CN102945316A - Failure rate calculation method for relay protection device in consideration of covariates - Google Patents

Abstract

A failure rate calculation method for a relay protection device in consideration of covariates belongs to the technical field of protection of electric power systems. The method comprises the following steps of: determining the function relationship between relay protection failure rate distribution parameters and the covariates by using a multiplication model; obtaining failure rate distribution functions under the Weibull distribution condition by the function relationship between the parameters and the covariates; and obtaining unknown parameters of the distribution functions through the formula (referring to the Specification) in order to calculate the failure rate of the relay protection device, wherein m and Eta in the formula respectively represent Weibull distribution shape parameters and scale parameters. According to the failure rate calculation method for the relay protection device in consideration of the covariates disclosed by the invention, the failure characteristics of the relay protection device are accurately simulated in consideration of the intrinsic characteristics of the relay protection and the external working conditions thereof, so that the covariates and failure rate calculation method for the relay protection is built. And the method is helpful to find out the principal factors which influence the reliability indexes of the method, and provides the guidance to improve the relay protection reliability.

Description

A kind of relay protection device crash rate computing method of considering covariant

Technical field

The present invention relates to consider the computing method of the protective relaying device crash rate of covariant, belong to relay protection of power system reliability field.

Background technology

Relay protection device is the first line of defence that ensures electric power netting safe running, and its reliability and power network safety operation are closely related.The research reliability of relay protection is implemented the reliability of relay protection assessment, finds out the factor that affects its reliability index, can provide certain theoretical direction for the relay protection maintenance work, improves and improve reliability of relay protection, ensures power network safety operation.

The failure model of determining protective relaying device is the basis of implementing reliability assessment, and the precision of model directly affects reliability assessment result's accuracy.Probability Model commonly used has two classes: a class is constant failure-rate models, and namely crash rate is constant, and the inefficacy of equipment is random occurrence and incident fully; One class is the time Dependent Failure model, and namely the crash rate function is not constant in whole time range, but obeys the distributions such as Weibull distribution, normal distribution, lognormal distribution.

At present, the failure model of existing relay protection device, Considering Failure rate rule is over time only namely regarded constant or time dependent variable only as.In fact, relay protection device is to be made of electronic devices and components, and the fault of electronic devices and components may be owing to the voltage that applies or the working temperature of equipment causes.Therefore, regard the relay protection crash rate as constant or the reliability model set up of temporal evolution only, do not consider relay protection intrinsic characteristic and operate outside condition thereof, can't accurately simulate the failure properties of protective relaying device.Simultaneously, consider relay protection intrinsic characteristic and operate outside condition thereof, set up relay protection covariant failure model, help to find out the principal element that affects its reliability index, provide guidance for improving reliability of relay protection.

Summary of the invention

The present invention is directed in the failure model of existing relay protection device; the problem of variation that can't the analog machine crash rate and the relation of its intrinsic characteristic and operate outside condition; a kind of relay protection failure model of considering covariant has been proposed; the rule that simulation relay protection device failure conditions changes with other metric parameter is in time calculated the relay protection device crash rate.

Technical scheme is, a kind of computing method of considering the relay protection device crash rate of covariant, and described method comprises the following steps:

Step 1: adopt multiplied model, determine the funtcional relationship of relay protection crash rate distribution parameter and covariant;

Step 2: by the funtcional relationship of parameter and covariant, obtain the crash rate distribution function in the Weibull distribution type situation;

Step 3: adopt the least square estimation method to obtain the distribution function unknown parameter, thereby calculate the relay protection device crash rate.

The present invention considers relay protection intrinsic characteristic and operate outside condition thereof, accurately simulates the failure properties of protective relaying device, sets up relay protection covariant crash rate computing method.The present invention helps to find out the principal element that affects its reliability index, provides guidance for improving reliability of relay protection.

Description of drawings

Fig. 1 is process flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that, following explanation only is exemplary, rather than in order to limit the scope of the invention and to use.

Fig. 1 is process flow diagram of the present invention.Among Fig. 1, consider relay protection intrinsic characteristic and operate outside condition thereof, introduce covariant, the failure properties of simulation protective relaying device is calculated relay protection device crash rate process, comprising:

Step 1: adopt multiplied model, determine the funtcional relationship of relay protection crash rate distribution parameter and covariant.

The fault of electronic devices and components may owing to inside or for external factor causes, this factor can be defined as covariant.Covariant may be other metric parameter such as working voltage, electric current, temperature, humidity and environment of relay protection device.The size of the parameter value of covariant can affect the failure conditions of relay protection device; therefore need to set up the two a kind of explicit relation; be the relation of covariant parameter value and relay protection crash rate distribution parameter, if η is the distribution function parameter of relay protection crash rate, then have

η(X)=f(x ₁,x ₂,…x _k)

In the formula, X=(x ₁, x ₂..., x _k), x _iBe _iIndividual covariant.

Because this relation is unknown, can suppose that so the relation between them is a kind of simple functional form.

Under multiplied model, have

$\mathrm{\η}\left(x\right)=\underset{i=0}{\overset{k}{\mathrm{\Π}}}{e}^{a_i{x}_i}=\exp \left(\underset{i=0}{\overset{k}{\mathrm{\Σ}}}{a}_i{x}_i\right)$

In the formula, a _iFor unknown parameter to be determined, a are arranged ₁=1.

Step 2: according to the covariant distribution function, obtain the crash rate distribution function in the Weibull distribution type situation.

