₍₁₎

_{where Iµ –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:

      (2)

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:

       (3)

where η_nom is the nominal UEC of the engine; tgφ_nom - a value corresponding to сosφ_ном; Р_nom 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)

      ₍₄₎

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

      (5)

By pouring the quantities Q₀ and Q_S into (2), will obtained the equation for determining total reactive power consumption by an induction motor:

      (6)

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:

       (7)

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 Ф_σ1, 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 Ф₁ and the scattering magnetic currents Ф_σ 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

      (8)

where L₁, L_µ - 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

      (9)

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

      (10)

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

      (11).

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

      (12)

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

      (13)

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 (Е_meas/=U_meas.) (13) the value of the mains voltage U₁ does not change, the U_meas. at the output of the measuring windings. The output voltage value is linearly related to the change in stator current value.

I. Introduction

The study of the physical and technical effects that form the basis of the structure of the inverter is required in the modeling of the elements and interconnections of the controlled output voltage converters of symmetrical quantities of reactive power of an induction motor [68,74]. The process of converting the value of primary three-phase currents into voltages and the algorithm for constructing a model of the converter structure include the principles of signal conversion of different types of physical nature, the relationship between the sizes and parameters of the converter structure and elements takes This algorithm is suitable for the process of controlling and controlling the reactive power of an induction motor [1,5].

II. Methods
When modeling the physical and technical effects of three-phase current magnetization parameters of an induction motor, the parametric structure scheme, which takes into account the physical and technical effects (FTE) used in the structure of the converter, changes the electrical magnitude and parameters, their a graph model of the interconnected structure is developed [2,6].
The structure of the primary current converter of an induction motor and a model based on FTEs are shown in pic-1.

Pic-1. A generalized model of an asynchronous motor based on the physical and technical effects of asymmetrical magnitude of reactive power applied to a controlled output voltage converter.
U_chik.. – output voltage generator; U_1.8 – is the component of the controlled output voltage in one ring, U_13.20 8 – is the component of the controlled output voltage in the second loop, ,- is the component of the total controlled output voltage in the common measuring ring.

In the process of supplying of electricity to an asynchronous motor from the mains, taking into account various external and internal parameters, writed as a graph model of the change in the output voltage, controlled by symmetrical quantities of reactive power consumed [8,9].

where:
I_A – is the primary current of phase A of the mains consumed by the induction motor;
f - current frequency;
w­­₂,w₁ – number of stator windings and sensing element windings;
 - resistance of the signal change part (magnetic);
ρ- is the specific resistance of the magnetic core material;
The asynchronous motor stator winding is calculated for phase A. The following is a summary parametric model of a single-element current converter with an output voltage controlled by symmetrical magnitudes of reactive power of an asynchronous motor (pic.2).
.
Pic-2. An asynchronous motor is a composite parametric model of a single-sensitive element converter of controlled voltage of symmetrical quantities of reactive power.

From this,
 (1)
 (2)
 (3)
 (4)
 (5)
The following is a distributed parametric model of a two-element element converter sensitive to the output voltage controlled by symmetrical quantities of reactive power of an induction motor.
Three-phase stator currents in the stator core of an induction motor generate magneto-moving forces F_μ [2,7,12].
The controlled output voltage at the output of the two sensitive element converters is formulated as follows:

 (6)
or
 (7)

The voltage across the first ring of the controlled output voltage, which is the symmetrical magnitude of the reactive power of an induction motor, that is, from a single sensing element, is expressed as follows.
 (8)
On the same basis we find the controlled output voltage in the second loop.
 (9)
The asynchronous motor reactive power symmetrical magnitudes of the controlled output voltage are expressed as a signal from two sensitive elements as follows.
 (10)
III. Results
Controlled output voltages based on scattered parameter of graph model written as following:
 (30)

 (31)
Based on these formulas, can writed the controlled output voltages of each phase of asynchronous motors as follows:
 (32)
IV. Conclusion
In the process of supplying electricity of asynchronous motor from the nets, taking into account various external and internal parameters, the symmetrical magnitudes of reactive power consumed are expressed for each phase current.
The magnetic processes in the stator windings of an induction motor can be clearly seen using a combined parametric model of currents consumed in all phases of e output voltage transducers, which controle the symmetrical magnitudes of reactive power of the asynchronous motor.