CN104091039A - Method for analyzing and calculating withstand voltage of composite insulator - Google Patents
Method for analyzing and calculating withstand voltage of composite insulator Download PDFInfo
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- CN104091039A CN104091039A CN201410154053.9A CN201410154053A CN104091039A CN 104091039 A CN104091039 A CN 104091039A CN 201410154053 A CN201410154053 A CN 201410154053A CN 104091039 A CN104091039 A CN 104091039A
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Abstract
The invention discloses a method for analyzing and calculating withstand voltage of a composite insulator. The method mainly comprises the following steps: in a statically-stable or constant electric field of an insulator, establishing a Laplace's equation based on a withstand voltage analysis process of the composite insulator to be tested; based on the established Laplace's equation, solving a functional extreme problem and a variational problem which are based on definite solution problem equivalence in the withstand voltage analysis process of the composite insulator to be tested; based on solving results of the functional extreme problem and the variational problem which are based on the definite solution problem equivalence, solving potential of each node of the composite insulator to be tested. Through the adoption of the method, defects of high operating difficulty, narrow application range, high cost and the like in the prior art can be overcome so as to achieve advantages of low operating difficulty, wide application range and low cost.
Description
Technical field
The present invention relates to power transmission and distribution technical field, particularly, relate to a kind of composite insulator breakdown Voltage Analysis computing method.
Background technology
Along with 750kV electric pressure electrical network becomes NORTHWEST CHINA area power grid main grid structure, operation scene is carried out the test of power frequency 1min withstand voltage to 750kV composite insulator and has been proposed requirement.But according to relevant criterion, the wet power frequency 1min withstand voltage value of 750kV composite insulator during height above sea level 2000m is 1185kV; The wet power frequency 1min withstand voltage of 750kV composite post insulator is 1085kV; When height above sea level 2000m is above, wet power frequency 1min withstand voltage value also will raise accordingly.
Will carry out at the scene the power frequency 1min withstand voltage test of such voltage levels, for testing equipment and test condition, all have higher requirements, a lot of units do not possess the ability that such test is carried out at scene.Or indivedual units have the ability, but also face all difficulties while carrying out at the scene, as problems such as equipment conveying, experimental technique economy.
In realizing process of the present invention, inventor finds at least to exist in prior art that operation easier is large, the scope of application is little and high in cost of production defect.
Summary of the invention
The object of the invention is to, for the problems referred to above, propose a kind of composite insulator breakdown Voltage Analysis computing method, to realize the advantage that operation easier is little, the scope of application is large and cost is low.
For achieving the above object, the technical solution used in the present invention is: a kind of composite insulator breakdown Voltage Analysis computing method, mainly comprise:
A, in the quiet steady or steady electric field of insulator, set up the Laplace's equation based on composite insulator breakdown Voltage Analysis process to be measured;
B, the Laplace's equation based on setting up, solve functional extreme value problem and variational problem based on determining solution problem equivalent in composite insulator breakdown Voltage Analysis process to be measured;
C, based on determining the functional extreme value problem of solution problem equivalent and the solving result of variational problem, solve the current potential of each node of composite insulator to be measured.
Further, described step a, specifically comprises:
In quiet steady or steady electric field, power taking position
for direct solution object, in isotropy, linear, uniform dielectric, current potential
meet Laplace's equation:
In formula
represent current potential.
