Anything in the 1-3A output current range and the PFC circuitry just dies (heatsink rapidly reaches 120C and the output turns off), not even a lot of airflow can seem to stop that.
That makes NO SENSE to me in Normal Operation.
See the Bottom of the Post for more abnormal Scenario.
I agree that if the Output Current is too low, then the Power Factor will be low and Oscillating quite a bit, since the DC-link Capacitors can hold most of the Power required by the Output Circuit on their own (without need for much Input Current). Thus there will be some "Pumping" Action from the Input from Time to Time at low Load.
I'd expect the Power Factor to oscillate in Time. Did you get your Measurement with an Oscilloscope or just a Kill-A-Watt Meter ?
That the Power Factor is bad a low Output Load is not a Surprise.
That it overheats it DEFINITELY is a big Surprise though

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I can only speculate that, for whatever Reason, the Oscillation Amplitude and/or Frequency is higher than expected.
This means that the PFC Switching Frequency is not fixed but somewhat Variable. Heck, at extremely low Load it might even switch Off from Time to Time. That can only be observed with an Oscilloscope though.
I'd expect at very low Load they might want to REDUCE the PFC Switching Frequency, which should reduce Losses, but increase current Ripple.
When you say that the "PFC Overheats", do you mean the Transistors ? Or the filter Choke ?
If you have a HV differential Probe (do NOT do this directly with an Oscilloscope) you could try to look at the Transistors Gate-Source Voltage and see if there is something weird happening with their Switching Pulses at low Load.
But again ... to overheat so badly at low-load is a bit of a Mistery.
Are you sure it's the PFC Circuit ?
At 10A and a little bit of airflow the PFC heatsink got to 64C equilibrium, increasing the output current to 14A and the temperature decreases further to 59C. Since the power factor on my 700W input power test was 0.98, I'd guess that anything under the optimal power factor causes that circuitry to not function properly. That also explains the sparking noise at no load (0.04 power factor with no 12V output, 0.09 with 12V output enabled, but no load).
Well that's roughly 3A Input Current, for a 10A Input Nominal Current (~ ish). Of course they don't design PFC to be optimal at 0.01% Load

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But that a bad PF causes the PFC to overheat is really weird to me.
Do you mean this Heatsink is getting very hot ?

Due to the way the PFC seems to function there doesn't seem to be any way to use this power supply passively. Too low output current and the PFC over heats and dies. Too high output current and 12V output stage heats up and requires airflow.
Again, that doesn't make much sense to me.
Unless ... Their PFC Circuit tries to over-compensate and thus INCREASES the Switching Frequency quite a bit at low-load.
Which IMHO is exactly the Opposite of what I'd expect, since that kills Efficiency (forget about the PF at low Load).
But also that shouldn't overheat, even 10x Switching Frequency shouldn't matter if current is 10x smaller than Nominal.
Except if they have a very bad Diode (Reverse Recovery).
When the PFC is the hottest component it seems hard to get airflow back there.
Back there ? The PFC is in the Front ...
A 120mm fan blowing air at the case doesn't do much.
Well, you have to blow Air
through the Case, not on the Case. Without a Duct you'd have zero Chance.
but even a little direct airflow from a blower fan at 0.6W (8V 0.075A) can cool the PFC heatsink just fine to 64C.
At which Input Current Load is that ?
At 215W input power the PFC is by far the hottest component in the system.
Again, weird. I'd say the Switching Frequency is going UP at low Load, which is the Opposite of what I'd expect.
But also THAT doesn't explain why it's overheating that much to be honest.
Like even if Switching Frequency is 10x Higher (and for the sake of Argument let's say that at Reasonable Load Switching Losses are 50% of the Total, other 50% being Conduction Losses), then that shouldn't really overheat, since the CURRENT is 10x lower than Nominal ...
At 700W input power the PFC cools itself passively (no airflow required), but the output stage gets to 110C.
Output Stage with no Airflow ? For ~ 30% Nominal Power I'd say it's not too Bad

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It's a bummer that this PSU seems to require a load around 7A for the PFC to not overheat. It's not the end of the world, but it kind of limits the versatility. When I have time I'll try to test up to 50A, but that's kind limit for my equipment.
If you have a Scope it would be interesting to investigate the PFC Circuit as to why it behaves like this and what changes between very low Load and 7A Load.
You will need HV Differential Probes and Oscilloscope (and lots of Caution).
I have those but ... right now I don't have much Time unfortunately

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Anecdotally, I have seen something similar-ish at work (NOT at very low load though) BUT ... to explain the Overheat Phenomenon, I think we have to look at abnormal Operation right now.
One such case is a Shoot-Through, but the only Way to have that for this Topology is if they do a Synchronous Rectification with MOSFET after the Boost. Basically 2 transistors shorting the DC Capacitor for a Fraction of a Microsecond each Time.
Another one could be having 2 Boost PFC interleaved with insufficient Inductance in-between them, so you kinda get current circulation between them. Again, not something I at first Sight see happening for this Topology.
And of course if anything causes the Semiconductor to heat up, the Switching Waveforms can SEVERELY be affected, thus the Turn On / Turn Off (Rise & Delay) Parameters can vary dramatically. A Semiconductor Timing at ambient Temperature is very different than when Hot.
It could also be caused by a slightly different Component Batch from the Semiconductor Supplier of course.
Funnily enough I saw this in a Paper, could indeed be what's going on, if the Controller things that we are always around Zero-Crossing:
Aside from that, the other Things that comes to Mind is: Diode Reverse Recovery.
IF the Switching Frequency increases at low Load, then the Diode of the PFC might be overheating.
MOSFET Conduction & Switching Losses are current dependent for the most Part (if you exclude the Gate Driver Losses).
Diode Reverse Recovery (Qrr/trr) is not. That mostly depends on the Switching Frequency.
So if Losses are definitively going up at low Load, the Switching Frequency is increasing, but there is no Shoot-Through or Current Circulation between Parallel Converters, Diode Reverse Recovery might be the explanation.
And if that is the Case, then I'm afraid we don't really have much Options.
I don't know if what they have installed right now is a PFC Diode + MOSFET in a single Package or as separate Discrete Components.
Depending what they have installed, it might be worth considering replacing those with a SIC/Schotty Variant.
With the Downside of course that we would have to find a way to "drive" the Diode (some SIC Diodes, at least when built inside a MOSFET Package/Module, have extremely high forward Voltage up to 4V, thus they need to be bypassed by the MOSFET !), if they do NOT have a Synchronous Bridge Rectifier Control already implemented.