RU2158472C2 - Method for evaluating adjustable signals of three- phase squirrel-cage induction motor - Google Patents

Abstract

FIELD: electric drives for electrified transport, mechanical engineering, and metallurgy. SUBSTANCE: classic equivalent T-circuit of induction motor phase is employed. Stator current, magnetization, and supply voltage signals are generated using new expressions. Analytic model of reference induction motor is devised. Method provides for evaluating adjustable variables of induction motor including saturation current, electromagnetic moment, and rotor speed within comprehensive range of sampling steps. Method may be found useful for vector control systems, for investigating transient operating conditions of induction motor, as well as for control systems, analytical synthesis of speed governors, and for electric drive adjusting devices. EFFECT: improved accuracy of evaluating controlled variables, enlarged functional capabilities. 3 cl, 25 dwg

Description

 The invention relates to electrical engineering and can be used in electric drives of electric trains, metal cutting machines, rolling mills and other mechanisms of mechanical engineering and metallurgy with high requirements for the quality of regulation, energy and regulation range, in particular as a reference model of a three-phase asynchronous motor (HELL) with a squirrel-cage rotor in systems with vector control, as well as for the study of dynamic modes of blood pressure and control systems, for the synthesis of regulators in devices I'm setting electric wires during their trial operation, to train students in the universities.

A known method for evaluating the controlled variables of a three-phase squirrel-cage motor with the Gorev-Park differential equations for a generalized electric machine, the equation of electromagnetic moment and the equation of motion [1]. This method for equations written through flux linkage has received the greatest recognition in the world for modeling dynamic modes of operation of a squirrel-cage rotor motor and for implementing a reference model (model of a control object) in systems with vector control of blood pressure and in the evaluation of controlled variables in simpler control systems. In this case, the transition from a real three-phase machine to a generalized two-phase machine is performed by projecting controlled variables from a real coordinate system with the abc axes along the stator phases onto the coordinate systems orthogonal to the α-β axis or the coordinate system orthogonal to the dq axis rotating relative to the stator with the frequency ω _{r of} rotation of the rotor of the engine, or on the orthogonal axis xy of the coordinate system rotating relative to the stator with some arbitrary speed ω _k .

Common disadvantages of all variants of the known method for evaluating the controlled variables of the engine are:
- low accuracy of flux linkage estimation according to Gorev-Park equations, and therefore, low accuracy of estimating electromagnetic moment and rotor speed;
- a large dependence of the accuracy of the estimation of variables on changes in the sampling step in a small range from 5 to 500 μs [2].

 Variants of the known method using projections of flux link signals onto the orthogonal axes of rotating coordinate systems have greater accuracy.

 There is a known [3] method for evaluating the controlled variables of a three-phase blood pressure, according to which, to increase the accuracy of the projection of the flux linkages onto the orthogonal axes dq of the rotating coordinate system, the stator phase currents and phase voltages are measured in the stationary coordinate system adc, and they are first converted to projections on the α-β axis a fixed coordinate system, and then, using the signal of the angle of rotation of the rotor, formed from the integral of the signal for setting the frequency of rotation of the stator field, in the projection on the dq axis of the rotating coordinate system.

The disadvantages of the method include:
- a large number of sensors used,
- additional coordinate converter (KP) α-β / dq;
- an inaccurate estimate of the angle of rotation of the rotor for a given frequency of rotation of the stator field, and not for the frequency of rotation of the rotor, and therefore
- low accuracy of the estimation of the flux linkage signal from the projections of the stator currents and voltages, the formation of which used an approximately estimated angle of rotation of the rotor,
- the impossibility of approximately estimated flux linkage to evaluate the signals of the electromagnetic moment and rotor speed.

 The most accurate method [4] is known for estimating the adjustable coordinates of a HELL with a squirrel-cage rotor according to the Gorev-Park equations for a generalized electric machine, the equation of electromagnetic moment and the equation of motion recorded in flux linkages in the rotor coordinate system with axes dq, according to which the electromagnetic moment of the engine is formed according to the vector the product of rotor currents and magnetization, presented in the form of projections on the orthogonal axis dq.

 This increased the accuracy of estimating the electromagnetic moment at a sampling step of up to 200 μs compared with other estimation methods. Moreover, the accuracy of estimating the magnetization current is low, since it is formed by an approximate expression relating the magnetization current, stator and rotor currents, and stator and rotor flux linkages.

The authors recommended this method for studying the operation of an induction motor in a control system during their simulation on a PC in the Pspice software package. In the case of its use in the regulation of blood pressure, among the disadvantages, in addition to the low accuracy of estimating the magnetization current, the use of an additional coefficient of α-β / dq should be attributed.
To reduce the number of coordinate converters used, it is advisable to simulate blood pressure using only fixed coordinate systems abc and α-β associated with the motor stator. Such models are analogues of the proposed model.

 When modeling blood pressure in the α-β axes, there is a need to improve the accuracy of solving Gorev-Park differential equations.

 Among the methods for numerically solving differential equations, the method of difference equations is known. To increase the accuracy of the estimation of controlled variables of blood pressure at discrete time instants, a voltage reference signal is supplied to the model input, which is equal to the arithmetic average between the voltage at the beginning and at the end of the interval and the actual voltage corresponding to the time moment half a period ahead [5]. Such a technique is unsuitable for real-time modeling, since the driving signal in a closed-loop control system is determined by the measured feedback signal.

 There is a method of evaluating the controlled variables of blood pressure with a short-circuited rotor according to the Gorev-Park equations written through flux linkages in the Cauchy form for modeling the engine using analogue [6] and digital computers [7], and in the latter case, to increase the accuracy and even stability of the solution the method of A.V.Basharin is used, which consists in the fact that at each step of the numerical solution of the differential equation two iterations are performed, each of which ends with the calculation of the average value of the controlled variables step integration.

 Despite this, the accuracy of the estimation of controlled variables in this way is low and depends, like the model stability, on the sampling step. The accuracy of the estimation of controlled variables by methods [7] and [5] is approximately the same.

 There is a known [8] method for evaluating the controlled variables of a three-phase squirrel-cage induction motor based on the operation of the mathematical model of the motor at discrete instants of time, which is tuned according to the parameters of the T-shaped equivalent circuit of the motor phase, for which the stator phase currents, phase voltages and position signal are measured, which form the projections of the stator current signal vectors and stator flux link signals onto the orthogonal axes α-β of the coordinate system fixed relative to the stator, according to the vector polar product which is multiplied by 1.5 is formed of the electromagnetic motor torque signal which, subject to the load torque and motor rotation direction is formed the dynamic engine torque signal. If necessary, the rotor speed of the engine is formed from the measured position signal.

 The main disadvantage is the low accuracy of the flux link signals, and hence the electromagnetic moment, as evidenced by the absence in the expression for calculating the electromagnetic moment of the product of the inductance of the magnetizing branch and the number of pole pairs.

 There is a known [9] method for evaluating the controlled variables of three-phase asynchronous squirrel-cage induction motors, which use a mathematical model of the motor when simulating an object of regulation at the input that operates at discrete moments of time and are configured according to the parameters of the T-shaped equivalent circuit of the motor phase and the given frequency of rotation of the stator field which supplies the signals for setting the supply voltage as a function of the frequency of rotation of the stator field, and a mathematical model with two observers: an observer of the flow and current stator and dual rotor speed observer. The mathematical model that simulates the engine as an object of regulation is based on the solution of the Gorev-Park equations for a generalized two-phase machine written in the Cauchy form with respect to the projections of the stator and rotor flux link vectors onto the orthogonal axes of the α-β coordinate system fixed relative to the stator. The output of the model is the projection of the stator current vector on the α-β axis, considered as the assumed current task. The mathematical model with observers of controlled variables is based on the solution of modified Gorev-Park equations. This model in its first part repeats the simulator model and is intended to improve the accuracy of estimating currents, flux linkages and rotor speed.

Disadvantages:
- Of all the known models of both engines, a model is used that has low resistance to change in the sampling step and the lowest accuracy in estimating flux linkages and stator currents;
- to increase the accuracy of the generated signals of flux linkages and stator current, on which the accuracy of estimating the rotor speed depends, several observers are introduced into the second model: an observer of the stator flux and current;
- to the input of both models, to set their parameters, a signal is given to set the frequency of rotation of the stator field, which differs by the magnitude of the absolute slip from the frequency of rotation of the rotor, which should determine the parameters of the motor model. As a result, the model may lose stability when the slope of the speed reference signal increases if it is linearly changed and is completely unsuitable for use when the reference signal is applied abruptly.

