# Conductor Temperature Rise, Three-Phase Vs. Single-Phase

• Leyden
In summary, the National Electrical Code allows for higher current on a select few conductors with one of the requisites being single phase. However, this allowance is only valid if all other conditions are met, such as the same size wire and same current.

#### Leyden

TL;DR Summary
Trying to determine whether three-phase current would produce more temperature rise in a conductor than single phase.
Good Morning,

I am not coming up with an answer in my search, could anyone confirm or deny whether a circuit conductor would experience more temperature rise with three-phase current than if the same R.M.S. current was single-phase. Alternating Current, 60 Hertz.

If you want to know why I want to know this, it is because in the National Electrical Code (NFPA 70) there is allowance (310.15(B)(7) (2017)) for higher current on a select few conductors with one of the requisites being single phase. And I am trying to figure out why, I am searching for the report of when this allowance was introduced (1956) but waiting on a reply from NFPA. If you have another theory why, I would also appreciate that, I have a few. I don't believe this is a legitimate reason why, because we use thermal OCPD but I want to know anyway.

Thank you

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3-phase currents flow in three different wires.
I am about 99% sure the answer is that 3-phase has three current carrying conductors so each conductor has heating from the other two, so it is derated to maintain the max allowable temperature.
Current ratings are as much about heat flow away from the conductor as it is about heat generation withing the conductor. The heat generated is determined by the RMS current value (that's pretty much the definition of RMS). But the current ratings are also determined by the local environment to keep the insulation from getting too hot.

Leyden said:
I am not coming up with an answer in my search, could anyone confirm or deny whether a circuit conductor would experience more temperature rise with three-phase current than if the same R.M.S. current was single-phase. Alternating Current, 60 Hertz.

Huh, that is manifestly unclear. A single conductor can not have three phases of current. It takes 3 conductors to make a 3 phase circuit. Can you rephrase your question?

@anorlunda is correct. It takes 3 wires to carry 3 phases. However, that really has nothing to do with anything. A given quantity of charge moving past a point in a wire in a given amount of time is what will determine the heating. 3 phases (3 separate wires) divides the current between conductors up in a way that is more efficient for transmission for the amount of metal used in the conductors given the same amount of power transmitted compared to single phase.
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All that being said, the NEC has guidelines that requires 3 current carrying conductors or less in a conduit unless we de-rate them. So, I can install 6 wires in a conduit that are all current carrying as long as there is an overcurrent protective device that protects the wires from overcurrent that would be appropriately less than 3 conductors would normally be protected at. I won't throw any real world numbers out since I don't know any off the top of my head.
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So concerning the specifics of your question about single vs. 3 phase which translates to number of conductors, which do you think will heat more in a conduit? 3 current carrying conductors or 2 assuming both cases use the same size wire? I think you already know the answer. A very wise man here on PF would say a question well stated is half answered. I feel guilty saying this after he is gone. We miss you @jim hardy

Asymptotic, Klystron, DaveE and 2 others
anorlunda said:
Huh, that is manifestly unclear. A single conductor can not have three phases of current. It takes 3 conductors to make a 3 phase circuit. Can you rephrase your question?

I apologize, as you can tell I have a lot to learn. The basis of my question is would a circuit conductor increase in temperature more if it were part of a three-phase circuit than if it were part of a single phase circuit, all other characteristics being the same.

For example, two same size and length conduit runs, with the same number of current carrying conductors in each conduit. all of the circuit conductors in both conduits are operating at the same current, but one conduit has three-phase circuits and the other conduit has single-phase circuits.

If it helps, I will put values to my example: (2) 2" conduits 100' long ran side by side. Both have (6) #1AWG copper XHHW(insulation) current carrying conductors, so (12) wires total, (6) in each conduit. All of the mentioned wires have 80 Amperes of RMS current measured. 60Hz Alternating Current. Would the three-phase conductors experience more temperature rise (would they be operating at a higher temperature)? I am allowed to have a larger overcurrent protection device on the single-phase circuits.

Thanks, I will post what I find out from the NFPA search if I ever get the old reports.

