RU2570363C1 - Method of determination of parameters of induction motor - Google Patents

Abstract

FIELD: electricity.SUBSTANCE: method of determination of parameters of the electric motor consists in that during starting and operation of the induction motor the instant values of currents and voltage of two stator phases and the frequency of rotation of the shaft of the induction motor are measured simultaneously; the measured instant values of currents and voltage are transformed from natural coordinate system into rectangular stationary system of coordinates, sequentially four temporary delays of the transformed currents and voltage and frequency of rotation of the shaft of the induction motor are performed, the obtained values are saved and used for determination of active resistance and equivalent inductance of the stator winding reduced to the stator of active resistance and equivalent inductance of the rotor winding, and the inductance pre-determined by the magnetic flux in the air gap of the electric motor in real time as follows:where R- active resistance of the stator winding, Ohm;- active resistance of the rotor winding reduced to the stator, Ohm; L- equivalent inductance of the stator winding, H; L- the resultant inductance pre-determined by the magnetic flux in the air gap of the induction motor, H; ? - rotor dispersion coefficient; T- rotor time constant, with; L- equivalent inductance of the rotor winding, H; K, K, K, K, K- the coefficients determined by the least squares method.EFFECT: simultaneous determination of all electromagnetic parameters of the induction motor in real time.2 cl, 4 dwg, 1 tbl

Description

The invention relates to electrical engineering and can be used to determine the parameters of induction motors.

ротора, приведенное к статору активное сопротивление $$R_2^{\text{'}}$$

ротора. С использованием полученных параметров рассчитывают по Т- или Г-образной схемам замещения с одним контуром на роторе рабочие характеристики.A known method of determining the parameters and performance of an induction motor without pairing with a load device [RU 2391680 C1, IPC G01R 31/24 (2006.01), publ. 06/10/2010], selected as a prototype, which consists in the fact that the power consumption, voltage and current in the no-load mode are measured and recorded at or near the rated voltage, the power factor and inductance of the stator are calculated from them, then the motor is disconnected from power source, register the stator voltage jump, the stator voltage damping curve and measure the stator resistance r ₁ . From the voltage jump, the current measured before shutdown, power factor and phase resistance, the stray reactance x ₁ is calculated. From the attenuation curve, the time constants T ₀ and T 'of the rotor are determined, respectively, with an open stator and a stator, conditionally connected to an infinitely large power network. Using the obtained values, the scattering coefficients σ ₁ and σ _{2 of the} stator and rotor, the reactance of mutual induction X ₁₂ , the reactance of dispersion reduced to the stator, are calculated $$X_2^{\text{'}\text{'}}$$

rotor reduced to stator resistance $$R_2^{\text{'}\text{'}}$$

rotor. Using the obtained parameters, the operating characteristics are calculated according to the T- or G-shaped equivalent circuits with one circuit on the rotor.

The disadvantage of this method is that for its implementation it is necessary to measure power consumption, voltage and current in idle mode.

The objective of the invention is to expand the arsenal of funds for similar purposes.

This is achieved by the fact that the method of determining the parameters of an induction motor, as in the prototype, consists in measuring the currents and voltages consumed by the induction motor and determining the stator resistance, the rotor time constant of the rotor scattering coefficient of the rotor, reduced to the rotor active resistance stator.

According to the invention, during the start-up and operation of an induction motor, the instantaneous values of currents and voltages at two phases of the stator and the rotational speed of the shaft of the induction motor are simultaneously measured. The measured instantaneous values of currents and voltages are converted from a natural coordinate system to a rectangular stationary coordinate system. Four time delays of the converted currents and voltages and the rotational speed of the induction motor shaft are sequentially performed. The obtained values are stored and used to determine the active resistance and the equivalent inductance of the stator winding, reduced to the stator of the active resistance and the equivalent inductance of the rotor winding, and the inductance due to the magnetic flux in the air gap of the electric motor in real time as follows:

where R ₁ is the active resistance of the stator winding, Ohm;

- приведенное к статору активное сопротивление обмотки ротора, Ом; $$R_2^{\text{'}\text{'}}$$

- reduced to the stator resistance of the rotor winding, Ohm;

L ₁ is the equivalent inductance of the stator winding, GN;

L _m - the resulting inductance due to the magnetic flux in the air gap of the induction motor, GN;

σ is the scattering coefficient of the rotor, p.u .;

T ₂ - rotor time constant, s;

L ₂ - equivalent inductance of the rotor winding, GN.