The disadvantages of all of the above methods are analogues:
- low accuracy in estimating the electromagnetic moment and engine speed from the projection of the flux linkage;
- the lack of an analytical solution that could be considered the standard and compare with it the results of modeling by numerical methods;
- the absence of an analytical description that allows the synthesis of regulators by analytical methods.

где U_sф(p), I_sф(p), I_mф(p) - преобразования по Лапласу соответственно фазных сигналов питающего напряжения, токов статора и намагничивания,
K₁ - коэффициент усиления,
T₀, T₁, T₂, T₃ - постоянные времени, зависящие от относительного скольжения s и параметров r₁, L₁, r'₂, L'₂, L_m T-образной схемы замещения двигателя,
при относительном скольжении s = 0
K₁ = 1/r₁,
T₁ = (L₁ + L_m)/r₁, T₀ = T₂ = T₃ = 0
Кроме того, формируют проекции i_sα,i_sβ и i_mα,i_mβ векторов сигналов тока статора и тока намагничивания на ортогональные оси α-β системы координат, неподвижной относительно статора, по векторному произведению которых формируют сигнал электромагнитного момента двигателя. Параметры передаточных функций зависят от величины относительного скольжения s, которая задается постоянной величиной. При формировании электромагнитного момента используется выражение для векторного произведения токов статора и намагничивания, представляющего собой произведение модулей векторов этих токов на синус угла между ними. При этом угол между векторами тока статора и тока намагничивания принимается постоянным и равным девяноста градусам минус угол между фазными током статора и напряжением в режиме короткого замыкания.There is a method [10] (prototype) for evaluating the controlled variables of a three-phase asynchronous squirrel-cage induction motor, which is closest to the proposed one, based on the operation of a mathematical model of the motor at discrete moments of time, which is configured according to the parameters of a simplified T-shaped circuit for replacing the motor phase. According to this method, at discrete time instants, a signal ω _{s of} setting the stator field rotation frequency is generated, signals U _{s of the} supply voltage are determined, signals of the phase currents i _sa , i _sb , i _{sc of the} stator and signals of the phase currents i _ma , i _mb , i _{mc of} magnetization are generated on transfer functions

where U _sf (p), I _sf (p), I _mf (p) are the Laplace transforms of respectively the phase signals of the supply voltage, stator currents and magnetization,
K ₁ - gain,
T ₀ , T ₁ , T ₂ , T ₃ - time constants depending on the relative slip s and the parameters r ₁ , L ₁ , r ' ₂ , L' ₂ , L _m T-shaped equivalent circuit of the engine,
with relative slip s = 0
K ₁ = 1 / r ₁ ,
T ₁ = (L ₁ + L _m ) / r ₁ , T ₀ = T ₂ = T ₃ = 0
In addition, the projections i _sα , i _sβ and i _mα , i _{mβ of the} vectors of the stator current and magnetization current signals are _generated on the orthogonal axes α-β of the coordinate system fixed relative to the stator, the vector product of which forms the electromagnetic signal of the motor. The parameters of the transfer functions depend on the relative slip value s, which is given by a constant value. When forming the electromagnetic moment, an expression is used for the vector product of stator currents and magnetization, which is the product of the moduli of the vectors of these currents by the sine of the angle between them. The angle between the vectors of the stator current and the magnetization current is assumed to be constant and equal to ninety degrees minus the angle between the phase current of the stator and the voltage in the short circuit mode.

The disadvantages of the described method include:
1) the possibility of using the model only for a qualitative assessment of transients due to:
- very low accuracy of the estimation of the signals of the stator currents and magnetization, due, firstly, to the use of a simplified T-shaped equivalent circuit of the motor phase and, secondly, to the assumption of constant relative slip in the study of motor dynamics;
- very low accuracy of the formation of the signal of the electromagnetic moment, due, firstly, the low accuracy of the signals of the stator currents and magnetization, and secondly, the assumption that the angle between the stator current vectors and the magnetization current is constant and, thirdly, the absence of the number in the expression for the electromagnetic moment pairs of motor poles;
2) the impossibility, due to the low accuracy of the estimation of stator currents and magnetization, to estimate the magnitude of the electromagnetic moment using a faster expression based on the vector product of the stator currents and magnetization expressed through the projections of the current vectors onto the orthogonal axes α-β of the coordinate system fixed relative to the stator .

 The advantages of the described method include the presentation of the model of an asynchronous motor in the form of transfer functions of phase currents with respect to the supply voltage, which, if the accuracy of the parameters included in these functions is improved, can make it possible to obtain an analytical model - a motor standard and to synthesize current regulators by analytical methods.

 The task: to improve the accuracy of the assessment of the controlled variables of a three-phase squirrel-cage induction motor.

 To solve this problem, the proposed method is directed.

T₃ = s (L'₂)/r'₂,
где r₁ и L₁ - активное сопротивление и индуктивность фазы статора,
r'₂ и L'₂ - приведенные к цепи статора активное сопротивление и индуктивность фазы ротора,
L_m - индуктивность ветви намагничивания,
формируют сигналы i_sa, i_sb, i_sc фазных токов статора по передаточным функциям (1) путем цифрового моделирования или по новым выражениям для фазных токов i_sф(t) статора в функции времени t при сигнале задания питающего напряжения в виде идеальной синусоиды с частотой ω₁ одной из гармоник

где U_m - максимум сигнала питающего напряжения,
ψ_ф - начальный фазовый сдвиг синусоиды питающего напряжения в соответствующей фазе двигателя,
φ₁ - фазовый сдвиг фазного тока статора по отношению к питающему напряжению фазы, вычисляемый в дискретные моменты времени по параметрам T-образной схемы замещения и новому значению относительного скольжения s,
Z_1M - модуль комплексного сопротивления фазному току статора, вычисляемый в дискретные моменты времени,
A₁, B₁ - коэффициенты, вычисляемые по выражениям

При цифровом моделировании токов статора в зависимости от его цели в качестве сигнала задания напряжения используется сформированный сигнал или измеренный по крайней мере в двух фазах статора двигателя.The problem is solved due to the fact that:
at discrete points in time
- form a signal of relative slip s,
- calculate the gain and time constants included in the transfer functions (1) with relative slip s ≠ 0 using new expressions that take into account all the parameters of the classical T-shaped equivalent circuit
K ₁ = 1 / r ₁ ,
T ₀ = s (L _m + L ' ₂ ) / r' ₂ ,
T ₁ = 2a / (bc),
T ₂ = 2a / (b + c),
a = L ₁ T ₀ + L _m T ₃ ,
b = r ₁ T ₀ + L ₁ + L _m ,

T ₃ = s (L ' ₂ ) / r' ₂ ,
where r ₁ and L ₁ - resistance and inductance of the stator phase,
r ' ₂ and L' ₂ - reduced to the stator circuit, the resistance and phase inductance of the rotor,
L _m - the inductance of the magnetization branch,
generate signals i _sa , i _sb , i _sc of stator phase currents according to the transfer functions (1) by digital modeling or by new expressions for phase stator currents i _sph (t) as a function of time t with a signal for setting the supply voltage in the form of an ideal sinusoid with a frequency ω _{1 of} one of the harmonics

where U _m is the maximum signal voltage
ψ _f - the initial phase shift of the sinusoid of the supply voltage in the corresponding phase of the motor,
φ ₁ is the phase shift of the phase current of the stator with respect to the supply voltage of the phase, calculated at discrete points in time by the parameters of the T-shaped equivalent circuit and the new value of the relative slip s,
Z _1M - the module of the complex resistance to the phase current of the stator, calculated at discrete points in time,
A ₁ , B ₁ - coefficients calculated by the expressions

In digital modeling of stator currents, depending on its purpose, the generated signal or measured in at least two phases of the motor stator is used as a voltage reference signal.

