# Negative power factor and PV systems

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#### Smart \$

##### Esteemed Member
...

If you want to look at it another way, the power factor is a measure of the percent of the used conductor path that is transporting real power. The percentage does not depend on the direction of power flow. In other words, +8 kW divided by 10 kVA means 80% of the path is used to transport real power. -8 kW divided by 10 kVA means 80% of the path is used to transport real power. Either way, it is 80%. The reverse flow does not mean we use -80% of the conductor path.

...
I see a possible hole in your premise, but I do not know enough about PV inverter output to challenge head on.

What I need to know is the PV-to-grid current data. For example, say a 208/120 service with a consumer load of 60A at 90% power factor (lagging). A grid-tied PV system connected to this system is producing 100A of current. What is the current waveform at the inverter output? ...at the service? Is it sinusoidal? Is it in or out of phase with the service voltage? Please elaborate to the extent of your knowledge (and/or willingness ) ...anyone???

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#### mivey

##### Senior Member
Why do you assume that inverter provides perfectly symmetric sinusoidal output?
Let's suppose it is not. In our connectivity rules, we allow a maximum 5% THD.

Here are the the differences between the displacement power factor and total power factor (with θ indicating the angle associated with displacement power factor):

θ = 0? | cosθ = 100.00% | pf = 99.88% | θ error = 2.86?
θ = 5? | cosθ = 99.62% | pf = 99.50% | θ error = 0.76? (15.20%)
θ = 10? | cosθ = 98.48% | pf = 98.36% | θ error = 0.40? (4.00%)
θ = 15? | cosθ = 96.59% | pf = 96.47% | θ error = 0.26? (1.73%)
θ = 20? | cosθ = 93.97% | pf = 93.85% | θ error = 0.20? (1.00%)
θ = 25? | cosθ = 90.63% | pf = 90.52% | θ error = 0.15? (0.60%)
θ = 30? | cosθ = 86.60% | pf = 86.49% | θ error = 0.12? (0.40%)
θ = 35? | cosθ = 81.92% | pf = 81.81% | θ error = 0.10? (0.29%)
θ = 40? | cosθ = 76.60% | pf = 76.51% | θ error = 0.09? (0.23%)
θ = 45? | cosθ = 70.71% | pf = 70.62% | θ error = 0.07? (0.16%)
θ = 50? | cosθ = 64.28% | pf = 64.20% | θ error = 0.06? (0.12%)
θ = 55? | cosθ = 57.36% | pf = 57.29% | θ error = 0.05? (0.09%)
θ = 60? | cosθ = 50.00% | pf = 49.94% | θ error = 0.04? (0.07%)
θ = 65? | cosθ = 42.26% | pf = 42.21% | θ error = 0.03? (0.05%)
θ = 70? | cosθ = 34.20% | pf = 34.16% | θ error = 0.03? (0.04%)
θ = 75? | cosθ = 25.88% | pf = 25.85% | θ error = 0.02? (0.03%)
θ = 80? | cosθ = 17.36% | pf = 17.34% | θ error = 0.01? (0.01%)
θ = 85? | cosθ = 8.72% | pf = 8.70% | θ error = 0.01? (0.01%)
θ = 90? | cosθ = 0.00% | pf = 0.00% | θ error = 0.00? (0.00%)

Compare the pf calculated from cosθ and the total power factor (what we actually get from the meter). As you can see, there is very little difference in the ranges we would expect to see from an inverter that meets the requirements.

#### mivey

##### Senior Member
I see a possible hole in your premise, but I do not know enough about PV inverter output to challenge head on.

What I need to know is the PV-to-grid current data. For example, say a 208/120 service with a consumer load of 60A at 90% power factor (lagging). A grid-tied PV system connected to this system is producing 100A of current. What is the current waveform at the inverter output? ...at the service? Is it sinusoidal? Is it in or out of phase with the service voltage? Please elaborate to the extent of your knowledge (and/or willingness ) ...anyone???
The meter does not use sinusoidal waveforms for the calculation.

The meter measures instantaneous values and accumulates blocks of watts and vars. For the reporting period, the power factor is calculated as cos(atan(varh/watth)). This is what is know as the total power factor and includes both the displacement (reactive) and distortion (harmonic) components.

Does that help?

#### mivey

##### Senior Member
What I need to know is the PV-to-grid current data. For example, say a 208/120 service with a consumer load of 60A at 90% power factor (lagging). A grid-tied PV system connected to this system is producing 100A of current. What is the current waveform at the inverter output? ...at the service? Is it sinusoidal? Is it in or out of phase with the service voltage? Please elaborate to the extent of your knowledge (and/or willingness ) ...anyone???
I have attempted to plot the different waveforms using the same layout as my earlier post. Please forgive any fat-fingering of the equations but this is the idea.