K ₁ , K ₂ , K ₃ , K ₄ , K ₅ are the coefficients determined by the least square method.

The coefficients K ₁ , K ₂ , K ₃ , K ₄ , K _{5 are} determined by the least squares method from the expression:

z _p - the number of pairs of poles of the motor;

- вектор коэффициентов, необходимых для нахождения параметров асинхронного электродвигателя; $$\left[\begin{array}{c}{K}_{\mathrm{one}}\\ K_2\\ K_3\\ K_{\mathrm{four}}\\ K_5\end{array}\right]$$

- the vector of coefficients necessary to find the parameters of the induction motor;

k is the time delay coefficient.

The proposed method, in contrast to the prototype, allows you to simultaneously determine all the electromagnetic parameters of an induction motor in real time without the need for measurements in idle mode and turning off the engine.

In FIG. 1 shows a diagram of a device that implements the considered method for determining the parameters of an induction motor.

In FIG. Figure 2 shows the transients of the currents I _1α {t}, I _1β (t) and the shaft speed of the induction motor ω (t)

$${\widehat{I}}_{1\beta }\left(t\right)$$

- расчетные кривые составляющих тока статоры статора в прямоугольной системе координат.In FIG. 3 shows graphs of current transients, where, I _1α (t), I _1β (t) are the experimental curves of the stator current components in a rectangular coordinate system, $${\widehat{I}}_{\mathrm{one}\alpha }\left(t\right),$$

$${\widehat{I}}_{\mathrm{one}\beta }\left(t\right)$$

- calculated curves of the stator stator current components in a rectangular coordinate system.

- расчетная кривая частоты вращения вала асинхронного электродвигателя.In FIG. 4 shows graphs of transient velocity processes, where ω (t) is the experimental curve of the shaft speed of an induction motor, $$\widehat{\omega }\left(t\right)$$

- calculated curve of the rotational speed of the shaft of the induction motor.

Table 1 shows the parameters of an induction motor, determined by the claimed method.

The method for determining the parameters of an induction motor is carried out using a device (Fig. 1), in which the phase current sensors 1 (ДТ1), 2 (ДТ2) and phase voltage sensors 3 (ДН1), 4 (ДН2) are connected to two power phases of the asynchronous electric motor. The shaft speed sensor of the induction motor 5 (DC) is mounted on its shaft. To current sensors 1 (ДТ1), 2 (ДТ2) and voltage sensors 3 (ДН1), 4 (ДН2) coordinate converter 6 (PC), the first block of time delay 7 (BV31), the second block of time delay 8 (BV32) are connected in series , the third block of time delay 9 (BV33), the fourth block of time delay 10 (BV34), the memory block 11 (PSU), the block determining the coefficients 12 (SOC), the block determining the parameters 13 (BOP). The sensor of the rotational speed of the shaft 5 (DS) is connected to the first block of time delay 7 (BV31) and the memory unit 11 (PSU). The memory block 11 (BP) is connected to the coordinate converter 6 (PC), the first time delay block 7 (BV31), the second time delay block 8 (BV32), and the third time delay block 9 (BV33). The control inputs of the memory unit 11 (PSU), the coefficient determination unit 12 (SOC) and the parameter determination unit of the asynchronous electric motor 13 (BOP) are connected to the control system of the asynchronous electric motor (not shown in Fig. 1). The unit for determining the parameters of the induction motor 13 (BOP) is connected to a computer (not shown in Fig. 1).