где U_m - максимум сигнала питающего напряжения,
φ_m/ - фазовый сдвиг фазного тока намагничивания по отношению к питающему напряжению фазы, вычисляемый в дискретные моменты времени по параметрам T-образной схемы замещения и новому значению относительного скольжения s,
Z_mM - модуль комплексного сопротивления фазному току намагничивания, вычисляемый в дискретные моменты времени,
A₂, B₂ - коэффициенты, вычисляемые по выражениям

формируют проекции i_mα и i_mβ вектора сигналов тока намагничивания на ортогональные оси α-β системы координат, неподвижной относительно статора, путем цифрового моделирования по новой передаточной функции сигналов токов намагничивания по сигналам токов статора

где I_m(p), I_s(p) - преобразования по Лапласу проекций на ортогональные оси координат α-β соответственно векторов сигналов токов статора и намагничивания.With the same accuracy, it is possible to generate signals of phase magnetization currents by expression (4), similar to expression (3):

where U _m is the maximum signal voltage
φ _{m /} is the phase shift of the phase magnetization current with respect to the supply voltage of the phase, calculated at discrete moments of time by the parameters of the T-shaped equivalent circuit and the new value of the relative slip s,
Z _mM is the module of the complex resistance to the phase magnetization current, calculated at discrete time instants,
A ₂ , B ₂ - coefficients calculated by the expressions

form the projections of i _mα and i _mβ of the magnetization current signal vector on the orthogonal axes α-β of the coordinate system fixed relative to the stator, by digital simulation of the magnetization current signals by the new transfer function using the stator current signals

where I _m (p), I _s (p) are the Laplace transforms of the projections onto the orthogonal coordinate axes α-β, respectively, of the signal vectors of the stator currents and magnetization.

где U_s(p), I_s(p) - преобразования по Лапласу соответственно сигнала питающего напряжения статора и сигнала тока статора,
K₂ - коэффициент усиления, вычисляемой по выражению K₂ = r₁;
T₄ - постоянная времени, вычисляемая по выражению T₄ = T₁ + T₂.In addition, the solution of the problem is achieved due to the fact that the signal u _s (t) of the supply voltage of the stator with relative slip s ≠ 0 is formed by digital modeling using the new transfer function

where U _s (p), I _s (p) are the Laplace transforms of the stator supply voltage signal and the stator current signal, respectively,
K ₂ is the gain calculated by the expression K ₂ = r ₁ ;
T ₄ is the time constant calculated by the expression T ₄ = T ₁ + T ₂ .

By the expression (6) by digital modeling, we can evaluate:
- signal at the stator clamps according to the stator currents measured in at least two phases
and / or
- voltage reference signal, intended for delivery to the frequency converter and generated by the measured stator current and the signal from the output of the current regulator.

In addition, the solution of this problem can be achieved due to the fact that, to take into account the spatial asymmetry of the phases of the stator of the motor, projections of signals are formed on the imaginary axis β of the orthogonal coordinate system stationary relative to the stator, according to new expressions
i _sβ = K [i _sb sin (ψ _ab ) -i _sc sin (ψ _ac )],
where K = i _sa / [i _sa + i _sb cos (ψ _ab ) + i _sc cos (ψ _ac )],
ψ _ab , ψ _ac are the spatial angles between phases a and b, respectively, and between phases a and c.

The high accuracy of estimating the stator currents i _s and magnetization currents i _m allows us to evaluate:
- phase current of the rotor or its projection onto orthogonal coordinate axes according to the expression
i ' _r = i _m - i _s ,
- electromagnetic moment M, in contrast to the prototype in terms of:
the most optimal in terms of speed
M = 1.5L _m p _τ (i _sβ i _mα -i _sα i _mβ ) (7)
or more accurate on p _τ compared to the prototype
M = 1.5L _m p _τ I _sM I _mM sinα, (8)
or the most accurate, different from the previous factor m _1/2
M = (m ₁ m _{2/4) L m p τ (i sβ} i mα -i sα i mβ) ( 9)
or
M = (m ₁ m _{2/4) L m p τ I sM I} mM sinα, ( 10)
where m ₁ and m ₂ are the number of phases respectively in the stator and rotor,
p _τ is the number of pole pairs in the motor,
I _sM and I _mM are the modules of the stator current and magnetization current vectors, respectively
α is the angle between the vectors of the stator current and the magnetization current, formed in contrast to the prototype according to one of the expressions:
α = arctan (i _sβ / i _sα ) -arctg (i _mβ / i _mα )
when following from expressions (9) and (10) for the electromagnetic moment
α = arcsin ((i _sβ i _mα -i _sα i _mβ ) / (I _sM I _mM ))
or
α = arctan ((i _sα i _mα + i _sβ i _mβ ) / (i _sβ i _mα -i _sα i _mβ )).
Increasing the accuracy of estimating the signal of the electromagnetic moment M according to expressions (8) and (10) to the accuracy of estimating using expressions (7) and (9), as well as introducing a new dependence of the magnetization current on the stator current by expression (5), opens up new possibilities for finding new laws of regulation of engine variables in systems with vector control.

Expression (10) can be obtained from the well-known expression of the electromagnetic moment through the resulting complex functions of flux linkage and current:
M = (m ₂ p _τ / 2) Im [ψ _rs i $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ ], (eleven)
where ψ _rs = L _rsm i _s e ^-jθ - (12) the resulting flux linkage vector,
i _r ^* is the vector conjugate to the resulting rotor current vector,
L _rsm = (m _1/2 ) L _m - (13) the mutual inductance of the rotor under the influence of the stator,
i _s is the resulting stator current vector, multiplied by e ^{-jθ is} reduced to a rotating coordinate system of the rotor,
θ is the angle of rotation of the rotor.

где

и т.д.It is known from the theory of a rotating field that the resulting vectors of stator current i _s , magnetization i _m and rotor i _r can be expressed as follows in terms of instantaneous values of the phase currents of the motor:

Where

etc.

Substituting expressions (12) - (14) in (11), we obtain the expression of the electromagnetic moment through the instantaneous values of the stator and rotor currents:
M = (m ₁ m _{2/4) L m p τ I sM I} rM sin (α s -α r -θ). (16)
Computer simulation of the moment according to expression (16) showed that it is unsuitable for estimating the electromagnetic moment, since the stator and rotor currents contained in it are very large in amplitude, and the angle between them, on the contrary, is very small. A small error in the estimation of the angle can lead to incorrect conclusions, in particular, about the dependence of the nature and time of the transition process on the initial position of the rotor, characterized by θ _{0 of the} initial displacement of the rotor axes with respect to the stator axes. Substituting in (11) i _r = i _m e ^jθ -i _s e ^jθ and taking into account that i _s xi _s = 0, we obtain expression (10) for the torque, from which it can be seen that the latter depends on the number of phases in the stator and rotor, inductance of the magnetization branch of the motor phase, the number of pole pairs, amplitudes and phase difference (α = α _s -α _r ) of the resulting stator and magnetization currents and does not depend on the position of the rotor.

 In the process of searching for analogues and selecting a prototype among the reviewed technical solutions, no signs were found that are similar to the hallmarks of the claimed technical solution.

 In the proposed technical solution, the problem of eliminating the disadvantages of the prototype is solved by taking into account all the parameters of the classical T-shaped circuit for replacing the HELL phase with a squirrel-cage rotor, generating signals of the stator currents and magnetization and supply voltage signals using new expressions, generating relative slip and angle signals at discrete times between vectors of stator currents and magnetization.

 All this, as will be shown below, can improve the accuracy of the assessment of controlled variables of blood pressure.

 The invention is illustrated by the drawings shown in FIG. 1-25.

 In FIG. 1 shows the classic T-shaped phase equivalent circuit of a three-phase squirrel-cage motor with a squirrel-cage rotor, which is the basis of the proposed method for evaluating controlled variables of blood pressure.

 In FIG. Figure 2-4 shows the variants of block diagrams of devices that implement the assessment of the most important controlled variables of blood pressure.

 In FIG. 5-11 are block diagrams of the functional blocks 1-7 of which the devices consist, diagrams of which are shown in FIG. 2-4.

 In FIG. 12-15 are block diagrams of functional blocks 9-12, which are part of the block 5 shown in Fig.9.

 In FIG. 16 is a block diagram of an analog device [9] using object models and models with variable observers, in which a device implemented by the proposed method is used as an object model.

 In FIG. 17 is a block diagram of a device that evaluates known controlled variables of blood pressure in a speed-optimal way.