Further, described step b, specifically comprises:
Solve and functional extreme value problem and the variational problem of determining solution problem equivalent, root Poisson equation solves the extreme value of functional with the Poisson field of homogeneous First Boundary Condition, in Poisson equation, generally determines equation and is:
when
field of definition while being volume V, definite condition:
the closed sides interface that in formula, S is field of definition;
The Laplace operator of homogeneous boundary condition is self-adjoint operator, has:
In above formula
with ψ be in field of definition two functions arbitrarily, wherein:
In above formula, γ is constant and is greater than zero, and the operator with above-mentioned character is called positive definite operator, if surely separate the operator of problem, is positive definite operator, this general determine equation must with following variational problem equivalence, and have unique solution:
After arrangement, can obtain:
In Electromagnetic Calculation, extreme value all refers to minimal value, and the integration item in formula (a) is called functional corresponding and Poisson equation, and in formula, V represents field domain, for above formula (a), by integral transformation, obtains:
In formula, S is for surrounding the closed surface of V;
For homogeneous First Boundary Condition and homogeneous second kind boundary condition, above formula (b) is reduced to:
Obtain thus the Poisson equation functional of above formula correspondence and First Boundary Condition and second kind boundary condition;
In like manner, can draw the functional of the Poisson equation of third boundary condition: during ρ=0, what function was corresponding is exactly the functional of the Poisson equation of First Boundary Condition and second kind boundary condition in formula; Derivation obtains, the Poisson field of corresponding and homogeneous second kind boundary condition and nonhomogeneous First Boundary Condition, and corresponding conditional problem of variation is:
ρ representation unit areal charge in formula.
Further, described step c, specifically comprises:
Under DC voltage effect, the Potential distribution of insulator should meet Laplace's equation, and its boundary condition belongs to Dirichlet problem;
If whole calculating field domain is divided into m unit, in unit e, the current potential of any point is expressed as with the function of the current potential at each fixed point place, unit:
In above formula, n0 represents subdivision unit number of vertex,
the potential value that represents each summit in unit,
be called element shape functions, variational problem variational problem equation approximate expression in whole field domain is expressed as:
The result of integral operation,
actual is all fixed points place current potential in whole field domain
i is from node 1 until the function of node sum m;
Utilize variational principle, order
right
derivative be zero, obtain a system of equations:
wherein matrix of coefficients [K] claims again stiffness matrix, and recycling boundary condition solves the current potential of each node
The composite insulator breakdown Voltage Analysis computing method of various embodiments of the present invention, owing to mainly comprising: in the quiet steady or steady electric field of insulator, set up the Laplace's equation based on composite insulator breakdown Voltage Analysis process to be measured; Laplace's equation based on setting up, solves functional extreme value problem and variational problem based on determining solution problem equivalent in composite insulator breakdown Voltage Analysis process to be measured; Based on determining the functional extreme value problem of solution problem equivalent and the solving result of variational problem, solve the current potential of each node of composite insulator to be measured; Can adopt finite element method, by insulator computation model discrete, combine, add and can obtain its Electric Field Distribution and Potential distribution by given boundary condition etc.; Thereby can overcome the defect that in prior art, operation easier is large, the scope of application is little and cost is high, to realize the advantage that operation easier is little, the scope of application is large and cost is low.
Other features and advantages of the present invention will be set forth in the following description, and, partly from instructions, become apparent, or understand by implementing the present invention.
Below by drawings and Examples, technical scheme of the present invention is described in further detail.
Accompanying drawing explanation
Accompanying drawing is used to provide a further understanding of the present invention, and forms a part for instructions, for explaining the present invention, is not construed as limiting the invention together with embodiments of the present invention.In the accompanying drawings:
Fig. 1 is the schematic flow sheet of composite insulator breakdown Voltage Analysis computing method of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described, should be appreciated that preferred embodiment described herein, only for description and interpretation the present invention, is not intended to limit the present invention.
According to the embodiment of the present invention, as shown in Figure 1, a kind of composite insulator breakdown Voltage Analysis computing method are provided.These composite insulator breakdown Voltage Analysis computing method, comprise in the quiet steady or steady electric field of insulator, set up Laplace's equation, solve and functional extreme value problem and the variational problem of determining solution problem equivalent, solve the current potential of each node; Adopt finite element method, by insulator computation model discrete, combine, add and can obtain its Electric Field Distribution and Potential distribution by given boundary condition etc.
