CN105808881B - The finite element optimum design method of high-voltage cable middle joint - Google Patents
The finite element optimum design method of high-voltage cable middle joint Download PDFInfo
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Abstract
The present invention relates to the finite element optimum design methods of high-voltage cable middle joint, include the following steps：S1）According to high-voltage cable middle joint two-dimensional axial symmetric overall structure, the overall structure geomery of semiconductive stress cone component is designed；S2）Establish stress cone finite element two dimension computation model；S3）FEM calculation is carried out to cable intermediate joint；S4）It is closed on cable insulation at shielded layer and takes a node using conical line as mapping path, obtain the relationship graph of electric field strength and S on the path；S4）Observe the relationship graph of electric field strength and S, if electric field strength E curve waveforms are that electric field is greatest around in metal screen layer incision, and with the increase of stress cone arcuate distance, electric field value is gradually decayed, to after certain distant place, electric field it is very small, it is concluded that high-voltage cable middle joint final structure model；It is no to then follow the steps S5）；S5）Again limited element calculation model parameter, return to step S2 are corrected）.
Description
Technical field
The present invention relates to high-voltage cable middle joint technical fields, more particularly, to a kind of having for high-voltage cable middle joint
The first optimum design method of limit.
Background technology
High-voltage cable middle joint is the weak spot of power cable line, in the statistics that power cable breaks down, electricity
The failure rate of cable fittings is about 70%.After the terminal of cable peels off the outer jacket and shielded layer of certain size, electricity is changed
The original field distribution of cable, produces electric field distortion, is more concentrated in shielding cut-off part power line, by high-voltage cable middle joint
Field strength calculation formula be apparent from, maximum field is happened at shielding cut off, in order to improve the field distribution of cable intermediate joint, adopts
With a variety of cable intermediate joint treatment measures for reducing electric field distortion:1. apply new insulating layer on cable insulation, it can
To increase equivalent insulation radius；2. the insulating surface at cable shield edge is coated with semiconductive varnish, it is possible to reduce along surface
Electric potential gradient near impedance and shielded layer；3. installing bonding ring additional near shielded layer, increase radius of curvature；4. using answering
Power is bored, and electric fields uniform distribution etc. is forced.Method is 4. planted the most commonly used is the both at home and abroad at present, mainly with room temperature liquid silicon rubber and solid
The stress tube and stress cone that body silastic material makes.
With growing continuously and fast for China's economic, electricity needs is also multiplied, and forms the power supply of large capacity centrality
Load center causes the demand of ultrahigh-voltage XLPE cable system also to increase sharply.The big cities such as BeiJing, China, Shanghai, Guangzhou at present
City is in operation 220kV cable runs, and 500kv cables are mainly or as power station, the high-pressure side of hydroenergy storage station
Lead-out wire uses, and with being continuously increased for urban distribution network load, 500kV cable systems are also being built on the ground such as Beijing, Shanghai, in
State has been provided with the ability that production includes the extra-high-tension cable of 500kV grades, but can provide 220kV and ratings above electricity at present
The producer of cable fittings is few, and 500kV cable accessories are also in the tackling key problem development phase.State's net DianKeYuan cable is pushing
The production domesticization of 500kV cable bodies and 220kV cable accessories.Since trend is thinned in the insulation thickness of extra-high-tension cable extruded insulation
Requirement, it will make cable body insulate work field strength improve, how to evaluate the attachment insulation performance run under high field intensity
It is extremely important.However, there is the difficulty in processing by the conical surface logarithmic curve of lathe forming in practical operation, common method is
Substitute ideal conical line with one or more straight line, or ideal using broken line and arc-spline curve close approximation
Conical line can not understand the distribution situation of stress cone internal electric field, also just can not design stress tapered end portion shape.
Invention content
The technical problem to be solved by the present invention is to：A kind of finite element optimum design side of high-voltage cable middle joint is provided
Method.By being analyzed with finite element method, according to the design controlling value of some key points, by adjusting stress cone curved shape
Shape and stress cone length are distributed to adjust high-voltage cable middle joint internal electric field, improve it by adjusting stress cone end curvature
Internal electric field is distributed, to well solve the problem for understanding stress cone internal electric field distribution situation, to overcome the prior art
It is insufficient.
