RU2402147C1 - Method of optimum vector control of asynchronous motor - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: at limitations of output voltage U₀ and current I₀ of power converter feeding the engine, which is typical for controlled drives, especially traction ones, there provided are: minimum losses in engine if at the current value of rotary speed and specified electromagnetic torque M_Z the limitations of maximum allowable values of amplitude of voltage and current at the output of power converter are not reached; conditional minimum of losses in engine at these voltage and current limitation levels at output of power converter if the specified torque M_Z cannot be implemented at optimum sliding value, but is implemented at large sliding values without exceeding voltage and current limitation levels; maximum implemented electromagnetic torque at these voltage and current limitation levels at the output of power converter if the specified torque M_Z cannot be implemented. In vector control method of asynchronous motor with short-circuited rotor fed from power converter, the value of magnetisation current vector mod(i_d) at each time point is equal to value of active current vector mod(i_q), which is divided by proportionality factor k. So at each point of time there met is ratio mod(i_dz)=mod(i_qz)/k; at that, for satisfactory operation of field changing model, value of magnetisation current vector mod(i_d)can be restricted with minimum allowable value mod(i_dmin).

EFFECT: providing maximum efficiency value of engine and implementing maximum electromagnetic torques in systems of vector control of asynchronous motors considering current and voltage limitation of power converter feeding the motor.

3 cl, 2 dwg

Description

The invention relates to a controlled asynchronous electric drive and can be used in the regulation of induction motors, in particular squirrel-cage motors, including traction. Specifically, the invention relates to asynchronous drive systems in which an induction motor is powered by a regulated voltage or current source, for example, an autonomous voltage or current inverter, a cycloconverter, and the like. Such sources make it possible to realize any desired voltage (current) and frequency of the motor supply with an accuracy, perhaps, up to the high-frequency modulation component, and within the known limitations of the output current and converter voltage determined by the used power devices.

Known methods of vector control of induction motors, in which the regulation of mechanical motion (electromagnetic moment) and the electromagnetic component (magnetic flux) is carried out separately, by regulating the active and magnetizing components of the current vector, due to the corresponding formation of the supply voltage (see book V.V. Rudakova: Asynchronous electric drives with vector control. - L .: - Energoatomizdat, 1987. - 134 p., P. 79-80). For the implementation of vector control systems, information is needed on the direction and magnitude of the magnetic field in the engine, for which, as a rule, models of electromagnetic processes are used. In vector control systems, the engine operating conditions with a constant field are usually used, in which the parameters of the field model vary slightly; with constant rotor flux linkage, the magnetizing component of the current is constant, and the active component and slip frequency are proportional to the electromagnetic moment.

, затем с помощью уравнений координатного преобразования из полученных mod(i_qz) и mod(i_dz) получают задания токов i_{A(B, C)z}, соответствующие требуемым значениям фазных токов обмоток статора асинхронного двигателя, и поддерживают в фазах асинхронного двигателя полученные требуемые токи с помощью питающего его силового преобразователя, причем L_r и L_h - индуктивности обмоток ротора и взаимоиндуктивность обмоток статора и ротора асинхронного двигателя, соответственно. При таком способе векторного управления активная составляющая тока i_q и, следовательно, частота скольжения ω_s пропорциональны требуемому электромагнитному моменту. Использование известных способов позволяет регулировать скорость вращения ротора двигателя в широком диапазоне с коэффициентом мощности и перегрузочной способностью, близкими к номинальным значениям.Closest to the invention among vector control systems is a vector control method - the Transvector system (Blaschke, F. Das Prinzip der Feldorientierung, die Grundlage fur die Transvektor-Regelung von Drehfeldmaschinen / F. Blaschke // Siemens Zeitschrift. - 1971, No. 45 , H.10). The vector control method of a squirrel-cage asynchronous motor fed from a power converter via the Transvector system consists in setting a constant magnitude of the magnetizing current component vector mod (i _dz ), at each instant of time, setting the required value of the electromagnetic moment M _z , measuring circular rotational speed of the rotor of the induction motor ω, obtain the value of mod (получают) and the direction Θ _Ψ of the flux linkage vector of the rotor of the induction motor, determine the required value of the vector of active t eye generalized electric machine from the expression

