In order to reduce input current harmonics and improve input power factor, a.r.prasad proposed a three-phase boost single switch SPWM PFC rectifier circuit in 1987, as shown in Figure 1-1. S in the figure is a single tube control switch, l is the input boost energy storage inductance, CD is the DC filter capacitor, and UD is the DC output voltage.
Assuming that the three-phase input voltage is a symmetrically balanced undistorted sine wave, as shown in Figure 1-1, then
The selected interval (as shown in Figure 1-1) is analyzed. In the interval, ua>0, uc > 50Hz, the input voltage can be considered to be constant during a switching cycle of switch s, so that the boost circuit can be established.
Since the three-phase boost single switch spwmpfc rectifier circuit cannot realize SPWM control, in order to simplify the control circuit, the main switch s here adopts the PWM control mode of constant switching frequency and constant conduction time, as shown in Figure 1-2.
D is the on duty ratio of switch s, then the average value of input current in the interval is
The values of current IA, IB and IC in the range of 0~2 π can be calculated according to the symmetry of the input current waveform. The value of harmonic distortion rate THDi can also be calculated from equation (3-9). The result shows that THDi is independent of duty cycle D (i.e. load factor) and is completely determined by voltage gain M. The relationship curve between THDi of input current and voltage gain m is shown in Figure 3-30. It can be seen from the figure that the current distortion rate THDi decreases with the increase of m value. When thdi<10%, the minimum value of M is 1.7.
Figure1-3 shows the two average waveforms of input phase current ia with input voltage of three-phase 380/220v for 6kW PFC rectifier at m=1.5 and m=2 and their comparison with fundamental current. It can be seen from the figure that the waveform of input current ia still contains 5th harmonic, which shows that the PWM control mode with constant switching frequency and constant conduction time cannot eliminate the 5th harmonic. The amplitude of the 5th harmonic is related to the value of voltage gain m, and the approximate expression of three-phase input current is
The initial phase angle of the 5th harmonic in equation (1-10) is obtained by the decomposition of Fourier series. The harmonic distortion rate of input current is
The input current waveform in a switching cycle TA is shown in Figure 1-3. The equivalent circuit and working mode corresponding to this waveform are shown in table 3-4.
During this period, ua>0>ub>uc, only 0, 2 or 3 diodes in the six rectifier diodes can be turned on at any time.
Mode 1, l energy storage [to~tm]: at the time of t=to, the switch S is turned on, the rectifier diodes VD1, vd6 and VD2 begin to conduct, the midpoint a, B and C of the bridge arm are short circuited, and the three-phase input currents IA, IB and IC. Start from zero and rise linearly. When t=ton, switch S is off and mode 1 ends.
Mode 2, three-phase l energy release [ton~t’off]: when t=ton, the switch S is turned off, and the inductors La, LB and LC simultaneously release energy and continue to supply power to CD and RL. When t=t’off, because the absolute value of Ub is the smallest, IB drops to zero, vd6 turns off naturally, and mode 2 ends.
Mode 3, three-phase energy release [t’off~toff]: when t=t’off, IB drops to zero, IA and IC continue to decline, and when t=toff, IA and IC fall to zero, and mode 3 ends.
Mode 4, cut-off [toff later]: three-phase currents IA, IB and IC. Both have fallen to zero, and vd1~vd6 are all cut off until mode 4 ends when switch S is reopened.
During ton in a switching cycle, s turns on, the input current (inductive current) rises linearly, and the inductance stores energy. During toff, s is turned off, and the inductance releases energy to the load. The length of toff is related to the absolute value of input voltage. In the interval, because the absolute value of Ub is the smallest, IB releases energy to zero when t ‘off<toff, vd6 is turned off, IA and IC continue to release energy, and the current IA and IC are zero when t=toff. Thus, a switching cycle is completed. Since toff ton = toff<ta<ton, the rectifier operates in the current intermittent mode (DCM), so the harmonic content of the input current is high.
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