Beneficial effects of the present invention are as follows：
In electromagnetic field analysis, FInite Element is more advanced one of method, is largely effective when solving bounded problem
, it is a kind of numerical computation method, the basic principle that it analyzes electric field is that handled object is first divided into limited list
Member (contain several nodes), the potential under certain boundary and primary condition at each node is solved further according to scalar electric potential, then into
One step solves other correlatives, which can be visually known the field distribution situation each put inside stress cone, by adjusting answering
Power bores curve shape and its axial length to adjust the distribution of its internal electric field, can also improve in it by adjusting stress tapered end curvature
Portion's field distribution.The present invention is based on finite element methods to be built using broken line and arc-spline curve approximate simulation conical line
Vertical electric field finite element two dimension computation model is calculated, and is analyzed according to existing result of calculation, and it is unfavorable constantly to repeat to adjust
The broken line or curve of field distribution, correct and establish electric field finite element two dimension computation model and calculated again, finally make calculating
Field distribution result afterwards reaches ideal standard requirement along conical line.By example, to the electricity of high-voltage cable middle joint
Field data is repeatedly calculated, is analyzed and is optimized.Verified through analysis, this method in the cable between the electric Field Calculation of connector and excellent
It is practicable to change in design, and a kind of new idea and method is provided for the design of high-voltage cable middle joint.
Description of the drawings
Fig. 1 is two-dimensional axial symmetric structural model figure of the present invention.
Fig. 2 is high-voltage cable middle joint finite element two dimension computation model figure of the present invention.
Fig. 3 (a) is the electric field strength Local Vector figure of high-voltage cable middle joint conical line of the present invention.
Fig. 3 (b) is the electric field strength part cloud atlas of high-voltage cable middle joint conical line of the present invention.
Fig. 4 is high-voltage cable middle joint E, EX of the present invention (electric field X-component), EY (electric field Y-component) value along conical line
Variation diagram.
Fig. 5 is the partial view of finite element two dimension computation model stress cone of the present invention.
Fig. 6 is E, EX (electric field X-component) after present invention adjustment computation model, EY (electric field Y-component) value is along conical line
Variation diagram.
Specific implementation mode
The embodiment of the present invention is described below in detail, examples of the embodiments are shown in the accompanying drawings, wherein from beginning to end
Same or similar label indicates same or similar element or element with the same or similar functions.Below with reference to attached
The embodiment of figure description is exemplary, and is only used for explaining the present invention, and is not considered as limiting the invention.
Cable termination and cable intermediate joint belong to axially symmetric structure, are built according to two-dimensional axial symmetric overall structure
Mould.There is power frequency work field strength and two class of impulse withstand voltage field strength in high-tension line, when cable main insulation design need to consider two classes simultaneously
Field strength, stress cone and the reagency cone of transition joint design the power frequency work field strength for only needing to consider insulation, the two table
Identical up to formula, alphabetical connotation is also identical in formula, they are also one of the principal element for determining cable intermediate joint length simultaneously, and two
Person's conical surface is by making the axial field strength on its surface be a constant (or be less than a constant), cable insulation not sublevel, and increases around insulation
Relative dielectric constant is equal to cable insulation relative dielectric constant.Traditionally design the overall structure of semiconductive stress cone component
Geomery mainly has thickness deltat t of the increasing around insulating layer, the stress cone axial length L of stress conek, and stress cone-shaped song
Line equation, model are as shown in Figure 1.
Wherein, ε1- cable body insulation relative dielectric constant；rc- conductor layer outer radius；R-ontology insulation outer radius；
U1- cable bears voltage, and design voltage U is taken according to various criterionAC；Rn- increase around insulating layer outer radius；εn--- cable increase around
The relative dielectric constant of insulation；Et- tangential field；En- normal direction field strength.
According to Fig. 1, since the conical surface of stress cone is connect with cable shield, current potential zero, so the stress cone conical surface is one
A equipotential surface takes up an official post in the stress cone conical surface and takes a point F, and the conical surface is equipotential surface, therefore power line is orthogonal.α was the tangent line of F points
With the angle of cut of cable radial direction, then the relationship of tangential field and normal direction field strength beCross the method for F points
To field strength EnStill can be approximate by cylindrical electric Field Calculation, then have for two layers of grade-insulated cableWhereinIt is integrated by the merging of two formulasEnable EtFor a constant, make cutting along surface
It is a constant to electric field strength, obtains conical line logarithmic curve equation：
The geomery that calculating transition joint is designed by (1) (2) (3) formula obtains the stress cone conical surface according to electric field distribution law
Model is logarithmic curve equation (4), and the conical surface logarithmic curve shaped by lathe in practical operation is commonly used in the presence of the difficulty in processing
Method be substitute ideal conical line with one or more straight line, or it is approximate using broken line and arc-spline curve
Ideal conical line is approached, the distribution situation of stress cone internal electric field can not be understood, it also just can not design stress tapered end portion
Shape.It is analyzed with the method for finite element, according to the design controlling value of some key points, by adjusting stress cone curved shape
Shape and stress cone length are distributed to adjust its internal electric field, improve the distribution of its internal electric field by adjusting stress cone end curvature,
This problem is well solved, ideal standard requirement is progressively reached.