then, using the coordinate transformation equations from the obtained mod (i _qz ) and mod (i _dz ), the currents i _{A (B, C) z} corresponding to the required values of the phase currents of the stator windings of the induction motor are obtained, and the obtained required phases are supported in the phases of the asynchronous motor currents using the power converter feeding it, and L _r and L _h are the inductors of the rotor windings and the mutual inductance of the stator windings and the rotor of the induction motor, respectively. With this vector control method, the active component of the current i _q and, therefore, the slip frequency ω _{s are} proportional to the required electromagnetic moment. Using known methods allows you to adjust the speed of rotation of the rotor of the engine in a wide range with power factor and overload capacity, close to the nominal values.

The disadvantages of the known methods is that due to a change in the slip frequency, losses in the engine increase compared with losses at an optimal constant slip frequency; in addition, an increase in the electromagnetic moment and an increase in the speed of rotation inevitably leads to a limitation of both the current and the voltage of the power converter supplying the induction motor, which makes it impossible to realize the maximum electromagnetic moment of the motor. Increasing the efficiency and maximizing the torque, taking into account current and voltage limitations, are especially important in traction drives due to limited power resources and the need to increase the efficiency of traction drives, in which efficiency and full use of the power converter resources are the main criteria for the quality of the drive.

The technical result, which is provided by the invention, is to ensure the maximum value of the motor efficiency, if such a regime is feasible, and to ensure the implementation of the maximum electromagnetic moments in the frequency control systems of induction motors, taking into account the current and voltage limitations of the power converter supplying the motor.

Given the limitations of the output voltage U ₀ and current I _{0 of the} power converter supplying the motor, which is typical for adjustable drives, especially traction:

- minimum losses in the engine are ensured if, at the current value of the rotor speed and a given electromagnetic moment M _{z, the} maximum permissible voltage and current amplitude limits at the output of the power converter are not reached;

- a conditional minimum of losses in the motor is provided at given levels of voltage and current limitation at the output of the power converter if the given moment M _{z is} not realized at the optimum slip value, but realized at large slip values without exceeding the voltage and current limitation levels;

- the maximum realized electromagnetic moment is provided at these levels, the voltage and current are limited at the output of the power converter, if the given moment M _{z is} not realized.

максимально допустимого напряжения на выходе силового преобразователя из выражения

и максимального электромагнитного момента M_zmax, развиваемого асинхронным двигателем, из выражения

задают минимальную величину вектора тока намагничивания mod(i_dmin) обобщенной электрической машины, имеющей параметры, соответствующие параметрам реального асинхронного двигателя, задают величину реализуемого электромагнитного момента M_zp либо равным значению электромагнитного момента M_z, либо, если требуемое значение электромагнитного момента M_z превышает M_zmax, равным M_zmax, причем знаки M_z и M_zp совпадают, определяют требуемую для обеспечения реализуемого электромагнитного момента M_zp величину вектора активного тока обобщенной электрической машины из выражения

, далее, если измеренная частота вращения ротора ω меньше

, а также в случае, если измеренная частота вращения ротора ω не меньше

, но величина реализуемого электромагнитного момента M_zp меньше значения электромагнитного момента, рассчитанного по формуле

The specified technical result is ensured by the fact that in the vector control method of a squirrel-cage induction motor powered by a power converter, the maximum permissible current value I _{0 is set} at the output of the power converter, at each instant of time, the required value of the electromagnetic moment M _{z is set} , the rotational speed is measured induction motor rotor ω, as well as voltage U _d of the power converter circuit DC current supplied to the motor, determine the value of mod (Ψ) and directed e Θ _Ψ rotor flux vector of the induction motor determine the optimal value of angular frequency ω _wholesale slip circular frequency critical slip from the expression

the maximum allowable voltage at the output of the power converter from the expression

and the maximum electromagnetic moment M _zmax developed by an induction motor, from the expression

set the minimum value of the magnetization current vector mod (i _dmin ) of a generalized electric machine having parameters corresponding to the parameters of a real induction motor, set the magnitude of the realized electromagnetic moment M _zp either equal to the value of the electromagnetic moment M _z , or if the required value of the electromagnetic moment M _z exceeds M _zmax, equal to M _zmax, wherein marks M _z and M _zp coincide is determined to provide the required electromagnetic torque realizable magnitude vector M _zp active current generalized Electrical tion of the machine from the expression

further, if the measured rotor speed ω is less

, as well as if the measured rotor speed ω is not less than

, but the magnitude of the realized electromagnetic moment M _{zp is} less than the value of the electromagnetic moment calculated by the formula

