• Technical differences between vector and scalar converters. Scalar frequency control applied to asynchronous motors

    Currently, motor speed control AC with the help of frequency converters is widely used in almost all industries.

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

    Control methods used in frequency converters to control AC motors

    Nowadays, speed control of AC motors using frequency converters is widely used in almost all industries. This is primarily due to great achievements in the field 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 has made it possible to significantly influence their cost and make them pay for themselves in fairly short periods 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 used based on two different control principles:
    1. U/f control (volt-frequency or scalar control);
    2. Vector control.

    U/f- speed control of asynchronous electric drive

    Scalar control or U/f regulation by an asynchronous motor is a change in motor speed by influencing the frequency of the voltage on the stator while simultaneously changing the modulus of this voltage. With V/f regulation, frequency and voltage act as two control actions, which are usually regulated together. In this case, the frequency is taken as an independent influence, 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., 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.
    At constant overload capacity, the rated power factor and efficiency of the engine over the entire range of rotation speed control practically do not change.
    The laws of U/f regulation include laws relating the magnitudes and frequencies of the voltage supplying the motor (U/f=const, U/f2=const and others). Their advantage is the ability to simultaneously control a group of electric motors. Scalar control is used for most practical applications of frequency drives with a range of motor speed control without the use of a sensor feedback until 1:40. Scalar control algorithms do not allow for monitoring and control of electric motor torque, as well as positioning mode. Most effective area of ​​application this method controls: 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 magnetic flux of the motor. Vector control is based on the idea of ​​voltages, currents, and flux linkages 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, today, electric drives with vector control have been developed, which are mass-produced by drive equipment manufacturers around the world.
    With vector control in an asynchronous electric drive in transition processes it is possible to maintain a constant rotor flux linkage, in contrast to scalar control, where the rotor flux linkage in transient processes changes when the stator and rotor currents change, which leads to a decrease in the rate of change of the electromagnetic torque. In a vector controlled drive, where the rotor flux linkage can be kept constant, the electromagnetic torque changes as quickly as the component of the stator current changes (analogous to the change in torque when the armature current changes in a machine DC).
    With vector control, the control link implies the presence of a mathematical model of an adjustable electric drive. 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:
    . Use of a mathematical model without additional clarifying measurements by the control device of electric motor parameters (only typical motor data entered by the user are used);
    The use of a mathematical model with additional clarifying measurements by a control device of electric motor parameters, i.e. active and reactive stator/rotor resistances, motor voltage and current.
    2. Based on 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 data from a mathematical model of the motor and values ​​obtained 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 stator and/or rotor current of the electric motor (as in the previous case), but also data on the rotor speed (position) from the sensor, which in some control tasks allows you to increase the accuracy of the electric drive's speed (position) setting.

    The basic 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 ensuring the constancy of the magnetic flux linkage of the air gap ψ0 (constancy of E/f);
    V. The law ensuring the constancy of the magnetic flux linkage of the rotor ψ2 (constancy of Evnut/f).
    The law of maintaining a constant stator flux linkage is implemented by maintaining a constant ratio of the stator emf to the angular frequency of the field. The main disadvantage of this law is the reduced overload capacity of the engine when operating at high frequencies. This is due to the increase inductive reactance stator and, consequently, a decrease in 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.
    When maintaining a constant rotor flux linkage, the motor torque does not have a maximum, however, as the load increases, 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 assessment 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 indicators of an asynchronous motor with a power of Рн = 18.5 kW under various laws frequency control, 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 under various control laws.” The results of the experiment carried out when testing this engine are also given there (frequency control law U/f = const). The engine operated at a load with a constant torque of 30.5 Nm in the speed range 500 - 2930 rpm.
    Comparing the obtained dependencies, we can conclude that in the low-speed zone, when using the control laws of the second group, the efficiency is 7-21% higher, and the power factor is 3-7% lower. As speed increases, the differences decrease.

    Fig.1. Change in efficiency (a) and cosφ (b) in the control range: 1 - experimental dependencies; calculated dependencies for different control laws: 2 - U/f = const, 3 - Evnesh /f = const, 4 - E/f= const, 5 - Evnesh /f= const.
    Thus, the laws of vector control provide not only better control electric drive in static and dynamic modes, but also an increase Engine efficiency and, accordingly, the entire drive. However, all laws maintaining constant flux linkage have their certain disadvantages.
    A common disadvantage of laws maintaining constant flux linkage is: low reliability due to the presence of sensors built into the engine, and losses in steel when the engine operates with a load torque less than the rated one. These losses are caused by the need to maintain a constant nominal flux linkage in various operating modes.
    The efficiency of the motor can be significantly increased by regulating the magnetic flux of the stator (rotor) depending on the magnitude of the load torque (slip). The disadvantages of such control are the low dynamic characteristics of the drive, due to the large value of the rotor time constant, 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, the group of laws with 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 a group of laws with the regulation of 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.

    Vector control

    Vector control is a method of controlling synchronous and asynchronous motors, not only generating harmonic currents (voltages) of the phases (scalar control), but also providing control of the rotor magnetic flux. The first implementations of the vector control principle and high-precision algorithms require the use of rotor position (speed) sensors.

