4+ Current Carrying Conductors -- Is voltage drop affected?

[Bonsai]

Hi all! I'm currently designing a system that involves long-distance single-phase distribution at 120V. In this design, I will be feeding several 20A GFCIs from a 3-phase, 4-wire 225 A panel. I am planning on running power to the receptacles in sets of pairs, that is, 2 hots and 2 neutral runs plus a ground in PVC conduit. Some of these runs are quite long -- between 400 and 650 ft one way. I am aware of the need to upsize conductors (and consequently the ground wire) to compensate for voltage drop and account for derating due to having more than 3 CCCs in a conduit. However, I'm wondering -- in calculating for voltage drop, should I be using different/adjusted numbers from table 9? I am aware that table is only intended to apply to runs of 3 or fewer CCCs in conduit, and am wondering if having 4 CCCs would significantly affect those figures for the purpose of calculating voltage drop.

My impression is that having more conductors would add to capacitance in the circuit, potentially negatively affecting the power factor. However, I have not been successful in finding any reference material that would corroborate this or allow me to calculate the total impact. Any help is much appreciated! I will be happy to provide more information if necessary.

 

[luckylerado]

I do not believe #of conductors in a raceway is part of the formula for calculatoing VD by any method.

 

[gar]

180702-1346 EDT

Bonsai:

Think about your question.

The table is based upon some assumption of the wire temperature rise based on the current. Virtual all wire used as normal conductors has a positive temperature coefficient of resistance. Thus, as current thru a specific wire increases this means the wire temperature rises, and resistance increases.

If you increase wire size with current held constant, then the temperature rise is less because the resistance is less. Increasing wire size with current held constant will very slightly reduce voltage drop for a fixed length of wire.

.

 

[Bonsai]

180702-1346 EDT

Bonsai:

Think about your question.

The table is based upon some assumption of the wire temperature rise based on the current. Virtual all wire used as normal conductors has a positive temperature coefficient of resistance. Thus, as current thru a specific wire increases this means the wire temperature rises, and resistance increases.

If you increase wire size with current held constant, then the temperature rise is less because the resistance is less. Increasing wire size with current held constant will very slightly reduce voltage drop for a fixed length of wire.

.

Understood! This makes a lot of sense. The VD saved by upsizing and therefore reducing resistance/heat loss through appropriately applying derating is far more than could potentially be incurred by AC wire interactions resulting from additional conductors. Do I understand your explanation correctly?

 

[ggunn]

Increasing wire size with current held constant will very slightly reduce voltage drop for a fixed length of wire.

Huh? Increasing wire size by enough to cut the resistance in half will decrease the voltage drop by half for a given amount of current in a given conductor length. V = IR.

 

[winnie]

I see what gar is saying; if you increase the wire size (say you exactly double the cross sectional area) then you expect a lower voltage drop because of the larger cross section.

In _addition_ to this reduction in voltage drop, you also see a reduction in temperature which slightly reduces voltage drop a bit more.

Back to the original poster, I presume that you are aware that using a shared neutral in your application can potentially reduce voltage drop, and that you have a design reason for not using a shared neutral.

-Jon

 

[kingpb]

Size the conductors to meet the VD requirements, then check to see if the current needed in that size conductor meets the de-rated capacity. Typically, the current is not an issue when upsizing for VD.

Example: 20A, 120V ckt; 650ft, limit VD to 3%. Your going to need a #1AWG copper conductor to go 650ft with 2.9% VD (18A max current)

A #1 AWG is good for 145A before you derate; so you can derate it 87.6% before current carrying capacity is an issue. So, you can see not really a consideration.

Probably want to consider increasing voltage to run longer lengths then drop down with a little transformer to 120V. #1 AWG for those long distances, plus increase in conduit size is probably not cost effective.

 

[Bonsai]

I've already sized the conductors with VD in mind, since that is the limiting factor due to the length of the runs -- my main question was that since Table 9's figures are based on 3 current carrying conductors in conduit, do they need to be adjusted if you have 4 or more conductors for the purposes of calculating VD, and is there a proper method for that? I did, of course, check the ampacity tables and derate appropriately to ensure that the conductors are safe.

To answer winnie's question about not having a shared neutral -- I was told to prioritize reliability over cost in this case. Having separate neutrals eliminates a shared point of failure.