I assumed a minimal harmonic distortion, and used a sinusoidal waveform as I have neither the time nor patience to create a distorted waveform. Not all inverters will produce a non-symmetrical current waveform and use a symmetrical pulse-train in a sinusoidal envelope (I'm not sure of the tech-speak as I do not have any references with me) to keep the power factor closer to unity. There are power supply & power conditioner builders on the site who can speak better on that topic than I can.

The last graph shows what happens when the inverter starts pushing 100 amps back on the grid:

#### mivey

##### Senior Member
The last graph shows what happens when the inverter starts pushing 100 amps back on the grid:
That should say pushing the net of 100 amps less the real load back on the grid.

#### tallgirl

##### Senior Member
If you want to look at it another way, the power factor is a measure of the percent of the used conductor path that is transporting real power. The percentage does not depend on the direction of power flow. In other words, +8 kW divided by 10 kVA means 80% of the path is used to transport real power. -8 kW divided by 10 kVA means 80% of the path is used to transport real power. Either way, it is 80%. The reverse flow does not mean we use -80% of the conductor path.

Work a few examples -- it'll either become very obvious to you, or you'll never figure out why the signs matter.

The short answer is that knowing the "sign" tells you how many VARs you have to make that you're also not making VAs for. This is the concern utilities have expressed -- if DRGs make VAs and not VARs, the ratio of VARs to VAs is worse than the power factors would indicate if you just look at power factor as some kind of "positive value only" number. There's a big difference between a 100KVA load with a 90% power factor and a 100KVA DRG with a 90% power factor. And that's why "signs matter".

It is good to be busy in today's economy.

I don't think that "dating" is a reflection of the state of the economy, but "dating" is more important than trying to explain how electricity works to someone who won't listen.

Work up some examples -- pay particular attention to examples where the DRG total becomes a large fraction of the total grid load. Either you'll "get it" or you won't. If you get it, great. If not, oh well.

#### Smart \$

##### Esteemed Member
...

Does that help?

I have attempted to plot the different waveforms using the same layout as my earlier post. ...
I will have to ponder the information plus develop and verify my own before responding with any substantial degree of certainty. Currently do not have enough time to devote to that end, but should next week...

... if DRGs ...

#### mivey

##### Senior Member
Work a few examples -- it'll either become very obvious to you, or you'll never figure out why the signs matter.
I have calculated many, many millions of bills. Untold thousands have had local generation as well. Putting a sign on the power factor to indicate power delivered or power received or a change in generating vs motoring status has never been an issue.

The short answer is that knowing the "sign" tells you how many VARs you have to make that you're also not making VAs for. This is the concern utilities have expressed -- if DRGs make VAs and not VARs, the ratio of VARs to VAs is worse than the power factors would indicate if you just look at power factor as some kind of "positive value only" number. There's a big difference between a 100KVA load with a 90% power factor and a 100KVA DRG with a 90% power factor. And that's why "signs matter".
You are working from a limited knowledge base, but are too set on what little you know to listen.

I don't think that "dating" is a reflection of the state of the economy, but "dating" is more important than trying to explain how electricity works to someone who won't listen.
If you ever want to be able to teach someone something, perhaps you need to work on your presentation skills first. Flapping your lips real fast with sounds emanating and stomping your foot when someone disagrees with you is not conducive to teaching anything.
Work up some examples -- pay particular attention to examples where the DRG total becomes a large fraction of the total grid load. Either you'll "get it" or you won't. If you get it, great. If not, oh well.
I will make an effort to do so. What effort have you made to understand what has been presented to you? From what I gather, you have no interest in reading material that disagrees with what you think.

#### mivey

##### Senior Member
Distributed generation

#### tallgirl

##### Senior Member
I will make an effort to do so. What effort have you made to understand what has been presented to you? From what I gather, you have no interest in reading material that disagrees with what you think.

I've put plenty of effort into the subject. I suggested you try a few examples on for size, and you've not, so I'm not putting a lot of truck into the comments you've made about my "teaching" skills.

The bottom line, regardless of what you or I may or may not know, is that utilities have concerns about declining power factor caused by PV installations. And while you seem to feel that slapping a negative sign in front of power factor is a dumb idea, and perhaps even that anyone who'd suggest doing so is an idiot, the facts are unavoidable -- completely and totally unavoidable -- that the grid operator will see two different ratios between VAs and VARs for a customer with 100KVA consumption at 90% PF and 100KVA production at 90% PF.