, а величина реализуемого электромагнитного момента M_zp не меньше значения электромагнитного момента, рассчитанного по формуле

provided that ω _s = ω _sopt , the required magnitude of the magnetization current vector of the generalized electric machine is determined from the expression mod (i _dz ) = mod (i _qz ); if the measured rotor speed ω is not less

, and the magnitude of the realized electromagnetic moment M _{zp is} not less than the value of the electromagnetic moment calculated by the formula

; если измеренная частота вращения ротора ω не меньше

, а величина реализуемого электромагнитного момента M_zp больше значения электромагнитного момента, рассчитанного по формуле

under the condition ω _s = ω _sopt , but not more than the value of the electromagnetic moment calculated by the same formula under the condition ω _s = ω _scrit , the required magnitude of the magnetization current vector of the generalized electric machine mod (i _dz ) is set equal to the magnitude of the active current vector mod (i _qz ) divided by the proportionality coefficient equal to

; if the measured rotor speed ω is not less

, and the magnitude of the realized electromagnetic moment M _{zp is} greater than the value of the electromagnetic moment calculated by the formula

, задают реализуемую величину вектора тока намагничивания mod(i_dp) обобщенной электрической машины либо равной требуемой величине вектора тока намагничивания mod(i_dz), либо, если требуемая величина вектора тока намагничивания mod(i_dz) меньше минимальной величины вектора тока намагничивания mod(i_dmin), равной минимальной величине вектора тока намагничивания mod(i_dmin), затем с помощью уравнений координатного преобразования, характеризующих переход от вращающейся системы ортогональных d-q-координат, ось 0-d которой ориентирована по направлению вектора потокосцепления Ψ ротора электрической машины в неподвижную систему фазных A-B-C-координат, из полученных требуемой величины вектора активного тока mod(i_qz) и реализуемой величины тока намагничивания mod(i_dp) обобщенной электрической машины определяют требуемые значения фазных токов i_A(B,C)z, которые поддерживают в фазах асинхронного двигателя с помощью питающего его силового преобразователя, причем L_s, L_r и L_h - индуктивности обмоток статора, ротора и их взаимоиндуктивность, R_s и R_r - активные сопротивления статора и ротора, соответственно.under the condition ω _s = ω _sopt , and more than the value of the electromagnetic moment calculated by the same formula under the condition ω _s = ω _scrit , the required magnitude of the magnetization current vector of the generalized electric machine mod (i _dz ) is set equal to the value of the active current vector of the generalized electric machine mod (i _qz ) divided by the proportionality coefficient equal to

, set the realizable magnitude of the magnetization current vector mod (i _dp ) of the generalized electric machine either equal to the required magnitude of the magnetization current vector mod (i _dz ), or if the required magnitude of the magnetization current vector mod (i _dz ) is less than the minimum magnitude of the magnetization current vector mod (i _dmin), mod equal to the minimum value of the magnetizing current vector (i _dmin), then using the coordinate transformation equations that characterize the transition from the rotating system dq-orthogonal coordinate axis 0-d which is oriented in the direction of the vector flux Ψ rotor electric machine in the fixed system phase ABC-coordinate from the obtained desired value vector active current mod (i _qz) and realizable value mod magnetizing current (i _dp) generalized electrical machine determine the required values of phase currents i _{A (B, C) z} , which are supported in the phases of the induction motor by means of a power converter supplying it, where L _s , L _r and L _h are the inductances of the stator and rotor windings and their mutual inductance, R _s and R _r are the active resistances of the stator and rotor, respectively.