    In general, under " vector control" refers to the interaction of the control device with the so-called "spatial vector", which rotates with the frequency of the motor field.

    Mathematical apparatus of vector control


    Wikimedia Foundation. 2010.

    See what “Vector control” is in other dictionaries:

      Tracing paper with him. Vektorregelung. A method of controlling the rotation speed and/or torque of an electric motor using the influence of an electric drive converter on the vector components of the electric motor stator current. In Russian-language literature in ... Wikipedia

      The solution to the optimal control problem of mathematical theory, in which the control action u=u(t) is formed in the form of a function of time (thereby it is assumed that during the process no information other than that given at the very beginning enters the system... ... Mathematical Encyclopedia

      - (frequency controlled drive, PNC, Variable Frequency Drive, VFD) system for controlling the rotor speed of an asynchronous (or synchronous) electric motor. It consists of the electric motor itself and a frequency converter... Wikipedia

      This term has other meanings, see CNC (meanings). This page is proposed to be merged with CNC. Explanation of reasons and discussion on the Wikipedia page: Toward unification/25 f... Wikipedia

      Stator and rotor of an asynchronous machine 0.75 kW, 1420 rpm, 50 Hz, 230-400 V, 3.4 2.0 A An asynchronous machine is electric car AC... Wikipedia

      - (DPR) part of an electric motor. In commutator electric motors, the rotor position sensor is a brush commutator unit, which is also a current switch. In brushless electric motors, the rotor position sensor can be different types... Wikipedia

      DS3 DS3 010 Basic data Country of construction ... Wikipedia

      An asynchronous machine is an alternating current electric machine, the rotor speed of which is not equal to (less than) the rotation speed of the magnetic field created by the stator winding current. Asynchronous machines are the most common electrical... ... Wikipedia

      This term has other meanings, see Frequency converter. This article should be Wikified. Please format it according to the rules for formatting articles... Wikipedia

      DS3 ... Wikipedia

    Books

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

    The use of a frequency converter is aimed at solving important problems. They consist in controlling the torque and speed of the electric motor. These requirements indicate the need to limit the motor current, as well as the torque, to values ​​that are permissible. This is done during starting, braking, and also during load changes.

    This is required in order to limit dynamic shock loads in the frequency converter mechanism. In this case, there are overloads during operation and the need to adjust the engine torque, which is performed continuously. Also, such actions are required when it is necessary to accurately support the forces on the mechanism that is working. Example in in this case drives used in metal processing machines become.

    Exist various methods frequency control, which allow you to solve various problems when adjusting speed and changing torque, including - two main methods - vector and scalar. Each of them has its own characteristic features, which should be discussed in more detail.

    The first control method is scalar. The peculiarity of scalar control lies in its prevalence, and its area of ​​application is related to pump and fan drives. In addition, frequency converters with a scalar control method are used where it is important to maintain a certain technological parameter. This could be, for example, pressure in a pipeline. Changing the amplitude as well as the frequency of the supply voltage acts as the basic principle on which it is based this method. In this case, the U/f law is used. The largest range for speed control is 1:10.
    Additional features of the scalar method are its inherent ease of implementation. There is also a drawback, which is that it is not possible to precisely regulate the speed of rotation of the shaft. Another feature is that a frequency converter with scalar control on the motor shaft does not make it possible to control the torque.

    The second method used in frequency converters is vector. This is a method of controlling synchronous and asynchronous motors, in which not only harmonic currents (voltages) of the phases are formed, but also provides control of the magnetic flux of the rotor, namely, the torque on the motor shaft. Vector control is used when during operation the load can change at the same frequency, i.e. there is no clear relationship between load torque and rotation speed, and also in cases where it is necessary to obtain an extended frequency control range at rated torques.

    Vector control systems are divided into two classes - sensorless and feedback. The scope allows you to define the application of a particular method. The use of sensorless systems is possible when the speed changes no more than 1:100, and the maintenance accuracy is no more than ±0.5%. With similar indicators of 1:1000 and ±0.01%, respectively, it is customary to use feedback systems.

    Advantages of the vector control method is the speed of response to changes in load, and in the region of low frequencies the rotation of the engine is characterized by smoothness and absence of jerks. Attention is drawn to the provision on the shaft under the condition of zero speed of the rated torque, if there is a speed sensor. Speed ​​adjustment is performed when high precision is achieved. All these advantages become important in practice.

    CONCLUSIONS:

    1. If in scalar frequency converters the object of monitoring and control is only the magnetic field of the stator, then in vector models the object of monitoring and control is both the magnetic field of the stator and the rotor, or rather, their interaction in order to optimize the torque at different speeds. As for monitoring and control methods, when the scalar control method is used, the output frequency and current of the frequency converter are used, and in the case of vector control, the output frequency, current and its phase are used.

    1.5.1 Control of an asynchronous electric motor in frequency mode until recently was big problem, although the theory of frequency regulation was developed back in the thirties. The development of variable frequency drives has been hampered by the high cost of frequency converters. The emergence of power circuits with IGBT transistors and the development of high-performance microprocessor control systems have allowed various companies in Europe, the USA and Japan to create modern frequency converters at an affordable price. It is known that the rotation speed of actuators can be controlled using various devices: mechanical variators, hydraulic couplings, resistors additionally inserted into the stator or rotor, electromechanical frequency converters, static frequency converters. The use of the first four devices does not provide high quality speed control, is uneconomical, and requires high costs during installation and operation. Static frequency converters are the most advanced asynchronous drive control devices at present.

