# Power factor relation with load

I was reading about power factor in electronic devices and I found charts showing that usually the power factor varies (usually decreases) with the load. So if you have a device that either works with 0% or 100% of load it's somehow easy to develop a power factor corrector (passive) but if your device varies the load from 0% to 100% it gets more complicated.

My question is: the device can be seen as a Z load. This Z (impedance) load is composed by a R (resistance) part with a X (reactance) part. So if my device varies the load by changing the relation between X and R (for example keeping same capacitors and inductors values but varying the resistance somehow), of course we then have a different final Z value so we have a different PF. But is it possible that in some cases the X varies like R so the resultant Z (and therefore the PF) remains the same for every load?

Furthermore, is it possible to map the device PF x Load curve and create a PFC that follows the same curve (even though if you change something in the device you have to do it again and considering simple devices where there's just a single dial to vary the load)?

• You use active PFCs to achive this. Mapping your load becomes unnessesary then. Moreover, up until recently, this passive PFC issue was always tuned to produce low enough harmonics/high enough PF at maximum load because that's (the only) thing the goverment/saftey agencies tested for. Partial load was not considered. – winny Aug 18 '16 at 10:42
• Interesting. But isn't the PFC something that has to be integrated to the power supply usually? Or I could buy a power supply with some PF and place a PFC around it to compensate it? – Felipe_Ribas Aug 18 '16 at 16:10
• There are many ways to implement PFC. Straight into the primary side on an existing power supply (uncommon), add a front end boost converter with average current sense 1/X^2 computation/trick to mimic it (very common) or just like you say an circuit in actual parallel to consume or produce the harmonics the power supply isn't (very uncommon but not unheard of). – winny Aug 18 '16 at 22:46
• You can have a capacitor bank where they are switched on/off according to the PF of the load. I have seen these things for industrial drilling machines (the large ones, big as a car). This is how it is: if you were to use an active power filter, you'd be paying a lot more, for virtually the same effect (nostly inductive loads, little noise), so in this case it's cheaper. But if you're thinking in small applications, then forget it, because the capacitor bank, alone, will drain your wallet. TL;DR: yes, it coan be done, but you'd better think well before you choose this; best use PFCs. – a concerned citizen Sep 17 '16 at 14:09

## 3 Answers

It is already what active (continuously tracking the complex power) compensation systems do.

Furthermore, is it possible to map the device PF x Load curve and create a PFC that follows the same curve (even though if you change something in the device you have to do it again and considering simple devices where there's just a single dial to vary the load)?

It is possible, why not, and also a good idea for few states. If you have a machine with 2 power states, then you need 2 pre-calculated reactance exclusively selected by a simple reactive power detection logic. Or it can even somehow be commutated by the dials on the machine itself.

But is it possible that in some cases the X varies like R so the resultant Z (and therefore the PF) remains the same for every load?

Take a look at this phasor diagram: -

For power factor correction (aka resonant tuning) the capacitor is chosen so that it's reactive current totally cancels the inductive reactive current and yields just a small current (I, due to R) taken from the supply (U).

So, if only R varies then a fixed value of C cannot keep power factor at unity because the inductive reactive current will change.

This is a specific case of a parallel tuned circuit where the resonant impedance (i.e. impedance where the phase angle is zero) is dependent on all three components at a particular operating frequency: -

$\omega_0 = \sqrt{\dfrac{1}{LC}-(\dfrac{R}{L})^2}$

Furthermore, is it possible to map the device PF x Load curve and create a PFC that follows the same curve (even though if you change something in the device you have to do it again and considering simple devices where there's just a single dial to vary the load)?

I have no idea what you mean.

• I think he is referring to a setup where the tuning capacitance changes in proportion with varying loads to keep an overall phase angle of 0, for any load. – jbord39 Aug 18 '16 at 9:38
• Yea that's right. If the tunning capacitor could vary accoringly to what you've already measured to be the PF x Load curve – Felipe_Ribas Aug 18 '16 at 10:30
• Automatic tuning of PF is of course very possible just as automatic tuning of radio receivers is - it's the same math applied to a different problem. – Andy aka Aug 18 '16 at 10:36
• Are you happy with this answer? If yes then please consider formally accepting it. If no, maybe there is something preventing you from doing this and would you like to explain this? – Andy aka Dec 1 '16 at 15:27

is it possible that in some cases the X varies like R so the resultant Z (and therefore the PF) remains the same for every load?

Very much possible. Imagine a plant with several identical machines, an office full of computers with non-PFC power supplies, or a hall with several groups of LED lights using similar drivers.

is it possible to map the device PF x Load curve and create a PFC that follows the same curve?

You don't really compensate for the power factor, you compensate for reactive currents which drive your power factor away from 1. Whether the reactive current in your load increased twofold because its internal R changed or because you have connected a second identical load is irrelevant, you'll still need to apply twice as much correction.