Moreover, the magnitude of mod (Ψ) and the direction Θ _Ψ of the flux linkage vector of the induction motor rotor are determined either from the measured instantaneous values of the phase currents of the stator winding of the induction motor i _{A (B, C)} and the circular rotational speed of the rotor of the induction motor ω using coordinate transformation equations characterizing the transition from a fixed system of phase ABC coordinates to a rotating system of orthogonal dq coordinates, the 0-d axis of which is oriented in the direction of the flux linkage vector Ψ of the rotor of the electric machine, and cal generalized model of the electric machine in the dq-coordinate system, or by means of magnetic field sensors mounted directly in the gap induction motor.

The difference of the proposed method from the existing ones is that the magnetization current during vector control is not constant or changing in proportion to the electromagnetic moment, but is changed in such a way as to ensure minimum losses in the motor, or the conditional minimum of losses at these levels of voltage and current limitation, or the maximum realized electromagnetic moment, if the given moment cannot be realized at given levels of voltage and current limitations.

In particular, the required magnitude of the magnetization current vector mod (i _dz ) at each moment of time is proportional to the required magnitude of the active current vector mod (i _qz ). In this case, the required value of the active current vector is divided by a certain proportionality coefficient k. Thus, the magnitude of the magnetization current vector at each instant of time is set equal to

,

,

moreover, for satisfactory operation of the field variation model, the magnitude of the magnetization current vector mod (i _dz ) can be limited from below to the minimum admissible value mod (i _dmin ).

The method of optimal vector control of an induction motor is illustrated in figure 1, which shows an example of a device that implements the method. In this case, an example of a vehicle (car, tractor, etc.) with an electric AC-transmission is given.

The block diagram of the algorithm for calculating the required parameters of the device is presented in figure 2.

The internal combustion engine 1 drives the alternator 2, which provides an alternating three-phase voltage to the input of the rectifier 3 of the power converter.

(см. Розанов Ю.К., Рябчицкий М.В., Кваснюк А.А.: Силовая электроника. Учебник - М.: Издательский дом МЭИ, 2007, 632 с., с.409).The output of the rectifier 3 and the input of the inverter 5 of the power converter form a DC link of the power converter, on which a voltage sensor 4 is mounted, which measures the instantaneous value of the voltage of the DC link U _d . In accordance with U _d according to known relations, the value of the maximum permissible value of the inverter output voltage U _{0 is set} . So, with pulse-width modulation of the output voltage of the power converter, the allowable amplitude of the sinusoidal linear voltage U ₀ cannot exceed

(see Rozanov Yu.K., Ryabchitsky M.V., Kvasnyuk A.A .: Power Electronics. Textbook - M .: Publishing House MPEI, 2007, 632 p., s. 409).

в блоке коэффициента 11, где p - число пар полюсов статора асинхронного двигателя. В результате, на выходе блока 11 получается значение мгновенной круговой частоты ω [c^-1] вращения ротора асинхронного двигателя 7.A block of current sensors 6 is connected to the output of the inverter 5, which measures the instantaneous values of the phase currents i _{A (B, C) of the} traction induction motor 7, also connected to the output of the inverter 5. A speed sensor 8 is installed on the same shaft as the motor 7, whose signal proportional to the rotor speed of the engine rotor n [rpm], is amplified by the amplifier 9, converted by analog-to-digital converter 10 and multiplied by a coefficient

in the coefficient block 11, where p is the number of pole pairs of the stator of an induction motor. As a result, at the output of block 11, the value of the instantaneous circular frequency ω [c ^-1 ] of rotation of the rotor of the induction motor 7 is obtained.

The required electromagnetic moment M _{z of the} traction induction motor 7 is set by the gas pedal 12 installed in the driver’s cab of the vehicle and transmitted through the amplifier 13 and the analog-to-digital converter 14.