The composite insulator breakdown Voltage Analysis computing method of the present embodiment, comprise the following steps:
1) in quiet steady or steady electric field, power taking position
for direct solution object, in isotropy, linear, uniform dielectric, current potential
meet Laplace's equation:
In formula
represent current potential;
2) solve and functional extreme value problem and the variational problem of determining solution problem equivalent, root Poisson equation solves the extreme value of functional with the Poisson field of homogeneous First Boundary Condition, in Poisson equation, generally determines equation and is:
when
field of definition while being volume V, definite condition:
the closed sides interface that in formula, S is field of definition;
The Laplace operator of homogeneous boundary condition is self-adjoint operator, has:
In above formula
with ψ be in field of definition two functions arbitrarily, wherein:
In above formula, γ is constant and is greater than zero, and the operator with above-mentioned character is called positive definite operator, if surely separate the operator of problem, is positive definite operator, this general determine equation must with following variational problem equivalence, and have unique solution:
After arrangement, can obtain:
In Electromagnetic Calculation, extreme value all refers to minimal value, and the integration item in formula is called functional corresponding and Poisson equation, and in formula, V represents field domain, for above formula (a), by integral transformation, can obtain:
In formula, S is for surrounding the closed surface of V;
For homogeneous First Boundary Condition and homogeneous second kind boundary condition, above formula (b) can be reduced to:
As can be seen here, the Poisson equation functional of above formula correspondence and First Boundary Condition and second kind boundary condition.In like manner can draw the functional of the Poisson equation of third boundary condition.In formula, during ρ=0, what function was corresponding is exactly the functional of the Poisson equation of First Boundary Condition and second kind boundary condition.
Derivation can obtain, the Poisson field of corresponding and homogeneous second kind boundary condition and nonhomogeneous First Boundary Condition, and corresponding conditional problem of variation is:
ρ representation unit areal charge in formula;
3) under DC voltage effect, the Potential distribution of insulator should meet Laplace's equation, and its boundary condition belongs to Dirichlet problem;
If whole calculating field domain is divided into m unit, in unit e, the current potential of any point is expressed as with the function of the current potential at each fixed point place, unit:
In above formula, n0 represents subdivision unit number of vertex,
the potential value that represents each summit in unit,
be called element shape functions, variational problem variational problem equation in whole field domain can approximate expression be expressed as:
The result of integral operation,
actual is all fixed points place current potential in whole field domain
the function of (i is from node 1 until node sum m), utilizes variational principle, order
right
derivative be zero, obtain a system of equations:
Wherein matrix of coefficients [K] claims again stiffness matrix, and recycling boundary condition solves the current potential of each node
The composite insulator breakdown Voltage Analysis computing method of above-described embodiment, adopt the finite element numerical computing method through secondary development, and application has software and the workstation of powerful solid modelling, calculating, data analysis and post-processing function, 750kV Composite Insulators in running status, whole section of power frequency withstand test, segmentation power frequency withstand test situation, has carried out respectively electric field numerical analysis; 750kV composite post insulator in whole section of power frequency withstand test, segmentation power frequency withstand test situation, has carried out respectively electric field numerical analysis.
Finite element method (Finite Element Method) is the method for utilizing mathematical approach, continuous engineering structure is separated into limited unit, with the unknown quantity of limited quantity, remove to approach unlimited unknown quantity, set up mathematical model, form panel load, introduce boundary condition, resolve Algebraic Equation set, actual physical system is carried out to analog computation analysis.The basic ideas of finite element method are " within one minute one, closing ".Dividing is in order to carry out element analysis, the object that calculate to be carried out to grid division, breaking the whole up into parts; Closing is for one-piece construction is comprehensively analyzed, and the unit collection of dividing zero, is whole.By to computation model discrete, combine, add and can obtain its Electric Field Distribution and Potential distribution by given boundary condition etc.Finite element numerical computing method is widely applied in the calculating such as mechanics, electric field, calorifics and fluid field.
In quiet steady or steady electric field, power taking position
for direct solution object, in isotropy, linear, uniform dielectric, current potential
meet Laplace's equation:
In formula
represent current potential.
In electromagnetic field field, definite condition is generally divided into Four types:
1) the borderline potential value of given whole field domain, is called Dirichlet problem;
2) given whole field domain border potential method guide functional value, is called neumann problem;
3) the borderline potential value of given whole field domain and its normal derivative linear combination, be called the 3rd class boundary value problem;
4) mix class boundary problem, i.e. given potential value on the segment boundary of whole field domain, and in the normal derivative value of the given current potential of remainder.