As sensors of phase currents 1 (ДТ1), 2 (ДТ2), current sensors - an industrial device KEI-0,1 were used, as sensors of phase voltages 3 (ДН1), 4 (ДН2) - voltage sensors LEM. As a sensor of the shaft rotation speed 5 (DS), a tachogenerator can be used. Coordinate Converter 6 (PC), the first block of time delay 7 (BV31), the second block of time delay 8 (BV32), the third block of time delay 9 (BV33), the fourth block of time delay 10 (BV34), memory block 11 (BP), coefficient determination unit 12 (BOK), parameter determination unit 13 (BOP), and an asynchronous motor control system are based on a TMS320C28346 microcontroller from Texas Instruments.

, $$I_{1{\alpha }_{j-1k}}$$

, $$I_{1{\alpha }_{j-2k}}$$

, $$I_{1{\alpha }_{j-3k}}$$

, $$I_{1{\alpha }_{j-4k}}$$

, $$I_{1{\beta }_j}$$

, $$I_{1{\beta }_{j-1k}}$$

, $$I_{1{\beta }_{j-2k}}$$

, $$I_{1{\beta }_{j-3k}}$$

, $$I_{1{\beta }_{j-4k}}$$

, напряжений в прямоугольной стационарной системе координат $$U_{1{\alpha }_j}$$

, $$U_{1{\alpha }_{j-1k}}$$

, $$U_{1{\alpha }_{j-2k}}$$

, $$U_{1{\alpha }_{j-3k}}$$

, $$U_{1{\alpha }_{j-4k}}$$

, $$U_{1{\beta }_j}$$

, $$U_{1{\beta }_{j-1k}}$$

, $$U_{1{\beta }_{j-2k}}$$

, $$U_{1{\beta }_{j-3k}}$$

, $$U_{1{\beta }_{j-4k}}$$

и частоты вращения ω_j, ω_j-1k, ω_j-2k, ω_j-3k, ω_j-4k передали в блок памяти 11 (БП).To test the operability of the proposed method for determining the parameters of an induction motor, phase current sensors 1 (ДТ1), 2 (ДТ2) and phase voltage sensors 3 (ДН1), 4 (ДН2) were connected to two phases of the asynchronous electric motor power supply (f _1н = 50 Hz, U _1н = 220 V, z _p = 2, ω ₀ = 157 rad / s). The rotational speed sensor of the shaft of the electric motor 5 (DS) was installed on the shaft of the asynchronous electric motor. During the start-up and operation of the induction motor, the instantaneous values of currents and voltages at two phases of the stator and the rotational speed of the motor shaft were simultaneously measured. The instantaneous values of currents and voltages were transferred to the coordinate transformer 6 (PC), where they were converted to instantaneous values of currents and voltages in a rectangular stationary coordinate system (Fig. 2). The instantaneous values of currents, voltages in a rectangular stationary coordinate system and the rotational speed of the induction motor shaft were transferred to time delay blocks 7-10 (BV31 - BV34), where four time delays of instantaneous values of currents, voltages in a rectangular stationary coordinate system and shaft rotation speed were sequentially performed engine 500 · 10 ^-6 seconds and the current received delayed once, twice, three times and four times the values of currents and voltages in a rectangular coordinate system and the fixed frequency ascheniya shaft of the induction motor. Received current and delayed once, twice, thrice and four times instantaneous values of currents in a rectangular stationary coordinate system $$I_{\mathrm{one}{\alpha }_j}$$

, $$I_{\mathrm{one}{\alpha }_{j-\mathrm{one}k}}$$

, $$I_{\mathrm{one}{\alpha }_{j-2k}}$$

, $$I_{\mathrm{one}{\alpha }_{j-3k}}$$

, $$I_{\mathrm{one}{\alpha }_{j-\mathrm{four}k}}$$

, $$I_{\mathrm{one}{\beta }_j}$$

, $$I_{\mathrm{one}{\beta }_{j-\mathrm{one}k}}$$

, $$I_{\mathrm{one}{\beta }_{j-2k}}$$

, $$I_{\mathrm{one}{\beta }_{j-3k}}$$

, $$I_{\mathrm{one}{\beta }_{j-\mathrm{four}k}}$$

stresses in a rectangular stationary coordinate system $$U_{\mathrm{one}{\alpha }_j}$$

