CONTENTS

ABSTRACT

        The purpose of this paper is to discover the character and parameters of the process, that determine combined effect of back electromotive force (EMF) of the group of asynchronous motors during running-down on the leakage current.

        The mathematical model of an electrotechnical system of a mine section during running-down of asynchronous motors after emergency shut-down was made up and analysed. This model allows to determine the effect of motor back EMF on the leakage current in case of emergency.

PROCESSES IN LOW-VOLTAGE ELECTROTECHNICAL COMPLEX DISCUSSION

        The vectorial method for the research of processes in case of simultaneous shut-down the group of asynchronous motors can be rationally used [2].

        The electric diagram in figure 1 shows an electrotechnical complex of a technological mine section in case of emergency shut-down. On this figure: AB — automatic circuit breaker; КМ — magnetic contactor switch.

Figure 1 — Electric diagram of the electrotechnical complex of a mine section in case of emergency shut-down

        The differential equations in coordinates for the equivalent circuit of an asynchronous motor (figure 2), which represent the electrical (all electrical variables and parameters are referred to the stator) and the mechanical part of the machine, can be written in the following way [2, 3]:

(1)

Figure 2 — Equivalent circuit of the i-motor network

        The processes in each trailing cable are described by such differential equation (see figure 2):

.

(2)

        Let us assume that:

(3)

        Using the above equations, the mathematical model of the i-motor network can be found:

(4)

        The last combined equations associate speed of rotation with voltage vector in the common part of the section power system :

.

(5)

        Operational impedance of the asynchronous motor is defined as follows [2]:

.

(6)

        Operational impedance of a trailing cable can be written in the next way:

.

(7)

        In view of expressions (6) and (7) the operational conductivity of the i-motor network can be written:

.

(8)

        During running-down of asynchronous motors , so:

.

(9)

        The last expression establishes functional dependence of operator on a rotation speed of motors in a running-down time:

.

(10)

        Taking into account a frequency modulation, voltage vector in the common part of the section power system, whose amplitude decreases on exponential law, is defined by expression:

.

(11)

        With the purpose of the analysis of a simultaneous running-down of n-motors it is necessary to make the generalized combined equations, which includes dependence (5) for a circuit of each engine, and also the equation (11):

(12)

        For definition of the effect of back EMF on leakage current through a body of the person, the equivalent circuit has been made (figure 3).

Figure 3 — Equivalent circuit of a cable section at occurrence of leakage current

        The given figure illustrates a touch of the person to a conductor of a trailing cable on an elementary section . Due to the given equivalent circuit it is possible to establish, that operational impedance of a leakage current circuit at zero entry conditions is equals to:

.

(13)

        Corresponding operational resistance is defined by the expression:

,

(14)

where ; ; ; .         Leakage current through a body of the person is defined in the following way:

.

(15)

        The formula (15) allows to define the leakage current through a body of the person under condition of the known value of a phase voltage in a place of leakage.

        According to the received mathematical model the computer model has been developed in case of simultaneous running-down two, three and four motors of various capacity (30-180 kw). As a result of computer modelling the diagrams shown on appendix 1 have been received.

CONCLUSION

REFERENCES

        2. Ковач К.П., Рац. И. Переходные процессы в машинах переменного тока. — М.-Л.: Госэнергоиздат, 1963. — 744 с.

        3. Шрейнер Р.Т. Математическое моделирование электроприводов переменного тока с полупроводниковыми преобразователями частоты. — Екатеринбург: УРО РАН, 2000. — 654с.

APPENDIX 1