Why Does Current Stay In Phase With Voltage in Active Power Factor Correction Circuits?

I broadly understand the way a control chip can follow the AC waveform and boost in a way that the current drawn will be corrected so as not to represent a spike but a sine type curve.

What I don't quite get, is I would assume that the current waveform would not be in phase with the voltage waveform, because the inductor is energized more at lower voltages than a the peak. I would have thought that the current would peak when the voltage is low? What am I missing?

The common PFC circuit uses a boost converter with a constant ON time. For a 240 VAC source the converter boosts to 350-400 VDC.

The energy stored in the boost inductor for each cycle is equal to one-half I squared L or 0.5(I^2)L. When the sine wave is at 30 degrees the voltage is 1/2 of the peak voltage, which occurs at 90 degrees. The energy stored in the boost inductor at 30 degrees is 1/4 the energy stored at 90 degrees. If a resistive load was connected it would draw 1/4 the power at 30 degrees as at 90 degrees. In this way a boost converter with a constant ON time looks like a resistive load.

thank you, by constant on do you mean continuous boost? the project i am working on using a VCO instead of a apfc controller, and results on simulator looks good but have 13 degree phase shift over shunt resistor in series with overall circuit. (prefer coding to these designs that can probably bought off shelf).. just wanted to understand. your answer however is so concise, i have respect for the guys on this forum. regards

The boost circuit runs in discontinous mode.