In actual electromagnetic field, field is continuous, and the every bit of the unlimited number of point in space has determining field amount (to have
There is mathematically so-called Infinite-dimensional degree of freedom).And FInite Element is that field domain is divided into limited a unit, with a simple function
As field variables model (also known as interpolating function), the trial solution of each unit midfield is constituted.FInite Element can will appoint in unit
The amount to be asked of a bit, with the field value on the intersection point (being known as node in FInite Element) of the elementary boundary and other elementary boundaries
It indicates.Therefore, the calculating of entire field can be attributed to the calculating of limited a node amount of entering the court, i.e., will inscribe and convert between Infinite-dimensional degree of freedom
For limited a degree of freedom the problem of.
The field distribution of cable termination and cable intermediate joint is an axially symmetric field, and field distribution meets Maxwell ▽
× E=0, ▽ D=ρ equations, it is assumed that axially and radially circle of the zero potential boundary definition in a diameter of terminal body diameter several times
On column bottom surface or curved surface, by uniqueness theorem, the conductor external electric field in model area uniquely determines, and Potential distribution meets Poisson
EquationDue to being distributed (i.e. ρ=0) without free charge outside conductor, Poisson's equation is reduced to Laplace's equationSolved in solution domainUse finite element methodThe step of be:1. finding out Laplce
The corresponding functional of equation (presses First Boundary Condition)WhereinIndicate electricity
PositionGradient, D indicate solve domain；2. the field domain progress to solution is discrete, go to divide with triangular element, it is general on entire domain
LetterIt can be expressed as functional in each unitThe sum of, L indicates the unit number being split into altogether in the domains D；3. using more
Item formulaTrue field distribution is approximatively indicated as field variables model, in formulaGeneration
The field amount at any point in table unit, x, y are the coordinate of the point, and α is coefficient；4. the Matrix Formula of determination unit characteristic, i.e.,X in formula1、y1,x2、y2,x3、y3For the coordinate on Atria vertex, For triangle
The functional value on three vertex of shape, factor alpha is related with the coordinate of three apexes of triangle and potential value, factor alpha1、α2、α3Point
It is not WhereinIts value is equal to the area of triangular element.
CollatedWhereinIt is in triangular element in linear interpolating function
Shape function,And haveAccording to square
The principle of battle array finding limit, corresponding cell matrix equation can basisIt willFunctional is substituted into, then carries out derivative operation and obtainsThe triangular unit matrix of equation
Feature formula
5. basisThe characteristic of total system model is acquired, just the characteristic of necessary " set " whole units,
Then the extreme value of functional, export simultaneous Algebraic Equation set (also known as finite element equation) are asked；6. solving finite element equation, introducing are forced
Boundary condition finds out the field value of any point in field.
Cable termination and cable intermediate joint belong to axially symmetric structure, their field distribution is also an axially symmetric field,
Field distribution meets Maxwell ▽ × E=0, ▽ D=ρ equations, using the high temperature vulcanized liquid silastic of import (LSR) material
And semiconductive material, while the filler of high-k is added, establish finite element model by static two dimensional field structure.Here with
For 66kV high-voltage cable middle joints, 66kV belongs to mesohigh voltage class, according to national standard " GB/Z 18890.1-
2002 rated voltage U kV (Um=(1+10%) U cross-linked polyethylene insulated power cables and its attachment part 1 ", for U kV
Cable, test voltageIndustrial frequency withstand voltage tests electricity UAC=2.5U0KV (66kV High-voltage Cable Design voltages UAC=
95kV), tolerance time 30 minutes.According to operating experience, line taking core section product is 240mm2, cable termination and cable intermediate joint
Contain silicon rubber (εn=2.3) and crosslinked polyethylene (ε1=2.3) 2 kinds of materials.According to known relevant parameter and (1), (2),
(3) expression formula calculates to obtain correspondence parameter in table 1, establishes limited element calculation model (Fig. 2) and is calculated.