 In FIG. 18-21 are block diagrams of functional blocks 8, 13, 14 and 15. which are part of the device, the circuit of which is shown in FIG. 17.

 In FIG. 22 shows a fragment of a device for evaluating stator currents and magnetization, as well as the electromagnetic moment of blood pressure with an asymmetric and non-sinusoidal supply voltage.

 In FIG. 23 shows a block 16 for generating signals of the supply voltage from the signals of the stator currents using the inventive transfer function.

In FIG. 24 and 25 are graphs of transients in the electromagnetic moment M and the rotor speed ω _r during direct start-up of the AM, confirming the high accuracy and stability of the proposed method for evaluating the controlled variables of the engine in a wide range of variation of the sampling step, including a sufficiently small 5 μs.

- векторы соответственно сигналов токов статора и намагничивания,

- в общем случае вектор сигнала напряжения статора в функции времени t и частоты вращения поля статора ω_s. Для блоков 2-1 и 3-1 это - U_m, ω₁ , t и ψ для каждой фазы, а для блоков 2-2- и 3-2 это -

- вектор сигнала напряжения статора, соответствующий моменту времени, определяемому переменной K, равной номеру шага дискретизации.In FIG. 2, 3 and 4 are indicated:
1 - protein parameter calculation (Fig. 5),
2 - block forming the stator current (Fig. 6),
3 - block forming the magnetization current or its projections on the orthogonal coordinate axis (Fig. 7),
4 - coordinate Converter (KP) 3F / 2F (3 phases / 2 phases) (Fig. 8),
5 - block forming the electromagnetic moment (Fig. 9),
6 - block forming the rotor speed (Fig. 10),
7 - block forming the relative slip (Fig. 11),

- vectors, respectively, of the signals of the stator currents and magnetization,

- in the general case, the stator voltage signal vector as a function of time t and the stator field rotation frequency ω _s . For blocks 2-1 and 3-1 it is U _m , ω ₁ , t and ψ for each phase, and for blocks 2-2- and 3-2 it is

is the vector of the stator voltage signal corresponding to the time instant determined by the variable K equal to the number of the sampling step.

 Each vector consists of phase a, d, and c signals.

- например, вектор сигнала тока статора, соответствующий моменту времени, определяемому переменной K, равной номеру шага дискретизации.In FIG. 6, 7, 19 are indicated:

- for example, the stator current signal vector corresponding to the time instant determined by the variable K equal to the number of the sampling step.

In block 1 (Fig. 5) is indicated:
1 - input for entering blood pressure parameters and its load,
2 - input for inputting a signal ω _s setting the frequency of rotation of the stator field,
3 - input for inputting the signal s relative slip,
4 - outputs.

 The number of input parameters at input 1 of block 1 and the number of outputs 4 is determined by the number of evaluated signals and the specific implementation of other blocks, the input of which receives parameters from output 4 of block 1.

In blocks 2, 3, 5, 6, 13 and 16 (Fig. 6, 7, 9, 10, 19 and 23) are indicated:
1 - input for entering the necessary variables from block 1, and the number of variables is determined by the mathematical expression that implements this block.

 In block 5 from block 1, at input 1, the coefficient Km of proportionality of the electromagnetic moment, determined by the expression (6), or (7), or (8), or (9), implemented in block 5, is introduced.

In block 6 from block 1 at input 1, a proportionality coefficient K _ω is introduced, determined by the basic equation of dynamics and equal to the ratio of the number of pole pairs of the motor p _τ to the value J of the total moment of inertia of the motor and its load.

 In control systems with a speed sensor and / or rotor position, block 6 is not used.

 The implementation of blocks 1 ... 8 and 11 is determined by the specific problem being solved.

вектор какого-либо сигнала, например тока или напряжения статора в реальных осях a-b-c статора,
i_α,i_β - проекции вектора какого-либо сигнала на ортогональные оси α-β системы координат, неподвижной относительно статора.In blocks 4-1, 4-2 (Fig. 8) is indicated:

the vector of a signal, for example, the current or voltage of the stator in the real axes abc of the stator,
i _α , i _β are the projections of the vector of a signal on the orthogonal axis α-β of the coordinate system, which is fixed relative to the stator.

векторов сигналов токов с выхода наблюдателя тока и потокосцеплений (блок II),
i₁ ^* - сигнал тока статора по способу, заявленному в [9],

соответственно проекции вектора тока статора на оси α-β ортогональной системы координат,
неподвижной относительно статора, и частота вращения ротора по способу, заявленному в [9],
На фиг. 17 обозначено:
8 - блок формирования угла поворота ротора (фиг. 18),
13 - блок формирования проекций потокосцеплений статора и ротора на ортогональные оси α-β (фиг. 19),
14 - блок формирования тока ротора (фиг. 20),
15 - известный координатный преобразователь (КП) 2ф/3ф (2 фазы / 2 фазы) (фиг. 21),
i_sx, i_sy, i_rx, i_ry, i_mx, i_my - соответственно проекции токов статора, ротора и намагничивания на оси системы координат, вращающейся относительно статора с произвольной скоростью ω_{k k}, ψ_sx,ψ_sy,ψ_rx,ψ_ry - соответственно проекции потокосцеплений статора и ротора на оси системы координат, вращающейся относительно статора с произвольной скоростью ω_k.
В частном случае ω_k= ω_r в системе координат с осями d-q вместо x-y.In FIG. 16 is indicated:
1 is a block that implements a model of an object of regulation, in particular three-phase HELL with a squirrel-cage rotor according to the claimed method,
II is a block that implements observers flux linkage and stator current according to the method claimed in [9],
III - a block that implements an observer of the rotor speed according to the method claimed in [9],
IV is a block that implements the conversion of the signal to set the voltage of the stator to the form according to the method claimed in [9],
V is a block that implements the projection of the stator current signals from the output of block I to a form according to the method [9],
8 is a block for subtracting projections i _sα , i _sβ of current signal vectors from the output of the model of the regulatory object (block I) and projections

vectors of current signals from the output of the current observer and flux linkage (block II),
i ₁ ^* is the stator current signal according to the method claimed in [9],

respectively, the projection of the stator current vector on the α-β axis of the orthogonal coordinate system,
stationary relative to the stator, and the rotor speed according to the method claimed in [9],
In FIG. 17 is indicated:
8 - block forming the angle of rotation of the rotor (Fig. 18),
13 is a block for the formation of projections of flux linkages of the stator and rotor on the orthogonal axis α-β (Fig. 19),
14 - block forming the rotor current (Fig. 20),
15 is a known coordinate Converter (KP) 2F / 3F (2 phases / 2 phases) (Fig. 21),
i _sx , i _sy , i _rx , i _ry , i _mx , i _my are, respectively, the projections of the stator, rotor and magnetization currents on the axis of the coordinate system rotating with respect to the stator at an arbitrary speed ω _{k k} , ψ _sx , ψ _sy , ψ _rx , ψ _ry are, respectively, the projections of the stator and rotor flux linkages on the axis of the coordinate system rotating relative to the stator with an arbitrary speed ω _k .
In the particular case, ω _k = ω _r in the coordinate system with the dq axes instead of xy.

