3 phase and 1 phase loads, What is my capacity?

[fostachild]

Hey All,

I'm trying to determine the remaining capacity in a panel which has loads that are both 3 phase (motors) and single phase (lighting). I would like to calculate amps drawn on a per phase basis. This is easy for the single phase loads, but I'm wanting to transform the three phase loads into their single phase components (mathematically).

I start by doing calculation for motors.

1) Find FLC using table 430.250 for each motor.
2) Sum FLCs for all motors, and add 25% of the largest motor FLC connected to panel to get total 3 phase load.

Now I'm hung up on how I would transform this current value (assuming 3 phase loads are balanced) into a current value for each of the 3 phases. The spreadsheet I have for the panelboard schedule which was created by the original designer has the current values being divided by 3, but I'm not sure that is correct.

I've tried searching the NEC for guidance on this but haven't come up with anything. Can anyone lend a hand?

Thanks in advance.

 

[jeremy.zinkofsky]

It is not technically correct, but a balanced load is typically assumed for panel and/or XFMR sizing so dividing by three is sufficient to gauge the load of each phase. The exact load for each phase is something that probably has to be measured in your situation given that you may not have enough information to do unbalanced 3 phase analysis.

 

[JoeStillman]

The spreadsheet is probably intended to show volt-amps or kVA , not amps. For a three-phase motor, full-load amps are the same on all three phases.

 

[charlie b]

I would like to calculate amps drawn on a per phase basis. This is easy for the single phase loads, but I'm wanting to transform the three phase loads into their single phase components (mathematically).

This might seem like extra work and it might not give you a different answer, but I believe you are going about this backwards. The safest (meaning the least likely to result in errors) way to do any such calculations is to convert everything into VA at the beginning, do all the addition in units of VA, and only convert back to amps at the very end. For your situation, take the amps for each of the motors from the table, multiply by 208 and again by 1.732 (the square root of 3). I generally use the approximate value of 360 for the factor of (208 * 1.732). That will give you the total VA (i.e., all three phases) for the motor. Add 25% to the largest motor, as you have already said. Then for each of the 120 volt loads, multiply its current value in amps times 120. Add all of these to the total motor load, without paying attention to which 120 volt load is powered by which phase. This gives you the total VA on the panel. We can only assume that you have done your best to balance the loads, as the mathematics behind unbalanced loading is way beyond what I can describe here in words. The final step is to take the total VA and divide by 360. That will give you the amps that any of the phases will be supplying.

 

[jeremy.zinkofsky]

This might seem like extra work and it might not give you a different answer, but I believe you are going about this backwards. The safest (meaning the least likely to result in errors) way to do any such calculations is to convert everything into VA at the beginning, do all the addition in units of VA, and only convert back to amps at the very end. For your situation, take the amps for each of the motors from the table, multiply by 208 and again by 1.732 (the square root of 3). I generally use the approximate value of 360 for the factor of (208 * 1.732). That will give you the total VA (i.e., all three phases) for the motor. Add 25% to the largest motor, as you have already said. Then for each of the 120 volt loads, multiply its current value in amps times 120. Add all of these to the total motor load, without paying attention to which 120 volt load is powered by which phase. This gives you the total VA on the panel. We can only assume that you have done your best to balance the loads, as the mathematics behind unbalanced loading is way beyond what I can describe here in words. The final step is to take the total VA and divide by 360. That will give you the amps that any of the phases will be supplying.

And it is some extremley complex math. Math that I am glad to say as a consultant engineer I never have to do again. Our whole understanding of designing low to medium voltage electrical systems for buildings is based on the assumption that the utility is providing us with a symmetrical source of power. The per unit system was developed to calculate asymmetrical (or unbalanced) values by eliminating the degree shift of each phase. If you could get the positive, negative, and zero sequence utility info in per unit and knew what values of voltage, amperage, and impedance they used for the per unit base, you may be able to do a phase by phase analysis on the service equipment. But there is a mixture of linear and non-linear loads in any given facility and without empirical data collected by precise load measuring devices you won't be able to make the unbalanced 3 phase equations work.

 

[fostachild]

This might seem like extra work and it might not give you a different answer, but I believe you are going about this backwards. The safest (meaning the least likely to result in errors) way to do any such calculations is to convert everything into VA at the beginning, do all the addition in units of VA, and only convert back to amps at the very end. For your situation, take the amps for each of the motors from the table, multiply by 208 and again by 1.732 (the square root of 3). I generally use the approximate value of 360 for the factor of (208 * 1.732). That will give you the total VA (i.e., all three phases) for the motor. Add 25% to the largest motor, as you have already said. Then for each of the 120 volt loads, multiply its current value in amps times 120. Add all of these to the total motor load, without paying attention to which 120 volt load is powered by which phase. This gives you the total VA on the panel. We can only assume that you have done your best to balance the loads, as the mathematics behind unbalanced loading is way beyond what I can describe here in words. The final step is to take the total VA and divide by 360. That will give you the amps that any of the phases will be supplying.

