# Would an AC induction motor rotate if the power factor were unity?

I know about active and reactive power as a big picture. Active power is what really does the job and the reactive power circulates back and forth in and out of the system. I also know the math behind them to some extend and active reactive components ect.

Where Im stuck as is that why power factor is set near unity like 0.8 or 0.9 but never unity. By adding capacitor banks why would power factor not made unity? In other words why is active power needed for inductive loads? I might be askng something foolish but I couldnt prove it to myself.

• I believe you're asking something that's completely impossible because of the laws of physics. If capacitance and inductance never existed, you could achieve unity. If money wasn't an issue, we could provide unity as well. – KingDuken Dec 18 '18 at 17:49
• Unity can be achived by compensation; isnt it? – user1245 Dec 18 '18 at 17:54
• It's possible to achieve unity pf with a parallel capacitor, but remember that the voltage across the resistive part of the load will always be less than the supply voltage. – Chu Dec 19 '18 at 0:05
• The power factor of a motor is a side effect of how it is constructed. Some places that run lots of big motors DO use capacitors to bring the power factor back closer to 1. – mkeith Dec 23 '18 at 3:27

Where Im stuck as is that why power factor is set near unity like 0.8 or 0.9 but never unity.

The Power Factor (to be precise, displacement power factor) isn't set to 0.8, 0.9.

A generator will be capable of producing VA. If a resistor was place across the terminals then the DPF & PF would be 1. It is the load that draws reactive current and the phase shift is dependent on the load. This can be compensated by some reactive components so the supply see's a DPF closer to unity, but this doesn't change the fact that the load will draw a non-unity DPF

• What I mean is setting the power factor of a system or a motor by adding capacitors. I mean the resonance condition. If you have a motor running with reactive power inductive Q, cant you add caps and make Q zero? Yes magnetizing current still flows but what is so difficult to achive exactly 1 PF? – user1245 Dec 18 '18 at 19:07
• practicalities. Capacitors are never really just capacitors not only in the dielectric but now you have added leads, which are inductive. Theoretically of course it can be done but out in industry it is done to reduce cost and while you could spend time creating the perfect circuit in front of the motor, how much time was spent to achieve this? at some point the costs involved (time, resource etc) outweigh chasing those final degree's – JonRB Dec 18 '18 at 19:08

Power factor is not "set", per se. Non-unity power factor happens, in spite of the fact that we'd like it to be exactly one.

In the US, large installations like mills or factories are often charged both for real power and reactive power, at different rates (or they're imposed with a surcharge for non-unity reactive power -- it's the same thing, but shows up differently on the accounting sheets). Such installations will go to some effort to bring the reactive power down, either with actual capacitor banks or with synchronous motors that aren't powering anything but are adjusted to look capacitive at 60Hz.

• I still dont understand why total reactive power Q cant be made zero leading a unity PF by a variable capacitor. – user1245 Dec 18 '18 at 18:24
• "...why total reactive power Q cant be made zero..." It can be. And if all of the contributors to the non-unity PF is at the same frequency rather than harmonics, the power factor can be made to be unity. Doing so costs money, though, so what is possible may not be what is economical. – TimWescott Dec 18 '18 at 19:51

Yes, it's a bit foolish. Ultimately, motors only care about current and the magnetic field that it produces, not the voltage that produces that current. The phase relationship between them (the power factor) doesn't matter at all.

Power factor limits are never exactly unity, because in practical terms, it's never possible to completely eliminate reactive elements in a circuit. For example, there is the leakage flux inside the motor — it's never possible to couple 100% of the flux between the stator and rotor — which makes it look like an inductor.

• For an induction motor the reactive power Q is inductive. If one adds capacitors across motor terminals and achives the total Q as zero; would the motor stop rotating? – user1245 Dec 18 '18 at 17:50
• I reread your answer I guess you mean therotically yes it will rotate but practically hard to tune it to 1. – user1245 Dec 18 '18 at 18:01

What sets the power factor below unity is the motor itself. This is true for many devices that need to produce a magnetic field: inductors, transformers, induction motors. They all need reactive power basically to create a magnetic field/flux.

The physical reasons lies in Lenz law between the emf $$\e\$$ and the magnetic flux $$\\phi\$$:

$$e(t) = -\frac{d \phi(t)}{d t}$$

$$\e\$$ is in phase with the voltage and $$\\phi\$$ with the current. So the current is lagging 90° behind the voltage, hence the reactive power consumption.

Note that, for the same power, an induction motor needs more reactive power than a transformer, because there is a need for an air gap between stator and rotor (if you want the motor to spin). This air gap requires more current to create the magnetic flux, and as a consequence more reactive power.

This image should help you understand unity power factor. Which is simply the phase difference between the voltage and the current sinusoids of the system. The photo below shows this in the time domain. You can see unity, leading and lagging power factors caused by balance or imbalance in this phase difference. However it is also useful to think about this in the phasor domain. Which is the left column in the image below. This allows us to simplify the math to understand how to "achieve" unity power factor. We need to align the voltage and current vectors. To do so we can either add capacitance into the system or add inductance to the system, depending on the initial system's capacitance or inductance. Your question title specifically appears to be about how your induction motor will operate in a system with unity power factor. It would rotate optimally. You should research the advantages of power factor correction in a system to understand why.

Now your other questions, why is power factor set to .8 or .9, once again the devices in the system whether they are inductive or capacitive loads will determine the power factor of the system.

The device itself will typically have a power factor rating as well which is how it will contribute to the overall system when it's in use. As you have already pointed out it is usually around .8 or .9, typically lagging, because most of our loads are inductive!

There are a ton of induction motors and machines connected to the US grid for example. Thus the grid typically requires adding reactive power to balance out the more typical inductive loads in the system. This is done to reduce the phase different between the voltage and current sinusoids in the system.