How do harmonics relate to power factor and displacement power factor?

A question we get a lot is how do harmonics relate to power factors specifically? What's the difference between total power factor and displacement power factor?

If you think about power factor,   and we think about the 60 Hertz part only – we have Watts on the X axis. We have VAs on the Y axis and the hypoth news is KVA or VA. If you think about harmonics, we add a third dimension to that graphic, and I'll show you a picture of that in a minute. But, the third dimension is the Z axis. So we have Watts, VAs and harmonics. And, as we add the harmonics, it doesn't extend the Watts. It doesn't really extend the VAs. What it does is extends the KVA or the VA. Let me show you what that means mathematically. If we take our power triangle and we draw the X axis here, this is our kilowatts and our Y axis, which is K V a R. 

And the hypotenuse, which is KVA. And, let's say the kilowatt equals 80 kilowatts. Say the KVA is a hundred. Then our power factor for the 60 Hertz part is kilowatts divided by KBA, which would be 80 over a hundred or 0.8.That's our power factor. And, we call that just the 60 Hertz part, the displacement power factor. Now, if I can add in the third dimension here, we have our 60 Hertz part again, kilowatt and K a R. And in KVA here, this is just KVA for 60 Hertz. If I add in harmonics, it's again adding to that Z axis. So my, my triangle looks like that. Now what I'm talking about from a new KVA is actually this number here, which is going to be bigger than the KVA 60 hertz. So KVA, total, let's say that's 120. 

So now my power factor total, including harmonics is going to be kilowatts divided by KVA total, which again, could be 80 divided by in this case one 20, which is six, seven. So again, my total power factor, if I have harmonics is always going to be lower than my displacement power factor which is just my 60 Hertz part. Now take keeping that in mind, let's talk about a little bit of history here. People always ask the question -  is that going to affect my power bill? And the answer is no. The reason is more historical than what we just showed you. So, if you are looking at the total power factor, utility companies could measure that and they could bill you for the lower power factor. But, what they do is they bill you for the 60 Hertz part only. 

The reason it's historical is at one point they only measured the 60 Hertz part. Then, we came along with all these new electronic meters and we had the capability to actually measure the total power factor. So a customer has a bill. One day, they have a 0.8 power factor. The utility comes out and puts a meter in the next day. They have a 0.67 power factor. Now, they get a power factor penalty. The problem is that a lot of customers complain and basically said that it's not fair, which in their case, they didn't change their load. So why should they be penalized? Utilities really build now only on displacement power factor, but the important part is to recognize that you are drawing more KVA. So your cables are going to draw more amps. Your transformers are going to see more KVA and your system capacity is going to be less. That really highlights the difference between 60 Hertz displacement power factor and the total power factor, which includes harmonics.