Relations corresponding to the mathematical model of a generalized electric machine and coordinate transformations characterizing the transition from the values of a real multiphase electric machine (in phase coordinates AB-С) to the values of a generalized two-phase electric machine (in rotating orthogonal coordinates dq, whose 0-d axis is oriented along the vector Ψ the flux linkage of the rotor of a real electric machine), are introduced by means of a personal computer 15 into the controller 16 (see examples of coordinate transformations and a mathematical model in: Vinogrado A.B .: Vector control of AC electric drives. Textbook - Ivanovo: Ivanovo State Power Engineering University named after V.I. Lenin, 2008, 298 pp., Pp. 8-15, 34-35, 187-195 ) Also, by means of a personal computer 15, the maximum permissible value of the output current I _{0 of the} inverter 5, the minimum permissible magnitude of the magnetization current vector, which ensures the stable operation of the mathematical model of the generalized electric machine mod (i _dmin ), as well as the equivalent circuit parameters of the traction induction motor R _r , are introduced into the controller 16, R _s , L _r , L _s , L _h . The values of the parameters L _s , L _r , L _h , R _s , R _r are taken according to the data of the phase equivalent circuit of an induction motor (see, for example, A. Bulgakov: Frequency control of asynchronous motors. M: Energoizdat, 1982, 216 p. , p.51-78) or can be obtained experimentally (see, for example, Vinogradov AB: Vector control of AC electric drives. Study Guide - Ivanovo: Ivanovo State Power Engineering University named after V.I. Lenin, 2008 , 298 p., Pp. 220-230).

From the measured instantaneous values of the phase currents i _{A (B, C)} and the rotational rotational frequency ω of the rotor of the traction induction motor 7 in the controller 16 at each moment of time by means of a coordinate transformation characterizing the transition from a stationary to a rotating coordinate system, the values of active i _q and magnetizing i _d component of currents corresponding to the mathematical model of electromagnetic processes in a generalized electric machine. Using i _q and i _d in the controller 16, at each instant of time, determine the value of mod (Ψ) and the direction Θ _{Ψ of the} vector Ψ of the flux linkage of the rotor of the induction motor 7.

Alternatively, to determine the magnitude of mod (Ψ) and the direction Θ _Ψ of the flux linkage vector, magnetic field sensors (Hall sensors) installed directly in the gap of an electric machine can be used (see, for example, Vinogradov AB: Vector control of AC electric drives. Training manual - Ivanovo: GOUVPO "Ivanovo State Power Engineering University named after V.I. Lenin", 2008, 298 p., Pp. 183-187). In this case, there is no need for current sensors 6.

The controller 16 also receives the task of the required moment M _{z of the} traction motor 7 and the measured instantaneous values of the voltage U _d , currents i _{A (B, C)} and frequency ω. The controller 16 implements an algorithm for generating the required magnitude of the active current vector mod (i _qz ) and the realized magnitude of the magnetization current vector mod (i _dp ), shown in FIG. 2.

In the controller 16, the required value of the active current vector is determined from the expression

Next, in the controller 16, the frequency of the optimal and critical slip is determined. In vector control, the slip frequency and the frequency of the supply voltage of the stator windings are not regulated. Despite this, in this algorithm, the optimal and critical slip frequencies are used to determine the proportionality coefficient k between the given active and magnetizing currents (i _qz and i _dz ). The value of the optimal slip ω _sopt can be determined by the values of resistances and inductances, for example, by the formula

where the absolute slip value, which is optimal for the stator current consumption, is indicated. Formula (3) determines the slip value that satisfies the law of regulation of M.P. Kostenko (see, for example, L.M. Piotrovsky. Electric machines - M.-L.: Gosenergoizdat, 1949, 528 p., P. 408). It is also possible to set the optimal slip value according to the results of experimental studies, as a function of the electromagnetic moment, speed, etc. (see, for example, Shreiner RT: Mathematical modeling of AC electric drives with semiconductor frequency converters. Yekaterinburg: Ural Branch of the Russian Academy of Sciences, 2000, 654 pp., p. 544-547).

The critical slip value is determined by the formula

The maximum permissible output voltage of the power converter supplying the motor is determined. For example, if it is necessary to ensure the sinusoidality of the output voltage of a power converter with pulse-width modulation, the maximum allowable output linear voltage is determined by the formula (5)

By the formula (6), the maximum electromagnetic moment M _zmax is determined, which limits the possible specification of the realized electromagnetic moment M _zp from the given maximum current value I ₀ . Thus, if the specification of the electromagnetic moment exceeds the obtained value, then M _{zp is} taken equal to M _zmax . Signs M _z and M _zp coincide.