Thanks Charles. I had seen you describe this strategy in another post, using VA instead of Amps, which I agree is a good approach in the event of a totally balanced load.

However as you identified, I'm trying to come at the problem with an amps per phase approach due to the single phase loads not being balanced (my assumption above was that the 3 phase motor loads were balanced).

I don't doubt that the analysis is complex, and maybe too complex to show on a message board, but if you could point me in the direction of some good resources I'd greatly appreciate it (whether that be texts or certain articles in the NEC, NEC being ideal since it will govern how this is handled).

 

[fostachild]

And it is some extremley complex math. Math that I am glad to say as a consultant engineer I never have to do again. Our whole understanding of designing low to medium voltage electrical systems for buildings is based on the assumption that the utility is providing us with a symmetrical source of power. The per unit system was developed to calculate asymmetrical (or unbalanced) values by eliminating the degree shift of each phase. If you could get the positive, negative, and zero sequence utility info in per unit and knew what values of voltage, amperage, and impedance they used for the per unit base, you may be able to do a phase by phase analysis on the service equipment. But there is a mixture of linear and non-linear loads in any given facility and without empirical data collected by precise load measuring devices you won't be able to make the unbalanced 3 phase equations work.

Thanks Jeremy,

Do you have any good resources for learning this type of analysis?

References to NEC articles would be especially helpful (as well as texts). I can't imagine that this is the first time that an unbalanced load has been put into service. How do inspectors handle this when they come across it, and what kind of information do they ask for? Do people just stay well under the limitations of the of the supply when putting an unbalanced load into service, assuming that with a large enough buffer they are safe?

Is this a fairly uncommon practice?

Thanks again.

 

[charlie b]

I'm trying to come at the problem with an amps per phase approach . . . .

Please don't do that. While you are at it, please try as best you can to immediately and forever hereafter drop the notion of "amps per phase" from your vocabulary. It is meaningless. Any current leaving the panel on Phase A will return to the panel via either Phase B or Phase C. It is the same amps. If there is more single phase load on Phase A, then there will be some current in the neutral conductor. There is a simple formula to calculate how much current will be on the neutral. But that is not what you are asking about. The analysis of unbalanced loading uses the same tool as the analysis of fault conditions. I first learned the process during my classes working towards an MSEE degree. It is not a trivial exercise, and it takes some very complicated math that begins with matrix algebra and can take you as far as differential calculus. From a designer's perspective, I would calculate the panel loading by starting with the assumption that all loads will be reasonably balanced, and then add in some safety margin to account for a reasonable amount of imbalance.

 

[charlie b]

References to NEC articles would be especially helpful (as well as texts).

The NEC will not help you here. It wants us to balance the loading.

Do you have any good resources for learning this type of analysis?

I suggest using Google or Bing to research the following terms:

• Symmetrical Components.
• Sequence Networks
• Positive, negative, and zero sequence impedance

 

[Smart $]

...
However as you identified, I'm trying to come at the problem with an amps per phase approach due to the single phase loads not being balanced (my assumption above was that the 3 phase motor loads were balanced).
...

Do it like this. For each load, provide three columns labeled A, B, and C. For 3Ø loads put 1/3 the load in VA in each column. For 1Ø line-to-line loads, put 1/2 the load in VA in each column representing the lines the load is connected to (A & B, B & C, or C & A). For 1Ø line-to-neutral loads, put the entire load in VA in the column representing the line the load is connected to (A, B, or C). When done, arithmetically sum each column and divide each total by 120V.

 

[electrofelon]

Hey All,

I'm trying to determine the remaining capacity in a panel which has loads that are both 3 phase (motors) and single phase (lighting). I would like to calculate amps drawn on a per phase basis. This is easy for the single phase loads, but I'm wanting to transform the three phase loads into their single phase components (mathematically).

I start by doing calculation for motors.

1) Find FLC using table 430.250 for each motor.
2) Sum FLCs for all motors, and add 25% of the largest motor FLC connected to panel to get total 3 phase load.

Now I'm hung up on how I would transform this current value (assuming 3 phase loads are balanced) into a current value for each of the 3 phases. The spreadsheet I have for the panelboard schedule which was created by the original designer has the current values being divided by 3, but I'm not sure that is correct.

I've tried searching the NEC for guidance on this but haven't come up with anything. Can anyone lend a hand?

Thanks in advance.

For existing installations, it may prove worthwhile to get away from NEC article 220 calculations and go with more of a real world load analysis. A 220.87 figure is best but where that data is not available from the utility or you are looking for an individual feeder and dont have the equipment to monitor, or dont want to take the elapsed time required , I admit to frequently using the "turn everything on and amp clamp it" method - which is actually a great oversimplification: its analyzing the loads, understanding the usage and diversity patterns, taking many readings over time, etc.

