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SUMMARY

Content

1. The urgency of the problem

Having analysed the statistics from 1985 to 2012 about failure of transformer substations 110/10 kV which are exploited in the Donbass power supply system, it found out that in most cases substations fail for the next reasons:

  1. Casual appearance of short circuit (SC) on the departing line, the failure of switch operation of Complete distributive device (CDD), the failure of lead-in switch operation 10 kV, through which were passed by thru abnormal current, and lead-in switch 110 kV isn't sensitive to SC which casually appears on the departing line;
  2. Casual appearance of SC in accessions to bus bar feeding CDD; the failure of lead-in switch operation 10 kV, the failure of lead-in switch operation 110 kV through which were passed by thru abnormal current, and the maximal current protection (MCP) of the switching device on lines 110 kV isn't sensitive to SC which casually appears in accessions to bus bar feeding CDD;
  3. Casual appearance of SC in the transformer 110/10 kV; the failure of lead-in switch operation 110 kV, the failure of MCP of the switching device on lines 110 kV, through which were passed by thru abnormal current.

The task consists in what is the necessary time to perform diagnostics of the system of disconnection of protective switching devices, that probability of coincidence in space and time of three casual events would be improbable value, i.e.

If this condition is followed the ignitions of the isolation won't be on substation

2. The aim of the work

In terms of a fire safety to define optimum of diagnostics of the systems of disconnection of protective switching devices of transformer substation. For this purpose it is necessary to solve the next problems:

  1. To receive the dependences of probability of failure during time of t of substation 110/10 kV from frequency of appearance of SC on the departing line, in accessions to bus bar 10 kV or in the transformer of substation, reliability of the systems of disconnection of lead-in switches 10 kV and 110 kV and terms of their diagnostics;
  2. To define average time before the first transformer substation failure and time dispersion between the failures.

3. Scientific novelty of the work

On the base of regular homogeneous markovsky processes with discrete number of conditions and continuous time the mathematical model explaining the process of transformer substation 110/10 kV failure during time of t was developed , differing from known for taking into account not only frequency of appearance of dangerous events, but also their duration.

4. Practical value of the work

The technique of calculations with which help it is possible to define in terms of a safety terms optimum of diagnostics of the system of disconnection of switching devices was developed, which provide the minor probability of isolation ignition on transformer substation.

5. The review of normative documents in the area of a fire safety

According to [1] the probability of fires in load center during the year shouldn't be higher, than H = 1·10-6. It means, That if N = 1000000 transformer substations were under supervision during the year the one fire (n = 1) for this period of time would be supposed.

The probability of fires during the year at H·t < 0.1 can be defined due to formula:

It means, it is necessary to receive dependence for the decision of a question of maintenance of a fire safety of transformer substations during their operation: probabilities of isolation ignition on substation during the year against the frequency of appearance of SC on a departing line, in accessions to bus bar 10 kV or in the transformer and duration of its existence, reliability of system of disconnection of lead-in switch 10 kV and 110 kV, and also periods of time between diagnostics of systems of disconnections of switches θ1, θ2 and θ3 (fig. 1).

Scheme of power supply of transformer substation 110/10 kV

Figure 1 – Scheme of power supply of transformer substation 110/10 kV

Due to the received dependence it will be possible to choose such periods of time between diagnostics of systems of disconnection of the switches θ1, θ2 and θ3, when the probability of fires will be admissible according to normative documents [1].

6. Development of the mathematical model describing processes of transformer substation failure

Let's enter some concepts. Under the Safe we will understand such condition of system of disconnection of the switch when at any moment it is ready to disconnect SC which appeared in an area of coverage of its relay protection, and Dangerous – in time of apperaring the SC on the protected element failure occurs in the system operation of the protective switching device. A dangerous condition of system of disconnection emerges as a result of its diagnostics: relay protection, drive of the switch, contact system, chamber of arc extinction etc.

Let's assign with ζk(t) the process of change of a condition of an element (SC, failure of the basic protection, failure of reserve protection), k = 1, 2, 3. Casual process ζ1(t), ζ2(t) of change of a condition of switching devices 1, 2 (2, 3; 3, 4) eventually can accept two values: 0 – the system of disconnection of the switch is in an efficient condition; 1 – the system of shutdown is in the refused condition. Casual period of time between apperances SC on a departing line, in accessions to bus bar 10 kV or in the transformer and duration of its existence we will characterize by the process ζ3(t).