    The principle of the frequency method of speed control of an asynchronous motor is that by changing the frequency f1 supply voltage, it is possible in accordance with the expression

    without changing the number of pole pairs p, change the angular velocity of the stator magnetic field. This method provides smooth speed control over a wide range, and the mechanical characteristics are highly rigid. Speed ​​regulation is not accompanied by an increase in the slip of the asynchronous motor, so power losses during regulation are small. To obtain high energy performance of an asynchronous motor - power factors, efficiency, overload capacity - it is necessary to change the input voltage simultaneously with the frequency.

    The law of voltage change depends on the nature of the load torque Ms. At constant load torque Mc=const The stator voltage must be regulated proportionally to the frequency :

    .

    For the fan nature of the load torque, this state has the form:

    With a load torque inversely proportional to speed:

    Thus, for smooth stepless regulation of the shaft speed of an asynchronous electric motor, the frequency converter must provide simultaneous regulation of the frequency and voltage on the stator of the asynchronous motor.

    With scalar control, the amplitude and frequency of the voltage applied to the motor are changed according to a certain law. A change in the frequency of the supply voltage leads to a deviation from the calculated values ​​of the maximum and starting torque of the engine, efficiency, and power factor. Therefore, to maintain the required engine performance characteristics, it is necessary to simultaneously change the voltage amplitude with a change in frequency.

    In existing frequency converters with scalar control, the ratio of the maximum motor torque is most often maintained constant M Max to the moment of resistance on the shaft M With. That is, when the frequency changes, the voltage amplitude changes in such a way that the ratio of the maximum motor torque to the current load torque remains unchanged. This ratio is called the overload capacity of the motor.

    At constant overload capacity, the rated power factor and efficiency of the engine over the entire range of rotation speed control practically do not change.

    The main feature when regulating blood pressure is that it is necessary to change the voltage U on the stator as a function of static torque M With resistance, and in accordance with the change in frequency.

    Thus, with the scalar control method, the dependence of the supply voltage on frequency is determined by the nature of the load on the electric motor shaft. In this case, for a constant load moment the relation is always maintained U/f = const, and, in fact, ensures a constant maximum engine torque. At the same time, at low frequencies, starting from a certain frequency value, the maximum motor torque begins to fall. To compensate for this and to increase the starting torque, an increase in the supply voltage level is used.

    Using the dependence of the maximum torque on voltage and frequency, you can plot a graph for U from f for any type of load.

    An important advantage of the scalar method is the ability to simultaneously control a group of electric motors.

    Scalar control is sufficient for most practical applications of variable-frequency electric drives with an engine speed control range of up to 1:40.

    Vector control allows you to significantly increase the control range, control accuracy, and increase the speed of the electric drive. This method provides direct control of motor torque.

    The torque is determined by the stator current, which creates an exciting magnetic field. With direct torque control, it is necessary to change, in addition to the amplitude and phase of the stator current, that is, the current vector. This is where the term “vector control” comes from.

    To control the current vector, and, consequently, the position of the stator magnetic flux relative to the rotating rotor, it is necessary to know the exact position of the rotor at any time. The problem is solved either using an external rotor position sensor, or by determining the rotor position by calculations using other engine parameters. The currents and voltages of the stator windings are used as these parameters.

    Less expensive is a variable-frequency electric drive with vector control without a speed feedback sensor, but vector control requires a large volume and high speed of calculations from the frequency converter.

    In addition, for direct torque control at low, close to zero rotation speeds, operation of a frequency-controlled electric drive without speed feedback is impossible.

    Vector control with a speed feedback sensor provides a control range of up to 1:1000 and higher, speed control accuracy is hundredths of a percent, torque accuracy is a few percent.

    A synchronous variable frequency drive uses the same control methods as an asynchronous drive.

    The control part of the inverter is executed on digital microprocessors and provides control of power electronic switches, as well as the solution of a large number of auxiliary tasks (monitoring, diagnostics, protection). In this case, a three-phase (or single-phase) alternating voltage of variable frequency and amplitude is formed at the output of the frequency converter ( And out = var, ƒ out = var).

    Mechanical characteristics of an asynchronous motor at frequency regulation speeds for various control objects have the form shown in Figure 1.2.

    So, for control objects with a constant moment of static load M c = Const, the power supply voltage must vary in proportion to its frequency U/ f = const in control objects requiring speed control at constant power P c = Const the control law will be: U/ f = const, at fan load the control law corresponds to U/ f 2 = const. For these reasons, the regulation method is most widely used for mechanisms M With = Const, although in principle the use of functional converters makes it possible to implement any of these laws.

    Until recently, electric drive systems for direct-flow drawing mills were built exclusively on the basis of DC motors. The reason for this was the lack of reliable frequency converters. At the same time, thyristor converter motor (TP-D) systems have such disadvantages as:

    Limitation of the rate of increase of the armature current, increased moment of inertia of the electric drive, leading to a decrease in the performance of automatic control systems;

    High weight and dimensions;

    Labor intensive to maintain.