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Averagesupernova said:
@anorlunda is correct. It takes 3 wires to carry 3 phases. However, that really has nothing to do with anything. A given quantity of charge moving past a point in a wire in a given amount of time is what will determine the heating. 3 phases (3 separate wires) divides the current between conductors up in a way that is more efficient for transmission for the amount of metal used in the conductors given the same amount of power transmitted compared to single phase.
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All that being said, the NEC has guidelines that requires 3 current carrying conductors or less in a conduit unless we de-rate them. So, I can install 6 wires in a conduit that are all current carrying as long as there is an overcurrent protective device that protects the wires from overcurrent that would be appropriately less than 3 conductors would normally be protected at. I won't throw any real world numbers out since I don't know any off the top of my head.
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So concerning the specifics of your question about single vs. 3 phase which translates to number of conductors, which do you think will heat more in a conduit? 3 current carrying conductors or 2 assuming both cases use the same size wire? I think you already know the answer. A very wise man here on PF would say a question well stated is half answered. I feel guilty saying this after he is gone. We miss you @jim hardy

The allowance is not for how many conductors are in a conduit I could have 6 single phase conductors in one conduit and 6 three-phase conductors in another conduit, same wire and conduit characteristics but I can use a larger overcurrent device on the single phase circuits.

The allowance I am investigating is 310.15(B)(7) (2017 NFPA 70(NEC))
"(7) Single-Phase Dwelling Services and Feeders. For onefamily dwellings and the individual dwelling units of two-family and multifamily dwellings, service and feeder conductors supplied by a single-phase, 120/240-volt system shall be permitted to be sized in accordance with 310.15(B)(7)(1) through (4). For one-family dwellings and the individual dwelling units of two-family and multifamily dwellings, single-phase feeder conductors consisting of 2 ungrounded conductors and the neutral conductor from a 208Y/120 volt system shall be permitted to be sized in accordance with 310.15(B)(7)(1) through (3).
(1) For a service rated 100 through 400 amperes, the service conductors supplying the entire load associated with a one-family dwelling, or the service conductors supplying the entire load associated with an individual dwelling unit in a two-family or multifamily dwelling, shall be permitted to have an ampacity not less than 83 percent of the service rating.
(2) For a feeder rated 100 through 400 amperes, the feeder conductors supplying the entire load associated with a one-family dwelling, or the feeder conductors supplying the entire load associated with an individual dwelling unit in a two-family or multifamily dwelling, shall be permitted to have an ampacity not less than 83 percent of the feeder rating.
(3) In no case shall a feeder for an individual dwelling unit be required to have an ampacity greater than that specified in 310.15(B)(7)(1) or (2).
(4) Grounded conductors shall be permitted to be sized smaller than the ungrounded conductors, if the requirements of 220.61 and 230.42 for service conductors or the requirements of 215.2 and 220.61 for feeder conductors are met."The requirement you are thinking of is 310.15(B)(3)(a) (More than three current-carrying conductors)

Averagesupernova said:
A very wise man here on PF would say a question well stated is half answered. I feel guilty saying this after he is gone. We miss you @jim hardy

When I was thinking about posting on here I was wondering if he specifically, might have an idea. I think he responded to about all of my few threads. I'm an infrequent user and just saw the announcement with this thread, I only corresponded with him a few times but man was he gracious to me with my lack of understanding. It's weird how much of a loss it feels to me, I can only try to imagine how much he means to some of you that were lucky enough to be close to him.

Asymptotic and anorlunda
I believe I need to add, I was reluctant to post the code section originally because I am more interested in my core question. I know of many of the industries reasons given for this code section such as load diversification, removing conductor safety factor and because another code section exception effectively allows no protection of service conductors. I have been researching this section and its history but my intent with this thread is the temperature rise of three-phase vs single-phase. Thought I should say that in fear of getting off in the weeds, looking at the current posts.

The heat generated within a conductor is only a function of the RMS value of the current in that conductor and the size of the conductor, it doesn't matter if the wire is part of a three phase or single phase system (assuming the RMS current value is the same). However, the temperature that results depends on lots of other stuff around the wire, like the type of insulation and what other heat sources (i.e. current carrying wires) are nearby.
A secondary effect is that metals have higher resistivity at higher temperatures, but this effect isn't huge.

Leyden
Thank you. That makes sense, I was just trying to picture the magnetic fields and thought maybe the three phases 120 degrees apart might produce more heat compared to single phase that decays to zero 120 times a second, while the three-phase system has a strong constant magnetic field. I'm still studying in this arena so I appreciate your patience and outreach.

If you are wondering why the code allows something with single phase that they don't allow with 3 phase the reason is likely statistical. I gave examples of number of wires in a conduit because of the obvious extra heat generated by having an extra wire as you would with 3 phase compared to only 2 wires with single phase.
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Trust the NEC. Years and years of real world experience goes into the code evolving into what it is. Nothing wrong wondering the reason why the code exists as it does, but the reasons are not always black and white.

