CN105116303B - A kind of method for estimating test number (TN) needed for 50% sparking voltage test - Google Patents
A kind of method for estimating test number (TN) needed for 50% sparking voltage test Download PDFInfo
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- CN105116303B CN105116303B CN201510557550.8A CN201510557550A CN105116303B CN 105116303 B CN105116303 B CN 105116303B CN 201510557550 A CN201510557550 A CN 201510557550A CN 105116303 B CN105116303 B CN 105116303B
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Abstract
The present invention relates to a kind of method for estimating test number (TN) needed for 50% sparking voltage test, this method includes：Structure one is on applying alive function；For giving confidence level, two constants for meeting condition are determined；Solution meets the confidence interval that equivalent inequality corresponds to unknown parameter；It is established and the associated inequality of standard deviation according to confidence interval；Test number (TN) is calculated according to constant M values, according to statistics uncertainty requirement selective value, the requirement for whether meeting overall uncertainty is chosen in verification；If being unsatisfactory for overall uncertainty requirement, by solving the value met the requirements, the test number (TN) of the condition of satisfaction is solved again according to the value calculated.Overall evaluation of a technical project provided by the invention considers that the factors such as discharge voltage standard deviation, confidence level requirement, uncertainty requirement and measuring instrument equipment, experiment ambient enviroment influence, and reference frame is provided for the accurate and effective of guarantee test result.
Description
Technical field
The present invention relates to a kind of high-voltage engineering test methods, and in particular to needed for a kind of 50% sparking voltage test of estimation
The method of test number (TN).
Background technology
Project of transmitting and converting electricity cost and operational reliability mainly depend on its dielectric level, with voltage class of electric power system not
Disconnected to improve, the contradiction between economy and reliability more highlights, it is therefore necessary to the rational insulation water of selection according to actual needs
It is flat.Insulation characterisitic of the selection of dielectric level depending on research object, to obtain the insulation characterisitic of certain research object, it is necessary to open
Disruptive discharge voltage test is opened up, 50% discharge voltage U is used in usual engineering50The exhausted of a certain definite object is evaluated with standard deviation
Edge characteristic.Since disruptive discharge voltage test is random experiment, result of the test has statistical property, as obtained by carrying out experimental study
There is the estimation of true value statistics uncertainty in result of the test, meanwhile, result of the test is subject to measuring instrument equipment, ambient enviroment etc.
Uncertain influence caused by factor.In general, the uncertainty of statistical result can be effectively reduced by increasing test number (TN), but
The increase of test number (TN) causes the increase of experimentation cost and to the possible destruction of testing equipment, it is necessary to selection rationally experiment time
Number.
50% impulse sparkover voltage U is provided in concerned countries standard50The lifting of 20 times can be no less than with efficiency test number
Method determines.Standard defines the lower limit of research number needed for lifting and lowering method, should be according to discharge voltage mark in practice lifting and lowering method
The factors such as quasi- deviation size and confidence level, uncertainty requirement select necessary pressurization number, guarantee test result it is accurate
Property and validity.
The content of the invention
To solve above-mentioned deficiency of the prior art, the object of the present invention is to provide a kind of 50% sparking voltage tests of estimation
The method of required test number (TN), this method consider discharge voltage standard deviation, confidence level requirement, uncertainty requirement and
The factors such as measuring instrument equipment, experiment ambient enviroment influence, and reference frame is provided for the accurate and effective of guarantee test result.
The purpose of the present invention is what is realized using following technical proposals：
The present invention provides a kind of method for estimating test number (TN) needed for 50% sparking voltage test, the 50% electric discharge electricity
Pressure is average voltage breakdown for continuous action voltage, is the breakdown voltage under 50% probability for surge voltage, improves it
It is in the described method includes following step：
1) structure is on applying alive function；
2) for giving confidence level, two constants for meeting condition are determined；
3) solve and meet the confidence interval that equivalent inequality corresponds to unknown parameter；
4) established and the associated inequality of standard deviation according to confidence interval；
5) according to statistics uncertainty requirement selection M values, whether verification M value selections meet the requirement of overall uncertainty；
If 6) be unsatisfactory for overall uncertainty requirement, by solving the M values met the requirements；
7) test number (TN) for the condition that meets is solved again according to the M values calculated.
