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Abstract

Introduction

First in the world the concept of vitality was formulated by the Russian admiral S.O. Makarov is ability of ship to continue a fight, having the damages in different battle parts [1].

Theme urgency

By a shove a failure which happened served to development of methods of estimation of reliability of structurally – difficult charts, prognostication of chain failures and vitality of grids on November, 9, 1965 in the USA. This failure resulted in that on territory with the population 30 million persons more than on 10 hours vital functions were halted. Harm from a failure made more than 100 million dollars [2].

More than 65 % large failures it is possible to attribute to chain, which take place in the dynamic mode at the short circuit (SC) in the element of network and refusal in work of row protective commutation apparatuses, through which got the through SC current and started going of them relay protections [3].

In power engineering under the loss of knot vitality of loading of the power supply system in the dynamic mode we will understand the process of coincidence in space and time of damages minimum number of electrical equipment, which emergency disconnection of substations of different voltage classes or their sections of buses, which provide industrial enterprises with electric power, is at: factories, power plants, mines and etc.

Under the loss of vitality of substation 110/6 – 10 kV in the dynamic mode we will understand the process of coincidence in space and time of damages minimum number of electrical equipment, at which even one of sections of buses 6 – 10 kV will be disconnected.

Therefore the work directed for development of new and perfection of the known mathematical models and methods as evaluated by vitality of knots of loading is an actual scientific task, the decision of which will allow practically to shut out cases appearance of cascade power interruptions, to death transformer substations feeding enterprises during the set time of t.

Purpose of work

Receipt of a new analytical dependence of probability of death during time of t transformer substation 110/6 – 10 kV, which provides industrial enterprises with electric power, depending on the parameter of stream of SC appearance in lines outgoing from the substation buses, and duration of its existence, reliability of the systems of disconnection of introductory, fider and sectional switches and terms of their diagnostics.

Scientific novelty

On the basis of regular homogeneous markovskykh processes with the discrete number of the states and a mathematical model which allows to estimate vitality of substation in the dynamic mode is continuous time got. A new analytical dependence of power supply probability of swithing off is got in the flow of time of t one of section of tires of a 6 – 10 kV substation 110/6 – 10 kV depending on frequency of the SC appearance in tires of lines outgoing from a section, reliability of the systems of disconnection of switches on substation and terms of their diagnostics.

Practical value of work

New analytical dependence got in work, and which allows to forecast vitality of knots and substation 110/6 – 10 kV, to compare the got result to the rationed level. In case that he will be more rationed 1/year, there is possibility to choose such diagnostics terms of the disconnection systems of switches, which the rationed level will be well-to-do at, that is 1/year.

Basic material

In energy under vitality of object property to resist to indignations is understood, shutting out their cascade development with mass violation of feed of users [4].

Under vitality of knot of loading we will understand ability of users and their automatic protection facilities to resist to indignations which bring him over to emergency disconnection [5].

A general formula is offered in work [6], by which it is possible to estimate vitality of concrete of grid.

                   (1)

where

r – frequency of appearance of failures, which characterizes the grid vitality (or separate its parts);

λj – parameter of the SC stream, happening in a j element;

ωi – the parameter of stream of refusals in work of protective commutation apparatus (PCA) through which got a through emergency current at SC in a j element of network and started going it current protection;

Θi – time domain between the diagnosticians of the system of the PCA disconnection, including current protection;

m – the PCA number, through which got a through emergency current and started going of them current protection;

r – number of grid or knot of loading;

n – number of the j SC elements, in which starts the i PCA going, through which got a through emergency current and started going of them current protection.

Than less Hr, that the grid vitality is higher.