, $$U_{\mathrm{one}{\alpha }_{j-\mathrm{one}k}}$$

, $$U_{\mathrm{one}{\alpha }_{j-2k}}$$

, $$U_{\mathrm{one}{\alpha }_{j-3k}}$$

, $$U_{\mathrm{one}{\alpha }_{j-\mathrm{four}k}}$$

, $$U_{\mathrm{one}{\beta }_j}$$

, $$U_{\mathrm{one}{\beta }_{j-\mathrm{one}k}}$$

, $$U_{\mathrm{one}{\beta }_{j-2k}}$$

, $$U_{\mathrm{one}{\beta }_{j-3k}}$$

, $$U_{\mathrm{one}{\beta }_{j-\mathrm{four}k}}$$

and rotation frequencies ω _j , ω _j-1k , ω _j-2k , ω _j-3k , ω _{j-4k were} transferred to the memory unit 11 (PSU).

When the asynchronous electric motor is connected to the network, the control system sends a signal to start the asynchronous electric motor to the control input of memory unit 11 (PSU), using this signal, during the start-up and operation of the asynchronous electric motor with a time delay, the current and voltage values are recorded in a rectangular stationary coordinate system and shaft speed of an induction motor. At the same time, when the induction motor is connected to the network, the control system supplies a signal to the control inputs of the coefficient determination unit 12 (BOC) and the parameter determination unit 13 (BOP). The transmission of signals from the memory block 11 (PSU) to the block determining the coefficients 12 (SOC) was carried out with a time delay of 500 · 10 ^-6 seconds. In the block for determining the coefficients 12 (BOC), the coefficients are determined by the least squares method [Least squares method and the basis of the mathematical-static theory of processing observations / Yu.V. Linnik. - State publishing house of physical and mathematical literature, 1958. P. 152-157] from the expression:

Where

z _p - the number of pairs of poles of the motor;

- вектор коэффициентов, необходимых для нахождения параметров асинхронного электродвигателя; $$\left[\begin{array}{c}{K}_{\mathrm{one}}\\ K_2\\ K_3\\ K_{\mathrm{four}}\\ K_5\end{array}\right]$$

- the vector of coefficients necessary to find the parameters of the induction motor;

k is the time delay coefficient.

The obtained coefficients K ₁ , K ₂ , K ₃ , K ₄ , K _{5 were} transferred to the parameter determination unit 13 (BOP), where they determined the resistance and equivalent stator winding inductance, the stator resistance and equivalent rotor winding inductance, and inductance, due to magnetic flux in the air gap of an induction motor in real time as follows:

where R ₁ is the active resistance of the stator winding, Ohm;

- приведенное к статору активное сопротивление обмотки ротора, Ом; $$R_2^{\text{'}\text{'}}$$

- reduced to the stator resistance of the rotor winding, Ohm;

L ₁ is the equivalent inductance of the stator winding, GN;

L _m - the resulting inductance due to the magnetic flux in the air gap of the induction motor, GN;

σ is the scattering coefficient of the rotor, p.u .;

T ₂ - rotor time constant, s;

L ₂ - equivalent inductance of the rotor winding, GN;

K ₁ , K ₂ , K ₃ , K ₄ , K ₅ are the coefficients determined by the least square method.