From Theory of Electromagnetic Field, all kinds of electromagnetic fields determine that solution problem is comprised of corresponding electromagnetic field equation group and definite condition.If by finite element model for solving, need first determine and surely separate functional problem and the variational problem of problem equivalent, due to a kind of special case that Laplace's equation in electromagnetic field equation is Poisson equation, the existing extreme-value problem that functional is described with the Poisson field of homogeneous First Boundary Condition.In Poisson equation, generally determine equation and be:
When
field of definition while being volume V, definite condition:
The closed sides interface that in formula, S is field of definition.
The Laplace operator of homogeneous boundary condition is self-adjoint operator, has
In formula
with ψ be in field of definition two functions arbitrarily, wherein:
In formula, γ is constant and is greater than zero, and the operator with above-mentioned character is called positive definite operator, if surely separate the operator of problem, is positive definite operator, this general determine equation must with following variational problem equivalence, and have unique solution.
After arrangement, can obtain:
In Electromagnetic Calculation, extreme value all refers to minimal value, and the integration item in formula is called functional corresponding and Poisson equation.In formula, V represents field domain, for above formula, by integral transformation, can obtain:
In formula, S is for surrounding the closed surface of V.
For homogeneous First Boundary Condition and homogeneous second kind boundary condition, above formula can be reduced to:
As can be seen here, the Poisson equation functional of above formula correspondence and First Boundary Condition and second kind boundary condition.In like manner can draw the functional of the Poisson equation of third boundary condition.In formula, during ρ=0, what function was corresponding is exactly the functional of the Poisson equation of First Boundary Condition and second kind boundary condition.
Derivation can obtain, the Poisson field of corresponding and homogeneous second kind boundary condition and nonhomogeneous First Boundary Condition, and corresponding conditional problem of variation is:
ρ representation unit areal charge in formula.
Getting functional
in the process of extreme value, automatically meet homogeneous third boundary condition, also meet nonhomogeneous second kind boundary condition and third boundary condition simultaneously.This boundary condition becomes natural boundary conditions.Its corresponding variational problem is called unconditional variational problem.Due in asking functional extreme value process, First Boundary Condition is not met automatically.So when processing Dirichlet problem and variational problem, also must process First Boundary Condition separately, conventionally claim this class boundary condition for forcing boundary condition, variational problem becomes condition variation relatively.
In multilayered medium, the region of homogeneous media still can be determined equation and describes with general, on medium decomposition face, should contact by the boundary condition on interphase.Owing to cancelling out each other on different interface conditions, so electric field when the multiple medium of finite element model for solving coexists is very convenient.
Under DC voltage effect, the Potential distribution of insulator should meet Laplace's equation, and its boundary condition belongs to Dirichlet problem.
If whole calculating field domain is divided into m unit, in unit e, the current potential of any point is expressed as with the function of the current potential at each fixed point place, unit:
In formula, n0 represents subdivision unit number of vertex,
the potential value that represents each summit in unit.
be called element shape functions, variational problem variational problem equation in whole field domain can approximate expression be expressed as:
The result of integral operation,
actual is all fixed points place current potential in whole field domain
the function of (i is from node 1 until node sum m), utilizes variational principle, order
right
derivative be zero, can obtain a system of equations:
Wherein matrix of coefficients [K] claims again stiffness matrix, and recycling boundary condition just can solve the current potential of each node
then by current potential, asked other electric field physical quantitys such as electric field intensity, electric density, electric current.
In sum, the composite insulator breakdown Voltage Analysis computing method of the various embodiments described above of the present invention, compared with prior art, have the following advantages: adopt finite element method, by to insulator computation model discrete, combine, add and can obtain its Electric Field Distribution and Potential distribution by given boundary condition etc.
Finally it should be noted that: the foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, although the present invention is had been described in detail with reference to previous embodiment, for a person skilled in the art, its technical scheme that still can record aforementioned each embodiment is modified, or part technical characterictic is wherein equal to replacement.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.