A study out of the University of Michigan, I believe it was (it came from Michigan -- not sure if UofMich did the work, but I know it was a Michigan thing) calculated costs for voltage and frequency regulation as PV penetration increased. As I recall, at 20% penetration, they put the regulation costs at about the same as the bulk (wholesale) generating costs. All this is from fuzzy memory, but that's beside the point -- there's going to be an impact and figuring out what it is and figuring out how to apportion the costs are going to be part of what goes on.

And while I suspect we're about fed up with each other, I'd encourage you to consider an example at the 20% point -- 1MVA at 90% PF with and without 200KVA at the same 90% PF being fed into the grid from a PV installation. Calculate the VARs that the utility needs to produce in both cases and the percentage of VARs to VAs from the utility perspective. Give that an honest go and you'll either see what I'm getting at or not.

#### Smart \$

##### Esteemed Member
I will have to ponder the information plus develop and verify my own before responding with any substantial degree of certainty. Currently do not have enough time to devote to that end, but should next week...
Here's what I came up with...

First, the waveforms of voltage and current, assuming the PV system outputs unity pf current:

Now the calculations:

See the "???"...? Why is the difference between VA and W not 720VAR???

#### mivey

##### Senior Member
I've put plenty of effort into the subject. I suggested you try a few examples on for size, and you've not, so I'm not putting a lot of truck into the comments you've made about my "teaching" skills.
You are just not following what I am saying. Look at my posts #136 and #144 and see if you can figure them out.

The bottom line, regardless of what you or I may or may not know, is that utilities have concerns about declining power factor caused by PV installations.
I'm well aware of the utilities' concerns as I am one of the utility people that addresses them and the associated costs. I design the system, design & verify the service, design & verify the meter setup, design & verify the utility rates, calculate the rates, verify the billing, analyze the financials, allocate the costs for the rates, develop software to help with all of these items, write policies and procedures for different utility areas including distributed generation and metering, as well as teach system design, rate design, billing, and cost allocation to utility personnel.

You might think the issue of generators not supplying vars is unique to PV systems but it is not.

And while you seem to feel that slapping a negative sign in front of power factor is a dumb idea, and perhaps even that anyone who'd suggest doing so is an idiot,
As I have said, there is no problem with using the sign as an indicator of other things and there are at least three ways that I have seen the sign in front of the pf used. The problem is with you trying to say that the power factor itself has a positive or negative nature.

Maybe that is where we have a misunderstanding.

The power factor is an indication of how the capacity is being utilized. It is strictly a percentage with no sign. To make the physical analogy, it is the percentage of the conductor carrying real current to the percentage of the conductor carrying real plus reactive current.

the facts are unavoidable -- completely and totally unavoidable -- that the grid operator will see two different ratios between VAs and VARs for a customer with 100KVA consumption at 90% PF and 100KVA production at 90% PF.
What the grid operator sees has nothing to do with the power factor value stored or any associated sign. What the grid operator sees is based on a kW and kvar measurement (and kVA but that is not important at this point). The power factor is a secondary piece of information and can be completely left out of the calculation with no impact. If the power factor number will not impact the calculations, neither will any sign you stick in front of it.

A study out of the University of Michigan, I believe it was (it came from Michigan -- not sure if UofMich did the work, but I know it was a Michigan thing) calculated costs for voltage and frequency regulation as PV penetration increased. As I recall, at 20% penetration, they put the regulation costs at about the same as the bulk (wholesale) generating costs. All this is from fuzzy memory, but that's beside the point -- there's going to be an impact and figuring out what it is and figuring out how to apportion the costs are going to be part of what goes on.
No doubt that if PV generators do not contribute vars, they will impact the grid costs. But this is the same scenario the power industry has faced with other generation on the grid. What made the PV inverter different from some is that they started out with no means to provide the vars. That is no longer the case with the new inverters.

And while I suspect we're about fed up with each other, I'd encourage you to consider an example at the 20% point -- 1MVA at 90% PF with and without 200KVA at the same 90% PF being fed into the grid from a PV installation. Calculate the VARs that the utility needs to produce in both cases and the percentage of VARs to VAs from the utility perspective. Give that an honest go and you'll either see what I'm getting at or not.
I already understand what you are getting at: it makes a difference whether or not the PV inverter provides vars to the grid or not. That has nothing to do with saying power factor can be positive or negative. The sign is an indicator of something else.

What you are not getting is that the calculations are not dependent on the number you use for power factor. That is not the way the utility meter works. Since you are concerned with what I see as a utility, let's look at the utility metering standards. The meter standards use quadrant metering and the power factor is a secondary calculation.

