KR100294335B1 - Velocity and flux estimation method for sensorless control of induction motor - Google Patents

Abstract

The present invention relates to a method for estimating the rotational speed and the rotor flux of an induction motor, and in the method for estimating the rotational speed and the rotor flux of an induction motor according to the present invention, a dynamic equation consisting of predetermined variables and characteristic characteristics of the induction motor. Setting an induction motor model represented by; A main velocity estimator and a second velocity estimator having a rotational speed and a flux estimation algorithm of the induction motor based on the dynamic equation, and converged in the electric and power generation regions among the three operating regions of the induction motor; Providing a sub-estimator, a first sub-estimator that converges in the transmission area and the braking area; Selecting one of the main estimator, the first sub estimator, and the second sub estimator according to the already estimated velocity and magnetic flux based on the stator voltage and the current; And estimating the rotational speed and rotor flux of the induction motor through the selected estimator. Accordingly, the magnetic flux and the rotation speed of the induction motor can be estimated stably in the low speed region.

Description

Velocity and Flux Estimation Method for SENSORLESS CONTROL OF INDUCTION MOTOR

The present invention relates to a method of estimating the rotational speed and rotor flux of an induction motor, and more particularly, to a method of estimating the rotational speed and rotor flux of an induction motor for sensorless vector control.

Induction motors have a simple structure, strong durability that requires little maintenance and repair, and are inexpensive, and are widely used as power sources for various machines in industrial sites.

On the other hand, since the induction motor does not include a permanent magnet in the rotor, the interference between the stator side and the rotor side variables is severe, so the nonlinearity has a very strong dynamic characteristic, which makes it difficult to control precisely compared to other motors. For this reason, induction motors are mainly used for constant speed operation, or have been driven using an open-loop control method called a voltage to frequency method that converts voltage and frequency proportionally. Since the V / F method is simple, it is not difficult to drive the induction motor. However, since the open loop control method is used, the V / F method cannot effectively cope with the load fluctuation.

Subsequently, the control technology of induction motors has been rapidly developed since the development of the vector control method which independently controls the torque and magnetic flux of induction motors.

On the other hand, breakthroughs in semiconductor technology, including power devices and microprocessors, enable the application of complex control theory, further promoting the development of control technology for induction motors. Therefore, based on this background, induction motors are gradually replacing DC motors in many applications.

For the control of the induction motor, information on the rotational speed and the magnetic flux of the rotor is required. The speed information is obtained using a speed sensor such as an encoder or tachometer, and the rotor flux is estimated using the rotational speed and current information. This has been used a lot. However, the attachment of the speed sensor results in the loss of the advantages of the induction motor, such as the durability, which is inherent in the induction motor, and a significant increase in price. For this reason, there have been many active researches on sensorless vector control to estimate the rotational speed and rotor flux of an induction motor without a speed sensor and to use the same to control the induction motor.

1 is a schematic diagram of a rotation speed estimation system of a conventional induction motor.

As shown, the rotational speed estimation system of an induction motor includes an induction motor 100, an induction motor model 101 implemented in a CPU so as to be simulated by software, an actual current and an induction motor model applied to the induction motor. And a speed estimator 103 for estimating the rotational speed of the induction motor by comparing the estimated current from the induction motor.

By such a configuration, when a voltage is applied to the induction motor model 101 implemented in the CPU, the current is estimated by the induction motor model 101. When the estimated current and the actual current are input, the speed estimator 103 compensates the error of both currents in the form of PI (proportional integration) control, estimates the rotational speed of the motor by a predetermined equation, and reflects it to the induction motor model 101. To keep it updated. In other words, the induction motor is regarded as a slowly varying system, and its rotation speed is changed to match the rotation speed of the actual induction motor.

However, in the conventional method as described above, when the induction motor operates in the power generation area, for example, when the elevator descends when the induction motor is driven by the induction motor, an estimation algorithm is emitted and the entire system becomes unstable. In addition, the gain setting of the PI controller is difficult.

In addition to the methods described above, many methods for estimating the rotational speed and rotor flux of induction motors without speed sensors have been proposed, but all the proposed methods include 1) pure integral calculation of current and voltage measurement values in the algorithm. It is vulnerable to the DC offset of the converter, making it impossible to operate in the low speed range. 2) It is difficult to set the value because it contains difficult parameters. It does not have such a defect.

