Design of three-phase sinusoidal pulse width modulation inverter for PEK-130 module

Brief description: ****

The principle of SPWM sinusoidal pulse width modulation technology is to compare the three-phase sinusoidal voltage command generated by the controller with the triangular wave, and generate a pulse width modulation signal to drive the inverter through the comparator, so that it outputs a voltage waveform that is similar to a sine wave and has equal amplitude but unequal width. According to the size and frequency of the sinusoidal voltage and the triangular wave, it can be defined as the following two indicators, one of which is the modulation index (Modulaton Index):

Where Vcontrol is the peak value of the three-phase sine wave voltage, and Vtri is the peak value of the triangle wave.

The second is the frequency modulation ratio, which is defined as:

Where fs is the triangular wave frequency and f1 is the sine wave voltage frequency.

The above figure is a three-phase inverter circuit diagram

Three-phase SPWM: ****

Taking phase A as an example, the peak value of the basic wave of voltage VAN can be expressed by the following formula:

The basic wave line-to-line voltage magnitude (RMS) is:

When ma≤1, it is called the linear modulation area of ​​the inverter, that is, when the peak value of the input sine wave voltage command is smaller than the peak value of the triangle wave, the input voltage will be proportional to the line-to-line voltage of the inverter output voltage basic wave. The triangle wave and sine wave are shown in the following figure:

Three-phase space vector SVPWM:

Space vector pulse width modulation is to use the concept of voltage space vector, that is, the rotating voltage vector space is generated by the switch switching state of the six power components of the inverter. The typical three-phase inverter is shown in the figure. Each phase has two switch components placed on the upper arm and the lower arm, which are S1, S3, S5 of the upper arm and S2, S4, S6 of the lower arm. In the control mode of space vector pulse width modulation, the conduction state of each phase switch component of the inverter is complementary, that is, if the upper arm is turned on, the lower arm is turned off, and vice versa, if the upper arm is turned off, the lower arm is turned on. In terms of control, a delay time is usually added before the switch is turned on to avoid the damage of the power components caused by the simultaneous conduction of the upper and lower arm power components. This delay time is called the dead time. Here, the switch conduction state of each arm of the a, b, and c phases is defined. If a=1, it means that the upper arm switch is turned on and the lower arm switch is turned off. A = 0 means that the upper arm switch is turned off and the lower arm switch is turned on. Therefore, there are eight output states of the three-phase inverter. The line-to-line voltage and phase voltage output results (DC link voltage is VDC) generated in each state are listed in the table below.

From the above table, we can know that the relationship between the phase voltage and the line voltage output by the three-phase inverter can be obtained by converting the coordinate axis to the αβ plane. The conversion relationship is:

Therefore, eight different voltage vectors can be obtained from these eight switch switching states. These eight voltage vectors are called basic voltage vectors, which are six effective voltage vectors V1, V2, V3, V4, V5, V6 and two zero vectors V0 and V7. Therefore, the voltage space plane can be divided into six intervals using these six effective voltage vectors, as shown in the figure below. The α-axis and β-axis of the αβ plane are relative to the horizontal axis and vertical axis of the AC motor stator, and Vref is the reference voltage vector of the output.

The reference voltage Vref of any output can be represented by any two of the six effective voltage vectors in the figure, and the components (conduction time) of this output voltage in these two effective voltage vectors can be obtained by algebraic methods.

Axis transformation:

Stationary axis transformation:

The three-phase abc stationary coordinate axis is converted to the αβ stationary coordinate axis system. This conversion is called Clark conversion. Based on the relationship between the two coordinate systems shown in the figure below, the following coordinate conversion formula is obtained:

fa, fb, fo are the variables of voltage and current under the αβ axis

fa, fb, fc are the variables of voltage and current on the abc axis

Conversely, the coordinate axes αβ are transformed into the three-phase abc coordinate system. This transformation is called the inverse Clark transformation, and the transformation formula can be expressed as:

The above is the relationship between the three-phase abc coordinate system and the stationary coordinate system. The undetermined coefficient before the conversion matrix is ​​3/2 if the non-power invariance law is used.

If the power invariance law is used, this is

This article adopts the non-power invariance law. In addition, for a three-phase balanced system, the zero-sequence component can be ignored when performing a stationary coordinate axis conversion. The figure below is a waveform diagram of the conversion of the abc stationary coordinate axis to the αβ stationary coordinate axis using PSIM simulation.

Synchronous rotation axis transformation:

In the previous section, the abc stationary coordinate system was transformed into the ab stationary coordinate axis system through coordinate axis transformation. In this section, the αβ stationary coordinate axes are further transformed into the DQ synchronous rotating coordinate axis system. This transformation is called Park transformation. At this time, it is assumed that the three-phase system is balanced, the zero axis component can be ignored, and the DQ axis and the αβ axis are placed on the two-dimensional vector plane at the same time, as shown in Figure 3.7. This rotating coordinate rotates at an angular velocity of ωe, so the coordinate transformation formula can be obtained:

in:

Conversely, the DQ axis of the rotating coordinate system is transformed to the ab coordinate system. This transformation is called the inverse Park transformation, and the transformation formula can be expressed as:

Experimental verification: