Faculty: Electrical Engineering
Speciality: Industrial Companies and Cities Electric Supply
Introduction
The main element of mine low voltage (up to 1000) system of the electricity supply is transformer substations. The main element of the sub-station is its windings. Failure of the transformer insulation occurs when the conductors of coils are failed (Coiled-circuit). In places with weak isolation is overheating, which leads eventually to the breakdown of isolation if the thermal protection will not give a signal to disable the substation. Consequently, the failure of the transformer substation is at the coincidence in time and space of two random events: the overheating of the transformer coils and insulation failure in the triggering of thermal protection. Consequently, the reliability of the transformer depends on the reliability of its thermal protection.
Winding transformer can fail while in the following modes: static, which is close to the nominal (in this mode, winding of the transformer fails, it is the breakdown because of the aging of insulation), repair, due to staff errors, dynamic, when unacceptable overloading of the transformer windings, and thermal protection is in the crashed state.
Failure of the transformer in the dynamic mode occurs at the coincidence in time and space of two casual events: the overload of the transformer and the refusal of the triggering of thermal protection.
The system of "winding of the transformer - thermal protection" account as the Markov process χ(t) with 4 discrete status and continuous time. The system for time t can be in one of the following states:
е1(0,0)
- winding of the transformer has permissible temperature, thermal protection is in working condition;
е2(1,0) - winding of the transformer is unacceptable under the terms of operation of the heating temperature, thermal protection is in working condition;
е3(0,1) - winding of the transformer is permissible temperature, thermal protection is in the crashed state;
е4(1,1) - winding of the transformer has unacceptable temperature of heating for the work, thermal protection is in the crashed state.
Denoting Рii(Δt) the probability that the system for a small time interval Δt remain in the status еi i = 1,4 and by Рij(Δt) - the probability that the system during Δt move from state to state ei еj , j = 1,4, j ≠ i.
These transition probabilities are defined as follows [14]:
The probability of finding the system «winding of the transformer - thermal protection» in each of the 4 possible states can be found from the following system of equations:
In the formula (2.1) the value of aij takes into account with accuracy up to the second order that during Δt will transition from state ei to state ej, and in formula (2.2) value (1 – aii) allows up to the second-order terms, that during Δt does not happen transition from state еi in any other state, process will remain in a state of еi.
where d1 - the average time interval between occurrences of overload of the transformer windings;
where d1 - the average existence of the overload of the transformer;
where d2 - the average time between failures of the thermal protection;
where d2 - average duration of finding the thermal protection in crashed undetected condition.
The system of linear differential equations (2.3) is solved with initial conditions Р1(0) = 1, Р2(0) = 0, Р3(0) = 0, Р4(0) = 0.
Applying to the system of equations (2.3) direct Laplace transform [1] and taking to account the initial conditions, we obtain:
From the system of equations (2.8) we find P1(s), P2(s), P3(s) and substituting them into (2.9) we find the function of the probability of failure of the transformer winding during time t:
Then
We proceed from the image (2.10) to the original, using the technique [12], we obtain:
where sk,к = 1,2,3 - the roots of the cubic equation
average time before the first breakdown of isolation winding transformer τ1, and the dispersion D1 is found from the equation [12]:
Using (2.12) (2.13) (2.14), we find:
If the state of thermal protection is controlling through the time interval 0 and verification considered absolutely reliable, the average time of protection being in crashed undetected condition can be found from the expression [2]:
In case if d1>d1, d2>d2, Θ2/d2 < 0,1 and runs the condition
then the probability of failure of the transformer winding during time t can be determined using the formula:
where
In this case, the time until the first breakdown of isolation transformer τ1, is inversely proportional to H:
What fallows from the formulas (2.20) and (2.21) that
The above formula can be used to determine the average time until the first breakdown of isolation transformer winding τ1, and dispersion D1, the determines of the average time location of defense in crashed undetected condition, as well as for finding the uptime of the transformer winding during the time t.
A topical issue: addressing challenges connected with forecasting the reliability of the transformer windings and prevent such events as inflammation of its isolation will extend the life of local stations, which operate in areas of coal mines.
The scientific value of the work: to improve the reliability of explosion of transformer substations. As a result of this work received a new dependence of the probability of failure of the transformer during the year on the frequency and duration of its congestion, reliability, thermal protection and the period of its diagnosis.
The practical significance of the work: is to develop methods of calculation to measure the reliability of the thermal protection of the substation. The method of assessing the reliability of transformer windings, which allows predict the failure of the transformer substation, proposed and justified solution to increase its reliability.
A review of research on the topic: there are published articles: "Assessing the reliability of the transformer in the dynamic mode in the scientist works of DonNTU - Electrotechnic and energy (2008, №8), and" Justification of recommendations to improve the reliability of thermal protection flameproof transformer substations in the scientist works of DonNTU - Electrotechnic and energy (2007, №7).
The question of improving reliability of the mine explosion-proof transformer substations with more than 1000 kVA nowhere else seen.
The main results of executed work are:
1. Provided review and analysis of explosion-proof transformer substations, used in Ukrainian mines.
2. A mathematical model to determine the reliability of the transformer in the dynamic mode is built.
3. A quantitative assessment of the reliability of the transformer in the dynamic mode is given.
4. is developed and quantify the technical solution to improve the reliability of thermal protection of the transformer substation TSVP-X / 6.
5. It is advised a principle new scheme for thermal protection of the transformer substation TSVP-X / 6.
6. It is found that the failure of the transformer explosion-proof transformer station TSVP-X / 6 occur when combining in time and space for at least three random events with different frequency and duration of existence.
7. A mathematical model that can explain the process of failure of the transformer explosion-proof transformer station TSVP-X / 6, with its operation is advised. Dependence of the probability of failure of transformer windings on the frequency and duration of protection in crashed undetected condition are given.
8. It is given a quantitative assessment of the reliability of the winding of the transformer substation, it is found the time before the first failure of the winding, the probability of failure of the transformer substation and the probability of it out of commission for a time t = 8760 hours (1 year).
Conclusion
In this work is given a solution of the actual mechanical industries of Ukraine scientific challenge consisting of the development technical solutions to improve the reliability of thermal protection flameproof transformer substation. To adopt the technical solutions it is developed a mathematical model that describes the process of failure of the transformer during operation of the transformer substation.
At the time of this writing, work is not finished. The final version of the work can be obtained from me or my scientific adviser after December 2010.
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