On the other hand, the present applicant proposes two types of speed estimator consisting of the main estimator and the sub-estimator as the rotational speed estimating system of the induction motor, and when the operation region of the induction motor is divided into three modes: the electric region, the power generation region, and the braking region. Since the main estimator can be used in the electric and braking areas, the sub-estimator can be used in the electric and braking areas. That is, the operating region of the induction motor is estimated from the estimated rotor flux and rotational speed of the induction motor and the estimation algorithm of the main or sub-estimator is operated according to the operating area of the induction motor. By repeating the process of obtaining the estimate, the rotor flux and rotational speed are updated.

However, the main estimator in this manner requires information on the direction of rotation of the induction motor and is sensitive to errors in the measured values. Therefore, when the main estimator operates in a low speed region where information about the rotation direction is easy and the signal to noise ratio of the measured values is large, there may be a problem that the estimate is divergent.

Accordingly, an object of the present invention is to provide a magnetic flux and rotational speed estimation system of an induction motor which can stably estimate the magnetic flux and rotational speed of an induction motor even in a low speed region.

1 is a schematic diagram of a rotation speed estimation system of a conventional induction motor,

Figure 2 illustrates the operation region of the induction motor represented by the relationship between the generated torque (T _e) and the rotational speed (ω _r) of the rotor in a normal state graph,

3 is a schematic diagram of a rotation speed and rotor flux estimation system of an induction motor according to the present invention;

4 is a flow chart showing a magnetic flux estimation method according to the present invention,

5 is a graph of simulation results according to the rotational speed and rotor flux estimation method of the induction motor according to the present invention.

According to the present invention, in the method of estimating the rotational speed and rotor flux of an induction motor, the method includes: setting an induction motor model represented by a dynamic equation consisting of predetermined variables and characteristic characteristics of induction motors; A main velocity estimator and a second velocity estimator having a rotational speed and a flux estimation algorithm of the induction motor based on the dynamic equation, and converged in the electric and power generation regions among the three operating regions of the induction motor; Providing a sub-estimator, a first sub-estimator that converges in the transmission area and the braking area; Selecting one of the main estimator, the first sub estimator, and the second sub estimator according to the already estimated velocity and magnetic flux based on the stator voltage and the current; And estimating the rotational speed and rotor flux of the induction motor through the selected estimator.

Here, the dynamic equation of the induction motor is as follows:

Where i _{ds and} i _qs are stator currents, ω _e is the rotational speed of the dq axis, ψ _dr, ψ _qr is the rotor flux, ω _r is the rotational speed of the motor, V _ds and V _qs are the stator voltages of the d and q axes, T _e is the generated torque, T _L is the load torque, and p is the polar pair number. In addition, a ₀ to a ₇ are characteristic constants of the induction motor defined as follows.

Where M is the mutual inductance, L _s is the stator magnetic inductance, L _r is the rotor magnetic inductance, R _s is the stator resistance, R _r is the rotor resistance, and σ is the leakage coefficient σ ≒ 1-M / L _s L _r is the friction coefficient of the induction motor, and J is the moment of inertia of the motor. Hereinafter, the same mathematical symbols have the same meanings, and thus repeated descriptions thereof will be omitted.

Also, selecting the estimator is effective based on the K value defined as follows:

Where T _e is the generated torque, ω _r is the mechanical rotational speed of the rotor, ψ _r is the magnitude of the rotor flux, and K _T is the torque constant.

Then, the estimation algorithm of the main estimator is given by

The estimation algorithm of the first sub estimator is given by

The estimation algorithm of the second sub estimator is preferably:

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

First, the process of configuring the three estimators will be described, and a method of estimating the rotational speed and the rotor flux of the induction motor by appropriately switching the estimators implemented as described above will be described.

The process of implementing the main estimator, the first sub estimator and the second sub estimator for estimating the rotor flux and the rotation speed of the induction motor according to the present invention is as follows. In order to estimate the rotor flux and rotation speed of an induction motor, a dynamic equation representing the dynamic characteristics of the induction motor is required. The dynamic equations of induction motors can take various forms depending on how the variables, coefficients and coordinate axes are defined, but the basic meanings are the same. The assumptions and constant definitions used in the dynamic equations used for the present invention are as follows. .