In case that , formula (1) will assume an air:

              (2)

Formulas (1) and (2) just at implementation of the following terms:

                                  (3)

– time domains between SC and time domains between the exposed refusals in the system of the PCA disconnection do not conflict with the exponential functions of probability distribution with parameters and accordingly;

– duration of the PCA finding in unfound out the saying no state does not conflict with the exponential function of probability distribution;

At the conclusion of formulas (1) and (2) the following assumptions were accepted:

– the devices of relay protection (RP) can fall out only then, when they are in the mode of expectation;

– if to the moment of the SC origin in a network, which RP must react on, it was in the capable of working state, its death in the mode of alarm is improbable [7];

– the refusals in the RP chart or drive of the PCA system disconnection come to light and is removed only as a result of absolutely reliable diagnostic verifications which take place with a time domain ΘI.

Under the refusal in work of PCA we will understand such, which results in the refusal in disconnection of the damaged element of network at SC in the area of action of its relay protection [8].

Probability of exit from the r grid line-up or separate its parts:

                   (4)

if , .

For transformer substation (fig. 1) any of buses sections can be the knot of loading – I or II.

Принципиальная chart of the substation 110/6-10 кВ

Picture 1 Principle scheme of the substation 110/6 – 10 кV

Vitality of knot of loading is determined in the dynamic mode, that, when in buses outgoing from a section lines or their users by chance there are the short circuits.

We will characterize vitality of knot of loading by the parameter of stream of its emergency disconnection at SC in the area of action of current protection of the i commutation apparatus added to the proper section of buses.

For example, if the line Л1 collects electric power from a bus I (fig. 1), the bus I will lose vitality at the coincidence in space and time of two random events: – SC happened in the line Л1 and – the refusal in work of switch under a number I happened. In this case switch under the number of m+2, which provides with electric power a section I, will disconnect it by current defence and except for an user which collected electric power from a section I on the line Л1, all users which collected electric power from this buses section through the proper switches will become disconnected (i=2...m).

If to designate through Н1 vitality of buses section I, that is parameter of stream of emergency disconnections of buses section, at SC in lines, the users of which collect electric power from the buses section I, then:

,                    (5)

where

,                                                                                        (6)

λj – parameter of the SC stream, happening in a j line which joins a bus I through the proper i commutation apparatus (j=1...n ), (i=1...m );

aj – number of fixed SC, which happened in a j segment of line in times of supervision;

Т – time of supervision after the state of lines which walk away from the buses sections I and II and electrical equipment of substation.

,                                                                                        (7)

ωi – parameter of stream of refusals in work of the system of the i PCA disconnection (i=1...m );

Θi – time domains between diagnostics of the system of the i PCA disconnection;

bi – number of the damages exposed as a result of diagnostics in the system of the PCA disconnection, which would bring to the refusal of it in work at SC in the area of action of him current protections.

Vitality of the Н2 buses section II is considered a similar appearance. In this case λj – there will be the parameter of the SC stream in lines, outgoing from the proper commutation apparatus added to the section II.

Probability of emergency disconnection of buses section I during time of t it is possible to define as follows:

,                                                                     (8)

where H1 – vitality sections of I substation (parameter of stream of emergency disconnections of buses section I at SC in lines, the users of which collect electric power from this buses section).

On a similar formula (8) probability of disconnection of II substation section is determined, if H2 is known.

Example

Under the supervision during the Т=12 years there was the electrical equipment of substation 110/6 kV, which provided one of Donbass mines with electric power. Away from the first buses system 4 lines walked and from II also 4. The scheme of transformer substation is similar to the scheme (fig. 1).

Next short circuits (SC) which happened in the lines Л1 were fixed for this time, Л2,…, Л8:

1=3; a2=4; a3=2; a4=6; a5=5; a6=3; a7=1;a8=0.

The systems of PCA disconnection substation were checked (it was diagnosed) up one time in a year, that is Θ=1 year. In times of supervision 12 years the following number of damages which would bring to the refusal him over in work at SC in the area of action of it current protection was exposed:

1=5; b2=4; b3=3; b4=6; b5=0; b6=0; b7=1;b8=7.

To build tree events and scheme of minimum sections, which explains the loss of vitality of the section I and II.