In the following sets, you could completely drop the power factor percentage with no difference in the result. I have shown the quadrant metering flag as well as the power factor that would come from the meter. I have added the signed pf notation used by Fluke PQ meters (what you are proposing) as well as two other notations I have found.

None of the signed pf values have any impact on the billing or cost as they are not used as part of the billing or cost calculation but are presented as secondary information. The reason they are not used is because there is no standard for that type notation and it can vary depending on who you are talking to. Four-quadrant metering is the IEEE standard for power metering and is what our utilities use.

Here is PV output (and/or load) that is less than the grid load for different PV load/output scenarios:

Here is PV output (and/or load) that is greater than the grid loads for different PV load/output scenarios:

Hopefully I have avoided any typos but either way, you should get the idea.

#### mivey

##### Senior Member
See the "???"...? Why is the difference between VA and W not 720VAR???
First off var= sqrt(VA^2-W^2) NOT VA-W.

I stopped when I saw that.

#### mivey

##### Senior Member
Here's what I came up with...

For post #136

For post #144

Also I get these values:

V = 120.00
A = 60.00
VA = 7200.04
W = 6,480.05
var = 3138.41
pf = 0.90

V = 120.00
I = 52.92
VA = 6349.84
W = (5,520.04)
var = 3138.41
pf = 0.869

#### Smart \$

##### Esteemed Member
First off var= sqrt(VA^2-W^2) NOT VA-W.

I stopped when I saw that.
My bad... but just a blip and corrected as depicted below.

But that's not what I see as controversial...

Take a look at the first 60?+ of the first cycle...

It seems to me that only the PV system can supply the reactive current until just after 60?. During the same timeframe, the service current is outgoing.

#### tallgirl

##### Senior Member
Smart,

You're looking at the wrong place -- for a 1MVA @ 90% PF chunk of grid that suddenly has 100KVA being added by a PV system, the utility is still providing all the VARs, but only 900KVA. That means the ratio of VAs to VARs -- which would normally be the power factor -- goes down.

There are other hypothetical problems as well -- the last time I looked at my peak demand it was about 5.4kW. Except that my minimum demand is around -2.5kW. So the difference between minimum and maximum is 7.9kW. Which is a lot more than the usual 0.3kW tare load for my place.

#### lga

##### Member
I believe this was the original question.

Am I correct in assuming that the POCO would prefer a PV system produce a more-negative (closer to -100%) power factor than just a small (further from -100%, but still negative) power factor?[/U]
There's a lot of stink about PV and power factor and I'm trying to understand what the heck the utilities want. Normally "smaller" is bad, but is it smaller in absolute value, or just plain smaller?

The correct answer is "no", as a utility engineer with 30+ years I can tell you the utility is not concerned with residentual PV systems. (they are concerned with your connecting to the grid)

To help clarify the term "smaller" the correct term is "lag". PF is a percent, from 0 to 1 (unity). We try to keep the distribution (and transmission) as close to unity (1) as possible to reduce the Var flow, however most loads are inductive and a system with .9, or .8 PF is acceptable, more than that and we begin shipping excess vars and this reduces our line capality. the solution is to install line capacitors to balance the induction motors or requiring our large induction loads to correct their inplant loads.

It shoud be noted a PF above 1 is called "lead" and this is bad, if the load is large and reaches the power plant this will do strange and expensive things to the generator.

Hope that helps

#### Smart \$

##### Esteemed Member
Smart,

You're looking at the wrong place...
No, I'm not.

As I see it, PV systems and the POCO share local VAR's, while outgoing PV power actually lessens POCO-generated VARs elsewhere. However, there is an anomoly in the means of measuring and associated calculation which permit the POCO to claim all the VARs, both locally and elsewhere.

#### tallgirl

##### Senior Member
No, I'm not.

As I see it, PV systems and the POCO share local VAR's, while outgoing PV power actually lessens POCO-generated VARs elsewhere. However, there is an anomoly in the means of measuring and associated calculation which permit the POCO to claim all the VARs, both locally and elsewhere.

Change your load to 100A @ 0.9 PF. Or better yet, 111A @ 0.9 PF. At 111 amps for the load, the real power consumed by the load is 12KW, and the real power produced by the PV system is also 12KW. Yet the PoCo is still responsible for the VARs.

Using your table, you'd have 13.3kVA, 12kW, and 5.8kVAR for the load. You'd still have 12kVA, 12kW and 0kVAR for the PV system. At the service, you now have 5.8kVAR and 0.0kW. And the power factor for that is ... ?

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