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Abstract

Content

Theme urgency

Over the last 10 years in Ukraine there were 528833 fires, from them 410562 fires in objects of inhabited sector. As a result of fires 36529 people were lost, from them 1176 children, the damage made 7,8 mlrd. grn [1].

All reasons of fires share on three main groups: natural, social, technogenic. The technogenic reasons of fires make about 40 %, them treat malfunction in electric networks and electrodevices. The fires caused by the electrotechnical reasons, average 22 % all fires in the world. In Ukraine in 2010 the fires caused by the electrotechnical reasons, made about 45 %, and across Donetsk region in 2009 about 25 %. The fires caused by the electrotechnical reasons, are distributed as follows: 62 % - ignitions of isolation of low-voltage electric networks, tension to 1 кV (LVEN); 10% - ignitions in electric heaters; 6 % - ignitions in introduction electric guards; 5 % - ignitions in household to electric equipment; 5 % - ignitions from not disconnected (vygorayemy) short circuits (sc); 12 % - the ignitions connected with other reasons (leakages of a current on the earth etc.) [2].

The analysis of networks of 0,4 kV of the industrial enterprises showed that isolation ignition in electric networks occurs generally at KZ in the protected element of a network and refusal of operations the next to a place of damage of switching devices through which passed a through emergency current and led in action their those protection [3].

Therefore, the works connected with forecasting and development of organizational and technical actions for prevention of ignitions isolation of LVEN of the objects connected with activity of the person, from emergence of SC, transitional resistance (TR) or sincere in the electric contact connections (ECC), are very actual tasks

Purpose of work

To define optimum, from the point of view of fire safety, terms of diagnostics of systems of shutdown of protective switching devices electric network, tension of 0,4 kV.

For achievement of a goal it is necessary:

  1. On the basis of regular, homogeneous markovsky processes with discrete number of conditions and continuous time to develop mathematical model, explaining process of ignition of isolation of protected conducting of 0,4 kV from casual emergence of OZ or SC, or weakened and dangerously scintillating power contact connection.
  2. To receive analytical dependences of probability of ignition of isolation during t time: from frequency of emergence of OZ or SC, or weakened ECC in a network; duration of their existence; from reliability of means of protection and terms of their diagnostics.
  3. To choose optimum rather fire safety terms of diagnostics of means of protection.
  4. To give an example calculations.

Question condition

The LVEN protective and switching devices existing today don't react to such emergency operation, as formation of PS or sincere in ESS that leads to ignition of isolation of LVEN, and it, in turn, leads to fires on the objects connected with activity of the person. In works [4], [5] technical solutions by means of which it is possible to protect are offered LVEN at formation of PS or sincere in the ESS. However, analysis of this development showed need of creation of devices more reliable, functional, small-sized and accepted concerning the price spark protection (PSP), and also organizational and technical actions for prevention of ignition of isolation to electric conducting at the weakened and dangerously sparking power contact connections.

Results of researches

Today the probability of emergence of ignition of isolation of LVEN in a year in Ukraine exceeds in 712 times size normalized GOST 12.1.004-91 in which it is said that the probability of fires in loading knot within a year shouldn't exceed size 1·10-6 [6].

Isolation ignition in low-voltage networks can occur at coincidence in space and time of two casual events: there was a damage to a protected network (either OZ, or SC, or NZ); there was a refusal in operation of appropriate means of protection.

Let ζ1(t) - casual regular homogeneous markovsky process which describes changes in time of a condition of a low-voltage electric network. Let's designate through «0» - in a network there are no damages which can lead to damage of isolation of the conductor, and through«1» - in a network there was a source, the capacity and which duration is capable to set fire to electric equipment isolation. Through ζ2(t) let's designate casual regular homogeneous markovsky process, which describes changes of a condition of the protective switching device. Let's designate through «0» - efficient condition of means of protection, and through «1» - the refused condition of protection.

Isolation ignition in a network will occur at the moment of a meeting of processes ζ1(t) and ζ2(t) in a condition «1», i.e. ζ1(t)=ζ2(t)=1.

Set of processes ζ1(t) and ζ2(t) let's consider as one regular homogeneous markovsky process of E (t) with four discrete conditions and continuous time.