First, each three-phase stator and rotor windings of the stator and rotor of the induction motor are wound so that the magnetomotive force is distributed in a sinusoidal wave and Y-connected with an electric angle displacement of 2π / 3. The rotor windings have the number of turns N _s and _{_} N _r , the equivalent resistances R _s and R _r , respectively. Third, the magnetization of the iron core is linear, assuming that it has a polar pair number p. The dynamic equations on the dq axis of three-phase induction motors can be derived. The maximum number means the number of magnetic poles formed in the induction motor, and the larger this value is, the larger the magnetization constant becomes. The dynamic equation derived under this assumption is

On the other hand, the dynamic equation of the mechanical system is given by

In addition, i _ds is the stator current of the d-axis, i _qs is the stator current of the q-axis, and ω _e is the rotational speed of the dq-axis. Φ _dr is the magnetic flux of the rotor of the d-axis, ψ _qr is the magnetic flux of the rotor of the q-axis, and ω _r means the mechanical rotational speed of the rotor. V _ds and V _qs are stator voltages of d and q axes, respectively, T _e is the generated torque, T _L is the load torque, and p is the maximum number. On the other hand, a ₀ to a ₇ to the values defined as follows may vary depending on the characteristics of the induction motor. Hereinafter, the same mathematical symbols have the same meanings, and thus repeated descriptions thereof will be omitted.

Where M is the mutual inductance, L _s is the stator magnetic inductance, L _r is the rotor magnetic inductance, R _s is the stator resistance, R _r is the rotor resistance, and σ is the leakage coefficient σ ≒ 1-M / L _s L _r is the friction coefficient of the induction motor, and J is the moment of inertia of the motor. Hereinafter, the same mathematical symbols have the same meanings, and thus repeated descriptions thereof will be omitted.

The process of implementing the estimator for estimating the rotational speed and the rotor flux based on the dynamic equation of the induction motor as described above is as follows.

First, the rotor fluxes φ _dr and ψ _dq on the dq axis are expressed by the magnitude ψ _r of the rotor flux and the position angle θ _r of the rotor flux as follows.

Next, i _ds , i _qs , V _ds , V _qs , Di _ds and Di _qs are the measurable values in the current equation [Equation 1] among the dynamic equations of the induction motor. And then define these values as α _d and α _q as follows: Here, Di _ds and Di _qs represent the differential equations of i _ds and i _ds , respectively, and these values are approximated using the average rate of change.

Therefore, α _d and α _q defined as above can be calculated by measuring the stator current and voltage.

Obtaining the rotational speed ω _r from [Equation 5] and [Equation 6] is as follows.

Here, sgn (ω _r ) means the sign of the rotational speed.

Meanwhile, using [Equation 5] and [Equation 1], which is the current equation of the induction motor, [Equation 2], which is the flux differential equation of the dynamic equation of the induction motor, can be rewritten as follows.

Moreover, if two expressions of [Equation 5] are differentiated with respect to time,

Get

In addition, the differential equations for ψ _r can be obtained from the above two equations and [Equation 5], [Equation 6] and [Equation 8].

[Equation 10]

The differential equations for the following θ _r can be obtained from equations (8) and (9).

On the other hand, ω _r can be expressed as follows from equations [Equation 5] and [Equation 6].

Then, the following differential equations of θ _r can be obtained from Equations 7, 11 and 12.

Therefore, the following rotational speed and rotor flux estimator can be constructed from Equation 10, Equation 12, and Equation 13.

Meanwhile, the estimation equation of the main estimator and the first sub estimator proposed at the time of filing is as follows.

Main estimator:

First Subestimator:

The estimation equations of the estimator are developed for the x-y axis, and reconstructed based on the d-q axis is as follows.

Main estimator:

First Subestimator:

The method of estimating the rotational speed and the magnetic flux of the induction motor including only the main estimator and the first sub estimator has been previously filed by the present applicant, and therefore, proof of their convergence is omitted.

Hereinafter, to show the convergence of the second sub estimator, K is defined as follows.

Where T _e is the generated torque, ω _r is the mechanical rotational speed of the rotor, and K _T is the torque constant.

The K value plays a very important role in the convergence analysis of the sensorless algorithm, which is directly related to the slip s. Slip refers to the difference between the rotational speed of the stator flux and the rotational speed of the rotor in the induction motor, and the value obtained by adding slip to the rotor speed satisfies the same relationship as the rotational speed of the stator flux. here

(%) slip = (ω _s -ω _r ) / ω _s

= a ₅ T _e / K _t ψ _r ² ω _s ≒ s

, The relationship of s = (K-1) / K holds. Thus, as shown in Fig. 2, the induction motor has its motorized area (0 <s <1), generating area (s <0) and breaking according to the value of slip s. It can be divided into three areas of the area (s> 0). Therefore, K <0, 0 <K <1, and K> 1 correspond to a braking area | region, a power generation area, and a transmission area, respectively.