Unfortunately I cannot use a higher voltage to distribute - the owner already determined that they would prefer all outlets sourced from a panel at a single given location. As a result, there's going to be a lot of copper in this system...

 

[winnie]

If you look closely at the various calculations and tables in the code, you will see that there are many approximations and simplifications. These all introduce some small amount of error in the calculations, but do not alter the result in any significant fashion.

For example, voltage drop calculations assume a particular conductor temperature. A different conductor temperature will mean that the voltage drop calculation is slightly incorrect.

As has already been discussed, more conductors in a conduit will change the conductor temperature, and this changes the voltage drop. For 120V circuits this simply gets ignored; the effect is so small that no calculations are necessary. If you want to estimate the range of possible different voltage drop values, simply run the calculation at (say) 0C and 60C and see how large the difference is.

If you want to see where such effects are relevant and calculated, look further in the code book to the duct bank calculations, for high current circuits run in multiple conduits buried in the ground. In this case the number of conduits, their arrangement, and the thermal conductivity of the soil all get considered for calculating ampacity.

Per kingpb's suggestion, you might consider running 240V to each receptacle location with a small single phase transformer at each.

-Jon

 

[Adamjamma]

I see what gar is saying; if you increase the wire size (say you exactly double the cross sectional area) then you expect a lower voltage drop because of the larger cross section.

In _addition_ to this reduction in voltage drop, you also see a reduction in temperature which slightly reduces voltage drop a bit more.

Back to the original poster, I presume that you are aware that using a shared neutral in your application can potentially reduce voltage drop, and that you have a design reason for not using a shared neutral.

-Jon

When using gfci or afci, you should not share neutral, is hat I have been taught.

 

[JoeStillman]

When using gfci or afci, you should not share neutral, is hat I have been taught.

Doesn't that depend on which end of the circuit the gfci is on? If its a gfci outlet, the upstream wiring is not monitored for ground fault. If its a gfci breaker, it can't be used for a multi-wire circuit.

Afci is something different. Wish I knew more about them.

 

[Adamjamma]

Doesn't that depend on which end of the circuit the gfci is on? If its a gfci outlet, the upstream wiring is not monitored for ground fault. If its a gfci breaker, it can't be used for a multi-wire circuit.

Afci is something different. Wish I knew more about them.

but with the breakers becoming a norm, and a requirement in some installations cases, one should treat the circuit as if it is a breaker situation just in case it later becomes one, as far as installation goes in new circuits or new construction, much like the requirement now for neutral in all switch locations that might need occupancy controls, making it easier just to install the neutral in all switch locations... not necessary by code but possibly better from the do it now so it is there later attitude.

 

[Frestly]

Voltage Drop Calculation with more than 4 conductors

Voltage Drop Calculation with more than 4 conductors

Same question - here is my take.

The impedance and inductance values for individual conductors in Chapter 9, Table 9 of the NEC are based upon 3 current carrying conductors in a raceway.
These are the values that are typically plugged into any voltage drop calculation but are invalid for more than 3 conductors.

These values must be adjusted by the proper Proximity Effect Multiplier:

AC Resistance = DC Resistance x (1 + Ys + Yp)

Ys = Skin Effect Multiplier
Yp = Proximity Effect Multiplier

See:

https://en.wikipedia.org/wiki/Proximity_effect_(electromagnetism)

I have searched the wire manufacturer web sites (South Wire, General Cable, Okonite, etc.) for a formula / table that gives the proximity effect multiplier for more than 3 conductors in a raceway without luck.

I disagree with other posters you should select the worst case wire size from either the NEC Table 315.(B)(3)(a) derating OR the voltage drop calculation.

In my mind, you need to adjust the impedance values in Chapter 9, Table 9 based on the number of conductors in a raceway and then calculate your voltage drop based upon these adjusted values. I have no idea where to find the proper adjustment factors.

Power = Current ^2 x Resistance

My guess - if the current capacity of a conductor is halved (50%) by Table 315.(B)(3)(a), then it's resistance should be 4 times the Table 9 listed value - No?

 

[MAC702]

...Afci is something different. Wish I knew more about them.

And we wish the code writers did, too.

 

[GoldDigger]

Same question - here is my take.

The impedance and inductance values for individual conductors in Chapter 9, Table 9 of the NEC are based upon 3 current carrying conductors in a raceway.
These are the values that are typically plugged into any voltage drop calculation but are invalid for more than 3 conductors.

