Simulation system for indirect vector control of an asynchronous motor. Control methods used in frequency converters to control AC motors

vector control

vector control is a control method for synchronous and asynchronous motors, which not only generates harmonic currents (voltages) of the phases (scalar control), but also provides control of the rotor magnetic flux. The first implementations of the vector control principle and algorithms of increased accuracy require the use of rotor position (speed) sensors.

In general, under vector control" is understood as the interaction of the control device with the so-called "space vector", which rotates with the frequency of the motor field.

Mathematical apparatus of vector control

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Books

• Energy-saving vector control of asynchronous motors: a review of the state and new results: Monograph , Borisevich A.V.. The monograph is devoted to methods for improving the energy efficiency of vector control of asynchronous motors. The model of an asynchronous electric motor is considered and the principle of the vector…

main idea vector control is to control not only the magnitude and frequency of the supply voltage, but also the phase. In other words, the magnitude and angle of the spatial vector is controlled. Vector control has better performance than with. Vector control eliminates almost all the disadvantages of scalar control.

Advantages of vector control:
• high accuracy of speed control;
• smooth start and smooth rotation of the engine in the entire frequency range;
• fast response to load changes: when the load changes, there is practically no change in speed;
• increased control range and regulation accuracy;
• heating and magnetization losses are reduced, and .

The disadvantages of vector control include:
• the need to set parameters;
• large fluctuations in speed under constant load;
• great computational complexity.

General functional diagram of vector control

The general block diagram of a high performance AC speed control system is shown in the figure above. The circuit is based on the magnetic flux linkage and moment control loops, together with an evaluation unit, which can be implemented in various ways. At the same time, the external speed control loop is largely unified and generates control signals for the torque controllers M * and magnetic flux linkage Ψ * (through the flow control unit). The motor speed can be measured by a sensor (speed / position) or obtained by means of an estimator allowing the implementation of .

Classification of vector control methods

Since the seventies of the twentieth century, many methods have been proposed to control the moment. Not all of them are widely used in industry. Therefore, this article discusses only the most popular management methods. Discussed torque control methods are presented for control systems and with sinusoidal back EMF.

Existing torque control methods can be classified in various ways.

Most often, torque control methods are divided into the following groups:
• linear (PI, PID) controllers;
• non-linear (hysteresis) controllers.

Note:

1. No feedback.
2. With feedback.
3. in steady state

Among the vector control, the most widely used are (FOC - field oriented control) and (DTC - direct torque control).

Linear Torque Regulators

Linear torque regulators work together with pulse-width modulation (PWM) voltage. Regulators determine the required stator voltage vector averaged over the sampling period. The voltage vector is finally synthesized by the PWM method, in most cases space vector modulation (SVM) is used. Unlike non-linear torque control schemes, where signals are processed by instantaneous values, in linear torque control schemes, a linear regulator (PI) operates with values ​​averaged over a sampling period. Therefore, the sampling frequency can be reduced from 40 kHz for non-linear torque controllers to 2-5 kHz in linear torque controller circuits.

Field Oriented Control

Field Oriented Control(POA, English field oriented control, FOC) - a control method that controls a brushless AC ( , ) as a DC machine with independent excitation, meaning that the field and can be controlled separately.

Field-oriented control, proposed in 1970 by Blaschke and Hasse, is based on an analogy with mechanically commutated control. In this motor, the field and armature windings are separated, the flux linkage is controlled by the field current, and the torque is independently controlled by the current regulation. Thus, the flux and torque currents are electrically and magnetically separated.

General functional diagram of sensorless field-oriented control 1

On the other hand, brushless AC motors ( , ) most often have a three-phase stator winding, and the stator current vector I s is used to control both flux and torque. Thus, the excitation current and the armature current united into the stator current vector and cannot be controlled separately. Decoupling can be achieved mathematically by decomposing the instantaneous value of the stator current vector I s into two components: the longitudinal component of the stator current I sd (creating a field) and the transverse component of the stator current I sq (creating a moment) in a rotating dq coordinate system oriented along the rotor field (R -FOC - rotor flux-oriented control) - figure above. Thus, the control of a brushless AC motor becomes identical to the control and can be implemented using a PWM inverter with a linear PI controller and space vector voltage modulation.

In field oriented control, the torque and field are controlled indirectly by controlling the stator current vector components.

The instantaneous stator currents are converted to a dq rotating frame using the αβ/dq Park transformation, which also requires knowledge of the rotor position. The field is controlled via the longitudinal current component I sd , while the torque is controlled via the transverse current component I sq . The Inverse Park Transform (dq/αβ), a coordinate transformation math module, calculates the voltage vector reference components V sα * and V sβ * .

