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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: (151)
When the switch is ON, the current in the boost inductor will increase from I_{l} to I_{h}: (152)
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}: (153)
We will eliminate now D between equations (152) and (153):
(154)
To find at what instantaneous input voltage the peak to peak ripple current will have a maximum, we need to analyze the function:
(155)
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:
(156)
The maximum instantaneous RMS value will be: (157)
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, 85276Vac, or 176276Vac, or 85138Vac, 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 85136Vac design with 400Vdc boost voltage witch is unusual. This particular case will not be discussed further.
RMS Ripple Current in the Boost PFC Inductor: Rewrite the formula (154) 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:
(158)
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 (152) and (153) and eliminating ripple current, we will have the following equation for the Boost duty cycle:
(159)
