Electronic – Why does low power factor make the LED bulb and clock radio flicker at 0.2 to 3 Hz

The power factor is managed ("corrected" is really the wrong term, although its the common one) by making the current follow the voltage. In your schematic, the bus voltage will be a bit higher than the peaks for the AC waveform. The inductor, FETs, diode, and capacitor form a boost converter. This converter takes the rectified AC input voltage and makes the bus voltage.

If the control system only regulated the output voltage, there would be no PFC happening. What it does instead is regulate the average current thru the diode to be proportional to the instantaneous rectified AC input voltage. Remember that the ideal load from a power factor point of view has the current in phase with the voltage. Another way of looking at it is that load on the AC line needs to look resistive. Just like a real resistor, you want to keep the current proportional to the voltage.

Of course that is at odds with regulating the bus voltage. This is handled by having a fast response to the AC input voltage but a much slower response to regulating the bus voltage. In other words, the AC line still sees a resistance, but the resistance value is slowly changed as needed to keep the bus voltage near its target value.

You can check out my Digital PFC Control writeup for more background on PFC and a way I came up with to keep the current proportional to the voltage without having to measure the current. I've got a patent on that, which also includes using digital computation to control the bus voltage more accurately. With a little computational power, you can know what ripple is caused on the bus due to following the AC line voltage, then use that to determine what changed due to varying demand from the load. This allows adjusting to load changes more quickly than the conventional approach but without defeating the PFC function.

The point you seem to be missing is that it does not require power transfer from the device back to the power line during part of the power cycle to have less than unity power factor.

There are various ways of looking at what power factor really is, although they all come out the same mathematically. One way is the ratio of real power delivered to the product relative to the RMS voltage and current. If the current is a sine (let's consider the voltage always a sine in this case, since the power line has such low impedance), then you have unity power factor when it is in phase with the voltage, and 0 when 90 degrees out of phase. In the case of a sine, power does have to flow back to the line during part of the cycle to have less than unity power factor.

However, lots of other waveforms are possible. You can have current that is always 0 or positive when the voltage is positive, or 0 or negative when the voltage is negative, but that is not a sine. The spikes you mention caused by a full wave bridge are a good example. Power never flows back to the power line, but yet the power factor is less than 1. Do some examples and calculate the RMS current drawn by a full wave bridge. You will see that the total real power drawn from the power line is less than the RMS current times the power line voltage (again, we are assuming the power line voltage is always a sine).

Another way to think of this is that losses in the tranmission system are proportional to the square of the current. The full wave bridge draws its current in short spikes of high magnitude. Because of the squared nature of the losses, this is worse than the same average current drawn more spread out. I you work out that math, you realize that the way to minimize the average square of the current is to make the current be a sine in phase with the voltage. That is the only way to achieve unity power fator.

Yet another way of looking at this, which you alluded to, is to think of the Fourier expansion of the current. We are assuming some current waveform that repeats every power line cycle, so it has a Fourier series. Any such repeating waveform can be expressed as a sum of a series of sine waves at the power line frequency and positive integer multiples thereof. For example with 60 Hz power, the waveform is a sum of sines at 60 Hz, 120 Hz, 180 Hz, 240 Hz, etc. The only question is what the amplitude and phase shift of each of these harmonics are. It should be obvious that only the fundamental (the 60 Hz component in this example) is capable of drawing any net power from the power line, and that only to the extent it is in phase with the voltage. Since all components are sines, each will draw power during part of the cycle and return the same power at another part of the cycle, except for the in-phase component of the fundamental. So your way of looking at power factor as having to put power back during part of the cycle is valid if you break up the current waveform into sine wave components. However, it is possible to have a set of sine wave components that take and return power to the power line at different times such that the net from all components at any one time is zero or positive. The full wave bridge current is one example of such a waveform.