In 1993, Ucecla et al. studied the three-phase single switch Boost PFC rectifier controlled by DCM mode variable frequency PWM with variable switching frequency fs. Its circuit is shown in Fig1-1. This is a single switch three-phase PFC rectifier circuit with Boost input inductance L.

For the convenience of analysis, it is assumed that:

① Switch tube S is an ideal switch. When S is on, its forward voltage drop Us=0; When S is off, its forward voltage drop Us=UM;

② Voltage gain of PFC rectifier M ‘=UM/Um. The value of Um depends on the DC/DC converter, such as the Ud in the DC/DCBoost converter.

Voltage gain is defined not by line voltage but by phase voltage amplitude, i.e

When constant switching frequency control is adopted, the waveforms of input currents ia, ib and ic are shown in Figure 1-2.

The following describes the function of the current id flowing out of the rectifier when the switch S adopts the constant on time ton=dTs and the variable off time Toff=t3 ton, that is, when the switching frequency fs is variable.

When switch S is on, there is id=0 (switch modulation). When constant conduction time ton and variable switching frequency fs are adopted, the waveforms of current ia, ib and ic are shown in Fig. 1-3.

It must be pointed out here that the current is always equal to the input current with the largest absolute value in ia, ib and ic, and the line current is different in ton of each phase, that is, it cannot reach zero in the same time.

In addition, in each cycle, the converter presents 6 different intervals depending on the diode conduction. In practical applications, the switching period Ts is always equal to t3 (as shown in Fig. ).

In the range of 0 ≤ wt ≤ 90 °, there are

Then the average input current ia avg is

Note that in equation ,

the input voltage UM is the voltage on switch S when switch S is turned off. The relationship curve between the fundamental wave current lf norm (root mean square value) normalized by the above three equations (equation (3-16)) and M ‘is shown in Figure .

The variable switching frequency shall be repeated every 60 ° (six times the frequency wave of the input AC frequency), and shall be less than or equal to – 30 ° ω The expression of switching frequency given in the interval of t ≤ 30 ° is

Standardized (normalized) switching frequency fston vs ω The relation curve of t (°) is shown in Fig, which is the formula when M ‘=2, 3, 5 and 10. Calculated fston vs ω T relationship curve.

For more information, please click here