To determine the rotor position, either a rotor position sensor installed in the electric motor or a sensorless control algorithm implemented in the control system is used, which calculates information about the rotor position in real time based on the data available in the control system.

A block diagram of direct torque control with space vector modulation with torque control and feedback flux linkage operating in a rectangular coordinate system oriented along the stator field is shown in the figure below. The PI outputs of the torque and flux linkage controllers are interpreted as the reference components of the stator voltage V ψ * and V M * in the coordinate system dq oriented along the stator field (English stator flux-oriented control, S-FOC). These commands (constant voltages) are then converted to a fixed coordinate system αβ, after which the control values ​​V sα * and V sβ * are fed to the space vector modulation module.

Functional diagram of direct torque control with space vector voltage modulation

Please note that this circuit can be considered as a simplified stator field-oriented control (S-FOC) without a current control loop or as a classic circuit (PUM-TV, English switching table DTC, ST DTC) in which the switching table is replaced by a modulator (PVM ), and the hysteresis torque and flux controllers are replaced by linear PI controllers.

In a Space Vector Modulation Direct Torque Control (SVM-SVM) scheme, the torque and flux linkage are directly controlled in a closed loop, so an accurate estimation of the motor flux and torque is required. Unlike the classic hysteresis algorithm, it works at a constant switching frequency. This significantly improves the performance of the control system: reduces torque and flux ripples, allows you to confidently start the engine and work at low speeds. However, this reduces the dynamic performance of the drive.

Nonlinear Torque Controllers

The presented group of torque controllers departs from the idea of ​​​​coordinate transformation and control by analogy with a DC collector motor, which is the basis for. Non-linear controllers offer to replace separate control with continuous (hysteresis) control, which corresponds to the ideology of operation (on-off) of inverter semiconductor devices.

Compared to field-oriented control, direct torque control schemes have the following characteristics:

Advantages:
• simple control scheme;
• there are no current loops and direct current regulation;
• no coordinate transformation required;
• there is no separate voltage modulation;
• position sensor is not required;
• good dynamics.

Flaws:
• an accurate estimate of the stator magnetic flux linkage vector and torque is required;
• strong ripples of torque and current due to a non-linear (hysteresis) controller and a variable switching frequency of the keys;
• noise with a wide spectrum due to the variable switching frequency.

Direct torque control

The direct torque control method with inclusion table was first described by Takahashi and Noguchi in an IEEJ paper presented in September 1984 and later in an IEEE paper published in September 1986. The scheme of the classical method of direct torque control (DTC) is much simpler than that of the field control method (), since it does not require the transformation of coordinate systems and measurement of the position of the rotor. The scheme of the direct torque control method (figure below) contains the stator torque and flux linkage estimator, hysteresis torque and flux linkage comparators, switching table and inverter.

Method principle direct torque control is to select the voltage vector for simultaneous control of both the torque and the stator flux linkage. The measured stator currents and inverter voltage are used to evaluate the flux linkage and torque. The estimated values ​​of the stator flux linkage and torque are compared with the control signals of the stator flux linkage ψ s * and motor torque M *, respectively, by means of a hysteresis comparator. The required motor control voltage vector is selected from the inclusion table based on the digitized flux linkage errors d Ψ and torque d M generated by hysteresis comparators, as well as based on the position sector of the stator flux vector obtained based on its angular position . Thus, the pulses S A , S B and S C for controlling the power switches of the inverter are generated by selecting a vector from the table.

Classic direct torque control circuit with switching table with speed sensor

Many variations of the classic circuit are available to improve starting, overload conditions, very low speed operation, reduced torque ripple, variable switching frequency operation and reduced noise levels.

The disadvantage of the classical method of direct torque control is the presence of high current ripples even in the steady state. The problem is eliminated by increasing the operating frequency of the inverter above 40kHz, which increases the overall cost of the control system.

Direct self-management

A patent application for the direct self-management method was filed by Depenbrock in October 1984. The block diagram of direct self-management is shown below.

Based on the stator flux commands ψ s * and the current phase components ψ sA , ψ sB and ψ sC , the flux comparators generate digital signals d A , d B and d C which correspond to active voltage states (V 1 to V 6). The hysteresis torque controller has an output signal d M , which determines the zero states. Thus, the stator flux controller sets the time interval of active voltage states that move the stator flux vector along a given trajectory, and the torque controller determines the time interval of zero voltage states that maintain the electric motor torque in a tolerance field defined by hysteresis.

