# Split phase residential power and power factor

#### JamesL

Joined Jul 3, 2012
3
We are working on a project that intends to provide some sort of power factor correction for a typical North American household... ie: residences using a 240V/200A split phase supply.

Now, I have a semi solid(or so Id like to think) grasp of power factor and how it applies to single and 3-phase systems. But in the case of a split phase supply, Im a little lost as to where the PF measurements need to be taken and the PF correction components placed...

Considering a typical split phase supply of the following type:

I understand that the voltage waveforms of each leg-to-neutral "phase" are, in fact, really in-phase with one another... and thus additive in nature. Which is why a measurement from one hot leg to the other results in twice the leg-to-neutral voltages. Etc, etc.

Where I need clarification is in regards to the following:

The way I understand it, we can find the reactive power consumed by the appliances on each leg of the split phase supply the good ol fashioned way: Q = sqrt[(VI)^2 - S^2] ... calculate Q for L1-to-neutral and L2-to-neutral.

Im guessing we also need to calculate the reactive power of the L1-to-L2 "phase" for the 240V appliances, right?

If I am on the right path here, we would have 3 reactive power measurements: Q1N, Q2N, and Q12. And summing these 3 measurements would give us the total reactive power that needs to be corrected for to improve the power factor, correct?

In regards to the actual power factor correction... say we are dealing with an overall inductive load that we will correct via placement of a parallel capacitor/capacitor bank. Where would this capacitor bank be placed? Obviously in parallel with the aggregate household load... but would that be across L1 and L2? Or do all 3 "phases" of the split phase supply need to have their own capacitors for correction?

Note: I do understand that using the term "phase" when discussing a split-phase supply is actually a bit of a misnomer...

Thanks for any insight you can provide!

#### Pich

Joined Mar 11, 2008
119
In ideal situation power factor correction should be done at the source (motor) that would allow less current to flow in the wires feeding the load and therefore less wire heating loss. As far as a central power factor correction, it can be done both ways depending on what voltage most of the loads are on.

#### #12

Joined Nov 30, 2010
18,210
Right now, my American house doesn't have any motors running. Hard to figure a correction for that unless you figure in 2 curly flourescent bulbs and this computer.

Typical motors are in the refrigerator, clothes dryer, clothes washer, air conditioner...well, that's all I have. Two motors at 120 V and the rest at 240V.
How bad is it to "correct" for motors that aren't running?

The answer would be 2 capacitors minimum because the 240V correction can be summed into the (2) 120 volt legs but putting the capacitors on the motors seems to make sense except for the surge current that happens when the contactors (relays) close. If you have an answer for that, I'd like to know.

#### bountyhunter

Joined Sep 7, 2009
2,512
We are working on a project that intends to provide some sort of power factor correction for a typical North American household... ie: residences using a 240V/200A split phase supply.

Now, I have a semi solid(or so Id like to think) grasp of power factor and how it applies to single and 3-phase systems. But in the case of a split phase supply, Im a little lost as to where the PF measurements need to be taken and the PF correction components placed...

Considering a typical split phase supply of the following type:

I understand that the voltage waveforms of each leg-to-neutral "phase" are, in fact, really in-phase with one another...
No, if two AC waveforms are in phase with each other, then going "across" the two hot lines would yield zero Volts since the voltages would move together. They are 180 out of phase with each other.

#### Papabravo

Joined Feb 24, 2006
13,909
You should already know from numerous credible sources that it is a complete waste of time.

#### WBahn

Joined Mar 31, 2012
25,899
Where would this capacitor bank be placed? Obviously in parallel with the aggregate household load... but would that be across L1 and L2? Or do all 3 "phases" of the split phase supply need to have their own capacitors for correction?
My thinking right now, based on just a bit of thought and nothing more, is that, in theory, you could put a single capacitor across any of the three options. My reasoning is this. The transformer providing all three circuits is seen as a single load from the primary side of the windings and so all it cares about is that the reactive power it sees is minimized. This can be done by adding an offseting reactive load anywhere on the other side.

Now, that's nice in theory, but I think there would be a number of practical factors at play. First, if you only put a single capacitor between L1 and L2, that means that the reactive currents on the two subcircuits L1-N and L2-N would have to travel from the neutral back to the transformer and then down the other hot line to get to the correcting element. That's a lot less wire to travel down than if it had to go through the transformer and back to the nearest substation, but we can do better. So I would think that putting three capacitors across all three possible pairings would be best because then the reactive loads in each circuit can exchange energy with the correcting element without sending it back to the transformer.

But now is when the real fun starts. What size capacitor do you use? If you use too small or too large, then you haven't corrected everything out. If you use too large, you might even make the power factor worse than without any correction at all. And there is your real problem because the capacitance needed this minute is different from the capacitance needed when the fridge kicks in and different again when furnace blower kicks and and different again when the home theatre system is fired up. And, for most homes, what is it most of the time? When people are sleeping or the house is empty while people are gone to work/school? The reactive loads may be so light that virtually no correction is needed. But when everyone is home and things are going and people are on the computer and using all kinds of switchers that power almost everything these days and the furnace and fridge and induction oven are all going, you might need quite a bit. But if you correct for that load, then the overwhelming majority of the time you are overcorrecting.