In FIG. 22 is indicated:
1 - block summing the projections of the vectors N harmonics of the stator currents on the axis α of the fixed coordinate system,
2 - block summing the projections of the vectors N harmonics of the stator currents on the axis β of the fixed coordinate system,
3 - block summation of the projections of the vectors N of harmonics of the magnetization currents on the axis α of the fixed coordinate system,
4 - block summation of the projections of the vectors N of harmonics of the magnetization currents on the axis β of the fixed coordinate system,
5 - unit for generating electromagnetic moment (Fig. 9), inputs 2-1, 2-2 and 3-1, 3-2 of block 1 correspond to inputs 2 and 3 in FIG. nine,
6-1 - block summing the projections of the vectors of the first harmonic of the stator currents of the forward and reverse sequences on the axis α of the fixed coordinate system,
7-1 - block summing the projections of the vectors of the first harmonic of the stator currents of the forward and reverse sequences on the axis β of the fixed coordinate system,
8-1 - block summing the projections of the vectors of the first harmonic of the magnetization currents of the forward and reverse sequences on the axis α of the fixed coordinate system,
9-1 - block summing the projections of the vectors of the first harmonic of the magnetization currents of the forward and reverse sequences on the axis β of a fixed coordinate system,
6-N - block summing the projections of the vectors of the Nth harmonic of the stator currents of the forward and reverse sequences on the axis α of the fixed coordinate system,
7-N - block summing the projections of the vectors of the Nth harmonic of the stator currents of the forward and reverse sequences on the axis β of the fixed coordinate system,
8-N - block summing the projections of the vectors of the Nth harmonic of the magnetization currents of the forward and reverse sequences on the axis α of the fixed coordinate system,
9-N is a block for summing the projections of the vectors of the Nth harmonic of the magnetizing currents of the forward and reverse sequences onto the β axis of a fixed coordinate system,
i _sα pr1, i _sβ pr1, i _sα prN, i _sβ prN are the projections of the current vectors of the direct sequence, for example, the stator of the first and Nth harmonics, respectively
i _sα obr1, i _sβ obr1, i _sα obrN, i _sβ obrN are the projections of the current vectors of the reverse sequence, for example, the stator of the first and Nth harmonics, respectively
i _sα 1, i _sα N - for example, the projection of the stator current vectors of the first and Nth harmonics, respectively.

 In FIG. 2 shows a block diagram of a device similar to the prototype. The device comprises a parameter calculation unit 1, the input 2 of which is connected to the input 1 of block 7, and the input 3 to the output 3 of block 7, the input 2 of which can be connected to the output 4 of block 6 or to the output of the rotor speed meter. The outputs 4 of block 1 are connected to the inputs 1 of blocks 2, 3 (blocks 3-1 or 3-2), 5 and 6. The input 2 of block 2 is connected to the input 2 of block 3. The outputs of 3 blocks 2 and 3 are connected to input 1 of a common or two different blocks 4. The outputs of 2 blocks or two blocks 4 are connected to the inputs 2 and 3 of block 5, the output 4 of which is connected to the input 3 of block 6, the output 4 of which can be connected to the input 2 of block 7.

 The device of FIG. 2 implements an estimate of the stator and magnetization phase currents according to the proposed method, their projections onto the orthogonal axis α-β of the coordinate system fixed relative to the stator, the electromagnetic moment of the motor, relative slip, and, if necessary, the rotor speed.

сигнала задания напряжения статора АД. Сформированные в блоках 2 и 3 векторы

сигналов токов соответственно статора и намагничивания с выходов 3 вышеназванных блоков подают на вход 1 одного или двух блоков 4, формирующих проекции векторов сигналов токов на ортогональные оси α-β системы координат, неподвижной относительно статора, которые с выходов 2 блоков 4 подают на входы 2 и 3 блока 5. Сформированный сигнал M электромагнитного момента с выхода 4 блока 5 подают на вход 3 блока 6, на вход 2 которого подают сигнал M_н момента нагрузки. Сформированный сигнал ω_s с выхода блока 6 подают, при необходимости, на вход 2 блока 1 в качестве сигнала обратной связи.The device of FIG. 2 operates as follows. At discrete time instants, inputs 1 and 2 of block 7-1 simultaneously receive respectively a signal ω _{s for} setting the stator field rotation frequency and a rotor speed signal measured or generated in block 6 (output 4) to generate a relative slip signal s, which is output 3 Block 7-1 is fed to input 3 of block 1. At the same time, signal ω _{s of} setting the stator field rotation frequency and input 1, parameters characterizing the motor and its load, are fed to input 2. From the outputs 4 of block 1, the generated coefficients and time constants are fed to the inputs 1 of blocks 2, 3, 5 and, if necessary, of block 6. In addition, the measured values are fed to the inputs of 2 blocks 2 and 3 (3-1 or 3-2) at least in two phases and (or) the vector formed in block 16 (Fig. 23)

signal setting voltage of the stator HELL. The vectors formed in blocks 2 and 3

the current signals of the stator and magnetization from the outputs 3 of the above blocks are fed to the input 1 of one or two blocks 4, forming projections of the current signal vectors onto the orthogonal axis α-β of the coordinate system, which is stationary relative to the stator, which from the outputs of 2 blocks 4 are fed to inputs 2 and 3 blocks 5. The generated signal M of the electromagnetic moment from the output 4 of block 5 is fed to the input 3 of block 6, to the input 2 of which a signal M _{n of} the load moment is supplied. The generated signal ω _s from the output of block 6 is fed, if necessary, to the input 2 of block 1 as a feedback signal.

 In FIG. 3 shows a block diagram of an embodiment of a device different from the device of FIG. 2 by the fact that the magnetization current generating unit 3-1 or 3-2 is replaced by a unit 3-3, the input 2 of which is connected to the output 3 of the unit 1. This device is advantageous in comparison with the analog device of the prototype shown in FIG. 2, a simpler implementation of block 3-3 is compared to blocks 3-1 and 3-2, while maintaining the same accuracy in estimating the signals of the phase magnetization currents.

 The general disadvantage of the devices of FIG. 2 and 3 is the presence of two coordinate converters implemented in block 4 or more complex block based on block 4, which sequentially receives signals from blocks 2 and 3 at one input and, having processed them, gives output signals to different outputs. In terms of speed and ease of implementation based on analogue technology, the advantage remains of using two coordinate converters based on block 4 in terms of the number of current signals, namely, stator current and magnetization current. In addition, when adjusting the ABP variables, the instantaneous values of the signals of the phase magnetization currents (outputs of blocks 3-1, or 3-2 in Fig. 2, or 3-3 in Fig. 3) are required only for generating projections of the signals of the magnetization currents on the orthogonal coordinate axes . Therefore, in these cases, it is advisable to use devices that allow "faster" to evaluate the controlled variables of blood pressure, depending on the signals of the magnetization current.

 For example, in FIG. 4 shows a block diagram of an embodiment of a device that implements the proposed method for evaluating the signals of stator currents and magnetization, increasing the speed of a device that evaluates, for example, signals of electromagnetic moment and, if necessary, rotor speed.

 The device comprises a parameter calculation unit 1, the input 2 of which is connected to the input 1 of block 7, and the input 3 to the output 3 of block 7, the input 2 of which can be connected to the output 4 of block 6 or the output of the rotor speed meter. The outputs 4 of block 1 are connected to the outputs 1 of blocks 2, 3-3, 5 and 6. The output 3 of block 2 is connected to the input 1 of a single coordinate converter based on block 4, the outputs 2 of which are connected to inputs 3 of block 5 and inputs 2 of block 3- 3, the output 3 of which is connected to the outputs 2 of block 5, the output 4 of which is connected to the input 3 of block 6, the output 4 of which can be connected to the input 2 of block 7 in the control system without a speed sensor and / or rotor position or with the output of the meter rotor speed if any.

 The device shown in FIG. 4, realizes the assessment by the proposed method of stator phase currents, their projections on the orthogonal axis α-β of the coordinate system of the projections on the same axis of the magnetization current vector, the motor electromagnetic moment, relative slip and, if necessary, the rotor speed, relative to the stator. In this device, in comparison with those shown in FIG. 2 and 3, only one coordinate converter is used on the basis of block 4 instead of two, two signals are input to input 2 of block 3-3 instead of three, and two signals instead of three are also received at output 3 of block 3-3.

 When evaluating the controlled variables, including the rotational speed of the rotor of a three-phase asynchronous motor with a short-circuited rotor, two device states are distinguished: start-up and cyclic operation at discrete time instants.

When starting up the device, initial values r ₁ , L ₁ , L _m , L ' ₂ , r' _{2 of the} parameters of the T-shaped equivalent circuit, the number P _{r of the} pairs of motor poles and the moment J of inertia of the motor with a load, are input 2 blocks 1 and input 1 of block 7 provide the initial value of the signal ω _{s for} setting the frequency of rotation of the stator field, and input 2 of block 7 - the initial zero value of the signal ω _{r of the} frequency of rotation of the motor rotor.