    The listed disadvantages are due to the presence of a commutator and, accordingly, switching processes and can be eliminated when constructing an electric drive system based on an asynchronous squirrel-cage motor.

    Currently, there is sufficient experience in the industrial use of electric drives using the IF-IM system in the power range of 35...100 kW.

    Thus, the IF-AM system, which has a control range of up to 1:1000 and higher, speed control accuracy - hundredths of a percent and torque accuracy - units of percent, can provide the necessary synchronization of the speeds of drive electric motors in a direct-flow drawing mill for the purpose of continuous drawing and a given value wire counter tension.

    1.5.2 Pumping stations with frequency electric drives. At pumping station No. 1 in Taldykorgan, a conventional squirrel-cage asynchronous pump motor with a power of 110 kW/h is connected through a PCT converter developed at the Khemz Research Institute. The electric drive control system is constructed similarly to those previously described, with the exception that the EKHO3 ultrasonic level gauge is used as a level transducer in the system. The use of a frequency electric drive in this installation reduces electricity consumption by 60 thousand kWh per year, thus by about 5%.

    In the pumping stations of Taldykorgan, frequency converters of the PChR-2 type and manufactured by the Finnish company Stromberg are also used, on the basis of which over 10 automatic control systems have been created and operate. pumping stations with units with power from 75 to 160 kW.

    Frequency converters from Stromberg are highly reliable and fairly compact means of regulating pumping units. To ensure uniform use of pumping units, a device is provided with which they can be alternately connected to one converter.

    1.5.3 Multi-speed electric motors in pumping units. The circulation pumping stations of some Taldykorgan thermal power plants are equipped with vertical pumping units with two-speed motors of the DVDA215/64-16-20K brand. Of the seven pumps at each station, two are driven by these electric motors. The rated power of the engines is 1400 kW, rotation speed is 375 and 300 rpm. The presence of such pumping units makes it possible to better adapt the operating mode of the pumping unit to the operating mode of the heating network. Two-speed electric motors are also used in water supply pumping installations.

    - What is vector control?
    - Keep the current at 90 degrees.

    The term “vector control” of electric motors is familiar to anyone who has been at least somewhat interested in the question of how to control an AC motor using a microcontroller. However, usually in any book on electric drives the chapter on vector control is located somewhere near the end, consisting of a bunch of hairy formulas with references to all the other chapters of the book. Why don’t you want to understand this issue at all? And even the most simple explanations still on their way through differential equations equilibria, vector diagrams and a bunch of other mathematics. Because of this, attempts like this appear to somehow turn on the engine without using the hardware. But in fact, vector control is very simple if you understand the principle of its operation “on your fingers”. And then it will be more fun to deal with formulas if necessary.

    Operating principle of a synchronous machine

    Let's consider the operating principle of the simplest AC motor - a permanent magnet synchronous machine. A convenient example is a compass: its magnetic needle is the rotor of a synchronous machine, and the Earth’s magnetic field is the magnetic field of the stator. Without an external load (and there is none in the compass, except for friction and fluid that dampens the oscillations of the needle), the rotor is always oriented along the stator field. If we hold a compass and rotate the Earth under it, the needle will spin along with it, doing work to mix the fluid inside the compass. But there is a slightly simpler way - you can take an external magnet, for example, in the form of a rod with poles at the ends, the field of which is much stronger than the Earth’s magnetic field, bring it to the compass from above and rotate the magnet. The arrow will move following the rotating magnetic field. In a real synchronous motor, the stator field is created by electromagnets - coils with current. The winding circuits there are complex, but the principle is the same - they create a magnetic field with the stator, directed in the desired direction and having the required amplitude. Let's look at the following figure (Figure 1). In the center there is a magnet - the rotor of a synchronous motor (the "arrow" of the compass), and on the sides there are two electromagnets - coils, each creating its own magnetic field, one in the vertical axis, the other in the horizontal.

    Figure 1. Operating principle of a synchronous electric machine

    The magnetic flux of the coil is proportional to the current in it (to a first approximation). We will be interested in the magnetic flux from the stator in the place where the rotor is located, i.e. in the center of the figure (we neglect edge effects, scattering and everything else). The magnetic fluxes of two perpendicularly located coils are added vectorially, forming one common flux for interaction with the rotor. But since the flux is proportional to the current in the coil, it is convenient to draw the current vectors directly, aligning them with the flux. The figure shows some currents I α And I β, creating magnetic fluxes along the α and β axes, respectively. Total stator current vector I s creates a co-directed stator magnetic flux. Those. essentially I s symbolizes the external magnet that we brought to the compass, but created by electromagnets - coils with current.
    In the figure, the rotor is located in an arbitrary position, but from this position the rotor will tend to rotate according to the magnetic flux of the stator, i.e. by vector I s(the rotor position in this case is shown dotted line). Accordingly, if you apply current only to the phase α , let's say I α= 1A, the rotor will stand horizontally, and if in β, vertically, and if you apply I β= -1 And then it will flip 180 degrees. If you supply current I α according to the law of sine, and I β according to the law of cosine of time, a rotating magnetic field will be created. The rotor will follow it and spin (like a compass needle follows the rotation of a magnet by hand). This basic principle operation of a synchronous machine, in this case two-phase with one pair of pluses.
    Let's draw a graph of the motor torque depending on the angular position of the rotor shaft and the current vector I s stator – angular characteristic of a synchronous motor. This dependence is sinusoidal (Figure 2).


