Detailed explanation of harmonic injection three-phase boost single-switch SPWMPFC rectifier

For the constant switching frequency and constant on-time (Ton) SPWMPFC rectifier introduced earlier, the 5th harmonic content of the mains input current is still on the high side. In 1995, Q. Huang proposed a variable control method of Ton. The method is to inject the 6th harmonic to change the duty cycle d, so as to reduce the 5th harmonic content in the mains input current. (click here to open
Read more about it)

The reason why the 5th harmonic content is large under the PWM control mode of constant switching frequency fs and constant on-time Ton can be explained by the detailed waveform of the input current in one switching cycle, as shown in Figure 2. Different circuit forms include Different waveform characteristics, the current discharge slope of the input inductor L is not proportional to the corresponding phase voltage, the discharge time Td depends on the three-phase voltage, and the maximum Td of a phase does not occur at its voltage peak, but occurs at the phase. At the moment when the voltage crosses zero, the result is to make the peak current lead and cause distortion, as shown in the figure, in this interval, the peak value of the input current ib is at π/3, when the B-phase voltage crosses zero (ub = 0), when M is small enough, the current peak will become the largest current peak. This disadvantage can be overcome by injecting the 6th harmonic to change the duty cycle d (Figure 1):

Figure 2 - Detailed waveform of input current in one switching cycle — Figure 2 – Detailed waveform of input current in one switching cycle

where m——modulation coefficient, m<l.

Replace the d in the constant frequency constant Ton=dTs with the variable duty cycle of the 6th harmonic injection defined by the formula (Fig. 1), and ignore the m2 (m2<<1) term and higher harmonics (n>7 ) term, the formula becomes Figure 3:

It can be seen from the formula (Figure 4) that the original 5th harmonic is suppressed by the 6th harmonic in the duty cycle. In the formula (Fig. 4), although the content of the 7th harmonic is increased, the total harmonic content is reduced. After injecting the 6th harmonic in d, the harmonic distortion rate THDi of the input current will be determined by the 5th and 7th harmonics, namely (Fig. 5):

If I5m>ml1m, and I5m>ml1m is the THDi of the input current ia of the constant switching frequency, constant on-time PFC rectifier circuit. Comparing the THDi’ of the formula THDi and the formula (Fig. 5), we can see that the PFC rectifier circuit after injecting the 6th harmonic cannot completely eliminate the 5th harmonic, but it can reduce the harmonic distortion rate THDi of the input current.

The 6th harmonic is injected into the duty cycle d, so that the characteristics of the PWM with variable Ton can also be expressed on the input current waveform, as shown in Figure 6. In this figure, if the duty ratio is changed, the distortion of the two phases can be reduced. In the interval a’~b, the duty ratio d is reduced, and the distortion of the b phase and the c phase is reduced; The interval, d increases the distortion of the a-phase and the c-phase, so that most of the interval distortion is improved.

Figure 6 - Input Average Phase Current — Figure 6 – Input Average Phase Current

The relationship between the optimal value of the modulation coefficient m and the voltage gain M is shown in Figure 7, and the relationship between the input current THDi (%) and the voltage gain M is shown in Figure 8. Figure (a) is the constant frequency fs, the constant frequency fs The relationship curve between THDi and M when Ton; Figure (b) is the relationship curve between THDi and M when fs is variable and Ton is constant; Figure (c) is the relationship curve between THDi and M when fs is constant and Ton is variable. It can be seen from Figure 8: To make THDi < 10%, for the curve (a) with constant fs and Ton, M should be greater than or equal to 1.7; for the curves (b) and (c) where one of fs and Ton is variable , M should be greater than or equal to 1.4. When M=l.7 of the curve (a), it can be seen from Fig. 7 that the optimum modulation coefficient m(%)=4.6.

Figure 7 - The relationship between the optimal value of the modulation factor m and the voltage gain M — Figure 7 – The relationship between the optimal value of the modulation factor m and the voltage gain M

Figure 8 - THDi(%) of input current versus voltage gain M — Figure 8 – THDi(%) of input current versus voltage gain M

For the actual three-phase PFC rectifier circuit, the input AC voltage is 220/120V, the output DC voltage is 800V, and M=1.485. The data obtained by testing with different harmonic injections are shown in Table 1, which corresponds to Table 1. The input average phase current waveforms at different injections are shown in Figure 9. From the figure and Table 1, it can be seen that the THDi value of m=4.6 and the injection that meets the requirements of IEC555-2 and m=6.3 and the “best state” injection case are both less than 10%, which can make the mains input power factor reach above 0.99.

Table 1 - Input average phase current waveforms at different injections — Table 1 – Input average phase current waveforms at different injections

Figure 9 - Input Average Phase Current Waveforms at Different Injections — Figure 9 – Input Average Phase Current Waveforms at Different Injections

Figure 10 - Simulation waveform of input current — Figure 10 – Simulation waveform of input current

Table 2 - Input current harmonic content — Table 2 – Input current harmonic content

For a 6kW PFC rectifier, when the 6th harmonic injection PWM control method is used, the input voltage is 220/120V, the frequency is 60Hz, the output voltage Ud=800V, the switching frequency fs=45kHz, the modulation factor m=4.6, and the control frequency bandwidth is When the EMI filter is 200Hz, the EMI filter is 100dB/30kHz, the input energy storage inductor L=50μH, and the output DC filter capacitor Cd=200uF, the harmonic content of the input current obtained by simulation and experiment is shown in Table 2. The simulation waveform is shown in Figure 10; the frequency spectrum of the input current is shown in Figure 11, and the test waveform of the input current is shown in Figure 12. The block diagram of the Boost PWMPFC rectifier circuit with harmonic injection is shown in Figure 13, and its control circuit uses a multiplier.