The plan

1. Introduction

2. Ungency of the problem

3. Equivalent circuit and the accepted assumptions

4. System of the equations

5. Òíå basik results

6. Conclusions

Introduction

This year I was luckly to me has had the luck to visit the all Ukrainian student's scientific and technical conference « Electrotechnical and electromechanical systems », which was held in Sevas-topol from April, 2 till April, 5, 2007. I represented the report on the theme master works « Model-ling of controlled magnetic circuit ». In spite of the fact that this material is more valuable to Don-bass, rather than for Crimea (having visited there for the first time, I paid attention that tourism and shipbuilding, rather than the coal-mining industry here are more advanced), all teachers and profes-sors unanimously recognized its actual and so interesting, that they gave me the diploma of the first degree!

Ungency of the problem

My theme master works is modelling controlled magnetic circuit. It is always actual; in fact there is nothing more important, than human life. The matter is that for last 10 years on minesof Donbass the quantity of accidents has essentially increased as a result of defeat by electric current at a casual touch to the current carrying parts which are taken place energized. Now one of the basic means on maintenance of safe operation of the electric equipment devices of the control of isolation and the protective switching-off, containing a throttle for automatic indemnification of a capacitor component of the ground outflow current. Moreover, inductance of such throttle is adjusted by magnetizing by the direct current [1] depending on length of a cable network (and, hence, from its capacity in relation to the ground). Experts say that presence of inductance in one circuit with ca-pacities of cables can represent potential danger of emergencies [2] are known. Besides «the expe-diency of application of nonlinear inductance for indemnification of currents of outflow now analytically is not proved» [3].

Such point of view has the right to existence from the following reasons:

1. Nonlinear inductance is a source of the maximum harmonics that reduces its compensating properties.

2. On any of the maximum harmonics the consecutive resonance is possible.

Equivalent circuit and the accepted assumptions

My problem is the research of management circuit influence on properties of a throttle. In the figure its circuit is given [1].

Image 1 - The figure of a throttle

It contains the Ø-shaped ferromagnetic core on which extreme cores working windings w are located, included consistently and in the same direction. Basic magnetic streams Ô₁ and Ô₂ become isolated accoding to them. On an average core is located management of the winding w_ó, the winding of the feedback w_îñ, and becomes isolated a stream magnetizing Ô₀. Working windings w extreme cores receive supply from the source of sine wave voltage. The winding of the feedback w_oc is supplys the straightened current, and the winding of management wó has the independent power supply.

Let's accept the following assumptions:

1. Let's not take into account streams of dispersion of cores as they do not worsen harmonious structure of the current.

2. And also neglect influence of working windings on the winding management current.

System of the equations

The magnetic circuit is described by system of the nonlinear equations connecting the sum of streams in one unit on first law Êirhgofa. And also the sum of magnetic voltage and magnetized forces, according to the full current law:
    
        Ô₁ + Ô₀ = Ô₂ ;

        H(B₁)• l₁ + H(B₂)• l₂ + (B₁• δ₁+ B₂• δ₂) / μ₀ = 2•i•w ;                        

        H(B₀)• l₀ + H(B₂)• l₂ + (B₀• δ₀+ B₂• δ₂) / μ₀=•|i|•w_oc + F₀ + i•w ;

where H – magnetic field intensity;
                      B_k = Ô_k / S_k – induction in magnetiz cores (ê =0, 1, 2);
                      l_k, S_k – length of the average line and section of magnetiz cores;
                      δ_k – length of air backlashes cores;
                      i – instant value of a current of working windings;
                      F₀ = i_y • w_y – magnetized force of management of the winding;
                      H(B) – an approximated curve magnetization.
    Voltage of working windings of the throttle is connected to the power supply the following equation:

w •d(Ô₁ + Ô2) / dt – i•(2•r + r_oc) = Uì • sin(ωt+ψ),                                                 

    where r, r_oc – active resistance of working windings and windings of the feedback;

U_m , ψ – amplitude and the initial phase of the having voltage.

Òíå basik results

Results of modelling are submitted as wave diagram magnetic induction three cores, and of working windings.

Ðèñóíîê 1 - Oscillograms of current i (t), induction of working cores B₀(t), B₁(t), B₂(t),
at constant magnetizing F₀ = 15 À.
(L/L_max=0,78; I_d = 55 ìÀ;I₍₁₎/_d= 99,76%; I₍₃₎/_d = 6,94%).

Ðèñóíîê 2 - Oscillograms of current i (t), induction of working cores B₀(t), B₁(t), B₂(t),
at constant magnetizing F₀ = 30 À.
(L/L_max=0,53; I_d = 82 ìÀ;I₍₁₎/_d= 99,33%; I₍₃₎/_d = 11,3%).

Conclusions

We’ve received mathematical model of the controlled nonlinear throttle for indemnifica-tion of capacitor source currents. It has been established, that the throttle is practically sine wave and the maximum harmonics do not influence its compensating and adjusting properties.

Thus « the expediency of nonlinear inductance application for indemnification of the ca-pacitor component of flow away currents » has been analytically proved.

THE LITERATURE

1. The directory power of a colliery: In 2ò. / V.S.Dzjuban, etc. – Donetsk: Open Company « the Southeast, Ltd. » 2001. Ò 1.: – 447 with.

2. Tsapenko E. F. Resonant an overstrain(overvoltage) in mine networks at indemnification of cur-rents of outflow on the ground. Industrial power. 1998, ¹ 10.

3. Tsapenko E.F., Mirskij M.I., Ñóõàðåâ O.K.Gornaja electrotechnic. Tsapenko E.F.: the Text-book for technical schools. – M.: Bowels, 1986.437 with.