The results of the determination of the parameters are received on the computer (table 1).

$${\widehat{I}}_{1\beta }\left(t\right)$$

и экспериментальных токов I_1α(t), I_1β(t) переходных процессов электродвигателя (фиг. 3) и сравнения расчетных кривых скорости $$\widehat{\omega }\left(t\right)$$

и экспериментальных кривых скорости ω(t) переходных процессов электродвигателя (фиг. 4). Для расчета переходных процессов использовали математическую модель в стационарной системе координат [Проектирование и исследование автоматизированных электроприводов. Часть 8. Асинхронный частотно-регулируемый электропривод / Л.С. Удут, О.П. Мальцева, Н.В. Кояин. - Томск: Изд. ТПУ, 2000. - С. 21-25].Validation of the determination of the parameters of the induction motor was carried out by comparing the calculated currents $${\widehat{I}}_{\mathrm{one}\alpha }\left(t\right),$$

$${\widehat{I}}_{\mathrm{one}\beta }\left(t\right)$$

and experimental currents I _1α (t), I _1β (t) transients of the electric motor (Fig. 3) and comparing the calculated velocity curves $$\widehat{\omega }\left(t\right)$$

and experimental velocity curves ω (t) of transients of the electric motor (Fig. 4). To calculate the transients, we used a mathematical model in a stationary coordinate system [Design and study of automated electric drives. Part 8. Asynchronous frequency-controlled electric drive / L.S. Udut, O.P. Maltseva, N.V. Koyain. - Tomsk: Ed. TPU, 2000. - S. 21-25].

After calculating the transients of the currents in a stationary rectangular coordinate system and the rotational speed of the induction motor shaft with the identified parameters, matching criteria were determined that showed the relative deviations of the current estimates in the rectangular stationary stator coordinate system σ _1α = 4.2%, σ _1β = 1.7 % - relative deviations of the components of the stator current, and the shaft speed of the induction motor - σ _ω = 0.6% - from the experimental values. It can be seen from the comparison that the calculated graphs correspond to the experimental ones; therefore, the error in determining the parameters is insignificant.

Table 1 Active resistance of stator winding, R ₁ , Ohm

The resistance of the rotor winding, brought to the stator, $$R_2^{\text{'}\text{'}},\text{Ohm}$$

Equivalent inductance of the stator winding, L ₁ , GN Equivalent inductance of the rotor winding, L ₂ , GN The resulting inductance due to the magnetic flux in the air gap of the machine, L _m , GN 0,095 0,067 0,02613 0,02609 0,02609

Claims (2)

1. The method of determining the parameters of an induction motor, including measuring the currents and voltages consumed by the induction motor, and determining the stator resistance, rotor time constant, rotor scattering coefficient reduced to the rotor resistance stator, characterized in that during the start-up and operation of the induction motor they are simultaneously measured instantaneous values of currents and voltages on two phases of the stator and the frequency of rotation of the shaft of an induction motor, measured instantaneous the values of currents and voltages are converted from a natural coordinate system to a rectangular stationary coordinate system, four time delays of the converted currents and voltages and rotational speeds of the induction motor shaft are successively performed, the obtained values are stored and used to determine the active resistance and equivalent inductance of the stator winding, reduced to the stator of the active resistance and equivalent inductance of the rotor winding, and inductance due to magnetic flow in the air gap of the motor in real time as follows:

where R ₁ is the active resistance of the stator winding, Ohm;
$$R_2^{\text{'}\text{'}}$$

- reduced to the stator resistance of the rotor winding, Ohm;
L ₁ is the equivalent inductance of the stator winding, GN;
L _m - the resulting inductance due to the magnetic flux in the air gap of the induction motor, GN;
σ is the scattering coefficient of the rotor, p.u .;
T ₂ - the time constant of the rotor, s;
L ₂ - equivalent inductance of the rotor winding, GN;
K ₁ , K ₂ , K ₃ , K ₄ , K ₅ are the coefficients determined by the least square method. 2. The method according to p. 1, characterized in that the coefficients K ₁ , K ₂ , K ₃ , K ₄ , K _{5 are} determined by the least squares method from the expression:

Where

z _p - the number of pairs of poles of the motor;
$$\left[\begin{array}{c}{K}_{\mathrm{one}}\\ K_2\\ K_3\\ K_{\mathrm{four}}\\ K_5\end{array}\right]$$

- the vector of coefficients necessary to find the parameters of the induction motor;
k is the time delay coefficient.

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