Each parameter list in 1 model of table
The Potential distribution on modelMeet two-dimentional Laplace's equation The boundary value problem of satisfaction such as formula (5)
Shown, potential units are volt, and length unit is millimeter.
According to cable intermediate joint model, in conjunction with the working characteristics equation of cable intermediate joint, the boundary condition of satisfaction and
Concrete structure parameter, while considering the performance of material, FEM calculation is carried out to cable intermediate joint, obtains cable intermediate joint
The electric field strength Local Vector figure and electric field strength part cloud atlas of conical line.It can see from Fig. 3 (a), either in stress
The straight line portion or curved portion of cone, it can be seen that electric field line is all perpendicular to the surface of stress cone, this is because stress cone
Surface voltage is all 0V, is an equipotential plane.In electromagnetic field, equipotential plane and etc. electric field lines be mutually perpendicular to, direction of an electric field
Stress poppet surface is directed toward by cable core.From in Fig. 3 (b) it can be seen that distribution of the electric field stress on conical line.
It is located on cable insulation to close at shielded layer and takes a node S and be defined as starting point, using conical line as mapping
Path, the path length of different nodal point separation start nodes is S (starting point S=0.0000mm) along the path, is obtained on the path
Electric field strength and the relationship of S such as Fig. 4 and table 2.
The corresponding field value of difference node along path of table 2 (takes the section near shielded layer incision, minimum value and maximum value
Point)
| S | E | EX | EY | |
| 0.0000 | 10747. | -1626.7 | 10623. | |
| 0.23450 | 11686. | -3179.3 | 11245. | Incision |
| 0.42712 | 10607. | -3767.0 | 9915.8 | |
| 24.986 | 5681.1 | -2439.7 | 5130.6 | |
| 25.674 | 5670.7 | -2507.7 | 5086.0 | At minimum |
| 26.220 | 5682.2 | -2572.2 | 5066.7 | |
| 29.035 | 6491.4 | -3743.9 | 5303.1 | |
| 29.427 | 6595.3 | -4136.6 | 5136.8 | Maximum |
| 29.818 | 6563.7 | -4438.2 | 4835.9 |
According to Fig. 4 and table 2 as can be seen that cable intermediate joint electric field maximum 11686V/mm is in metal screen layer notch
Near place, boring internal maximum field intensity 6595.3V/mm, (maximum of conventional design silicon rubber outer surface is cut much smaller than 25kV/mm
To electric field strength controlling value), silicon rubber is much smaller than 25kV/mm (conventional design controls with crosslinked polyethylene interface field strength 11686V/mm
Value processed), the tangential electric field strength of maximum of silicon rubber outer surface is less than 22kV/mm, is much smaller than silastic surface flashover electric field strength,
Generally speaking, cable intermediate joint stress cone improves the distribution of electric field, illustrates that the scheme of design is reasonable, is feasible.Make
Electric field is more uniform, does not occur, and avoids the generation of the sliding elephant that flashes, and then reduces the generation of accident, optimizes cable end
Electric field is uniformly distributed at end, technical indicator realize and far more than the target in table 3 generally speaking, cable intermediate joint stress
Cone improves the distribution of junction electric field, but local maximum 6595.3V/mm occurs inside conical line, illustrates stress cone
Conical line has unreasonable place.In order to keep field distribution more uniform, analyzed according to existing result of calculation, it is comprehensive
The extreme coordinates for considering and adjusting the broken line near stress concentration point, arc-spline curve change simultaneously the slope and circle of broken line
The radius of curvature of arc spline curve remodifies limited element calculation model and is calculated, and changes conical line (shown in Fig. 5) here
1 coordinate of endpoint:Δ x=-3.89mm, Δ y=-1.92mm, 2 coordinate of endpoint：Δ x=-4.28mm, Δ y=0mm, while by R6
It is changed to R7, obtains electric field strength and the relational graph (Fig. 6) and field scale (table 3) of S again.
The corresponding field value of difference node along path of table 3 (takes the section near shielded layer incision, minimum value and maximum value
Point)
By comparing Fig. 4, Fig. 6 and table 2, table 3, the variation of the E values on conical line is observed, E values are relatively more flat in Fig. 6
It is slow, illustrate that boring internal electric field is distributed to have obtained further uniformly optimization.Same reason, (Fig. 5) endpoint 3 in adjustable integral mould
Coordinate and relevant parameter, can also make the electric field concentration point of the point uniformly optimize along conical line, constantly repeat adjust it is unfavorable
The curve of field distribution can make field distribution progressively reach ideal requirement.It is final that technical indicator is allowed to realize and far more than table 4
In target.