The probability of transitions from a safe condition to dangerous for a period Δt is equal λkΔt+0(t), where 0(t) means, that probability of appearance more than one dangerous condition in the period of time t+Δt is improbable value in comparison with Δt. Probability of transitions from a dangerous condition in the safe during the time Δt is equal μkΔt+0(t). The parameter λk characterizes intensity or speed of replacement safe periods of time by dangerous, and μk – frequence or speed of replacement dangerous periods of time by safe [2].

Substation failure (isolation ignition) will come at the moment, when all three processes ζk(t) will be in a condition 1, i.e. when ζ1(t)=ζ2(t)=ζ3(t)=1.

Casual time to the first fire we will assign with τ(0). Let's express value of average time to the first fire by parameters of processes θ1, θ2 and θ3.

The complex of the specified processes we will consider as regular homogeneous markovsky process with eight discrete conditions and continuous time. The behavior in time of such system is defined entirely by a matrix of transitions of P which in our case looks like:

Average time before the first transformer substation failure we will assess from system of the equations [3]:

where N=1-Q, Q - fundamental matrix, which turns out from a matrix of transitions due to exception of the absorbing condition (last line and last column).

Probability of isolation ignition of transformer substation during the time of t we will find using the general system of the equations for regular homogeneous discrete markovsky process with the absorbing condition and continuous time [5]:

where – row-vector; – row-vector; , I – singular matrix.

Time dispersion before the first isolation ignition of transformer substation [4], i.e. before the first transition to the absorbing condition:

where .

7. Assessment of a fire safety of transformer substations and development of the recommendations for its improvement

Fire safety of transformer substations must be provided at level of requirements of GOST 12.1.004.91 [4]. For the scheme (fig. 1), we will represent the tree of formation of a fire of substation (fig. 2) and the scheme of the minimum sections (fig. 3).

The tree of formation of the events, which coincidence leads to isolation ignition (fire) and to substation failure

Figure 2 – The tree of formation of the events, which coincidence leads to isolation ignition (fire) and to substation failure

where – SC happened; – the failure of system of disconnection switch with number i happened.

the scheme of the minimum sections

Figure 3 – The scheme of the minimum sections

Conclusion

Received in M.Eng's work the calculation formula and schemes of the minimum sections allow to estimate fire safety of transformer substation of any class of voltage and to choose optimum in terms of safety the diagnostics of systems of disconnection of protective switching devices.

The list of sources

  1. Ковалев А.П. Оценка пожарной безопасности передвижных трансформаторных подстанций 110/35/6 кВ / А.П. Ковалев, А.В. Шевченко, И.В. Белоусенко // Промышленная энергетика. – 1991. – №6. – С. 28-31.
  2. Тихонов В.И. Марковские процессы / В.И. Тихонов, М.А. Миронов. – М.: Советское радио, 1977. – 488 с.
  3. Кемени Дж. Конечные цепи Маркова / Дж. Кемени, Дж. Сиел – М.: Наука, 1970. – 272 с.
  4. ГОСТ 12.1.004-91 ССБТ. Пожарная безопасность. Общие требования. – М.: Изд-во стандартов, 1991.
  5. Гнеденко Б.В. Математические методы в теории надежности / Б.В. Гнеденко, Ю.К. Беляев, А.Д. Соловьев – М.: Наука, 1965. – 524 с.
  6. Кельберт М.Я. Вероятность и статистика в примерах и задачах. Том 2. Марковские цепи как отправная точка теории случайных процессов и их приложения / М.Я. Кельберт, Ю.М. Сухов – М.: МЦНМО, 2009. – 586 с.
  7. Чжун Кай-лай Однородные цепи Маркова / Чжун Кай-лай Перев. с англ. – М.: Мир, 1964. – 426 с.
  8. Ковалев А.П. О проблемах оценки безопасности электротехнических объектов / А.П. Ковалев // Электричество. – 1991. – № 8. – С. 50-55.
  9. Лобанова И.С. Оценка пожарной безопасности передвижных подстанций – Автореферат [Электронный ресурс]. – Режим доступа: http://masters.donntu.ru/2008....