Space vector modulation
Under the name space vector modulation ( English space vector modulation (SVM, SVPWM) or English space vector control ) refers to the power electronics , a method for controlling the rotating electrical machines based on the pulse width modulation .
Based on this type of modulation , it is possible to electronically simulate a multi-phase three-phase system , as is required for the operation of three-phase machines. With the space vector representation, two variables , the angle of the space vector and its amount or real and imaginary part, are sufficient to specify the flux density distribution in the machine.
functionality
requirement
If a three-phase system is to be simulated, a half-bridge ( HB1 , HB2 , HB3 ) is required for each of the three phases . This means that the output voltage of the phase ( U , V , W ) can be applied to both the positive and the negative intermediate circuit potential ( UDC ). As can already be seen from the circuit, only one switch may be closed for each half bridge, otherwise the intermediate circuit voltage will be short-circuited. For further considerations it is assumed that one switch is closed for each half bridge. This means that there is a certain potential at every point in time in every phase . From this it follows that every half bridge can assume two states. In the first state the upper switch (state "1") and in the second state the lower switch (state "0") is closed.
Basic voltage space vector
Each half bridge can have two different switch positions. Since three half bridges are necessary for a three-phase three-phase system, this results in possible switch positions and thus 8 switching states. Each switch position results in a different voltage constellation between the phases and thus also a different voltage space vector. The two switch positions in which either all three upper or all three lower switches are closed are an exception. With these switch positions, all three phases are short-circuited. This means that no voltage can be measured between the phases. These two voltage vectors are called zero voltage space vector . From this, 6 active and two passive voltage space vectors can be displayed. The following table shows the linked output voltages of the 8 switch positions that can occur.
| Basic voltage space vector | Half bridge 1 S U1 / S U0 |
Half bridge 2 S V1 / S V0 |
Half bridge 3 S W1 / S W0 |
U UV | U VW | U WU |
|---|---|---|---|---|---|---|
| U 0 | 0 | 0 | 0 | 0V | 0V | 0V |
| U 1 | 1 | 0 | 0 | + U DC | 0V | -U DC |
| U 2 | 1 | 1 | 0 | 0V | + U DC | -U DC |
| U 3 | 0 | 1 | 0 | -U DC | + U DC | 0V |
| U 4 | 0 | 1 | 1 | -U DC | 0V | + U DC |
| U 5 | 0 | 0 | 1 | 0V | -U DC | + U DC |
| U 6 | 1 | 0 | 1 | + U DC | -U DC | 0V |
| U 7 | 1 | 1 | 1 | 0V | 0V | 0V |
modulation
Each voltage space vector also generates a specific alignment of the flux density distribution in a three-phase machine. In order to be able to commutate a three-phase machine continuously (sinusoidally), the 6 active basic voltage space vectors are not sufficient, as voltage space vectors must be switched to the machine with any angles and amounts.
To achieve this, the basic principle of pulse width modulation is used. For example, if you want to output a voltage space vector ( Ua ) that has exactly half the angle of the voltage space vector U1 and U2 , this can be achieved by outputting the voltage space vector U1 alternately with the voltage space vector U2 . The duration that each voltage space vector is applied depends on the switching frequency of the modulation. Only the ratio of the two times is decisive for the resulting voltage space vector. In the example given, the two times must be selected to be of exactly the same length in order to obtain the desired voltage space vector. Due to the low-pass effect of the stator windings, there is an averaged current in the machine and thus the desired space vector, the desired alignment of the magnetic flux density.
The control logic must first check in which of the 6 sectors the desired voltage space vector is located and output the two affected basic voltage space vector alternately. The ratio of the times that each of the two voltage space vectors must be present results from the relative angle of the desired voltage space vector in relation to the angles of the basic voltage space vector concerned.
So far it has been described how any voltage space vector can be output with the maximum amount. For the commutation of an induction machine, however, it is essential to be able to choose the amplitude of the output voltage, i.e. the amount of the voltage space vector, as desired. To realize this, the two zero-voltage space vectors are required. If you want to output the voltage space vector Ub , for example , the ratio of the output times of the voltage space vector U1 and U2 must be exactly the same, as in the previous example. In order to be able to reduce the amount of the resulting voltage space vector, an additional time is introduced in which a zero voltage space vector is output. The amount of the resulting voltage space vector depends on the ratio of the switch-on time of the active voltage space vector and the switch-on time of the zero voltage space vector.
For the output of any voltage space vector, each switching period is divided into three time spans. The two active voltage space vectors are output in two of these time periods and a passive voltage space vector is output in the third time period. The three voltage space vectors involved (and thus switch positions) are pulse-width modulated.
Optimization and overmodulation
A zero-voltage space vector is always required to output any voltage space vector. Since the machine current in the stator winding of a three-phase machine is smoother, the higher the switching frequency is selected, it is advisable to halve the time that the zero-voltage space vector must be output. This ensures that several switching processes are performed per switching period and thus the frequency is increased. At the beginning of each switching period, the first half of the zero voltage space vector, then the first active voltage space vector, the second half of the zero voltage space vector and finally the second active voltage space vector are output.
In order to minimize the switching losses, the control logic can be designed in such a way that it outputs the more favorable of the two zero-voltage space vectors. The more favorable zero-voltage space vector is the one for which the fewest switches have to be switched in the respective switch position.
So that the linked output voltage remains sinusoidal when the voltage space vector rotates, each voltage space vector may only move on the circle drawn in the space vector diagram. For special applications (briefly higher torque) the output voltage is overmodulated. In this case, the voltage space vector is no longer moved on a circular path, but - in the extreme case - along the hexagon drawn in the space vector diagram. It should be noted, however, that the resulting output voltages are no longer sinusoidal, but are superimposed with harmonics. This results in higher losses in an induction machine.
practice
implementation
The space vector modulation is usually implemented with microcontrollers or digital signal processors . The technical implementation can take place in software or directly in hardware , depending on the type of processor used . Special controllers already have a corresponding switching logic in the hardware, which takes over the output of the required voltage space vector. The user only has to transfer the desired voltage space vector to a register and the hardware part of the controller ensures the correct modulation in order to obtain the desired voltage space vector.
application
The space vector modulation is used in frequency converters for rotary field machines, and in some cases in converters for brushless DC motors (especially PMSM), which are very similar to a frequency converter. Space vector modulation plays an important role especially in converters that commutate induction machines with the help of field-oriented control , since the control is already carried out here on the basis of the space vector display.
Another application is special three-phase rectifiers such as the Vienna rectifier , where this technology is used to reduce harmonics .
literature
- Dierk Schröder: Electric drives - basics . 1st edition. Springer, Berlin, Heidelberg 2009, ISBN 978-3-642-02989-9 .
- Dierk Schröder: Electric drives - control of drive systems . 3. Edition. Springer, Berlin, Heidelberg 2009, ISBN 978-3-540-89612-8 .