4 test data of table and technical standard
The present invention analyzes the mathematical model of cable intermediate joint, finite element theory and method, establishes limited
Relationship simultaneously carries out simulation calculation, and emulation has obtained the field distribution of the cable intermediate joint stress cone conical surface, and will emulation
As a result it is compared with theory analysis, is analyzed according to existing result of calculation, considered and adjust stress concentration point
The parameter of neighbouring curve, remodifies limited element calculation model and is calculated, finally make along conical line field distribution gradually
Reach ideal requirement, i.e. cable intermediate joint electric field maximum is near metal screen layer cut-off port, and with stress cone
The increase of arcuate distance, electric field value are gradually decayed, and after arriving certain distant place, electric field is very small.With finite element optimum design method
Realize the correctness and validity of cable intermediate joint field distribution, with obvious effects, the uniform electricity for how further of optimization
The research of cable transition joint field distribution and practical application are of great significance.
Although an embodiment of the present invention has been shown and described, it will be understood by those of ordinary skill in the art that：Not
In the case of being detached from the principle of the present invention and objective a variety of change, modification, replacement and modification can be carried out to these embodiments, this
The range of invention is limited by claim and its equivalent replacement, without creative work improvements introduced etc., should all include
Within protection scope of the present invention.
Claims (1)
1. a kind of finite element optimum design method of high-voltage cable middle joint：It is gone forward side by side by establishing finite element two dimension computation model
Row simulation calculation, to obtain the field distribution of cable intermediate joint stress cone conical line, it is characterised in that including following step
Suddenly：
S1) according to high-voltage cable middle joint two-dimensional axial symmetric overall structure, the overall structure of semiconductive stress cone component is designed
Geomery, including thickness deltat t of the increasing around insulating layer of stress cone, stress cone axial length Lk, stress cone conical surface pattern curve
Equation；
S2) according to electric field distribution law and relevant criterion, model parameter table is acquired, stress cone finite element two dimension is established and calculates mould
Type executes step S3)；
S3) according to cable intermediate joint model, in conjunction with the working characteristics equation of cable intermediate joint, the boundary condition and tool of satisfaction
Body structural parameters carry out FEM calculation to cable intermediate joint, obtain the electric field strength office of cable intermediate joint conical line
Portion's polar plot and electric field strength part cloud atlas；
S4 it) is closed on cable insulation at shielded layer and takes a node and be defined as starting point, using conical line as mapping path,
The path length of different nodal point separation start nodes is S along the path, obtains the relationship graph of electric field strength and S on the path；
S5 the relationship graph of electric field strength and S) is observed, if electric field strength E curve waveforms are electric fields in metal screen layer incision
It is greatest around, and with the increase of stress cone arcuate distance, electric field value is gradually decayed, after arriving certain distant place, electric field is very small,
Then obtain the final structure model of high-voltage cable middle joint；It is no to then follow the steps S6)；
S6) according to the relationship graph of electric field strength and S, the endpoint of broken line near stress concentration point, arc-spline curve is adjusted
Coordinate changes simultaneously the slope of broken line and the radius of curvature of arc-spline curve, corrects limited element calculation model parameter again, returns
Return step S2).
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106934152A (en) * | 2017-03-13 | 2017-07-07 | 顺德职业技术学院 | The modeling method of many stress interface accessory devices of high-tension cable |
| CN107944100B (en) * | 2017-11-13 | 2020-10-30 | 青岛汉缆股份有限公司 | Linear design method for comprehensively producing umbilical cable |
| CN107769148B (en) * | 2017-11-24 | 2019-12-06 | 广东电网有限责任公司珠海供电局 | design method of high-voltage alternating-current cable intermediate joint stress cone |
| CN109408901B (en) * | 2018-09-29 | 2023-05-09 | 国网山西省电力公司太原供电公司 | Modeling method of three-dimensional simulation model of cable joint electric field distribution |
| CN111814266B (en) * | 2020-05-29 | 2024-05-14 | 深圳供电局有限公司 | Parameter optimization method, device, equipment and storage medium for cable intermediate connector |
| CN115828710B (en) * | 2023-01-28 | 2023-09-08 | 湖南经研电力设计有限公司 | Uneven thickness design method and system for cable support hardware fitting |
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