In case the condition is satisfied

the resources of the power converter are enough to realize the engine operating mode with minimal losses and at the same time achieve the realizable value of the electromagnetic moment M _zp , and the voltage and current limitations at the output of the power converter, taking into account (6), are not achieved. Take k = 1. Then

If condition (7) is not satisfied, the ratio is used to calculate the electromagnetic moment

The following three cases are possible.

Case 1. The magnitude of the moment M calculated by relation (9) under the condition that ω _s = ω _sopt is greater than the value of the required moment M _zp .

In this case, the inverter 5 can ensure the operation of the induction motor 7 with the realized moment M _zp with minimal losses, but with the output current of the power converter limited to no more than I ₀ . It is _assumed that k = 1, which corresponds to mod (i _dz ) = mod (i _qz ). The operating mode of an induction motor with minimal losses at an electromagnetic moment M = M _{zp is realized} .

Case 2. The magnitude of the moment M, calculated by the relation (9) for ω _s = ω _scrit , is less than the value of the realized moment M _zp .

The fulfillment of condition (11) means that, given the current and voltage restrictions of the power converter, it is impossible to obtain a realizable electromagnetic moment M _zp . Therefore, the moment is set, the maximum achievable under the existing restrictions of voltage and current at the output of the power converter U ₀ and I ₀ . Then accepted

and the magnitude of the magnetization current vector mod (i _dz ) is determined by (1) taking into account (12).

The achieved moment is determined in accordance with (9).

Case 3. Otherwise (that is, if neither (10) nor (11) is satisfied), the realized moment cannot be ensured in the mode of minimal losses, but this moment can be obtained by slightly increasing the ratio of the active and magnetizing components of the current. In this case, relation (9) is used to calculate the required value of the coefficient k at M = M _zp and the maximum voltage U ₀ .

To simplify the solution of (9) with respect to ω _s , the assumption is used that at high rotational speeds characteristic of the traction drive during regulation in the second zone with a limited motor supply voltage, the slip frequency and the terms dependent on it in the denominator (9) are negligible: ω>> ω _s (ω _s → 0); the stator resistance and the terms dependent on it in the denominator (9) are also negligible: R _s → 0. Then, taking into account (3), the coefficient k is

If ω _sopt is specified not according to (3), otherwise the solution of (9) with respect to k is found similarly. The magnitude of the magnetization current vector is determined by (1) with (13) taken into account.

Then, in the controller 16, the realizable magnitude of the magnetization current vector mod (i _dp ) is set. This value is set equal to the required magnitude of the magnetization current mod (i _dz ) or, if the required magnitude of the magnetization current vector mod (i _dz ) is less than mod (i _dmin ), equal to mod (i _dmin ).

The signals proportional to the instantaneous values mod (i _dz ) and mod (i _dp ) previously determined in the controller 16, by means of a coordinate transformation corresponding to the transition from a rotating system of dq coordinates to a fixed system of phase ABC coordinates, are converted into driving signals of instantaneous output phase currents i _Az , i _Bz , i _Cz , received at the input of the inverter controller 17, which generates output signals for switching the power keys of the inverter 5, received at the input of the driver 18 of the inverter power keys. The driver controls the power switches of the inverter, switching them in such a way that a three-phase current of a given instantaneous value is formed at the inverter output (in the stator windings of the induction motor).

The proposed method allows to realize a large range of changes in the magnitude of the magnetic field and to provide a small level of losses in an induction motor in a wide range of rotational speeds and moments.