On the other hand, the main estimator converges at K <0 and the first sub estimator at K <0 or K> 1. Therefore, when the K value is positive, the main estimator must be operated, and when the negative value is negative, the first sub estimator must be operated. However, in the low speed region, the error appears as a relatively large value. Especially, since the main estimator needs information about the rotation speed code from the first sub estimator and has no ability to determine the sign of the rotation speed by itself, the first sub estimator If the timing of switching from the main estimator to the wrong one is wrong, the whole system may become unstable. Such a case is particularly likely to occur when the rotational direction of the rotor is changed or during low speed driving. Therefore, the second sub estimator proposed to supplement the above point in the low speed region is used in combination with the main estimator 4 in the low speed region.

The convergence of the second sub estimator is as follows. However, to prove this, we need the following assumptions. First, the stator current is limited by some constant I _max . In other words,

Second, there exist positive constants ψ _m and ψ _M satisfying

Third, there are positive constants ω _m and ω _M satisfying

Where ω _M satisfies the following.

Fourth, the sign of the speed estimate coincides with the sign of the actual speed. In other words,

Finally, K defined above satisfies K> 0.

In practically all induction motor control systems, the first assumption is natural because the magnitude of the current is limited to prevent damage to the motor and inverter due to overcurrent. In addition, the induction motor cannot operate at ψ _r = 0, so the second assumption is also natural. The third assumption is the speed range in which the second sub-estimator can operate. Ω _m can be set to a very small value, not zero, and in the case of the induction motor of the specification to be simulated below, the value is about 90 rpm. The ω _M value can be large up to approximately 80-90 rpm.

The fourth assumption is that the sign of the speed estimate coincides with the sign of the actual speed, which may not be satisfied in cases such as when the rotational speed of the motor changes, but this is usually the case that occurs instantaneously and is satisfied in most cases. . This assumption is for the convenience of analyzing the convergence of the proposed estimator. For reference, even if the sign of the speed estimate is different from the sign of the actual speed, it can be proved that the estimate is not diverged and the magnitude of the estimated error is limited. The final assumption is that the second subestimator will operate in the transmission or power generation area.

Assuming that the above assumptions are satisfied, the estimation error converges to zero.

Hereinafter will be described in detail the configuration and the method of estimating the speed and rotor flux estimation system of the induction motor including the second sub-estimator, the main estimator and the first sub-estimator configured as described above.

3 is a schematic diagram of a rotation speed and rotor flux estimation system of an induction motor according to the present invention, and FIG. 4 is a flow chart illustrating a flux estimation method according to the present invention.

As shown, the rotational speed and rotor flux estimation system of an induction motor uses dynamic equations of a predetermined induction motor to estimate the rotational speed of the induction motor and the magnetic flux of the rotor from the phase current and phase voltage applied to the induction motor. A pre-processing part 1 for processing necessary information and a main estimator 4 for estimating the rotor flux by a predetermined estimation algorithm based on the information processed by the pre-processing part 1, and Select whether to operate the first sub-estimator 5 and the second sub-estimator 6 and the main estimator 4, the first sub-estimator 5, and the second sub-estimator 6 according to the operating area of the motor. And an estimator selecting section (2).

By the above configuration, the rotor flux and the rotation speed of the induction motor are estimated as follows. However, since the initial driving is ω _r ≒ 0, the rotational speed and the rotor flux estimation of the induction motor are made through the first sub estimator 5.

The preprocessor 1 detects the stator current and stator voltage from a sensor (not shown), and based on the detected current value, voltage value, characteristic constant values of the induction motor, and dynamic equation, K value necessary for proper selection of the estimator as described above. Various variables and constant values are calculated (100). However, this requires information on the characteristic constant values of the motor, such as stator resistance R _s , rotor resistance R _r , and mutual inductance M. These values fluctuate greatly as the driving conditions of the induction motor change. In particular, in the case of R _r , the difference between the values at room temperature and high temperature may be 1.5 times or more. Therefore, in order to apply the rotational speed and rotor flux estimation method of induction motor, it is necessary to estimate the characteristic constants of the motor online. However, in the present invention, these points are left out and it is assumed that the characteristic constants of the motor are perfectly known.

The estimator selecting unit 2 determines whether the driving region of the current induction motor is a power generation region based on the processed K value (200). If K> 1 or K <0, it corresponds to the electric and braking area, so the first sub estimator 5 is selected. Accordingly, the first sub estimator 5 uses the above-described estimation algorithm to determine the rotational speed of the induction motor. The rotor flux is estimated (400).