    Figure 2. Angular characteristic of a synchronous machine (there is some historical confusion here with the signs of moment and angle, which is why the characteristic is often drawn inverted relative to the horizontal axis).

    To obtain this graph in practice, you can put a torque sensor on the rotor shaft, then turn on any current vector, for example, simply apply current to phase α. The rotor will rotate to the appropriate position, which must be taken as zero. Then, through the torque sensor, you need to turn the rotor “by hand”, fixing the angle on the graph at each point θ , which was turned, and the moment that the sensor showed. Those. you need to stretch the “magnetic spring” of the engine through the torque sensor. The largest moment will be at an angle of 90 degrees from the current vector (from the beginning). The amplitude of the resulting maximum torque M max is proportional to the amplitude of the applied current vector. If 1A is applied, we get, say, M max = 1 N∙m (newton*meter, unit of measurement of torque), if we apply 2A, we get M max = 2 N∙m.

    From this characteristic it follows that the motor develops the greatest torque when the rotor is at 90° to the current vector. Since, when creating a control system on a microcontroller, we want to get the highest torque from the motor with a minimum of losses, and losses, first of all, are the current in the windings, it is most rational to always set the current vector at 90° to magnetic field rotor, i.e. perpendicular to the magnet in Figure 1. We need to change everything the other way around - the rotor does not move towards the current vector we set, but we always set the current vector at 90° to the rotor, no matter how it rotates there, i.e. “nail” the current vector to the rotor. We will regulate the motor torque by the amplitude of the current. The greater the amplitude, the higher the torque. But the rotation frequency, the frequency of the current in the windings is no longer “our” business - what happens, how the rotor rotates, so it will be - we control the torque on the shaft. Oddly enough, this is exactly what is called vector control - when we control the stator current vector so that it is at 90° to the rotor magnetic field. Although some textbooks give broader definitions, to the point that vector control generally refers to any control laws where “vectors” are involved, but usually vector control refers to precisely the above control method.

    Building a vector control structure

    But how is vector control achieved in practice? Obviously, first you need to know the position of the rotor so that you have something to measure 90° relative to. The easiest way to do this is by installing the position sensor itself on the rotor shaft. Then you need to figure out how to create a current vector, maintaining the desired currents in phases α And β . We apply voltage to the motor, not current... But since we want to support something, we need to measure it. Therefore, for vector control you will need phase current sensors. Next, you need to assemble a vector control structure in the form of a program on a microcontroller that will do the rest. So that this explanation does not look like an instruction on “how to draw an owl,” let’s continue the dive.
    You can maintain the current with the microcontroller using a software PI (proportional-integral) current regulator and PWM. For example, a structure with a current regulator for one phase α is shown below (Figure 3).


    Figure 3. Current-closed control structure for one phase

    Here is the current setting i α_back– a certain constant, the current that we want to maintain for this phase, for example 1A. The task is sent to the current regulator adder, the disclosed structure of which is shown above. If the reader does not know how the PI controller works, then alas. I can only recommend some of this. The output current regulator sets the phase voltage U α. The voltage is supplied to the PWM block, which calculates the duty cycle settings (comparison settings) for the PWM timers of the microcontroller, which generate PWM on a bridge inverter of four switches to generate this U α. The algorithm can be different, for example, for positive voltage, the PWM of the right rack is proportional to the voltage setting, the lower switch is closed on the left, for negative PWM, the left switch is closed, the lower switch is closed on the right. Don't forget to add dead time! As a result, such a structure makes the software a “current source” at the expense of a voltage source: we set the value we need i α_back, A this structure implements it with a certain speed.

    Further, perhaps some readers have already thought that the vector control structure is only a small matter away - you need to install two current regulators, one regulator for each phase, and form a task on them depending on the angle from the rotor position sensor (RPS), i.e. e. make something like this structure (Figure 4):


    Figure 4. Incorrect (naive) vector control structure

    You can't do that. When the rotor rotates, the variables i α_back And i β_back will be sinusoidal, i.e. the task for the current regulators will change all the time. The speed of the controller is not infinite, so when the task changes, it does not immediately process it. If the task is constantly changed, then the regulator will always catch up with it, never reaching it. And as the engine rotation speed increases, the lag of the real current from the set one will become larger and larger, until the desired angle of 90° between the current and the rotor magnet ceases to be similar to it at all, and the vector control ceases to be so. That's why they do it differently. Correct structure next (Figure 5):


    Figure 5. Vector sensor control structure for two-phase synchronous machine

    Two blocks have been added here - BKP_1 and BKP_2: blocks of coordinate transformations. They do very simple thing: rotate the input vector by a given angle. Moreover, BOD_1 turns to + ϴ , and BKP_2 on - ϴ . That's all the difference between them. In foreign literature they are called Park transformations. BKP_2 performs coordinate transformation for currents: from fixed axes α And β , tied to the motor stator, to the rotating axes d And q, tied to the engine rotor (using the rotor position angle ϴ ). And BKP_1 makes the reverse transformation, from setting the voltage along the axes d And q makes the transition to the axes α And β . I don’t provide any formulas for converting coordinates, but they are simple and very easy to find. Actually, there is nothing more complicated than school geometry (Figure 6):