Further, in the step 1), build on application voltage U1,U2,…,UnFunction be：F=F (U1,
U2,…,Un；λ), it is desirable that the distribution of function F is known and independent of any unknown parameter including λ；Facility making alive U1,
U2,…,UnIt is from normal distribution totality U~N (μ, σ2) sample, haveConstructor
That is the distribution of function F is it is known that comprising unknown parameter μ, and independent of any unknown parameter；Wherein：Wherein λ is unknown parameter；Represent sample mean, μ represents population mean, and σ is standard deviation in population, and n indicates n application voltage.
Further, in the step 2), for given confidence level 1- α, two constants a, b is determined, represent two points of positions
Point so that P { a ＜ F (U1,U2,…,Un；λ) ＜ b }=1- α；P represents that distribution function is in a, the probability between b；By standard just
The property of state distribution obtains：
Wherein：N indicates n application voltage, and μ represents population mean, and σ is overall standard deviation, zα/2Expression standard
The quantile of normal distribution α/2.
Further, in the step 3), from a ＜ F (U1,U2,…,Un；λ) ＜ b draw equivalent inequality
WhereinWithRespectively confidence level is the confidence lower limit and confidence upper limit of the two-sided confidence interval of 1- α；
It solvesInequality in corresponding left side braces：
Wherein：Represent sample mean, μ represents population mean, and σ is standard deviation in population, and n indicates n application
Voltage；zα/2Represent the quantile of standardized normal distribution α/2.
Further, in the step 4)：OrderThe test number (TN) for the condition that meets is solved, wherein
usFor the statistics uncertainty of sample, M is constant, and σ is overall standard deviation；
Number needed for experiment is calculated under given uncertainty and confidence level.
Further, in the step 6), if being unsatisfactory for overall uncertainty requirement, pass throughIt solves full
The M values required enough, if M selections are unsatisfactory for the requirement of overall uncertainty, (measurement result has overall measurement uncertainty, total uncertain
The uncertainty as caused by the factors such as the statistics uncertainty and measuring apparatus of measurement data, measuring environment is spent to collectively constitute),
It is calculated by following formula after meeting the M values of overall uncertainty requirement, recalculates number needed for experiment：
Wherein：ut、uaAnd ueRespectively caused by overall uncertainty, measuring instrument equipment uncertainty and ambient enviroment because
Uncertainty caused by element；For constant, (M represents a certain constant to M, can directly give, can also calculate and provide, purpose is exactly to select certain
One percentage such as M selections 2, represents the 50% of standard deviation).
The excellent effect that technical solution provided by the invention has is：
The calculating side of test number (TN) needed for 50% discharge voltage is estimated in high-voltage engineering insulation applications provided by the invention
Method, this method consider discharge voltage standard deviation, confidence level requirement, uncertainty requirement and measuring instrument equipment, examination
The influence of the factors such as ambient enviroment is tested, the validity of result of the test is evaluated in advance, is provided for the improvement of high-voltage test method
With reference to.
Description of the drawings
Fig. 1 is the flow chart of the computational methods of test number (TN) needed for 50% discharge voltage of estimation provided by the invention.
Specific embodiment
The specific embodiment of the present invention is described in further detail below in conjunction with the accompanying drawings.
The following description and drawings fully show specific embodiments of the present invention, to enable those skilled in the art to
Put into practice them.Other embodiments can include structure, logic, it is electrical, process and other change.Embodiment
Only represent possible variation.Unless explicitly requested, otherwise individual component and function are optional, and the order operated can be with
Variation.The part of some embodiments and feature can be included in or replace part and the feature of other embodiments.This hair
The scope of bright embodiment includes equivalent obtained by the gamut of claims and all of claims
Object.Herein, these embodiments of the invention can individually or generally be represented that this is only with term " invention "
For convenience, and if in fact disclosing the invention more than one, it is not meant to automatically limit the scope of the application to appoint
What single invention or inventive concept.