Claims (3)

1. The method of controlling an squirrel-cage induction motor powered by a power converter, which consists in setting the maximum permissible current value I ₀ at the output of the power converter, at each instant of time, setting the required value of the electromagnetic moment M _z , measuring the rotational speed of the asynchronous rotor of the motor ω, as well as the voltage U _d of the DC link of the power converter supplying the motor, determine the magnitude of mod (Ψ) and the direction Θ _Ψ of the asynchronous rotor flux linkage vector engine, determine the values of the circular frequency of the optimal slip ω _opt , the circular frequency of the critical slip from the expression

the maximum allowable voltage at the output of the power converter from the expression

and the maximum electromagnetic moment M _zmax developed by an induction motor, from the expression

set the minimum magnitude of the magnetization current vector mod (i _dmin ) of a generalized electric machine having parameters corresponding to the parameters of a real induction motor, set the magnitude of the realized electromagnetic moment M _zp , either equal to the value of the electromagnetic moment M _z , or if the required value of the electromagnetic moment M _z exceeds M _zmax, equal to M _zmax, wherein marks M _z and M _zp coincide is determined to provide the required electromagnetic torque realizable magnitude vector M _zp active current generalized RE eskoy machine of expression

further, if the measured rotor speed ω is less

as well as if the measured rotor speed ω is not less

but the magnitude of the realized electromagnetic moment M _{zp is} less than the value of the electromagnetic moment calculated by the formula

provided that ω _s = ω _{s opt} ,
determine the required magnitude of the magnetization current vector of the generalized electrical machine from the expression mod (i _dz ) = mod (i _qz ); if the measured rotor speed ω is not less

and the magnitude of the realized electromagnetic moment M _{zp is} not less than the value of the electromagnetic moment calculated by the formula

provided that ω _s = ω _{s opt} ,
but not more than the value of the electromagnetic moment calculated by the same formula under the condition ω _s = ω _{s crit} , the required magnitude of the magnetization current vector of the generalized electric machine mod (i _dz ) is set equal to the magnitude of the active current vector mod (i _qz ) divided by the proportionality coefficient equal to

if the measured rotor speed ω is not less

and the magnitude of the realized electromagnetic moment M _{zp is} greater than the value of the electromagnetic moment calculated by the formula

provided that ω _s = ω _{s opt} ,
and more than the value of the electromagnetic moment calculated by the same formula under the condition ω _s = ω _{s crit} , the required magnitude of the magnetization current vector of the generalized electric machine mod (i _dz ) is set equal to the value of the active current vector of the generalized electric machine mod (i _qz ) divided by the coefficient proportionality equal

specify the realizable magnitude of the magnetization current vector mod (i _dp ) of the generalized electric machine either equal to the required magnitude of the magnetization current vector mod (i _dz ), or if the required magnitude of the magnetization current vector mod (i _dz ) is less than the minimum magnitude of the magnetization current vector mod (i _dmin ), equal to the minimum magnitude of the magnetization current vector mod (i _dmin ), then using the coordinate transformation equations characterizing the transition from a rotating system of orthogonal dq-coordinates, the 0-d axis of which is oriented in the direction of the vector the flux link Ψ of the rotor of an electric machine into a stationary system of phase A-B-C coordinates, from the obtained required magnitude of the active current vector mod (i _qz ) and the realized magnitude of the magnetizing current mod (i _dp ) of the generalized electric machine, determine the required values of phase currents i _{A ( B, C) z} , which are supported in the phases of an induction motor by means of a power converter supplying it, where L _s , L _r and L _h are the inductances of the stator and rotor windings and their mutual inductance, R _s and R _r are the active resistances of the stator and rotor, respectively . 2. The method of controlling an induction motor according to claim 1, characterized in that at each moment of time, currents in each phase of the stator winding of the induction motor are measured i _{A (B, C)} , and the quantity mod (Ψ) and the direction Θ _Ψ of the flux linkage vector of the asynchronous rotor the motor is determined by the measured instantaneous phase currents of the stator winding of the induction motor i _{A (B, C)} and the circular rotational speed of the rotor of the induction motor ω using the coordinate transformation equations characterizing the transition from a stationary system of phase A-B-C-coordinate tension into the rotating system of orthogonal dq-coordinates, the 0-d axis of which is oriented in the direction of the flux linkage vector Ψ of the rotor of the electric machine, and the mathematical model of the generalized electric machine in the dq-coordinate system. 3. The method of controlling an induction motor according to claim 1, characterized in that the magnitude of mod (Ψ) and the direction Θ _Ψ of the flux linkage vector of the rotor of the induction motor are determined using magnetic field sensors installed directly in the gap of the induction motor.

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