The system can be at any moment in one of a set of conditions , where
е1(0,0) - in a network there are no damages which can lead to OZ, SC, weakened the LVEN; means of protection are in an efficient condition;
е2(1,0) - in a network there was OZ damage, or KZ, or the weakened ECC means of protection are in an efficient condition;
е3(0,1) - in a network there are no damages which can lead to OZ, SC, weakened the ECC; means of protection are in the refused condition;
е4(1,1) - in a network there was OZ damage, either SC, or the weakened ECC; means of protection are in the refused condition.

At casual hit of system in a condition е4(1,1) there is an isolation ignition that can lead to a fire in a place of damage of isolation. Parameters of processes ζ1(t) and ζ2(t) let's designate through λ1, μ1; λ2, μ2 respectively, where
 - average interval of time between emergence of dangerous damage of a network;
 - average duration of existence of a dangerous source;
 - average interval of time between refusals of means of protection;
 - average duration of finding of means of protection in the undetected refused condition.

Probability of ignition of isolation during t time because of damages to a network and refusals in operation of means of protection:

Probabilities P1(t), P2(t), P3(t), findings of system in each of possible conditions е1(0,0), е2(1,0), е3(0,1) we find from system of the linear differential equations of a look:

The system of the equations (2) decides under entry conditions P1(0)=1, P2(0)=0, P3(0)=0.

From system of the equations we find P1(t), P2(t), P3(t) by numerical method and the received values it is substituted in a formula (1).

Average time before isolation ignition if the system is in one of conditions: е1(0,0), е2(1,0), е3(0,1) because of damage, accompanied either OZ, or SC, or ECC and refusal in operation of the corresponding protection, we will receive:

From system (3) we find:

Time dispersion before ignition of isolation of the conductor of LVEN provided that during the initial moment of time the system was in one of conditions: е1(0,0), е2(1,0), е3(0,1), let's find from system of the linear algebraic equations:

where

From system of the linear algebraic equations (7) we find:

Systems of the equations (2), (3) and (7) completely characterize fire-dangerous knot. If as a result of calculations we will receive thatτ1=σ1, then it is possible to determine probability of ignition of isolation of LVEN by a formula:

In that case, when λ1«μ1 and λ2«μ2, and then, using a formula (4), we find intensity of ignition of isolation of the conductor of LVEN:

where

 – average interval of time between emergence or SC, either TR, or sincere in ECC protected LVEN;

 – average time of existence or SC, either TR, or sincere in ECC protected LVEN;

 – average interval of time between refusals or SC, or IZ, or PSP;

 – average time of finding of system of shutdown of the switching device in an undetected condition.

If time intervals between carrying out diagnostics of a condition ECC are set (Θ1), then intensity of restoration μ1 it is possible to define, on a formula:

If λ1Θ1<0,1, then the formula (11) will become:

If time intervals between diagnostics are set Θ2 protective switching device, that is similarly calculated and μ2, i.e.:

If λ2Θ2<0,1, then the formula (11) will become:

If λ1<<μ2 and λ2<<μ1, then:

Example

To estimate fire safety of LVEN of 0,4 kV (fig. 1):

The scheme of the protected knot of loading

Figure 1 – The Scheme of the protected knot of loading

Let's designate the following events:

 – there was SC in a protected network;

 – there was a leakage of a current on the earth in a network;

 – there was a weakened and dangerously sparking power contact;

 – there was a refusal in operation (MZ);

 – there was a refusal in operation (RU);

 – there was a refusal in operation (PSP).

We build "tree" of events which explains emergence of ignition of isolation in low-voltage networks because of their various damages:

Animation: 8 shots, 5 repetitions, duration of each shot - 120 ms, 54,8 KB

Figure 2 - The "Tree" of events explaining process of ignition of isolation in LVEN

the Scheme of the minimum sections

Figure 3 – The Scheme of the minimum sections

Using the formula (15) received above, we find:

In view of that means of protection 4, 5 and 6 (fig. 1) are in one case, then:

Let's write down a formula (15) in the following look:

Knowing basic data: x1, x2, x3, y4, y5, y6, and Θ2 , it is possible to define probability of ignition of isolation during t time as follows:

Conclusions

The settlement formula received in a master's thesis and schemes of the minimum sections allow to estimate fire an electric network, as tension of 0,4 kV and to choose optimum from the point of view of safety terms of diagnostics of systems of shutdown of the protective switching devices.

List of references

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