Asymptotic, Klystron, Leyden and 1 other person
Averagesupernova said:
If you are wondering why the code allows something with single phase that they don't allow with 3 phase the reason is likely statistical. I gave examples of number of wires in a conduit because of the obvious extra heat generated by having an extra wire as you would with 3 phase compared to only 2 wires with single phase.
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Trust the NEC. Years and years of real world experience goes into the code evolving into what it is. Nothing wrong wondering the reason why the code exists as it does, but the reasons are not always black and white.

Thanks, this section currently has different and conflicting interpretations in the industry. I would probably still be researching it even if everyone agreed on one interpretation, but it is especially frustrating with different interpretations and methods of application. I have been reading the different code-making-panel reports through the years on this section and even the panel members through the years have disagreed.

This is one of a few code sections that have conflicting interpretations that I am working to try to clear up. I am planning on doing some actual temperature measurement experiments, I have been researching temperature rise calculations but they are quite complex to me. I also expect to get this last report to give me what is hopefully a clear understanding of the reasoning, should be hearing from NFPA anytime.

Leyden said:
I have been researching temperature rise calculations but they are quite complex to me.
Yes, and everyone else too. I don't think the standards are intended to be that accurate. I'm not sure they will ever agree completely. If you want real accuracy you will have to model (like FEA thermal models) and the verify with testing for each implementation. That is why equipment safety certifications require actual thermal measurements to verify it's been designed right.
Also, as I'm sure you've seen, the footnotes and the small print is often as, or more, important than the number in the table.

Asymptotic
DaveE said:
Yes, and everyone else too. I don't think the standards are intended to be that accurate. I'm not sure they will ever agree completely. If you want real accuracy you will have to model (like FEA thermal models) and the verify with testing for each implementation. That is why equipment safety certifications require actual thermal measurements to verify it's been designed right.
Also, as I'm sure you've seen, the footnotes and the small print is often as, or more, important than the number in the table.

Yep, thanks. I don't expect the conductors insulation to degrade or for the conductor to be operating precisely on the table temperature at the specific current in the table, I would expect some safety factor in there.

But a huge concern of mine if you are interested, is time current curves of over-current protection devices and them being based on 40 degrees C ambient. For example, say we have a 175 amp thermal magnetic circuit breaker, say a standard Square D QO, see the trip curve in the link below.

QOM FAMILY MOLDED CASE CIRCUIT BREAKERS CHARACTERISTIC TRIP CURVE NO. 736-6
175A breaker at 180 amps will take 16 minutes to 2.7 hours to trip at 40*c ambient temp cold start

218 amps(175 x 1.25) is 5.8 minutes to 2.7 hoursNow, let's say this main breaker is in an outdoor meter and main combination enclosure for a house in say Minnesota. Now say it is the dead of winter, the main feeder runs quite a way in the house inside insulation. And say for whatever reason they use a lot of electric heat and other electric loads.Below is the table that was used in this code section prior to 2014 and is returning in 2020, I included it so you don't have to do the 83% calculation required in 2017.

One of the common interpretations that I have heard from actually well respected NEC aficionados is that you are allowed to use 310.15(B)(7) and have a calculated load for the house which is above the 310.15(B)(16) table ampacity for the conductor, and that is not by using a lower ambient temperature or anything, that is just in general, you are allowed to do that. I don't believe that interpretation if you hadn't guessed that already, but the other interpretations pose similar problems. If the breaker is in a low enough ambient temperature, the circuit conductors could run well above 310.15(B)(16) ampacity indefinitely, the breaker operating properly and as expected(by anyone that knows the trip curve and 40 degree C rating) would never trip until the circuit conductors melt and then it would hopefully trip on short circuit current(magnetic trip element) before they ignite the structure.

But service conductors on the line side of the breaker are only protected by overcurrent protection downstream of the conductors, they would likely burn the structure to the ground before the utility cutout fuse would open, albeit these will likely not be buried in hot insulation. But it can go the other way as well, overcurrent device in air conditioned space with the service conductors outdoors in the Arizona summer operating above their 310.15(B)(16) ampacity indefinitely.Just a related side note, the table was removed for 2014 because of misapplication in the industry.

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Three phase runs slightly hotter, I finally got my hands on an old AIEE study(IEEE before it was IEEE) that was discussed in the old NEC code panel discussions. I haven't read the study completely though I think my original question may have more to do with what you all were trying to get in my head about effectively having 2 wires, even though the current code does not prohibit more than that. It is possible to have more than that since the allowance gives leeway for multi-family dwellings. Thank you all for your input.

Does anyone have any theories why three-phase is hotter?