 

[iwire]

I admit to frequently using the "turn everything on and amp clamp it" method - which is actually a great oversimplification: its analyzing the loads, understanding the usage and diversity patterns, taking many readings over time, etc.

That is also a direct NEC violation and if an inspector asks how you arrived at your figures you would likely fail.

 

[jeremy.zinkofsky]

Thanks Jeremy,

Do you have any good resources for learning this type of analysis?

References to NEC articles would be especially helpful (as well as texts). I can't imagine that this is the first time that an unbalanced load has been put into service. How do inspectors handle this when they come across it, and what kind of information do they ask for? Do people just stay well under the limitations of the of the supply when putting an unbalanced load into service, assuming that with a large enough buffer they are safe?

Is this a fairly uncommon practice?

Thanks again.

You can find a lot of books on the subject if you google "power system analysis" or "per unit equations".

Basically, it is a linear algebra excerise using matrix equations. So look up "Z" matrix and "Y" matrix as well. Surprisingly the math really isn't complicated, it's just rigorous which makes it hard to understand the core principle of what is going on.

Good luck & have fun...

 

[electrofelon]

That is also a direct NEC violation.

Yes I am aware of that. In the real world most of us rarely do a load calculation every time we add a load to an electrical system. Besides my figure would be more conservative than 220.87 would be. Also There was that thread a while back where some of the engineers on here were discussing how MCC's rarely meet a 220 calculation.

Regardless, my point was that for an existing installation when judging system capacity, one is likely to save a ton of money and hassle by going off measured load rather than calculated load - yes 220.87 followed to the letter is the correct way to measure load.

 

[fostachild]

Please don't do that. While you are at it, please try as best you can to immediately and forever hereafter drop the notion of "amps per phase" from your vocabulary. It is meaningless. Any current leaving the panel on Phase A will return to the panel via either Phase B or Phase C. It is the same amps. If there is more single phase load on Phase A, then there will be some current in the neutral conductor. There is a simple formula to calculate how much current will be on the neutral. But that is not what you are asking about. The analysis of unbalanced loading uses the same tool as the analysis of fault conditions. I first learned the process during my classes working towards an MSEE degree. It is not a trivial exercise, and it takes some very complicated math that begins with matrix algebra and can take you as far as differential calculus. From a designer's perspective, I would calculate the panel loading by starting with the assumption that all loads will be reasonably balanced, and then add in some safety margin to account for a reasonable amount of imbalance.

Hey Charles,

I don't see why amps per phase is such a terrible statement, as long as it is understood what the return path will be of a line to line load.

Besides I love me some matrix algebra and differential calculus, but maybe I'm a bit of a masochist like that. :slaphead:

Thanks again for the resources, and all of your help.

 

[fostachild]

Do it like this. For each load, provide three columns labeled A, B, and C. For 3Ø loads put 1/3 the load in VA in each column. For 1Ø line-to-line loads, put 1/2 the load in VA in each column representing the lines the load is connected to (A & B, B & C, or C & A). For 1Ø line-to-neutral loads, put the entire load in VA in the column representing the line the load is connected to (A, B, or C). When done, arithmetically sum each column and divide each total by 120V.

Hey Smart$,

After tracing out the equations in the spreadsheet of the original panelboard schedule, this is the approach that was taken. However,the columns were incorrectly labeled, which is what led to my confusion (A instead of VA).

Thanks for the help.

 

[Smart $]

Hey Charles,

I don't see why amps per phase is such a terrible statement, as long as it is understood what the return path will be of a line to line load.

Besides I love me some matrix algebra and differential calculus, but maybe I'm a bit of a masochist like that. :slaphead:

State it as amps per line and maybe y'all will :hug:

Technically a "phase" is measured between two line conductors. What people generally refer to as Phase A, B, or C, is actually Line A, B, or C.

 

[Smart $]

Hey Smart$,

After tracing out the equations in the spreadsheet of the original panelboard schedule, this is the approach that was taken. However,the columns were incorrectly labeled, which is what led to my confusion (A instead of VA).

Thanks for the help.

You're quite welcome. :thumbsup:

 

[Besoeker]

Any current leaving the panel on Phase A will return to the panel via either Phase B or Phase C.

Or the neutral in which case it wouldn't be in B or C.

 

[iwire]

Yes I am aware of that. In the real world most of us rarely do a load calculation every time we add a load to an electrical system. Besides my figure would be more conservative than 220.87 would be. Also There was that thread a while back where some of the engineers on here were discussing how MCC's rarely meet a 220 calculation.

Regardless, my point was that for an existing installation when judging system capacity, one is likely to save a ton of money and hassle by going off measured load rather than calculated load - yes 220.87 followed to the letter is the correct way to measure load.

Regardless, my point was that your method can result in a legitimate failed inspection and for that reason in my opinion it is bad advice to give on a code forum.