Direct self-government scheme

The characteristic features of the direct self-government scheme are:
• non-sinusoidal forms of flux linkage and stator current;
• the stator flux vector moves along a hexagonal path;
• there is no margin for supply voltage, the capabilities of the inverter are fully used;
• inverter switching frequency is lower than direct torque control with switching table;
• excellent dynamics in the constant and weak field ranges.

Note that the operation of the direct control method can be reproduced using the circuit with a flow hysteresis width of 14%.

At present, speed control of AC motors with frequency converters is widely used in almost all industries.

In practice, speed control systems for three-phase AC motors are applied based on two different control principles:
2. Vector control.

Control methods used in frequency converters to control AC motors

At present, speed control of AC motors with frequency converters is widely used in almost all industries. This is primarily due to the great achievements in the field of power electronics and microprocessor technology, on the basis of which frequency converters were developed. On the other hand, the unification of the production of frequency converters by manufacturers made it possible to influence their cost quite strongly and made them pay off in a fairly short period of time. Saving energy resources when using converters to control asynchronous motors in some cases can reach 40% or more.
In practice, speed control systems for three-phase AC motors are applied based on two different control principles:
1. V/f-regulation (volt-frequency or scalar control);
2. Vector control.

V/f - speed regulation of asynchronous electric drive

Scalar control or V / f-regulation of an asynchronous motor is a change in the speed of the motor by influencing the frequency of the voltage on the stator while simultaneously changing the module of this voltage. With V/f control, frequency and voltage act as two control variables that are usually controlled together. In this case, the frequency is taken as an independent effect, and the voltage value at a given frequency is determined based on how the type of mechanical characteristics of the drive should change when the frequency changes, i.e., on how the critical moment should change depending on the frequency. To implement such a control law, it is necessary to ensure the constancy of the ratio U / f = const, where U is the voltage on the stator, and f is the frequency of the stator voltage.
With a constant overload capacity, the rated power factor and efficiency engine over the entire speed control range practically do not change.
The laws of U / f-regulation include laws that relate the magnitude and frequency of the voltage supplying the motor (U / f = const, U / f2 = const and others). Their advantage is the possibility of simultaneous control of a group of electric motors. Scalar control is used for most practical applications of a frequency electric drive with a range of motor speed control without the use of a feedback sensor up to 1:40. Scalar control algorithms do not allow realizing the control and management of the motor torque, as well as the positioning mode. The most effective area of ​​application of this control method: fans, pumps, conveyors, etc.

vector control

Vector control is a method of controlling synchronous and asynchronous motors, which not only generates harmonic currents and phase voltages (scalar control), but also provides control of the motor magnetic flux. At the heart of vector control is the idea of ​​voltages, currents, flux links as spatial vectors.
The basic principles were developed in the 70s of the 20th century. As a result of fundamental theoretical research and advances in the field of power semiconductor electronics and microprocessor systems, to date, electric drives with vector control have been developed, which are mass-produced by manufacturers of drive technology around the world.
With vector control in an asynchronous electric drive in transients, it is possible to maintain a constant rotor flux linkage, in contrast to scalar control, where the rotor flux linkage in transients changes when the stator and rotor currents change, which leads to a decrease in the rate of change in the electromagnetic torque. In a vector control drive, where the rotor flux linkage can be kept constant, the electromagnetic torque changes as fast as the stator current component changes rapidly (similar to the change in torque when the armature current changes in a DC machine).
With vector control in the control link, the presence of a mathematical model of an adjustable electric drive is implied. Vector control modes can be classified as follows:
1. According to the accuracy of the mathematical model of the electric motor used in the control link:
. The use of a mathematical model without additional refining measurements by the control device of the parameters of the electric motor (only typical motor data entered by the user is used);
The use of a mathematical model with additional refining measurements by the control device of the parameters of the electric motor, i.e. stator/rotor active and reactive resistances, motor voltage and current.
2. According to the presence or absence of speed feedback (speed sensor), vector control can be divided into:
Motor control without speed feedback - in this case, the control device uses the data of the mathematical model of the motor and the values ​​\u200b\u200bobtained by measuring the stator and / or rotor current;
Motor control with speed feedback - in this case, the device uses not only the values ​​​​obtained by measuring the current of the stator and / or rotor of the electric motor (as in the previous case), but also data on the speed (position) of the rotor from the sensor, which in some control tasks allows to increase the accuracy of working out by the electric drive of the speed (position) command.