To define:

1) vitality of the section I and II;

2) how vitality of buses section will change I and II, if to diagnose the system of the PCA disconnection we will be through Θ=0,5 years;

3) probability is which of that during 10 years at Θ=1 year of the section I and II will lose vitality.

Decision. Using basic data of example of formula (6), (7) we find the following parameters of the SC streams in lines and in the system of the PCA disconnection:

а) for the buses of lines outgoing from a section:

λ1=0,25 1/year; λ2=0,33 1/year; λ3=0,17 1/year; λ4=0,5 1/year; λ5=0,42 1/year; λ6=0,25 1/year; λ7=0,08 1/year;λ8=0.

б) for the system of the PCA disconnection:

ω1=0,42 1/year; ω2=0,33 1/year; ω3=0,25 1/year; ω4=0,5 1/year; ω5=0; ω6=0; ω7=0,08 1/year; ω8=0,58 1/year;

Analysing the results of supervisions (Т=12 years) fixed in operative magazines after the SC appearances in the I and II lines outgoing from a section, exposed and removed in the PCA refusals in the disconnection system, which would bring to the refusal them over in work, at the casual appearance SC in the area of action of them current protections - we build «trees» and schemes of minimum sections which allow to account for the loss of vitality of knots of loading (section I and II) of substation 110/6 kV [9].

We will designate through – event, SC happened in a j line; – event, the refusal in the system of the i PCA disconnection happened.

Each of events and is characterized by the parameters of the SC stream – λj and parameter of stream of refusals in the system of the PCA disconnection – ωi.

Tree of events, which explains the loss of vitality of the section I and II has the appearance of fig. 2 a,c.

Using a fig. 2 a,c in we build the schemes of minimum sections of fig. 2 b,d.

Using a formula (1), values of parameters λj and ωi, got by formulas (2) and (3) and schemes of minimum sections of fig. 2 b, d we find:

If to conduct diagnostics of the system of the PCA disconnection through Θ=0,5 years, then:

«Tree» events and chart of minimum sections
«Tree» events and chart of minimum сечений

Picture 2 - Tree events and scheme of minimum section
а) an event happened – SC in the line Лj (j=1...4 ) and – said no in the PCA work (i=1...4 ); b) scheme of minimum sections, made for estimation of vitality of the section I;
c) an event happened – SC in the lines Л7, j=7 and event – said no in the PCA, i=7 work; d) scheme of minimum sections, made for estimation of vitality of the section II.

We will define in how many times will be multiplied vitality of buses sections I and II at diminishment of diagnostics terms of the disconnection system of commutation apparatus with Θ=1 year on Θ=0,5 years.

Probability of that during t=10 years at Θ=1 year of section of I and II substation will lose vitality it is possible to estimate by a formula (8):

Conclusions

1. For determination of the most exact estimation of vitality of knots of loading of substation 110/6 – 10 kV, by the electrical equipment it follows to conduct the supervision not after the groups of the same types elements, and concrete after every it unit. Than anymore time of supervision after the equipment of substation, the more precisely value of vitality of knot of loading.

2. By work of electrical substation equipment it follows to begin the supervision from the moment of its starting in exploitation to the moment of utilization.

3. Supervision during the T=12 years after the electrical equipment of substation 110/6 kV, which provides a coal mine with electric power, it is set that vitality of buses sections:H1=0,108 1/year, and H2=2,56*10-3 1/year.

4. It is shown that change of diagnostics term of the system of PCA disconnection 6 kV with Θ=1 year to Θ=0,5 years allows to multiply vitality of section I and II in 4 times.

5. Probability is certain of that during the t=10 years of section I and II substations will lose vitality: F1(10)=0,66, and F2(10)=2,56*10-3.

At writing of this abstract master's degree work is not yet completed. Final completion: December, 2012. Complete text of work and materials on a theme can be got at an author or his leader after the indicated date.

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