CN102945316B - A kind of relay protection device crash rate computing method considering covariant - Google Patents

Abstract

Consider relay protection device crash rate computing method for covariant, belong to technical field of electric system protection.Adopt multiplied model, determine the funtcional relationship of relay protection crash rate distribution parameter and covariant; By the funtcional relationship of parameter and covariant, obtain the crash rate distribution function in Weibull distribution type situation; The least square estimation method is adopted to obtain distribution function unknown parameter, thus, calculate relay protection device crash rate , in formula, m and η is respectively Weibull Distribution Form Parameter and scale parameter.The present invention considers relay protection intrinsic characteristic and operate outside condition thereof, the failure properties of accurate simulation protective relaying device, sets up relay protection covariant crash rate computing method.The present invention contributes to finding out the principal element affecting its reliability index, provides guidance for improving reliability of relay protection.<!--1-->

Description

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

Technical field

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

Background technology

Relay protection device ensures the first line of defence of electric power netting safe running, its reliability and power network safety operation closely related.Research reliability of relay protection, implements reliability of relay protection assessment, finds out the factor affecting its reliability index, can provide certain theoretical direction, improve and improve reliability of relay protection for relay protection maintenance work, ensure power network safety operation.

Determine that the failure model of protective relaying device is the basis of implementing reliability assessment, the precision of model directly affects the accuracy of reliability assessment result.Conventional Probability Model has two classes: a class is constant failure rate model, and namely crash rate is constant, and the inefficacy of equipment is random occurrence and incident completely; One class is time Dependent Failure model, and namely failure rate estimation is not constant in whole time range, but obeys Weibull distribution, normal distribution, lognormal distribution equal distribution.

At present, the failure model of existing relay protection device, only considers crash rate rule over time, namely regards constant or only time dependent variable as.In fact, relay protection device is made up of electronic devices and components, and the fault of electronic devices and components may be voltage owing to applying or the working temperature of equipment causes.Therefore, relay protection crash rate is regarded as constant or only change the reliability model of foundation in time, do not consider relay protection intrinsic characteristic and operate outside condition thereof, cannot the failure properties of accurate simulation protective relaying device.Meanwhile, considering relay protection intrinsic characteristic and operate outside condition thereof, set up relay protection covariant failure model, contribute to finding out the principal element affecting its reliability index, providing 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; cannot the problem of the change of analog machine crash rate and the relation of its intrinsic characteristic and operate outside condition; propose a kind of relay protection failure model considering covariant; the rule that simulation relay protection device failure conditions changes with other metric parameter in time, calculates relay protection device crash rate.

Technical scheme is, a kind of computing method considering the relay protection device crash rate of covariant, 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 Weibull distribution type situation;

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

The present invention considers relay protection intrinsic characteristic and operate outside condition thereof, the failure properties of accurate simulation protective relaying device, sets up relay protection covariant crash rate computing method.The present invention contributes to finding out the principal element affecting its reliability index, provides guidance for improving reliability of relay protection.

Accompanying drawing explanation

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

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.It is emphasized that following explanation is only exemplary, instead of in order to limit the scope of the invention and apply.

Fig. 1 is process flow diagram of the present invention.In Fig. 1, consider relay protection intrinsic characteristic and operate outside condition thereof, introduce covariant that the failure properties of simulation protective relaying device calculates 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 due to inner or cause for external factor, and this factor can be defined as covariant.Covariant may be working voltage, electric current, temperature, other metric parameter such as 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 a kind of explicit relation of both foundation is needed; namely 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 has

η(X)=f(x ₁,x ₂,…x _k)

In formula, X=(x ₁, x ₂..., x _k), x _ibe _iindividual covariant.

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

For under multiplied model, have

$\mathrm{\&eta;}\left(x\right)=\underset{i=0}{\overset{k}{\mathrm{\&Pi;}}}{e}^{a_i{x}_i}=\exp \left(\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{a}_i{x}_i\right)$

In formula, a _ifor having unknown parameter to be determined, a ₁=1.

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

For Weibull distribution, Reliability Function is

R(t)=exp[-(t/η) ^m]

Accumulative inefficacy function is

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

Failure rate estimation is

$\mathrm{\&lambda;\&lambda;}(t)=\frac{m}{\mathrm{\&eta;}}{\left(\frac{t}{\mathrm{\&eta;}}\right)}^{m?1}$

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

Suppose to only have scale parameter to be determined by covariant in two parameters.Substitute into the distribution function parameter η under multiplied model, the Reliability Function obtaining the consideration covariant in Weibull type situation is

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

Failure rate estimation is

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

Step 3: adopt the least square estimation method to obtain distribution function unknown parameter, thus calculate 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 ..., k n) corresponding covariant parameter value (x _1j, x _2j..., x _kj), then least squares estimate can be adopted to obtain the location parameter of distribution function.

By

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

F(t)=1-R(t)

Obtain

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

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

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

One group of empirical distribution function value F (t can be obtained _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, order

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

By least square method, solving equation group

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

The estimated value of unknown quantity can be obtained

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

By b _i=ma _i, thus obtain unknown parameter (m, a of failure rate estimation ₁, a ₂..., a _k), thus obtain the relay protection device crash rate considering 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, the failure properties of accurate simulation protective relaying device, sets up relay protection covariant crash rate computing method.The present invention contributes to finding out the principal element affecting its reliability index, provides guidance for improving reliability of relay protection.

The above; be only the present invention's preferably embodiment, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; the change 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 (1)

1. consider relay protection device crash rate computing method for covariant, it 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 Weibull distribution type situation;

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

Described multiplied model η (x) is: wherein, k be greater than zero integer, represent the number of covariant; x _ibe i-th covariant; a _ifor the multiplication factor that covariant is corresponding, a ₁=1;

Consideration covariant failure rate estimation in described Weibull type situation is: suppose to only have scale parameter to be determined by covariant in the form parameter of Weibull distribution and scale parameter, the failure rate estimation of acquisition is in formula, m and η is respectively Weibull Distribution Form Parameter and scale parameter; T represents the time; x _ibe i-th covariant; a _ifor the multiplication factor that covariant is corresponding, a ₁=1; K be greater than zero integer, represent the number of covariant.