The three-phase half-bridge SPWM inverter VSV-PWM state space modulation mapping method is also called the six-step PWM mapping method. It is a drawing method that makes the magnetic flux trajectory tend to be circular, or a method of finding the magnetic flux trajectory using the drawing method. The basic idea is to use numerical control to make the polygonal magnetic flux trajectory formed by the motor when the three-phase half-bridge inverter supplies power to approximate the circular magnetic flux trajectory of the motor when the three-phase symmetrical sine wave voltage is supplied. The higher the approximation, the smaller the harmonic content of the output voltage.

When the output voltage of the inverter is a pure square wave waveform of 180°, the magnetic flux increment of the formed regular hexagonal magnetic flux trajectory is

In the time ΔT, if Ù* is a constant phasor, then we have

For example,

In the formula, Ù is the phasor voltage that generates the magnetic flux linkage. There are a total of 8 phasor voltages, namely Ù0, Ù1, …, Ù7. in. The zero phasors of Ù0 and Ù7 do not correspond to any voltage output, and there are only 6 real effective phasors. In the complex space, the 6 phasors act in sequence within the time T=6·ΔT, resulting in the output shown in Figure (a) Magnetic flux trajectory shown; T is the period of the output fundamental voltage.

Its model is

In the formula, E is the DC power supply voltage of the inverter; △T is the action time of the voltage phasor.

As shown in Figure (a) , the magnetic flux trajectory is a regular hexagon, so that the torque and angular velocity of the load motor have 6 times the output frequency of the pulsation. In order to make the magnetic flux trajectory tend to be round, the top corners of the regular hexagon can be cut off by the multi-segment polyline method. The specific method is as follows.

(1) Taking the midpoint of each side of the regular hexagon as the boundary, divide the regular hexagon into six sectors I, II, …, VI, as shown in Figure (a) . Each sector includes two flux linkage phasors, such as the I sector is

(2) Divide the length of each side of the regular hexagon into N segments equally, then the magnetic flux linkage phasor on both sides of each corner is divided into N/2 units (N must be an even number), and the magnetic flux linkage phasor of each unit is divided into N/2 units. mold

(3) Make parallel lines parallel to the two adjacent sides at each sub-point, and form (N/2) 2 rhombic grids in each sector, as shown in Figure (b) . Assuming that the final approximation of the trajectory is a regular hexagonal inscribed circle, and its radius is R0,

it is taken as the radius, and two concentric circles are made, including the diamond mesh between the two concentric circles, which is the desired polygonal magnetic flux trajectory. When N≥12, the magnetic flux trajectory can finally approach the inscribed circle of the regular hexagon.

It can be seen from Figure (b) that the phasor action sequence of the magnetic flux chain in sector I is △ψ6, △ψ6, △ψ1, △ψ6, △ψ1, Δψ6, Δψ1, Δψ1. Using the symmetry of each sector Then we can get all the magnetic flux linkage phasor sequence on the whole periphery. One-to-one correspondence between this sequence and the corresponding voltage phasor, the conversion state sequence of the inverter switch tube in one fundamental wave cycle can be obtained, as shown in Figure (e). The waveforms of the corresponding three-phase line voltages are shown below the figure (e). It can be known from the above drawing method that the phasor action time of each switch state is equal, and it is very convenient to implement with circuit hardware. In addition, the regulation of the inverter output voltage is achieved by appropriately adding a zero phasor during the switching transition. In this scheme, zero phasors are added to each unit uniformly. The method is to add Ù0 (000) after Ù1 (100), Ù3 (010), Ù5 (001); add Ù7 (111) after Ù2 (110), Ù4 (011), Ù6 (101). Its action time only depends on the modulation degree M, and there is no need to calculate or build a table, so the control method is simplified, and it is easy to implement in hardware. Using the new driver IR2130 can easily get a miniaturized all-digital control circuit. This control method is very good for low-power variable frequency speed regulation systems such as refrigerators and air conditioners. By adjusting the voltage of the voltage-controlled oscillator in the control circuit, the constant U/f ratio variable voltage variable frequency (VVVF) control with a constant pulse width can be realized. Of course, a properly designed control circuit can also achieve constant voltage constant frequency (CVCF) control.

In addition to using the 6-step PWM mapping method (also known as the state-space modulation mapping method) described above to increase the segment N of each side and make the magnetic flux trajectory tend to be circular, it is also possible to eliminate specific harmonics. method to make the magnetic flux trajectory tend to be circular. It should be pointed out here that both the 6-step drawing method and the specific harmonic elimination method can make the magnetic flux trajectory tend to circle well at less switching frequency, so the switching loss is correspondingly somewhat reduced.