into the resistivity rho at the cable insulation r₁(r) is expressed as:

${\mathrm{\ρ}}_1\left(r\right)=c_1{c_5}^{-{\mathrm{\γ}}_1}{r}^{c_2-{\mathrm{\γ}}_1{c}_6}{I}^{-\frac{{\mathrm{\γ}}_1}{1+{\mathrm{\γ}}_1}}$

the specific resistance r (y) from the inner surface of the enhanced insulating layer to the stress cone curve y is thus obtained by the following expression:

$R\left(y\right)=c_9{I}^{-\frac{{\mathrm{\γ}}_1}{1+{\mathrm{\γ}}_1}}+c_{10}{y}^{c_4-{\mathrm{\γ}}_2{c}_8}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}-c_{11}{I}^{-\frac{{\mathrm{\γ}}_2}{1+{\mathrm{\γ}}_2}}$

the radial electric field intensity E at the stress cone curve y is obtained by combining the expression of the unit resistance R (y) from the inner surface of the enhanced insulating layer to the stress cone curve y and the expression of the resistivity at the strong insulating layer y₂(y) is:

$E_2\left(y\right)=c_{12}{y}^{c_{13}}\frac{1}{c_9{\[\frac{E_2\left(y\right)}{C_7{y}^{c_8}}\]}^{\[{\mathrm{\γ}}_2-\frac{{\mathrm{\γ}}_1(1+{\mathrm{\γ}}_2)}{1+{\mathrm{\γ}}_1}\]}+c_{10}{y}^{c_4-{\mathrm{\γ}}_2{c}_8}-c_{11}}$

the letters referred to in the foregoing calculation represent the following meanings:

θ_cis the cable conductor temperature, theta_RIs the temperature of the outer surface of the cable insulation, theta₁Is the temperature at the outer diameter r of the cable insulation, theta₂To increase the temperature at the outer diameter R' of the insulation, R is the radius of the insulation of the cable, W_cLoss of cable conductors; r is_cIs the cable conductor radius; rho_T2To enhance the thermal resistivity of the insulating layer, ρ_T1Is the thermal resistivity, rho, of the cable insulation_1,0Is the resistivity coefficient, rho, of the cable insulation_2,0To enhance the resistivity coefficient of the insulating layer, a₁Is the temperature coefficient of resistivity of the cable insulation layer, a₂To enhance the temperature coefficient of resistivity, gamma, of the insulating layer₁Is the resistivity field coefficient, gamma, of the cable insulation₂To enhance the resistivity-electric field coefficient of the insulating layer, E₁(r) radial electric field intensity at radius r of the cable insulation layer, E₂(r ') is the radial electric field strength at radius r' of the reinforcing insulation layer;

$c_1={\mathrm{\ρ}}_{1,0}{e}^{-a_1{\mathrm{\θ}}_c}{r_c}^{-a_1{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}}},$ $c_2=a_1{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}},$ $c_3={\mathrm{\ρ}}_{2,0}{e}^{-a_2{\mathrm{\θ}}_c}{\left(\frac{R}{r_c}\right)}^{-a_2{\mathrm{\ρ}}_{T1}\frac{w_c}{2\mathrm{\π}}}{R}^{-a_2{\mathrm{\ρ}}_{T2}\frac{w_c}{2\mathrm{\π}}},$ $c_4=a_2{\mathrm{\ρ}}_{T2}\frac{w_c}{2\mathrm{\π}},c_5={\left(\frac{c_1}{2\mathrm{\π}}\right)}^{\frac{1}{1+{\mathrm{\γ}}_1}},$ $c_6=\frac{c_2-1}{1+{\mathrm{\γ}}_1},$ $c_7={\left(\frac{c_3}{2\mathrm{\π}}\right)}^{\frac{1}{1+{\mathrm{\γ}}_2}},$ $c_8=\frac{c_4-1}{1+{\mathrm{\γ}}_2},$ $c_9=\frac{1}{2\mathrm{\π}}{c}_1{c_5}^{-{\mathrm{\γ}}_1}\[\frac{R^{c_2-{\mathrm{\γ}}_1{c}_6}}{c_2-{\mathrm{\γ}}_1{c}_6}-\frac{{r_c}^{c_2-{\mathrm{\γ}}_1{c}_6}}{c_2-{\mathrm{\γ}}_1{c}_6}\],$ c₁₃＝c₄-γ₂c₈-1。