    Figure 6. Coordinate transformations from fixed axes α and β, tied to the motor stator, to rotating axes. d And q, tied to the rotor

    That is, instead of “rotating” the settings of the regulators (as was the case in the previous structure), their inputs and outputs rotate, and the regulators themselves operate in static mode: currents d, q and the outputs of the controllers in steady state are constant. Axles d And q rotate together with the rotor (as they are rotated by a signal from the rotor position sensor), while the axis regulator q regulates exactly the current that at the beginning of the article I called “perpendicular to the rotor field”, that is, it is a torque-generating current, and the current d is aligned with the “rotor magnet”, so we don’t need it and we set it equal to zero. This structure is free from the disadvantage of the first structure - the current regulators do not even know that something is spinning somewhere. They work in a static mode: they have adjusted each of their currents, reached the specified voltage - and that’s it, just like the rotor, don’t run away from them, they won’t even know about it: all the work of turning is done by coordinate transformation blocks.

    To explain “on the fingers” you can give some analogy.

    For linear traffic, let it be, for example, a city bus. It constantly accelerates, then slows down, then goes backwards and generally behaves as it wants: it is an engine rotor. Also, you are in a car nearby, driving in parallel: your task is to be exactly in the middle of the bus: “keep 90°”, you are the current regulators. If the bus changes speed all the time, you should also change the speed accordingly and monitor it all the time. But now we’ll do “vector control” for you. You climbed inside the bus, stood in the middle and held on to the handrail - like the bus, don’t run away, you can easily cope with the task of “being in the middle of the bus.” Similarly, current regulators, “rolling” in the rotating axes d, q of the rotor, live an easy life.

    The above structure actually works and is used in modern electric drives. Only it lacks a whole bunch of small “improvements”, without which it is no longer customary to make it, such as compensation for cross-connections, various restrictions, field weakening, etc. But this is the basic principle.

    And if you need to regulate not the drive torque, but still the speed (the correct angular speed, rotation frequency)? Well then we install another PI controller - a speed controller (RS). We apply a speed command to the input, and at the output we have a torque command. Since the axis current q is proportional to the torque, then to simplify it, the output of the speed controller can be fed directly to the input of the axis current controller q, like this (Figure 7):


    Figure 7. Speed ​​controller for vector control
    Here the SI, the intensity setter, smoothly changes its output so that the engine accelerates at the desired pace, and does not drive at full current until the speed is set. Current speed ω taken from the rotor position sensor handler, since ω this is the derivative of the angular position ϴ . Well, or you can simply measure the time between sensor pulses...

    How to do the same for three phase motor? Well, actually, nothing special, add another block and change the PWM module (Figure 8).


    Figure 8. Vector sensor control structure for three-phase synchronous machine

    Three-phase currents, just like two-phase ones, serve one purpose - to create a stator current vector I s, directed in the desired direction and having the desired amplitude. That's why three-phase currents you can simply convert them to two-phase, and then leave the same control system that has already been assembled for a two-phase machine. In English-language literature, such a “recalculation” is called Clarke transformation (Edith Clarke is her), in our country it is called phase transformations. In the structure in Figure 8, accordingly, this is done by the phase transformation block. They are done again using the school geometry course (Figure 9):

    Figure 9. Phase conversions - from three phases to two. For convenience, we assume that the amplitude of the vector I s is equal to the amplitude of the current in the phase

    I think no comments are needed. A few words about the current of phase C. There is no need to install a current sensor there, since the three phases of the motor are connected in a star, and according to Kirchhoff’s law, everything that flows through two phases must flow out of the third (unless, of course, there is a hole in your motor insulation, and half did not leak somewhere onto the housing), therefore the current of phase C is calculated as the scalar sum of the currents of phases A and B with a minus sign. Although a third sensor is sometimes installed to reduce measurement error.

    A complete rework of the PWM module is also required. Typically, a three-phase six-switch inverter is used for three-phase motors. In the figure, the voltage command still arrives in two-phase axes. Inside the PWM module, using reverse phase transformations, this can be converted into voltages of phases A, B, C, which must be applied to the motor at this moment. But what to do next... Options are possible. A naive method is to set a duty cycle for each inverter rack proportional to the desired voltage plus 0.5. This is called sine wave PWM. This is exactly the method that the author used in habrahabr.ru/post/128407. Everything is good in this method, except that this method will underutilize the voltage inverter - i.e. maximum voltage, which will be obtained will be less than what you could get if you used a more advanced PWM method.