Claims (4)
1. composite insulator breakdown Voltage Analysis computing method, is characterized in that, mainly comprise:
A, in the quiet steady or steady electric field of insulator, set up the Laplace's equation based on composite insulator breakdown Voltage Analysis process to be measured;
B, the Laplace's equation based on setting up, solve functional extreme value problem and variational problem based on determining solution problem equivalent in composite insulator breakdown Voltage Analysis process to be measured;
C, based on determining the functional extreme value problem of solution problem equivalent and the solving result of variational problem, solve the current potential of each node of composite insulator to be measured.
2. composite insulator breakdown Voltage Analysis computing method according to claim 1, is characterized in that, described step a, specifically comprises:
In quiet steady or steady electric field, power taking position
for direct solution object, in isotropy, linear, uniform dielectric, current potential
meet Laplace's equation:
In formula
represent current potential.
3. composite insulator breakdown Voltage Analysis computing method according to claim 2, is characterized in that, described step b, specifically comprises:
Solve and functional extreme value problem and the variational problem of determining solution problem equivalent, root Poisson equation solves the extreme value of functional with the Poisson field of homogeneous First Boundary Condition, in Poisson equation, generally determines equation and is:
when
field of definition while being volume V, definite condition:
the closed sides interface that in formula, S is field of definition;
The Laplace operator of homogeneous boundary condition is self-adjoint operator, has:
In above formula
with ψ be in field of definition two functions arbitrarily, wherein:
In above formula, γ is constant and is greater than zero, and the operator with above-mentioned character is called positive definite operator, if surely separate the operator of problem, is positive definite operator, this general determine equation must with following variational problem equivalence, and have unique solution:
After arrangement, can obtain:
In Electromagnetic Calculation, extreme value all refers to minimal value, and the integration item in formula (a) is called functional corresponding and Poisson equation, and in formula, V represents field domain, for above formula (a), by integral transformation, obtains:
In formula, S is for surrounding the closed surface of V;
For homogeneous First Boundary Condition and homogeneous second kind boundary condition, above formula (b) is reduced to:
Obtain thus the Poisson equation functional of above formula correspondence and First Boundary Condition and second kind boundary condition;
In like manner, can draw the functional of the Poisson equation of third boundary condition: during ρ=0, what function was corresponding is exactly the functional of the Poisson equation of First Boundary Condition and second kind boundary condition in formula; Derivation obtains, the Poisson field of corresponding and homogeneous second kind boundary condition and nonhomogeneous First Boundary Condition, and corresponding conditional problem of variation is:
ρ representation unit areal charge in formula.
4. composite insulator breakdown Voltage Analysis computing method according to claim 3, is characterized in that, described step c, specifically comprises:
Under DC voltage effect, the Potential distribution of insulator should meet Laplace's equation, and its boundary condition belongs to Dirichlet problem;
If whole calculating field domain is divided into m unit, in unit e, the current potential of any point is expressed as with the function of the current potential at each fixed point place, unit:
In above formula, n0 represents subdivision unit number of vertex,
the potential value that represents each summit in unit,
be called element shape functions, variational problem variational problem equation approximate expression in whole field domain is expressed as:
The result of integral operation,
actual is all fixed points place current potential in whole field domain
i is from node 1 until the function of node sum m;
Utilize variational principle, order
right
derivative be zero, obtain a system of equations:
wherein matrix of coefficients [K] claims again stiffness matrix, and recycling boundary condition solves the current potential of each node
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106570324A (en) * | 2016-11-03 | 2017-04-19 | 合肥华义电气科技有限公司 | Substation power frequency electric field computing method |
| CN110705006A (en) * | 2019-08-16 | 2020-01-17 | 北京航空航天大学 | Method for solving optimal additional magnetic field position type of plasma vortex driving device |
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| CN102694358A (en) * | 2012-06-07 | 2012-09-26 | 甘肃省电力公司电力科学研究院 | Method for improving potential distribution of insulators in transmission line in filthy and wet environment |
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Cited By (2)
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| CN106570324A (en) * | 2016-11-03 | 2017-04-19 | 合肥华义电气科技有限公司 | Substation power frequency electric field computing method |
| CN110705006A (en) * | 2019-08-16 | 2020-01-17 | 北京航空航天大学 | Method for solving optimal additional magnetic field position type of plasma vortex driving device |
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