сигналов напряжения статора (измерение и формирование сигналов задания напряжения могут выполняться до начала очередного цикла функционирования устройства по фиг. 4, но с тем же периодом дискретизации dt), который подают на вход 2 блока 2, с выхода 3 которого сформированный вектор

тока статора подают на вход 1 блока 4, с выхода 2 которого сформированные проекции i_sα,i_sβ на ортогональные оси α-β сигналов токов статора подают на вход 2 блока 3-3 и вход 3 блока 5, на вход 2 которого также подают проекции i_mα,i_mβ на ортогональные оси α-β сигналов токов намагничивания, сформированный сигнал M электромагнитного момента с выхода 4 блока 5 подают на вход блока 6, на вход 2 которого также подают сигнал M_н момента нагрузки, на выходе 4 блока 6 получают сигнал ω_r частоты вращения ротора.Then, at discrete time instants, input 2 of block 1 and input 1 of block 2 is supplied with the next value of the signal ω _{s for} setting the rotational speed of the stator field; input 2 of block 7 is supplied with a feedback signal ω _{r with} respect to the rotor speed, for example, from output 4 of block 6 , from the output 3 of block 7 to the input 3 of block 1, the feedback signal relative to the slip s formed in block 7 is supplied, the parameters r ₁ , L ₁ , L _m , L ' ₂ , r' ₂ T-shaped are fed to the input 1 of block 1 replacement scheme engine (which may be constant or vary from heating and (or) metal saturation), the number p _τ n pairs luces of the engine and the moment J of the inertia of the engine with the load, from the outputs 4 of block 1, apply the necessary coefficients and time constants to the inputs 1 of blocks 2, 3-3, 5 and 6, measure at least two phases and (or) form, for example, in block 16, vector

the stator voltage signals (the measurement and generation of voltage setting signals can be performed before the start of the next operation cycle of the device in Fig. 4, but with the same sampling period dt), which is fed to input 2 of block 2, from output 3 of which the generated vector

the stator current is fed to input 1 of block 4, from the output 2 of which the formed projections i _sα , i _sβ to the orthogonal axes α-β of the signals of the stator currents are fed to input 2 of block 3-3 and input 3 of block 5, input 2 of which also serves i _mα , i _mβ on the orthogonal axes α-β of the magnetization current signals, the generated signal M of the electromagnetic moment from the output 4 of block 5 is fed to the input of block 6, to the input 2 of which also a signal M _{n of} the load moment is received, at the output 4 of block 6 receive a signal ω _r rotor speed.

 Further, the device operates in a cycle with a period dt according to the described algorithm.

 In FIG. 16 is a block diagram of an analog device [9] operating in a closed-loop control system with increased requirements for regulatory quality. This device uses the model of the regulatory object (block I), implemented by the proposed method, and models with observers of variables (blocks II and III), implemented by the method described in [9].

 The device of FIG. 16 differs from that described in [9] only in block I simulating an object of regulation by the claimed method. In this case, block I is implemented according to the structure shown in FIG. 4. As in the known device, block I has one output connected to the input of block V of the known device, and one common input signal with block IV of the known device.

 The advantage of this device in comparison with the known is the greater accuracy of estimating the stator current by the claimed method, which will increase the accuracy of the evaluation of other variables by the known method.

по заданному, например, с выхода регулятора тока или измеренному току статора

фазных токов статора

их проекций i_sα,i_sβ на ортогональные оси α-β неподвижной относительно статора системы координат, проекций i_mα,i_mβ на те же оси векторов токов намагничивания и i_rα,i_rβ ротора и ψ_sα,ψ_sβ векторов потокосцеплений статора и ψ_rα,ψ_rβ ротора, электромагнитного момента двигателя M относительного скольжения S, частоты вращения ротора ω_r угла поворота ротора θ, проекций i_sx, i_sy на ортогональные оси x-y вращающейся системы координат векторов токов статора, i_mx, i_my намагничивания и i_rx, i_ru ротора, проекций ψ_sx,ψ_sy на те же оси векторов потокосцеплений статора и ψ_rx,ψ_sy ротора, модулей векторов токов статора I_sM и намагничивания I_mM, фазовых сдвигов α_s между вектором ток статора и вещественной осью координат, α_m между вектором тока намагничивания и вещественной осью координат и α между векторами токов статора и намагничивания. Повышение точности оценки перечисленных регулируемых переменных AD открывает новые возможности при реализации систем управления вектором.In FIG. 17 shows a block diagram of a device that evaluates with high accuracy the optimal speed by the method of the following adjustable variables of blood pressure: supply voltage

for a given, for example, from the output of the current regulator or the measured stator current

stator phase currents

their projections i _sα , i _sβ on the orthogonal axis α-β of the coordinate system fixed relative to the stator, projections i _mα , i _mβ on the same axis of the magnetization current vectors and i _rα , i _{rβ of the} rotor and ψ _sα , ψ _sβ of the stator flux link vectors and ψ _rα , ψ _{rβ of the} rotor, the electromagnetic moment of the motor M relative slip S, the rotor speed ω _{r of the} angle of rotation of the rotor θ, the projections i _sx , i _sy on the orthogonal axis xy of the rotating coordinate system of the stator current vectors, i _mx , i _my magnetization and i _rx , i _{ru of the} rotor, projections ψ _sx , ψ _sy on the same axis of the stator flux link vectors and ψ _rx , ψ _{sy of the} rotor, the stator current vector modules I _sM and magnetization I _mM , phase shifts α _s between the stator current vector and the real coordinate axis, α _m between the magnetization current vector and the real coordinate axis and α between the stator current vectors and magnetization. Improving the accuracy of evaluating the listed controlled variables AD opens up new possibilities for the implementation of vector control systems.

The device of FIG. 17 the device of FIG. 4. It is supplemented by:
- block 16, the output 3 of which is connected to the input 2 of block 2,
- block 14 - 2, the input 1 of which is connected to the output 3 of the block 3 - 3, and the output 2 - with the output 2 of the block 4 - 1, from the output 3 of the block 14 receive projection signals of the rotor current vector on the α-β axis;
- one or two blocks 15, the inputs 1 of which are connected to the output 2 of the block 4 - 1, the inputs 2 - with the output 2 of the additional block 8 - 1, and the outputs 3 - with the inputs 1 and 2 of the additional block 14 - 2, from the output 3 of which receive signals of projections of the rotor current vector on the x - y axis;
- one or two blocks 13, inputs 1 of which are connected to the output 4 of block 1, inputs 2 - with the output 2 of blocks 4 - 1, inputs 3 - with the output 3 of blocks 3 - 3, and outputs 4 and 5 with the input 1 of one or two additional blocks 15, the inputs 2 of which are connected to the output 2 of the block 8 - 1, and the outputs 3 of which receive the signals of the projections of the flux linkage vectors of the stator and rotor on the x - y axis;
- block 11 - 1, input 1 of which is connected to the output 2 of block 4 - 1, input 2 - with the output of block 3 - 3, output 3 receives a phase shift signal between the stator currents and magnetization vectors, and output 4 - a phase shift signal between the stator current vector and the α axis, from output 5, a phase shift signal between the magnetization current vector and the α axis;
- one or two blocks 9, the inputs 1 of which are connected to the output 2 of the block 4 - 1 and the output 3 of the block 3 - 3, and with the output 2 receive signals, respectively, of the modules of the stator currents and magnetization.

 In FIG. Figure 22 shows a fragment of a device designed to improve the accuracy of estimating stator currents and motor variables depending on them at asymmetric and non-sinusoidal supply voltages. This fragment may be connected before block 5 to the device shown in FIG. 4, which, in turn, becomes a fragment of a more complex device.

 In a fragment of the device of FIG. 22 to the inputs 1 of blocks 6 - 1, 7 - 1, 8 - 1, 9 - 1 ... 6 - N, 7 - N, 9 - N provide projection signals on the α-β axis of the stator current vectors and the direct sequence magnetization for N harmonics, inputs 2 - similar signals for currents of the negative sequence, outputs 2 of blocks 6 - 1, 6 - 2 ... 6 - N are connected to the inputs 1,2..N of block 1, the output N + 1 of which is connected to the input 2 - 1 of block 5, outputs 2 of blocks 7 - 1, 7 - 2 ... 7 - N are connected to inputs 1, 2..N of block 2, output N + 1 of which is connected to input 2 - 2 of block 5, outputs 2 blocks 8 - 1, 8 - 2 ... 8 - N are connected to the inputs 1,2. ..N of block 3, the output of N + 1 of which is connected to the input 3 - 1 of block 5, the outputs of 2 blocks of 9 - 1, 9 - 2 ... 9 - N are connected to the inputs 1,2..N of block 4, the output of N + 1 which is connected to the input 3 - 4 of block 5, from the output 4 of which receive the signal M of the electromagnetic moment.