These values must be adjusted by the proper Proximity Effect Multiplier:

AC Resistance = DC Resistance x (1 + Ys + Yp)

Ys = Skin Effect Multiplier
Yp = Proximity Effect Multiplier

See:

https://en.wikipedia.org/wiki/Proximity_effect_(electromagnetism)

I have searched the wire manufacturer web sites (South Wire, General Cable, Okonite, etc.) for a formula / table that gives the proximity effect multiplier for more than 3 conductors in a raceway without luck.

I disagree with other posters you should select the worst case wire size from either the NEC Table 315.(B)(3)(a) derating OR the voltage drop calculation.

In my mind, you need to adjust the impedance values in Chapter 9, Table 9 based on the number of conductors in a raceway and then calculate your voltage drop based upon these adjusted values. I have no idea where to find the proper adjustment factors.

Power = Current ^2 x Resistance

My guess - if the current capacity of a conductor is halved (50%) by Table 315.(B)(3)(a), then it's resistance should be 4 times the Table 9 listed value - No?

No. The table is based on maximum insulation temperature as affected by less ability to lose heat to the environment when the fill level of a raceway is high. The temperature has very little effect on the resistance of copper or aluminum over the temperature range involved. To a first approximation the resistance is unchanged by fill, even though the inductive component of the impedance may change significantly for large wires carrying balanced current.

 

[Frestly]

4+ Current Carrying Conductors

4+ Current Carrying Conductors

No. The table is based on maximum insulation temperature as affected by less ability to lose heat to the environment when the fill level of a raceway is high. The temperature has very little effect on the resistance of copper or aluminum over the temperature range involved. To a first approximation the resistance is unchanged by fill, even though the inductive component of the impedance may change significantly for large wires carrying balanced current.

Okay, so I can't use NEC table 310.15(B)(3)(a) to estimate the change in AC resistance via the proximity effect when more than 3 current carrying conductors are installed in a conduit.
What can I use? The resistance and impedance values listed in Chapter 9, Table 9 are only valid when 3 conductors are installed in a raceway.

My understanding is that % fill of a raceway is limited by Chapter 9, Table 1 (40% fill for 2 or more conductors).
Yes, I understand the heating effects, but my impression was that those increased heating effects are a result of more resistive heat being given off by the larger quantity of conductors.

For instance, I have 16 amps flowing through each of three #8 conductors in PVC conduit (balanced 3 phase loading).
From table 9, chapter 9, the AC resistance of #8 Copper is 0.78 Ohms / 1000 Feet.
And so, the power dissipated per 1000 feet by the 3 conductors will be approximately 3 x 16 Amps x (0.78 Ohms) ^ 2 = 29.20 Watts / 1000 Feet.
As a first approximation, tripling the quantity of conductors from 3 to 9 also triples the heat output of those conductors from 29.20 Watts / 1000 Feet to 87.6 Watts / 1000 Feet.

However, depending on how this conduit is installed (by itself underground, in a ductbank with other conduits, etc.) consideration must also be given to the thermal resistivity of the conduit's surroundings to determine
what the operating temperature of these conductors will be. If the thermal resistivity of a conduit's surrounding is relatively high such that the heat generated by the conductors raises the ambient temperature, then
an ambient temperature correction factor must be used (NEC Table 310.15.(B)(2)(a)). The effect of this increase in ambient temperature is to raise the resistance of the conductors.

And so, just for temperature effects, an iterative approach must be used (Neher McGrath calculations - see NEC Annex B).
Pick a conductor size and installation configuration, select the table 9 resistance, calculate the heat dissipated, calculate the ambient temperature, adjust the resistance based upon the ambient temperature, rinse and repeat until the solution converges.

I suspect that NEC table 310.15(B)(3)(a) makes some assumptions about how the conduit is installed to limit the ambient temperature increase resulting from more than 3 conductors installed in a raceway.

My question is, does that table also take into account the proximity effect from conductors being installed next to each other?

If it does, how do I use that table to calculate an "effective" resistance value that I can use for voltage drop considerations.
But from your response, the answer seems to be no.

I believe that I am correct in saying that there are really two different effects (increased resistance from increase in ambient temperature and increased resistance from the proximity effect) that must be evaluated cumulatively.
I just don't know how to do it yet.

Thank you.