I don't see much of a chance of this working unless the amount of correction is controllable in real time somehow so that the amount of correction can be kept reasonably close to what is required by the load at that moment. But is it worth it? How much lost energy is associated with an individual home's reactive load? Perhaps it would be better to accept a compromise approach and perform the correction at the substation level. Then you have a lot more customers and the loads are evened out quite a bit more and then, perhaps, a bank of capacitors can be used that switch in different cells according to a nominal schedule based on the average daily VAR profile. If that isn't good enough, then you can devise an active control approach and afford to put some money into it because it is serving dozens or perhaps hundreds of homes.

#### t_n_k

Joined Mar 6, 2009
5,455
In principle you would calculate the VAR for each load and then sum the lot to give the total consumer VARs.

I think one would probably place the PFC correction cap directly across the incoming [secondary side] HV [240V] terminals. This would make sense since capacitive compensating VARs would be proportional to the square of the HV voltage - the bigger the voltage the smaller the compensating capacitor required for the same VARs. Of course the voltage rating has to be double that of the alternative compensation cap placed across the LV [120V] connection. Irrespective of the placement the compensation cap it has to be able to provide the required VARs at the appropriate current and voltage rating.

#### JamesL

Joined Jul 3, 2012
3
No, if two AC waveforms are in phase with each other, then going "across" the two hot lines would yield zero Volts since the voltages would move together. They are 180 out of phase with each other.
From what I understand, they are 180* out of phase with respect to the reference point/neutral leg.

#### JamesL

Joined Jul 3, 2012
3
Fellas, thanks for the good insight. You have given me some things to think about. The idea is for the device to be a type of "central" PFC for a single residence.

WBahn, the amount of correction will be controllable. The idea was to use a polyphase energy metering device to take measurements of the voltage/current and apparent/true/reactive power from each "phase", have a microcontroller that has logic in place to determine what size capacitor or inductor would need to be tied into the load to correct for the given amount of reactive power... and then switch such an element on to provide the correction.

t_n_k... thanks. By the secondary side, Im assuming you mean the "load" side of the transformer, correct?

I bounced around t_n_k's idea a bit more..

The neutral leg should typically carry zero current, or a minimal amount if there is a delta b/w the two hot legs. If we know the total VARs to be corrected for, we should be able to accomplish the correction via placement of a single capacitor across the 240V legs. Obviously the size and voltage/current ratings would need to be established.

We would want to put the capacitor between the secondary side of the transformer and the aggregate load, correct?

#### crutschow

Joined Mar 14, 2008
25,098
If you are switching capacitors in and out as needed, you could use capacitors from each leg to neutral as required for unbalanced 120V loads. For 240V correction you could add an equal capacitor to each phase. The correction would be provided by the two capacitors in series (with their junction connected to neutral). Of course their effective capacitance is reduced by one-half (for equal value capacitors).

#### WBahn

Joined Mar 31, 2012
25,899
The idea was to use a polyphase energy metering device to take measurements of the voltage/current and apparent/true/reactive power from each "phase", have a microcontroller that has logic in place to determine what size capacitor or inductor would need to be tied into the load to correct for the given amount of reactive power... and then switch such an element on to provide the correction.
Have you looked at how much the potential savings is compared to doing the same thing at far few points a bit higher in the distribution chain? Over any given set of N houses, they will, to some degree, balance each other out and all the PFC system at the higher node has to do is balance out the net. You could even do something as simple as determine the fixed element (probably a cap) that would need to be placed at each service entrance to make the net correction at the higher node as small as possible. Getting a bit more sophisticated, you could have each service entrance have a limited number of choices and then send control signals over the powerline to each unit to choice the amount of correction to use.

I really do suspect that you're going to find that the cost of doing independent house-by-house correction is going to exceed the marginal benefit compared to something that is slightly more centralized.

The neutral leg should typically carry zero current, or a minimal amount if there is a delta b/w the two hot legs.
I don't think you can make such an assumption. What is true on the average over a long time frame does not hold at the time scales you are interested it. The assignment of circuits in a house is intended to but roughly equal loads, on average, onto the two circuits, but at any given time it is highly likely that one or the other will strongly dominate and you have to deal with both.

We would want to put the capacitor between the secondary side of the transformer and the aggregate load, correct?
You want to put the correction element as close (electrically) to the load being corrected as possible. If you put the correcting element across the secondary of the transformer, then the reactive currents on the two branches using the neutral have to travel back to the transformer before they can make it to the correcting element. So, if you are only going to have one correcting element, it is probably best placed at the transformer. But this is going to be dependent on the profile of your reactive loads. For instance, if the bulk of the reactive loads are things that run off L1-L2, then it might be better to put the correcting element at the service entrance and accept the penalty for the L1-N and L2-N reactive loads. That's something that is just going to have to be characterized, modelled, and simulated.

#### Audioguru

Joined Dec 20, 2007
11,249
Why do you want to correct the power factor in a North American household?
Housholds are not charged extra for a poor power factor, industry is charged.

#### WBahn

Joined Mar 31, 2012
25,899
Why do you want to correct the power factor in a North American household?
Housholds are not charged extra for a poor power factor, industry is charged.
They are not charged directly ... yet.

They are already charged for the average, it is simply included in the base rate.

But there is growing interest in charging households directly because the types of loads in residential usage are placing a growing reactive burden on the utility. Instead of just continuing to increase the base rates to cover the expenses, utilities are having to increase production capacity, as well. They want to reduce the residential reactive burden to forestall the need for new capacity. They have two choices (or some mix of the two): Perform the correction themselves and pass on the costs to everyone, or pass on the costs to customers in proportion to how much they are contributing to the problem in order to incentivize them to correct their portion of it themselves. I expect a hybrid of the two to develop over time (probably the next ten years or so).