When 0 <K <1, the estimator selecting unit 2 again determines whether or not the rotational speed omega _r of the induction motor is low or high speed based on the predetermined value omega _M (300). Here, ω _M is a suitable value satisfying the following equation, and it is sufficient to set smaller than min [(2 / p) * sqrt {a ₄ (a ₄ -2)}]. Where sqrt means √.

[Equation 24]

That is, the main estimator 4 is selected in the high speed region where | ω _r |> ω _M , and the second sub estimator 6 is selected in the low speed region where | ω _r | <ω _M (300). Accordingly, the selected estimators 4 and 6 estimate the rotational speed and the rotor magnetic flux of the induction motor by using the above-described estimation algorithm, respectively (500 and 600).

The main estimator 4 cannot find out the sign of the rotational speed of the induction motor by itself, but the actual implementation requires the sign of the rotational speed, and it is sensitive to the error of the measurement because the estimate of the magnetic flux angle is algebraically obtained and the inverse of the measured values is used. Do. Therefore, if the main estimator is driven in the low speed region, the estimate may diverge.

On the other hand, the second subestimator 6 newly proposed in the present invention obtains an estimate of the magnetic flux angle through a filter type estimator without requiring the sign of the rotational speed in the implementation of the algorithm. It has a strong advantage. This second sub-estimator converges in the transmission and power generation regions similarly to the main estimator in the low speed region. Therefore, the main estimator solves the problems of the main estimator in the low speed region by substituting the newly proposed second sub estimator for the operation in the low speed region.

5 is a graph showing the simulation results of the rotational speed and rotor flux estimation method of the induction motor according to the present invention. This shows the result of forward and reverse operation when a 20% load (0.86 Nm) of the rated load (4.3 Nm) is applied at a low speed (18 rpm). A load is applied when t = 3.5 sec, and at t = 6 sec the speed command changes from 18 rpm to -18 rpm. When K> 0 and | ωr | <30 rpm in the steady state, the second sub estimator operates. As can be seen from the simulation results, the speed and flux estimates converge well with the actual values even at high loads at low speeds.

As described above, the rotor speed and rotor magnetic flux estimation method of the induction motor according to the present invention measures the stator current and the voltage to determine the rotor flux and the rotation speed through the magnetic flux estimator obtained by displaying the rotor flux in polar coordinates in the dq coordinate system. Use the method of obtaining. The simulation showed that it does not include the integrating operation and does not include the difficult variables to be set, and has excellent estimation performance from low speed to high speed through simulation.

As described above, according to the present invention, the magnetic flux and the rotational speed of the induction motor can be estimated stably in the low speed region.

Claims (6)

In the method of estimating the rotational speed and rotor flux of an induction motor, Setting an induction motor model represented by a dynamic equation consisting of predetermined variables and induction motor characteristic constants; A main velocity estimator and a second velocity estimator having a rotational speed and a flux estimation algorithm of the induction motor based on the dynamic equation, and converged in the electric and power generation regions among the three operating regions of the induction motor; Providing a sub-estimator, a first sub-estimator that converges in the transmission area and the braking area; Selecting one of the main estimator, the first sub estimator, and the second sub estimator according to the speed and the magnetic flux already estimated based on the stator voltage and the current; And Estimating the rotational speed and rotor flux of the induction motor through the selected estimator. The method of claim 1, The dynamic equation of the induction motor is a rotational speed and rotor flux estimation method of the induction motor, characterized in that: Where i _{ds and} i _qs are stator currents, ω _e is the rotational speed of the dq axis, ψ _dr, ψ _qr is the rotor flux, ω _r is the rotational speed of the motor, V _ds and V _qs are the stator voltages of the d and q axes, T _e is the generated torque and T _L is the load torque. Also, a ₀ to a ₇ are characteristic constants of the induction motor. The method according to claim 1 or 2, The selecting of the estimator is based on the K value defined as follows: Rotational speed and rotor magnetic flux estimation method of the induction motor: The method according to claim 1 or 2, The estimation algorithm of the main estimator is a rotation speed and rotor flux estimation method of the induction motor, characterized in that the following equation: The method according to claim 1 or 2, The estimation algorithm of the first sub estimator is a rotation speed and rotor flux estimation method of the induction motor, characterized in that the following equation: The method according to claim 1 or 2, The estimation algorithm of the second sub estimator is a rotation speed and rotor flux estimation method of an induction motor, characterized in that: