Issue. The term “object survivability” in power engineering is concerned as a property of system to resist disturbances and forbid its cascade evolution and total consumer power interruption [1].

There are so called open-chain failures at short circuits (SC) in the electrical network nodes and at protection switching units (PSU) malfunctions when through current [2]. There were 75 such open-chain failures in 25 local electrical systems and in 2 united power grids for the period of 5 years in USSR. In 81% of cases failures were occurred as a result of network damages and PSU malfunctions [3-4]. 99% of consumer supply damnification is related with it [4].

Let’s interpret survivability of substation as the property of its input and feeder PSU and other automatic protection facilities to resist disturbances (external and internal SC) which may cause substation failure.

Among strong requirements at substation reconstruction there must be survivability increase over the basic (initial) level.

For this purpose it is necessary to develop simple and understandable for engineers design procedures to define survivability. Therefore, new mathematical models and design procedures development are issue of scientific and practical problem.

The object of master work consists in definition of survival characteristics main parameters.

For this purpose it is necessary to solve the following problems:

- Mathematical model development to estimate substation survivability (substation failure temporal probability, average time period of earliest substation failure, time dispersion of earliest substation failure).

- Development of “trees” and minimal cross-section scheme to define substation survivability.

•- Survivability evaluation of substation “Tsentralnaya” 330/110/35 kV.

Scientific novelty. New dependence of substation survivability loss during time t from the frequency of SC appearance at PSU range, PSU reliability and test terms was obtained.

Practical value of work. Design procedure to estimate substation survivability and choose most effective substation alternative design taking into account its survivability and reduced costs is being worked out.

In the first part of the work there is existing substation scheme 330/110/35 kV (applied in Ukraine) with its description of advantages and disadvantages, operating regimes at transformer and bus-tie circuit-breaker maintenance, etc. Also shown reconstructed substation scheme with more reliable circuit-breakers and PSU. Possible operating regimes are described too. There was chosen basic design of substation for survivability estimation.

The second part of work is devoted to the mathematical model development for estimation of substation survivability. At mathematical model working up several assumptions were accepted: probable PSU malfunction at standby; at SC appearances in operative relay protection system (RPS) range its failure improbable [5, 6].

RPS failures and circuit-breaker’s drives are discovered and eliminated only as a result of absolutely reliable testing. Under PSU failure is concerned cutoff failure of damage network element at SC in RPS range [7].

As survivability index could be accepted frequency of substation damage at SC over output transmission lines. For this purpose following formula can be used [8]:

where τ₁ – average time period before substation failure.

Formula (1) is true at following conditions: time intervals between SCs over transmission lines and time intervals between PSU failures do not contradict to exponential functions of probability distribution with parameters correspondingly λ_i, λ_s.i, λ_o.j.

If following case is true:

Formula (1) could be presented as:

where m – number of PSU under through current;
                         n – number of malfunction circuit-breaker cut-off cause substation failure at SC at output transmission line;
                         λ_k – index of failure flow as SCs transmission lines;

where r – numder of output transmission line;
                         l – total output transmission line length;
                         λ_s.i – index of failure flow at PSU malfunctions;
                         θ_i – time period of circuit-breakers relation system;
                         λ_o.j – index of breakdown failure flow ;
                         θ_j – time period between test terms of circuit-breakers cutoff system;

If case (2) is false than average time before substation fault could be determined from [9]:

where
                         r – number of cases promote substation fault;
                         N=(I-Q) – fundamental matrix;
                         I – unit matrix;
                         Q – result from traffic matrix P exclusion of last row and column;
                         ξ – вcolumn vector with all elements equals 1.

Probability of substation fault during time period t could be found from solving of linear differential equation system like [9]:

where – row vector;
                          – row vector;
                         A=(P-I);
                         I – unit matrix.

Equation system (5) could be solved at initial condition:

Р₁(0)=1, Р₂(0)=Р₃(0)=…=Р_2^r(0)=0.

Time interval distribution function between substation faults at time period t could be defined from equation (5):

F₁(t)= Р_2^r(t).

Time dispersion before earliest substation fault [9]:

D=(2N-I)τ-C,                                                                        (6)

where – column vector;
                         – column vector.

In the case when following condition is true:

So, substation fault probability during time period t could be determined with:

Knowing F_i(t) or H_i it is able choose most effective substation scheme taking into account its survivability and reduced costs З_i with a help of efficient factor:

where Н₁ – substation survivability of first variant;
                         З₁ – calculated costs over first variant;
                         Н₂ – substation survivability of second variant;
                         З₂ – calculated costs over second variant.

In the case when cost of circuit-breaker equals equal (10%) cost of two disconnectors efficient factor will be:

where N₁ – number of circuit-breakers in substation scheme of first variant;
                         n₁ – number of disconnectors in substation scheme of first variant;
                         N₂ – number of circuit-breakers in substation scheme of second variant;
                         n₂ – number of disconnectors in substation scheme of second variant.

Using procedure below it was evaluated the scheme of existing substation “Tsentralnaya” 330/110/35 kV and its scheme after reconstruction.

CONCLUSIONS:

1. Were developed mathematical models, obtained formulas to choose most effective scheme of substation taking into account its survivability and reduced costs.

2. Was presented calculation sample of reconstructing substation scheme survivability evaluation. Being chosen most effective its structrure.

REFERENCE:

1. Надежность систем энергетики. Терминология. – М.: Наука, 1980, вып. 95.

2. Китушин В. Г. Определение характеристик отказов системы при цепочечном развитии аварий. – Изв. АН СССР. Энергетика и транспорт 1977, №3.

3. Гук Ю. Б. Теория надежности в электроэнергетике: Учеб. пособие для вузов. – Л.: Энергоатомиздат, 1990.

4. Гук Ю. Б. Анализ надежности электроэнергетических установок. – М.–Л.: Энергоатомиздат. Ленингр. отд-ние, 1998.

5. Фабрикант В. П. О применении теории надежности к оценке устройств релейной защиты. – Электричество, 1965, №9.

6. О расчете надежности систем электроснабжения газовых промыслов / И. В. Белоусенко, М. С. Ершов, А. П. Ковалев и др. – Электричество, 2004, №3.

7. Эндрени Дж. Моделирование при расчетах надежности в электроэнергетических системах. Пер. с англ./ Под ред. Ю. И. Руденко. – М.: Энергоатомиздат, 1983.

8. Гнеденко Б. В. Курс теории вероятности. – изд. Наука. Главная редакция физико-математической литературы, Москва, 1969, с.400

9. Ковалев А. П. О проблемах безопасности технологических объектов топливно-энергетического комплекса Украины. Наукові праці Донецького національного технічного університету. Серія «Електротехніка і енергетика», випуск 79: Донецьк: ДонНТУ, 2004. – с.111 – 118.

10. Руденко Ю. Н., Ушаков И. А. Надежность систем энергетики. – М.: Наука, 1986.

11. Ермилов А. А. Основы электроснабжения промышленных предприятий. 3-е изд., перераб. и доп. – М.: Энергия, 1976.

12. Розанов М. Н. Надежность электроэнергетических систем – М.: Энергоатомиздат, 1984.

13. Ковалев А. П., Чурсинов В. И., Якимишина В. В. Оценка вероятности появлений цепочечных аварий в энергосистемах. – Вестник Кременчугского гос. политехн. ун-та, 2004, вып. 3/2004(26).

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