    Let's do the math. Let you have a classic frequency converter powered by industrial three-phase network 380V 50Hz. Here 380V is linear (between phases) effective voltage. Since the converter contains a rectifier, it will rectify this voltage and the DC bus will have a voltage equal to the amplitude linear voltage, i.e. 380∙√2=540V DC voltage(at least without load). If we apply a sinusoidal calculation algorithm in the PWM module, then the amplitude of the maximum phase voltage that we can achieve will be equal to half the voltage on the DC bus, i.e. 540/2=270V. Let's convert into effective phase: 270/√2=191V. And now to the current linear: 191∙√3=330V. Now we can compare: 380V came in, but 330V came out... And you can’t do anything else with this type of PWM. To correct this problem, the so-called vector type PWM is used. Its output will again be 380V (ideally, without taking into account all voltage drops). Vector PWM has nothing to do with vector control of an electric motor. It's just that its rationale again uses a little school geometry, which is why it's called vector. However, his work cannot be explained on the fingers, so I will refer the reader to books (at the end of the article) or to Wikipedia. I can also give you a picture that slightly hints at the difference in the operation of sinusoidal and vector PWM (Figure 10):


    Figure 10. Change in phase potentials for scalar and vector PWM

    Types of position sensors

    By the way, what position sensors are used for vector control? There are four types of sensors most commonly used. These are a quadrature incremental encoder, a Hall element-based encoder, an absolute position encoder, and a synchronous encoder.
    Quadrature encoder does not indicate the absolute position of the rotor - by its impulses it only allows you to determine how far you have traveled, but not where and from where (how the beginning and end are related to the location of the rotor magnet). Therefore, it is not suitable for vector control of a synchronous machine. Its reference mark (index) saves the situation a little - there is only one per mechanical revolution, if you reach it, then the absolute position becomes known, and from it you can already count how much you have traveled using a quadrature signal. But how to get to this mark at the beginning of work? In general, this is not always inconvenient.
    Hall element sensor- This is a rough sensor. It produces only a few pulses per revolution (depending on the number of Hall elements; for three-phase motors there are usually three, i.e. six pulses), allowing you to know the position in absolute value, but with low accuracy. Accuracy is usually enough to keep the angle of the current vector so that the motor at least moves forward and not backward, but the torque and currents will pulsate. If the engine has accelerated, then you can start programmatically extrapolating the signal from the sensor over time - i.e. construct a linearly varying angle from a rough discrete angle. This is done based on the assumption that the motor rotates at approximately constant speed, something like this (Figure 11):


    Figure 11. Operation of a Hall element position sensor for a three-phase machine and extrapolation of its signal

    Often a combination of an encoder and a Hall effect sensor is used for servo motors. In this case, you can make a single software module their processing, eliminating the disadvantages of both: extrapolate the angle given above, but not by time, but by marks from the encoder. Those. An encoder operates inside the Hall sensor from edge to edge, and each Hall edge clearly initializes the current absolute angular position. In this case, only the first movement of the drive will be non-optimal (not at 90°), until it reaches some front of the Hall sensor. A separate problem in this case is the processing of non-idealities of both sensors - rarely does anyone arrange the Hall elements symmetrically and evenly...

    In even more expensive applications they use absolute encoder With digital interface(absolute encoder), which immediately outputs the absolute position and allows you to avoid the problems described above.

    If the electric motor is very hot, and also when required increased accuracy angle measurements, use “analog” synchronous sensor(resolver, rotating transformer). This is a small electrical machine used as a sensor. Imagine that in the synchronous machine we considered in Figure 1, instead of magnets, there is another coil to which we apply a high-frequency signal. If the rotor is horizontal, the signal will be induced only into the phase stator coil α , if vertical - then only in β , if you turn it 180, the phase of the signal will change, and in intermediate positions it is induced both here and there according to the sine/cosine law. Accordingly, by measuring the signal amplitude in two coils, the position can also be determined from the ratio of this amplitude and the phase shift. By installing such a machine as a sensor to the main one, you can find out the position of the rotor.
    There are many more exotic position sensors, especially for ultra-high precision applications such as electronic chip making. There are already any physical phenomena, just to find out the position most accurately. We will not consider them.

    Simplifying vector control

    As you understand, vector control is quite demanding - give it position sensors, current sensors, PWM vector control, and no microcontroller to calculate all this mathematics. Therefore for simple applications it is simplified. To begin with, you can eliminate the position sensor by making sensorless vector control. To do this, use a little more mathematical magic, located in the yellow rectangle (Figure 12):


    Figure 12. Sensorless vector control structure

    An observer is a block that receives information about the voltage applied to the motor (for example, from a job on a PWM module) and about the currents in the motor from sensors. Inside the observer there is a model of an electric motor, which, roughly speaking, tries to adjust its currents in the stator to those measured from a real motor. If she succeeded, then we can assume that the position of the rotor simulated inside the shaft also coincides with the real one and can be used for the needs of vector control. Well, this is, of course, completely simplified. There are countless types of observers like these. Every graduate student specializing in electric drives tries to invent his own, which is somehow better than others. The basic principle is monitoring the EMF of the electric motor. Therefore, most often a sensorless control system is only operational for a relatively high frequency rotation, where the EMF is large. It also has a number of disadvantages compared to the presence of a sensor: you need to know the engine parameters, the speed of the drive is limited (if the rotation speed changes sharply, the observer may not have time to track it and “lie” for some time, or even “fall apart” completely) , setting up an observer is a whole procedure; for its high-quality operation, you need to know exactly the voltage on the motor, accurately measure its currents, etc.