For Weibull distribution, Reliability Function is

R(t)=exp[-(t/η) ^m]

The function that adds up to lose efficacy is

$F(t)=1?\exp [?{(\frac{t}{\mathrm{\η}})}^m]$

The crash rate function is

$\mathrm{\λ\λ}(t)=\frac{m}{\mathrm{\η}}{\left(\frac{t}{\mathrm{\η}}\right)}^{m?1}$

In the formula, m and η are respectively Weibull Distribution Form Parameter and scale parameter.

Suppose to only have scale parameter to be determined by covariant in two parameters.Distribution function parameter η under the substitution multiplied model, the Reliability Function that obtains the consideration covariant in the Weibull type situation is

$R(t)=\exp \left[\text{-}{\left(\frac{\text{t}}{\mathrm{\η}(x)}\right)}^m\right]$

The crash rate function is

$\mathrm{\λ}\left(t\right|x)=\frac{{\mathrm{mt}}^{(m-1)}}{{\mathrm{\η}}^m}={\mathrm{mt}}^{m-1}{\left[\exp \left(\underset{i=0}{\overset{k}{\mathrm{\Σ}}}{a}_i{x}_i\right)\right]}^{-m}$

Step 3: adopt the least square estimation method to obtain the distribution function unknown parameter, thereby calculate the relay protection device crash rate.

If known one group of relay protection device out-of-service time sequence (t ₁, t ₂..., t _n), and time t _j(j=1,2 ..., n) k corresponding covariant parameter value (x _1j, x _2j..., x _Kj), then can adopt least squares estimate to obtain the location parameter of distribution function.

By

$R\left(t\right)=\exp \{-{\left(\frac{t}{\exp \left(\underset{i=0}{\overset{k}{\mathrm{\Σ}}}{a}_i{x}_i\right)}\right)}^m\}$

F(t)=1-R(t)

Obtain

$\ln \left[\mathrm{<figure-callout\; id="1"\; label="ln"\; filenames="HDA00002303321200011.png"\; state="\{\{state\}\}">ln</figure-callout>}\frac{1}{1-F\left(t\right)}\right]=m\ln t-m\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{a}_i{x}_i$

By known out-of-service time sequence (t ₁, t ₂..., t _n), by meta order formula

F(t _j)=(j-0.3)/n+0.4

Can obtain one group of empirical distribution function value F (t _j) (j=1,2 ..., n).

Make y _j=lnln[1/ (1-F (t _j))], b _i=ma _i, then

To y _jWith corresponding independent variable (t _j, 1, x _1j, x _2j..., x _Kj) carry out linear regression, make

$Q=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{[y_j-(m\ln t_j-\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{b}_i{x}_{\mathrm{ij}})]}^2$

By least square method, the solving equation group

$\left\{\begin{array}{c}{\frac{Q}{m}|}_{m=\hat{m},b_i=\widehat{b_i}}=0\\ .\\ .\\ .\\ {\frac{Q}{b_i}|}_{m=\hat{m},b_i=\widehat{b_i}}=0\end{array}\right.---(i=\mathrm{1,2},...k)$

Can obtain the estimated value of unknown quantity

$\left\{\begin{array}{c}m=\hat{m}\\ .\\ .\\ .\\ b_i=\widehat{b_i}\end{array}\right.(i=\mathrm{1,2},...k)$

By b _i=ma _iThereby, obtain unknown parameter (m, a of crash rate function ₁, a ₂..., a _k), thereby obtain considering the relay protection device crash rate of covariant

$\mathrm{\&eta;}\left(t\right|x)=\frac{{\mathrm{mt}}^{(m-1)}}{{\mathrm{\&eta;}}^m}={\mathrm{mt}}^{m-1}{\left[\exp \left(\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{a}_i{x}_i\right)\right]}^{-m}$

The present invention considers relay protection intrinsic characteristic and operate outside condition thereof, accurately simulates the failure properties of protective relaying device, sets up relay protection covariant crash rate computing method.The present invention helps to find out the principal element that affects its reliability index, provides guidance for improving reliability of relay protection.

The above; only for the better embodiment of the present invention, but protection scope of the present invention is not limited to this, anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (4)

1. relay protection device crash rate computing method of considering covariant is characterized in that, the method comprising the steps of:

Step 1: adopt multiplied model, determine the funtcional relationship of relay protection crash rate distribution parameter and covariant;

Step 2: by the funtcional relationship of parameter and covariant, obtain the crash rate distribution function in the Weibull distribution type situation;

Step 3: adopt the least square estimation method to obtain the distribution function unknown parameter, thereby, calculate the relay protection device crash rate.

2. a kind of relay protection device crash rate computing method of considering covariant according to claim 1 is characterized in that, described multiplied model is:

, wherein, x _iBe i covariant, a _iFor unknown parameter to be determined, a are arranged ₁=1.

3. a kind of relay protection device crash rate computing method of considering covariant according to claim 1; it is characterized in that; consideration covariant crash rate function in the described Weibull type situation is: suppose to only have scale parameter to be determined by covariant in the form parameter of Weibull distribution and the scale parameter, the crash rate function of acquisition is , in the formula, m and η are respectively Weibull Distribution Form Parameter and scale parameter.

4. a kind of relay protection device crash rate computing method of considering covariant according to claim 1 is characterized in that, described the least square estimation method is: by meta order formula F (t _j)=(j-0.3)/n+0.4 obtains empirical distribution function value F (t _j) (j=1,2 ..., n).Make y _j=lnln[1/ (1-F (t _j))], b _i=ma _i, then By to y _jWith corresponding independent variable (t _j, 1, x _1j, x _2j..., x _Kj) carry out linear regression, namely obtain the estimated value of unknown parameter.

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