The object of the present invention is to provide experiment time needed for 50% discharge voltage is estimated in a kind of high-voltage engineering insulation applications
Several computational methods, 50% discharge voltage are average voltage breakdown for continuous action voltage, for surge voltage
It says as the breakdown voltage under 50% probability.The described method includes following step：
1) one is built on application voltage U1,U2,…,UnFunction：F=F (U1,U2,…,Un；λ), wherein λ is unknown
Parameter；It is required that the distribution of F is known and independent of any unknown parameter including λ.U might as well be set1,U2,…,UnCome
From normal distribution totality U~N (μ, σ2) sample, therefore haveSo as to buildI.e.
The distribution of F is it is known that comprising unknown parameter μ, and independent of any unknown parameter.Wherein λ is unknown parameter；Represent that sample is put down
Average, μ represent population mean, and σ is standard deviation in population, and n indicates n application voltage.
2) for given confidence level 1- α, two constants a, b are determined so that P { a ＜ F (U1,U2,…,Un；λ) ＜ b }=1-
α；
It can be obtained by the property of standardized normal distribution：
3) from a ＜ F (U1,U2,…,Un；λ) ＜ b draw equivalent inequalityWhereinWithRespectively confidence level
For the confidence lower limit and confidence upper limit of the two-sided confidence interval of 1- α；
Equivalent inequality is drawn according to step 2)
4) makeSolve the test number (TN) for the condition that meets, wherein usStatistics from sample is not true
Fixed degree, M are constant, and σ is overall standard deviation；
It can obtain
So as to calculate number needed for experiment under given uncertainty and confidence level.
5) according to statistics uncertainty requirement selection M values, whether verification M selections meet the requirement of overall uncertainty；
If 6) be unsatisfactory for overall uncertainty requirement, pass throughSolve the M values met the requirements, wherein ut,
ua, ueRespectively overall uncertainty is not known caused by the factors such as uncertainty, ambient enviroment caused by measuring instrument equipment
Degree；
If M chooses the requirement for being unsatisfactory for overall uncertainty, pass through
It calculates after meeting the M values of overall uncertainty requirement, recalculates number needed for experiment.
7) test number (TN) for the condition that meets is solved again according to the M values calculated.
Embodiment
When carrying out the design of 1000kV project of transmitting and converting electricity external insulations the air gap, it is necessary to according to typical electrode different excessively electric
It presses and carries out discharge test research under type action.It is generally necessary to carry out thunder and lightning, switching impulse discharge test, typical electrode is obtained
Thunder and lightning, 50% discharge characteristic curve of switching impulse.Now illustrate opening by taking the air gap that 8 split conductors form shaft tower as an example
Rational test number (TN) how is selected before exhibition experimental study.
According to foregoing, it is believed that 8 split conductors are to shaft tower thunder and lightning, switching impulse sparkover voltage and discharge probability in normal state point
Cloth, i.e. U~N (μ, σ2), wherein μ is unknown, according to previous development experimental study as a result, for lightning impulse, σ≤3%；Behaviour
Make impact σ≤6%, build distribution functionFor giving under confidence level 1- α=95%, according to step
2) it is described, it can be obtained by the property of standardized normal distribution：
Above-mentioned equivalent inequality is solved to obtain：
It can be obtained by formula (1)：
σ=3% is taken for lightning impulse, σ=6% is taken for switching impulse.
As M=3, lightning impulse and the lower required statistics uncertainty of operating impulse voltage experiment can respectively reach
1% and 2%, then under 95% confidence level, test number (TN) only needs to meetz0.025Standard normal point can be looked into
Bu Biao get 1.96.N >=34.6 are calculated, take 35.
As M=2, lightning impulse and the lower required statistics uncertainty of operating impulse voltage experiment can respectively reach
1.5% and 3%, then under 95% confidence level, n >=15.4 are calculated, take 16.Obviously 3% for switching impulse
Overall measurement uncertainty is naturally larger than 3% under statistics uncertainty, and bigger than normal, therefore, M needs to ask for by formula (2).
Assuming that overall uncertainty requirement is 3%, the uncertainty caused by the factors such as measuring instrument equipment, ambient enviroment is such as
Fruit can calculate, and calculating provides, if can not calculate can be estimated, might as well take ua=1.5%, ue=1%, calculate to obtain M=
2.4, test number (TN) n >=22.1 take 23.