    There is another simplification option. For example, you can do so-called “auto-switching”. In this case, for a three-phase motor, they abandon the complex PWM method, abandon the complex vector structure and begin to simply turn on the motor phases using a position sensor on Hall elements, even sometimes without any current limitation. The current in the phases is not sinusoidal, but trapezoidal, rectangular, or even more distorted. But they try to make sure that the average current vector is still at 90 degrees to the “rotor magnet” by choosing the moment when the phases are turned on. At the same time, turning on the phase under voltage, it is not known when the current will increase in the motor phase. At a low rotation speed it does this faster, at a high speed, where the EMF of the machine interferes, it does it more slowly; the rate of increase in current also depends on the inductance of the motor, etc. Therefore, even including the phases exactly at the right time, it is not at all a fact that the average current vector will be in in the right place and with the required phase - it can either advance or lag relative to the optimal 90 degrees. Therefore, in such systems, a “switching advance” setting is introduced - essentially just the time, how much earlier voltage needs to be applied to the motor phase, so that in the end the phase of the current vector is closer to 90 degrees. Simply put, this is called “setting timings.” Since the current in an electric motor during autocommutation is not sinusoidal, then if you take the sinusoidal machine discussed above and control it in this way, the torque on the shaft will pulsate. Therefore, in motors designed for autocommutation, the magnetic geometry of the rotor and stator is often changed in a special way to make them more suitable for this type of control: the EMF of such machines is made trapezoidal, due to which they work better in autocommutation mode. Synchronous machines optimized for autocommutation are called brushless direct current motors (BLDC) or in English BLDC (Brushless Direct Current Motor). The auto-commutation mode is also often called the valve mode, and motors operating with it are valve-type. But these are all just different names that do not affect the essence in any way (but seasoned electric drive operators often suffer from CPGS in matters related to these names). There is a good video illustrating the principle of operation of such machines. It shows an inverted motor, with the rotor on the outside and the stator on the inside:

    But there is a course of articles on such engines and the hardware of the control system.

    You can go for even greater simplification. Switch the windings so that one phase is always “free” and no PWM is applied to it. Then it is possible to measure the EMF (voltage induced in the phase coil), and when this voltage passes through zero, use this as a signal from the rotor position sensor, because the phase of this induced voltage depends precisely on the position of the rotor. This results in sensorless auto-commutation, which is widely used in various simple drives, for example, in “regulators” for aircraft model propellers. It must be remembered that the EMF of the machine appears only at a relatively high rotation speed, therefore, to start, such control systems simply slowly switch phases, hoping that the motor rotor will follow the supplied current. As soon as the EMF appears, the auto-commutation mode is activated. Therefore, a sensorless system (so simple, and most often complex too) is not suitable for tasks where the engine must be able to develop torque at near-zero speeds, for example, for a traction drive of a car (or its model), a servo drive of some mechanism, etc. p. But the sensorless system is successfully suitable for pumps and fans, where it is used.

    But sometimes they make even greater simplifications. You can completely abandon the microcontroller, keys, position sensors and other things by switching phases with a special mechanical switch (Figure 13):

    Figure 13. Mechanical switch for switching windings

    When rotating, the rotor itself switches its parts of the windings, changing the voltage applied to them, while an alternating current flows in the rotor. The commutator is positioned in such a way that the magnetic flux of the rotor and stator is again close to 90 degrees in order to achieve maximum torque. Such motors are naively called DC motors, but completely undeservedly: inside, after the collector, the current is still alternating!

    Conclusion

    All electric machines work in a similar way. In the theory of electric drives, there is even the concept of a “generalized electric machine”, to which the work of others is reduced. The finger-tip explanations shown in the article can in no way serve practical guide to writing microcontroller code. The article discusses well if one percent of the information that is required to implement real vector control. To do something in practice, you need, firstly, to know TAU, at least at the level of understanding how the PI controller works. Then you still need to study mathematical description both synchronous machine and vector control synthesis. Also study vector PWM, find out what pole pairs are, get acquainted with the types of machine windings, etc. This can be done in the latest book “Anuchin A.S. Electric drive control systems. MPEI, 2015”, as well as in “Kalachev Yu. N. Vector regulation (practice notes)”. The reader should be warned against diving into the formulas of “old” textbooks on drives, where the main emphasis is on considering the characteristics of electric motors when powered directly from a three-phase industrial network, without any microcontrollers and position sensors. The behavior of the motors in this case is described by complex formulas and dependencies, but for the problem of vector control they are of almost no use (if only studied for self-development). You should be especially careful about the recommendations of old textbooks, where, for example, it is said that a synchronous machine should not operate at its maximum torque, since the operation there is unstable and threatens to tip over - all this is “bad advice” for vector control.

    On which microcontroller you can make full-fledged vector control, read, for example, in our article New domestic motor-control microcontroller K1921VK01T JSC NIIET, and how to debug it in the article Methods for debugging microcontroller software in an electric drive. Also visit our website: in particular, there are two boring videos posted there, which show in practice how to set up a PI current controller, as well as how a current-closed and vector sensorless control structure works. In addition, you can purchase a debugging kit with a ready-made sensor vector control structure on a domestic microcontroller.

    P.S.
    I apologize to the experts for the not entirely correct handling of some terms, in particular the terms “flow”, “flux linkage”, “magnetic field” and others - simplicity requires sacrifice...

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