Реджабов Зайлобиддин1, Гуломов Ахмадулло1, Абдурашидов Елдорбек1
1Андижанский машиностроительный институт


Rejabov Zaylobitdin1, Gulomov Ahmadullo1, Abdurashidov Eldorbek1
1Andijon machine-building institute

Keywords: asynchronous motor, magnetic force, phase rotor induction motor

Рубрика: 05.00.00 ТЕХНИЧЕСКИЕ НАУКИ

Библиографическая ссылка на статью:
Реджабов З., Гуломов А., Абдурашидов Е. Equations of magnetic force of a phase rotor induction motor // Современные научные исследования и инновации. 2022. № 1 [Электронный ресурс]. URL: https://web.snauka.ru/issues/2022/01/97368 (дата обращения: 21.05.2024).

New methods and tools are being developed for control of the reactive power consumption in asynchronous motors and to expand the capabilities of control system elements and devices. The use of measuring flat measuring windings as sensor elements of system of control and automatization of reactive power consumption in asynchronous motors provides unified values of output current – 100 mA and voltage – 20V [1-2].
The reactive power consumption of an asinchronous motor can be described as follows equation [3-4]


where  –salt walking current; Q0 and Qs are the reactive powers in the stand-alone and short-circuit (scattering) modes, the value of Qs depends on the applied load current of the motor.
The reactive power consumption of an asynchronous motor varies from the load-dependent reactive power Qo to the nominal load Qnom, while the reactive power at the motor nominal load varies. It can be seen from the working description that the cosφ value has the smallest value in the regime, with the have highest speed (Fig. 1, b).
The reactive power consumed by an inductionous motor at rated voltage is as follows:


where β is the load factor of the asynchronous motor.
According to the reference data, the nominal reactive power of an induction motor can be determined as:


where ηnom is the nominal UEC of the engine; tgφnom - a value corresponding to сosφномРnom is the rated active power of the motor at rated voltage.
In asynchronous motors in the single-stroke mode сosφ0=0,1 – 0,2 and the corresponding sinφ0=0,99 – 0,97. Considering the small size of the steel core and mechanical losses during the activity, can be get as sinφ0=1
The of three-phase reactive power consumption determined as follows:

or according to (1.3)


The reactive power of the motor scattering currents, depending on the load, is presented as follows:


By pouring the quantities Qand QS into (2), will obtained the equation for determining total reactive power consumption by an induction motor:


where P, tgφ, and η are the quantities corresponding to the known load of the engine. (6) shows that the reactive power consumption of induction motors depends on its load in the operating mode
Load factor will determined as:


The change of reactive power consumption in asynchronous motors depends on the change in stator current (load current). From equation (6) and (7) understanding, that obtaining information about the value of stator current in the supply of reactive power to asynchronous motors through accurate, fast, continuous and uncomplicated changes, expands the capabilities of asynchronous motor reactive power control and control system and energy-resource savings leads. In determining the value of the stator current of an asynchronous motor, mainly the elements of the measuring and control systems are connected to the mains via measuring transformers or electromagnetic current transducers. The criteria such as output values of unified values, errors, and time are minimal size. The use of a measuring element located directly in the stator part of motor and the magnetic system in determining the stator current value for asynchronous motor reactive power control and automation systems satisfies the above criteria [3].
The measuring element between the main stator winding in the stator groove and the dielectric tqin (wedge, which can also be special wood) allows to detect changes in the scattering current Фσ1, which causes the consumption of reactive power.
In this case, as a measuring element is taken flat measuring windings.
The main reason for this is to obtain a magnitude in the form of voltage from the measuring coil transforming to the change of the main magnetic flux Ф1 in the stator part of the asynchronous motor [4].
Derive of the value of voltage obtained from the measuring coil from the value of the stator current.
When the outputs of the asynchronous motor stator winding are connected to a voltage power supply U1, the main current Фand the scattering magnetic currents Фσ are generated by the current I1 in the winding
For the stator circuit, applying Kirchhoff’s second law can be reaseached switching scheme given in Figure 1.a


where L1, Lµ - are the inductances of the stator winding and the magnetic field, respectively; U1 - stator winding phase; I1, Iµ - currents of stator windings and magnetizing substations;  stator scattering current and main current.
After some modifications, equation (8) becomes


From equation (9) will finded on the basic of magnetic flux.


Move from the vector view of the main magnetic flux to the effect value:


where Z1=R1+jX1 is the total resistance of the stator winding.
The measuring coil we are proposing is a transformer-like secondary coil relative to the stator coil, from which voltage is formed as a result of the passage of the main magnetic flux Ф1. The value that affects this voltage is as follows


w2 –is the number of wraps of the measuring tape
Puting (11) to (12) will get next


Where - is the transformation coefficient of the stator winding relative to the measuring windin.
On the basis of using and installing flat measure windings in inside of asynchronous motor and connecting their output voltage to measuring and control devices assumed that, this measuring tape is working properly (Еmeas/=Umeas.) (13) the value of the mains voltage U1 does not change, the Umeas. at the output of the measuring windings. The output voltage value is linearly related to the change in stator current value.

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