It in confidence level is 95% that above-described embodiment, which is, and the requirement of different uncertainties of measurement is lower to calculate demonstration.For given
Uncertainty of measurement during confidence level value difference, can equally provide, details are not described herein again according to this method.Obviously in order to reach
To higher confidence level, although adding credibility, test number (TN) can also increase.
The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, although with reference to above-described embodiment pair
The present invention is described in detail, those of ordinary skill in the art still can to the present invention specific embodiment into
Row modification either equivalent substitution these without departing from any modification of spirit and scope of the invention or equivalent substitution, applying
Within the claims of the pending present invention.
Claims (4)
1. a kind of method for estimating test number (TN) needed for 50% sparking voltage test, 50% discharge voltage, for lasting work
It is average voltage breakdown with voltage, is the breakdown voltage under 50% probability for surge voltage, which is characterized in that the method bag
Include following step：
1) structure is on applying alive function；
2) for giving confidence level, two constants for meeting condition are determined；
3) solve and meet the confidence interval that equivalent inequality corresponds to unknown parameter；
4) established and the associated inequality of standard deviation according to confidence interval；
In the step 4)：OrderSolve the test number (TN) for the condition that meets, wherein usFor the statistics of sample
Uncertainty, M are constant, and σ is overall standard deviation；
Number needed for experiment is calculated under given uncertainty and confidence level；λWithRespectively confidence level is the bilateral of 1- α
The confidence lower limit and confidence upper limit of confidence interval；
5) according to statistics uncertainty requirement selection M values, whether verification M value selections meet the requirement of overall uncertainty；
If 6) be unsatisfactory for overall uncertainty requirement, the M values met the requirements are solved by following calculation expressions；
In the step 6), if being unsatisfactory for overall uncertainty requirement, pass throughThe M values met the requirements are solved, if
M chooses the requirement for being unsatisfactory for overall uncertainty, is calculated after meeting the M values of overall uncertainty requirement, recalculated by following formula
Go out number needed for experiment：
Wherein：ut、uaAnd ueRespectively uncertainty and ambient environmental factors draw caused by overall uncertainty, measuring instrument equipment
The uncertainty risen；M is constant；
7) test number (TN) for the condition that meets is solved again according to the M values calculated.
2. the method as described in claim 1, which is characterized in that in the step 1), build on application voltage U1,U2,…,
UnFunction be：F=F (U1,U2,…,Un；λ), it is desirable that the distribution of function F it is known and independent of including λ it is any not
Know parameter；Facility making alive U1,U2,…,UnIt is from normal distribution totality U~N (μ, σ2) sample, have
ConstructorThat is the distribution of function F is it is known that comprising unknown parameter μ, and independent of any unknown ginseng
Number；Wherein λ is unknown parameter；Represent sample mean, μ represents population mean, and σ is standard deviation in population, and n indicates n
A application voltage.
3. the method as described in claim 1, which is characterized in that in the step 2), for given confidence level 1- α, determine two
A constant a, b represent two quantiles so that P { a ＜ F (U1,U2,…,Un；λ) ＜ b }=1- α；P represents that distribution function is in
Probability between a, b；It is obtained by the property of standardized normal distribution：
Wherein：N indicates n application voltage, and μ represents population mean, and σ is overall standard deviation, zα/2Represent standard normal
It is distributed the quantile of α/2；F=F (U1,U2,…,Un；It is λ) application voltage U1,U2,…,UnFunction；Represent sample mean.
4. the method as described in claim 1, which is characterized in that in the step 3), from a ＜ F (U1,U2,…,Un；λ) ＜ b are obtained
Go out equivalent inequalityWhereinλWithRespectively confidence level is the confidence lower limit and confidence of the two-sided confidence interval of 1- α
The upper limit；
It solvesInequality in corresponding left side braces：
Wherein：Represent sample mean, μ represents population mean, and σ is standard deviation in population, and n indicates n application voltage；
zα/2Represent the quantile of standardized normal distribution α/2.
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| CN109116195B (en) * | 2018-06-27 | 2020-08-14 | 中国南方电网有限责任公司超高压输电公司大理局 | Method and device for calculating 50% flashover voltage of hot-line work combination gap of power transmission line |
| CN110516363B (en) * | 2019-08-28 | 2022-12-06 | 西安西热节能技术有限公司 | Method for determining performance test duration of steam turbine |
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