формируют (блоки 6 - 1, 7 - 1, 8 - 1, 9 - 1...6 - N, 7 - N, 8 - N, 9 - N, фиг. 22) проекции на те же оси векторов сигналов токов статора i_sα1,i_sβ1...i_sαN,i_sβN и намагничивания i_mα1,i_mβ1...i_mαN,i_mβN, формируют (блоки 1, 2, 3, 4, фиг. 22) проекции на те же оси векторов сигналов токов статора i_sα,i_sβ и намагничивания i_mα,i_mβ, по векторному произведению которых формируют (блок 5, фиг. 22) сигнал M электромагнитного момента двигателя.When the supply voltage is asymmetric, voltage signals of the forward and reverse sequences are generated for three phases, form (block 7 - 2, Fig. 11) for signals of the negative sequence, the relative slip signal equal to "two" minus the relative slip s formed (block 7 - 1, Fig. 11) for currents of the direct sequence, time constants and gain factors included in the transfer functions and other parameters depending on the relative slip value are calculated for the signals of the forward and reverse sequences (block 1, Fig. 5), form for the currents of the forward and reverse sequences of projection onto the orthogonal axes α-β the vectors of the stator current signals i _sα pr1, i _sβ pr1 ... i _sα prN, i _sβ prN, i _sα obr1, i _sβ arr1 ... and magnetization

form (blocks 6 - 1, 7 - 1, 8 - 1, 9 - 1 ... 6 - N, 7 - N, 8 - N, 9 - N, Fig. 22) projections on the same axis of the stator current signal vectors i _sα 1, i _sβ 1 ... i _sα N, i _sβ N and magnetizations i _mα 1, i _mβ 1 ... i _mα N, i _mβ N, form (blocks 1, 2, 3, 4, FIG. 22) projections on the same axis of the vectors of signals of the stator currents i _sα , i _sβ and magnetization i _mα , i _mβ , the vector product of which form (block 5, Fig. 22) a signal M of the motor electromagnetic moment.

 When the supply voltage is non-sinusoidal, signals corresponding to the 1st through the Nth harmonics are extracted from its signals, projections of the stator and magnetization current signal vectors onto the orthogonal α-β axes are formed for each harmonic, the vector product of the same sums generating the motor electromagnetic moment signal .

 In the case of spatial asymmetry of the phases of the stator HELL in all devices, the coordinate converter 3ph / 2ph, implemented according to the structure of block 4-1 (Fig. 8), is replaced by a converter according to the structure of block 4-2 (Fig. 8).

 In the general case, the sequence of signal formation is determined by their functional relationships. Independent signals from each other can be formed in any sequence. If the device is designed to evaluate the controlled variables of an engine that has any parameters that do not change over time during the operation of the engine, for example, the number of pole pairs, in some cases the moment of inertia of the engine with a load, etc., then entering these parameters or calculating them performed once before the cyclic functioning of the device at discrete points in time.

 The inventive method is implemented in the form of a software package for a PC running in a Windows environment and allowing to study a three-phase asynchronous motor with a cage rotor as an object of regulation.

 The inventive method for evaluating the controlled variables of a three-phase squirrel-cage induction motor is based on analytical and digital models.

 The analytical model is implemented using blocks 2 - 1, 4 - 1 (for blood pressure with spatial stator symmetry) or 4 - 2 (for blood pressure with spatial stator asymmetry), 3 - 1, 5 - 1 or 5 - 2, 6 - 1, 7 - 1. Blocks 3 - 1 and 5 - 1 are implemented by digital modeling. The analytical model has good stability at a sampling step in the range of 5 - 200 μs.

 The analytical model of the engine implemented at a sampling step of 50 μs can be considered a reference, since the results of analytical modeling at a sampling step of 5–50 μs range are practically the same.

The following advantages and areas of application of the analytical model of a three-phase squirrel-cage induction motor can be noted:
1) high accuracy of the estimation of controlled variables, making the model a reference for digital models created on the basis of a T-shaped equivalent circuit and Gorev-Park equations describing the electromagnetic processes occurring in the engine, and allowing it to be used to simulate an object of regulation in direct microprocessor control systems with increased requirements for quality and range of regulation;
2) the possibility of synthesis of regulators by analytical methods for the transfer functions;
3) the ability to analyze the engine as an object of regulation to select the type of regulators and control laws.

 The digital model is implemented using blocks 2 - 2, 4 - 1 (for blood pressure with spatial stator symmetry) or 4 - 2 (for blood pressure with spatial stator asymmetry), 3 - 1, 5 - 1 or 5 - 2, 6 - 1, 7 - 1. Blocks 2 - 2, 3 - 1 and 5 - 1 are implemented by digital modeling. The digital model has good stability with a sampling step in the range of 0.005 - 1.8 ms.

In FIG. 24 and 25 are graphs of transients in the electromagnetic moment M and the rotor speed ω _r for direct start of the 4A100 / L4Y3 engine at a voltage U _max = 380 V with a frequency f ₁ = 50 Hz with an abrupt change in frequency and load moment Mn = 0, obtained with using the above software package.

 The graphs shown in FIG. 24 make it possible to compare the accuracy of the claimed engine model with the analog model [7], which describes the engine by the Gorev-Park differential equation system, written in the Cauchy form and solved in increments using the AB method. Bashirin to increase the accuracy and stability of the model; The electromagnetic moment of the engine is expressed through the projection of the stator and rotor flux linkages onto the orthogonal axes α-β of the coordinate system, which is fixed relative to the stator.

 In FIG. 24: 1 - reference analytical model (dt = 50 μs), 2 - digital model with discretization by the method, 3 - digital model with discretization by the method of equations in finite differences, 4 - analog model [7]. Sampling step dt = 50 μs for the standard and dt = 1 ms for the rest of the models.

The closest to analytical model 1 was model 2 with trapezoid discretization. From graphs 1 and 2 of FIG. 24 it is seen that the evaluation of the rotor speed ω _r by the trapezoidal method gives high accuracy, despite the significant difference from the reference graph of the instantaneous values of the engine torque determined by the trapezoidal method. This can be explained by the high accuracy of coincidence with the reference average moment obtained by modeling by the trapezoidal method. The simulation results of the instantaneous values of the electromagnetic moment according to expressions (6) and (7) differ from the simulation results by the expressions (8) and (9) by m _1/2 times, which is significant when controlling the moment according to its instantaneous values and is indifferent when adjusting the average moment or estimates of the moment of rotation of the rotor.

 Thus, the accuracy of estimating the electromagnetic moment, and according to it the rotational speed of the motor rotor by the stator and magnetization currents, is much higher than by the flux linkages of the stator and rotor.

 In FIG. 25 are graphs confirming the high accuracy and stability of the proposed method for evaluating the controlled variables of the engine in a wide range of variation of the sampling step, including with a sufficiently small 5 μs.

 In FIG. 25: 1 - reference analytical model with a sampling step dt = 50 μs, 2 - a digital model with discretization by the trapezoidal method and step dt = 50 μs, 3 - a digital model with discretization by the trapezoidal method and step dt = 1 ms.

 The proposed digital model with trapezoid discretization, in contrast to analogs and prototype, has good stability and accuracy without additional measures that increase them when changing the sampling step from 5 μs to 1.8 ms.

 Control systems for electric drives with increased dynamic and adjusting characteristics are traditionally implemented on digital-analog technology. In each case, the functional blocks of the control system are built on the element base that optimally meets the requirements for speed, accuracy, noise immunity and cost.

When implementing the proposed method as part of a direct microprocessor control system for electric drives, you can use various elements of modern digital-analog technology. These funds include:
- digital signal processors (DSPs) of the TMS320 series from TEXAS INSTRUMENTS [11] and DSP controllers based on them, on which additional system modeling is implemented;
- analog, digital-analog and digital microsystems of ANALOG DEVICES firm [12];
- programmable logic devices of the company ALTERA [13, 14],
- based on the RISC + CISC process C167 from Siemens [15].

 A device from TEXAS INSTRUMENTS has many features, but is the most expensive of those listed.