1956
(The Heating and Mechanical Effects of Installing Insulated Conductors in Steel Raceways, M. M. BRANDON, L. M. KLINE, K. S. GEIGES, F. V. PARADISE. ) https://ieeexplore.ieee.org/document/4499473/

"SINGLE- VERSUS 3-PHASE HEATING
To determine the effect on conductor heating by single- and 3-phase currents, 12 type RH-RW, no. 6 AWG wires were installed in 2-inch rigid conduit in air, and tested by first using single-phase current and then 3-phase current of a Y connected supply. See Table IX. "
This is a rich study by the way, if anyone is interested, especially those that deal with the NEC and NEC wiring practices. This is the study that is the basis for our ampacity derating for more than three conductors, they did extensive testing.

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Leyden said:
Does anyone have any theories why three-phase is hotter?
It's not. This has been explained in several replies. This is a thermal problem that has nearly nothing to due with electrical circuits, except that there is a source of current. The temperature, or ampacity limits, only depend on the construction (insulation, conduit, etc.) the number of current carrying conductors and the current in those conductors. What you are seeing is ampacity limits in a few different configurations. 3 phase ampacity assumes 3 current carrying conductors in the bundle. Single phase ampacity assumes 2 current carrying conductors. That is why you are allowed to have higher current in single phase vs. 3 phase.

DaveE said:
It's not. This has been explained in several replies. This is a thermal problem that has nearly nothing to due with electrical circuits, except that there is a source of current. The temperature, or ampacity limits, only depend on the construction (insulation, conduit, etc.) the number of current carrying conductors and the current in those conductors. What you are seeing is ampacity limits in a few different configurations. 3 phase ampacity assumes 3 current carrying conductors in the bundle. Single phase ampacity assumes 2 current carrying conductors. That is why you are allowed to have higher current in single phase vs. 3 phase.

I believe you may have missed this part in my post

"SINGLE- VERSUS 3-PHASE HEATING
To determine the effect on conductor heating by single- and 3-phase currents, 12 type RH-RW, no. 6 AWG wires were installed in 2-inch rigid conduit in air, and tested by first using single-phase current and then 3-phase current of a Y connected supply. See Table IX. "
This above text is from the study explaining the table I posted, the only difference is three-phase circuits and single-phase circuits, both having the same 12 conductors in the same conduit. It took higher current for the single phase test to reach the same temperature.

That IEEE paper is behind a paywall, so I can't read it. If the 12 conductors are just laid in the duct without any special arrangement (like on the perimeter of a circle) then there are many combinations of how they can be wired as closed circuits. With single phase there are 66 combinations of 12 things taken 2 at a time. With 3 phase, there are 220 combinations of 12 things taken 3 at a time.

Each combination would have different mutual inductances to other pairs, and capacitance to ground. So it makes it exceedingly difficult to guess what is behind those numbers without reading the paper.

It would also be possible to make it a 12 phase system with 12 conductors. That too would be slightly different.

But back to basics, the OP question was about power losses. Losses in a conductor are ##I^2R## single phase or 3 phase or even DC. If there is some arrangement that gives different currents, that is a different question.

Leyden
Given the (small) magnitude of the difference between the single / 3 phase currents required to produce a constant temperature (and assuming proper experiment construction), I would initially attribute the difference to some combination of:

Dielectric heating of the conductor insulation (this is the 'big' difference for 3-phase)
Inductive heating of the conduit (and other conductors)

-Some conductor 'voltage drop' values from the experiment would be a useful way to verify that the effect is 'real.'

Leyden
"HEATING TEST SETUPS
Conduit in Air, EMT in Air

In the heating tests on wires installed in rigid-steel conduit or EMT the wires were laid out in series and folded back on themselves a sufficient number of times to provide the number of wires to be tested. Thermocouples were inserted, as previously described, and the wires were pulled into the conduit. The assembly was placed in the test enclosure. The feeder conductors were connected to the current transformers through the fuse board (see Fig. 2), and the thermocouples were connected to the instrument in order to record the temperatures reached on the conductors (see Fig. 1). The heating source was adjusted to enable the thermostats to maintain the enclosure temperature at 30 C 41 0.5 C. The current was adjusted to give the steady-state operating temperatures desired of 60 C or 75 C.

The voltage drop in the conductors under test was recorded at the steady state operating temperatures.

For determining the steady-state operating temperature, the temperature on the hottest conductor was adjusted to the maximum value desired. This test setup also was used for load diversity, transient heating, and single versus 3-phase heating tests."

1956
(The Heating and Mechanical Effects of Installing Insulated Conductors in Steel Raceways, M. M. BRANDON, L. M. KLINE, K. S. GEIGES, F. V. PARADISE. ) https://ieeexplore.ieee.org/document/4499473/
This is a 17 page paper, if anyone thinks I am posting too much of it please let me know.

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