The main laws of vector control include the following:
a. The law ensuring the constancy of the magnetic flux linkage of the stator ψ1 (corresponding to the constancy of Evnesh /f).
b. The law that ensures the constancy of the magnetic flux linkage of the air gap ψ0 (constancy of E / f);
in. The law that ensures the constancy of the magnetic flux linkage of the rotor ψ2 (the constancy of Evnut/f).
The law of maintaining the constancy of the stator flux linkage is implemented while maintaining a constant ratio of the stator EMF to the angular frequency of the field. The main disadvantage of such a law is the reduced overload capacity of the motor when operating at high frequencies. This is due to an increase in the inductive resistance of the stator and, consequently, a decrease in the flux linkage in the air gap between the stator and the rotor with increasing load.
Maintaining a constant main flow increases the overload capacity of the engine, but complicates the hardware implementation of the control system and requires either changes in the design of the machine or the presence of special sensors.
While maintaining a constant rotor flux linkage, the motor torque does not have a maximum, however, with an increase in load, the main magnetic flux increases, leading to saturation of the magnetic circuits and, consequently, to the impossibility of maintaining a constant rotor flux linkage.

Comparative evaluation of the laws of speed control by an asynchronous electric drive by changing the voltage frequency on the stator

Figure 1 shows the results of theoretical studies of the energy performance of an asynchronous motor with a power of Rn = 18.5 kW for various frequency control laws, which were carried out in the work of V.S. Petrushin and Ph.D. A.A. Tankov "Energy indicators of an asynchronous motor in a frequency electric drive with various control laws." The results of an experiment carried out during testing of this motor are also given there (frequency control law U/f = const). The engine was loaded with a constant torque of 30.5 Nm in the speed range of 500 - 2930 rpm.
Comparing the obtained dependences, we can conclude that in the zone of low speeds, when using the control laws of the second group, the efficiency is higher by 7-21%, and the power factor is lower by 3-7%. As the speed increases, the differences decrease.

Fig.1. Change in efficiency (a) and cosφ (b) in the control range: 1 - experimental dependences; calculated dependences for different control laws: 2 - U/f = const, 3 - Evnesh /f = const, 4 - Е/f= const, 5 - Evnut /f= const.
Thus, the laws of vector control provide not only better control of the electric drive in static and dynamic modes, but also an increase in the efficiency of the motor and, accordingly, the entire drive. However, all laws with maintaining the constancy of the flux linkage have their own certain disadvantages.
A common disadvantage of laws with maintaining the constancy of the flux linkage are: low reliability due to the presence of sensors built into the motor, and losses in steel when the motor is running with a load torque less than the nominal one. These losses are caused by the need to maintain a constant nominal flux linkage in various operating modes.
It is possible to significantly increase the efficiency of the motor by regulating the magnetic flux of the stator (rotor) depending on the magnitude of the load torque (slip). The disadvantages of this control are the low dynamic characteristics of the drive, due to the large value of the time constant of the rotor, due to which the magnetic flux of the machine is restored with some delay and the complexity of the technical implementation of the control system.
In practice, a group of laws with a constant magnetic flux has become widespread for dynamic electric drives operating with a constant moment of resistance on the shaft and with frequent shock load applications. While the group of laws with the regulation of the magnetic flux as a function of the load on the shaft is used for low-dynamic electric drives and for drives with a “fan” load.

To implement the ability to control torque and speed in modern electric drives, the following methods of frequency control are used, such as:

• Vector;
• Scalar.

The most widespread are asynchronous electric drives with scalar control. It is used in drives of compressors, fans, pumps and other mechanisms in which it is necessary to keep at a certain level either the speed of rotation of the motor shaft (a speed sensor is used), or some technological parameter (for example, pressure in the pipeline, using an appropriate sensor).

The principle of operation of the scalar control of an asynchronous motor - the amplitude and frequency of the supply voltage change according to the law U/f^n = const, where n>=1. How this dependence will look in a particular case depends on the requirements imposed by the load on the electric drive. As a rule, frequency acts as an independent influence, and the voltage at a certain frequency is determined by the type of mechanical characteristic, as well as by the values ​​of the critical and starting torques. The scalar control ensures that the induction motor has a constant overload capacity independent of the voltage frequency, and yet at fairly low frequencies a significant reduction in motor torque can occur. The maximum value of the scalar control range, at which it is possible to regulate the value of the rotation speed of the rotor of the electric motor, without loss of the resistance torque does not exceed 1:10.