 ALTERA devices are the cheapest and fastest, but a signal processor is under construction. Therefore, it is advisable to use these devices only for the implementation of individual functions, such as coordinate transformations, fast Fourier transform, filters.

From the device company ANALOG DEVICES for controlling AC machines found application [12]:
- digital high-speed signal processors ADSP-21XX series,
- specialized vector coprocessors ADMC200 and ADMC201, allowing you to create various types of coordinate converters.

 A digital model was developed and tested on IBM486 (processor clock frequency 66 MHz + coprocessor for floating point operations) that simulates the estimation of controlled variables of a three-phase asynchronous motor with direct microprocessor control based on the main harmonic of the stator supply voltage. The execution time for one cycle of estimation of controlled variables is about 700 μs, which provides acceptable accuracy for drives with low accuracy requirements and engine rotor speeds up to 60 Hz.

 Based on the processor C167 from Siemens, the device according to the claimed method can be implemented with a sampling step of dt ≈ 500 μs at a processor frequency of 16 MHz. When implementing the method based on signal processors, the sampling step will be tens of times smaller, which allows implementing systems with vector control. With such a small sampling step, methods for estimating controlled variables using projections of flux linkages onto the orthogonal axes of rotating coordinate systems do not provide the necessary estimation accuracy [2].

When implementing the proposed method, the following positive technical effect will be obtained:
1) creating stable in a wide range of sampling step analytical and digital reference models of a three-phase asynchronous motor with a squirrel-cage rotor, which allows to solve the complex problem of creating a drive control system based on AM with a squirrel-cage rotor, namely:
- analysis of the engine as an object of regulation,
- analytical synthesis of regulators,
- digital modeling of the regulatory system in order to optimally configure regulators and select regulatory laws,
- direct microprocessor control,
- setting up electric drives when putting them into trial operation;
2) reducing the number of sensors and coordinate converters used in direct microprocessor control.

Sources of information
1. Kopylov I.P. Mathematical modeling of electrical machines: Textbook. for universities for special. "Electric machines." - M .: Higher. school., 1987, p. 30-39, p. 51-52.

 2. Analysis of dynamic induction motor dehavoir / Andonov Zdravko, Mirceviski Slobodan A. // Comput. Syst. and Res. Autom .: Proc. 9th Int. Conf. "Syst. Autom. Cong. And Res." (SAER '95) and DECUS Wat. Users Group Semin. 95, Varna, Sept. 24-26, 1995.- Sofia, 1995.- S. 188-192. - English

 3. US patent N 5481172, CL. H 02 M 7/00 (318-800), 1996.

 4. Salo J., Pyrhonen J., Niemela M. A. Space Vector Induction Motor Model for the Pspice Circuit Simulator // EPE Journal. - 1996 .-- Vol. 5. - N 3/4. -WITH. 56-62.

 5. Kopylov I. P. Electromechanical energy converters. - M .: Energy, 1973, p. 134-138.

 6. Kopylov I. P. Electromechanical energy converters. - M .: Energy, 1973, p. 164, p. 189.

 7. Basharin A.V., Postnikov Yu.V. Examples of calculating an automated electric drive on a computer: Textbook for universities. - 3rd ed. - L .: Energoatomizdat. Leningrad Separation, 1990, p. 225-228, p. 177-180, p. 483.

 8. US patent N 4904920, CL. H 02 P 5/40 (318-800), 1990.

 9. German patent N 4433551, cl. H 02 P 7/44, 1996.

10. Kovach K.P. and Ratz I. Transients in AC machines. - M. -L .: Gosenergoizdat, 1963, p. 493-548 (prototype)
11. New tools accelerate the development of modern digital control of electric motors: Based on materials from the monthly DETAILS ON SIGNAL PROCESSING (July 1997) // CHIP NEWS. - 1997. N 7-8 (16-17). S. 27.

 12. Denisov K., Ermilov A., Karpenko D. Methods of controlling AC machines and their practical implementation based on components of ANALOG DEVICES // CHIP NEWS. - 1997. - N 7-8 (16-17). - S. 18-26.

 13. Bratenev V. and Bratenov G. ALTERA suggests creating your own signal processor // CHIP NEWS. - 1997. - N 7-8 (16-17). - S. 39-41.

 14. Gubanov D., Steshenko V. et al. Prospects for the implementation of digital filtering algorithms based on FPGAs from ALTERA // CHIP NEWS. - 1997.-N 9-10 (18-19). - S. 26-33.

 15. C167 Derivatives. 16-Bit CMOS Single-Chip Microcontrollers. User's Manual 03.96, Version 2.0. Siemens, 1996.

Claims (3)

1. A method for evaluating the adjustable signals of a three-phase squirrel-cage induction motor, by which a relative slip signal S is generated, at a discrete time instant, a signal ω _{s for} setting the stator field rotation frequency is generated, the supply voltage signals U _s are set, calculated according to the parameters of the T-shaped equivalent circuit phase of the motor, gain K ₁ and time constants T ₀ , T ₁ , T ₂ included in the transfer functions of the signals of the phase currents of the stator according to the supply voltage signals

where U _sf (p), I _sf (p) are the Laplace transforms of respectively the supply voltage and stator current signals in the motor phase, form the phase current signals i _sa , i _sb , i _{sc of the} stator according to the transfer functions, form the projections i _sα , i _sβ and i _mα, i _mβ vectors stator current signals and magnetization on orthogonal axes α-β coordinate system fixed relative to the stator, characterized in that the discrete time form of relative sliding signal S, is calculated included in the transfer functions of said gain and constant s time during relative sliding S ≠ 0 by the expressions:
K ₁ = 1 / r ₁ ,
T ₀ = S (L _m + L ₂ ¹ ) / r ₂ ¹ ,
T ₁ = 2a / (b - c),
T ₂ = 2a / (b + c),
a = L ₁ T ₀ + L _m T ₃ ,
b = r ₁ T ₀ + L ₁ + L _m ,

T ₃ = S (L ₂ ¹ ) / r ₂ ¹ ,
r ₁ and L ₁ - resistance and inductance of the stator phase,
r ₂ ¹ and L ₂ ¹ - reduced to the stator circuit active resistance and inductance of the phase of the rotor,
L _m is the inductance of the magnetization branch, the indicated signals i _sa , i _sb , i _sc of the stator phase currents are generated by the transfer functions by digital modeling or by the expressions for the phase currents i _sf (t) of the stator as a function of time t with a signal for setting the supply voltage in the form ideal sinusoid with a frequency w _{1 of} one of the harmonics:

where U _m is the maximum signal voltage
ψ _f - the initial phase shift of the sinusoid of the supply voltage in the corresponding phase of the motor,
φ ₁ - phase shift of the phase current of the stator with respect to the supply voltage of the phase, calculated at discrete points in time,
Z _{1 m} - the module of the complex resistance to the phase current of the stator, calculated at discrete points in time,
A ₁ , B ₁ - coefficients calculated by the expressions:

form the indicated projections i _mα and i _mβ of the magnetization current signal vector on the orthogonal axes α-β of the coordinate system fixed relative to the stator, by digital simulation of the transfer function of the magnetization current signals by the stator current signals

where I _m (p), I _s (p) are the Laplace transforms of the projections onto the orthogonal coordinate axes α-β, respectively, of the signal vectors of the magnetization currents and stator. 2. The method according to claim 1, characterized in that the signal U _{s of the} supply voltage of the stator with relative slip S ≠ 0 is formed by digital simulation of the transfer function

where U _s (p), I _s (p) are the Laplace transforms of the stator supply voltage signal and the stator current signal, respectively,
K ₂ - gain calculated by the expression
K ₂ = r ₁ ,
T ₄ - time constant calculated by the expression:
T ₄ = T ₁ + T ₂ . 3. The method according to p. 1 or p. 2, characterized in that in order to take into account the spatial asymmetry of the phases of the stator of the engine, projections of the signals are formed on the imaginary axis β of the orthogonal coordinate system stationary relative to the stator, according to the expression
i _sβ = K [i _sb sin (ψ _ab ) -i _sc sin (Ψ _ac )],
Where
K = i _sa / [i _sa + i _sb cos (ψ _ab ) + i _sc cos (ψ _ac )],
ψ _ab , ψ _ac are the spatial angles between phases a and b, respectively, and between phases a and c.

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