Chapter 15.

Boost Power Factor Correction

Maximum Peak to Peak Ripple Current in the Boost PFC Inductor:

Because the switching frequency is usually more than three orders of magnitude higher than the line frequency, for a single switching cycle the inductor can be considered as having a triangle AC switching current with the instantaneous line current as a DC bias. After making this approximation, the following equations can be developed:

In general, for an inductor the following equation will apply:

                                             (15-1)

When the switch is ON, the current in the boost inductor will increase from I_l to I_h:

                                              (15-2)

Where V_i is the instantaneous input voltage.

When the switch is OFF, the current in the boost inductor will decrease from I_h to I_l:

                                 (15-3)

We will eliminate now D between equations (15-2) and (15-3):

                                  (15-4)

To find at what instantaneous input voltage the peak to peak ripple current will have a maximum, we need to analyze the function:

                                    (15-5)

From the above equation, we see that:

a) If the instantaneous input voltage can reach half of the boost voltage, the peak to peak ripple current has a maximum in this point. This maximum is:

                                           (15-6)

The maximum instantaneous RMS value will be:

                     (15-7)

b) If the instantaneous input voltage cannot reach half of the boost voltage, the peak to peak ripple current has a maximum when the instantaneous input line reach its peak.

In a normal design, 85-276Vac, or 176-276Vac, or 85-138Vac, the instantaneous input voltage would always reach a value equal with half of the boost voltage. The only situation when the instantaneous input voltage will not reach half of the boost voltage, is in a 85-136Vac design with 400Vdc boost voltage witch is unusual. This particular case will not be discussed further.

RMS Ripple Current in the Boost PFC Inductor:

Re-write the formula (15-4) function of time:

The RMS value of this current will be:

Boost PFC Inductor Calculation:

We will try now to determine a formula for calculating the boost inductor having as input data: PFC output power, PFC boost voltage, Minimum AC input voltage, PFC switching frequency and Maximum boost ripple current as a percentage from the peak Input AC current:

                                         (15-8)

Maximum Boost PFC Inductor Peak Current:

Analyzing the above equation, the conclusion will be that the inductor peak current will occur at the minimum AC line voltage (V_rms), and when the instantaneous line voltage reaches its peak. Therefore, the maximum peak current in the boost inductor will be:

Now, going back to the equations (15-2) and (15-3) and eliminating ripple current, will we have the following equation for the Boost duty cycle:

                                                  (15-9)