Scalar control of an induction motor is quite simple to implement, but there are still two significant drawbacks. Firstly, if a speed sensor is not installed on the shaft, then it is impossible to control the value of the shaft rotation speed, since it depends on the load acting on the electric drive. Installing a speed sensor easily solves this problem, but another significant drawback remains - the inability to control the torque value on the motor shaft. Of course, you can install a torque sensor, but the cost of such sensors, as a rule, exceeds the cost of the electric drive itself. Moreover, even if you install a torque control sensor, the process of controlling this very moment will turn out to be incredibly inertial. Another "but" - scalar control of an asynchronous motor is characterized by the fact that it is impossible to simultaneously control the speed and torque, therefore, it is necessary to regulate the value that is most important at a given time due to the conditions of the technological process.

In order to eliminate the shortcomings that scalar motor control has, back in the 71st year of the last century, SIEMENS proposed the introduction of a vector motor control method. The first electric drives with vector control used motors with built-in flow sensors, which significantly limited the scope of such drives.

The control system of modern electric drives contains a mathematical model of the engine, which allows you to calculate the rotation speed and shaft torque. Moreover, only current sensors of the motor stator phases are installed as the necessary sensors. The specially designed structure of the control system provides independence and almost inertialess regulation of the main parameters - the shaft moment and the shaft rotation speed.

To date, the following vector control systems for an asynchronous motor have been formed:

• Sensorless - there is no speed sensor on the motor shaft,
• Systems with speed feedback.

The application of vector control methods depends on the application of the electric drive. If the measurement range of the speed value does not exceed 1:100, and the requirements for accuracy fluctuate within ± 1.5%, then a sensorless control system is used. If the speed measurement is carried out within values ​​reaching 1: 10000 or more, and the level of accuracy must be quite high (±0.2% at a speed below 1 Hz), or it is necessary to position the shaft or control the torque on the shaft at low speeds , then a system with speed feedback is applied.

Advantages of the vector method for controlling an asynchronous motor:

• High level of accuracy in controlling the speed of rotation of the shaft, despite the possible absence of a speed sensor,
• The implementation of the rotation of the engine at low frequencies occurs without jerks, smoothly,
• If a speed sensor is installed, it is possible to achieve the nominal value of the torque on the shaft even at zero speed,
• Quick response to a possible load change - sudden load jumps practically do not affect the speed of the electric drive,
• High level of motor efficiency due to reduced losses due to magnetization and heating.

Despite the obvious advantages, the vector control method also has certain disadvantages - the great complexity of calculations, knowledge of the motor parameters is required for operation. Among other things, the fluctuations in the speed value at a constant load are much larger than with the scalar control method. By the way, there are such areas where electric drives are used exclusively with a scalar control method. For example, a group electric drive, in which one converter feeds several motors.

Scalar control(frequency) - a method of controlling a brushless alternating current, which consists in maintaining a constant voltage / frequency ratio (V / Hz) over the entire operating speed range, while only the magnitude and frequency of the supply voltage are controlled.

The V/Hz ratio is calculated based on the rated values ​​(and frequency) of the controlled AC motor. By keeping the V/Hz ratio constant, we can keep the magnetic flux in the motor gap relatively constant. If the V/Hz ratio increases then the motor becomes overexcited and vice versa if the ratio decreases the motor is in an underexcited state.

Changing the supply voltage of the electric motor with scalar control

At low speeds, it is necessary to compensate for the voltage drop across the stator resistance, so the V/Hz ratio at low speeds is set higher than the nominal value. The scalar control method is most widely used to control asynchronous motors.

Applied to asynchronous motors

With the scalar control method, the speed is controlled by setting the voltage and frequency of the stator so that the magnetic field in the gap is maintained at the desired value. To maintain a constant magnetic field across the gap, the V/Hz ratio must be constant at different speeds.

As the speed increases, the stator supply voltage should also increase proportionally. However, the synchronous frequency of an induction motor is not equal to the shaft speed, but depends on the load. Thus, an open loop scalar control system cannot accurately control the speed when there is a load. To solve this problem, speed feedback can be added to the system, and hence slip compensation.

Disadvantages of scalar control

Method scalar control relatively simple to implement, but has several significant drawbacks:
• firstly, if a speed sensor is not installed, it is impossible to control the shaft rotation speed, since it depends on the load (the presence of a speed sensor solves this problem), and in the case of when the load changes, you can completely lose control;
• Second, you can't manage. Of course, this problem can be solved using a torque sensor, but the cost of its installation is very high, and will most likely be higher than the electric drive itself. In this case, the torque control will be very inertial;
• it is also impossible to control torque and speed at the same time.

Scalar control is sufficient for most applications where an electric drive is used with a motor speed control range of up to 1:10.

When maximum speed is required, the ability to control a wide range of speeds and the ability to control the torque of the electric motor is used.