Phase and Ground Wire Impedance

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mbrooke

mbrooke

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Picture the following scenario:



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Chapter 9, Table 9 lists 500kcmil as have a resistance of 0.027 ohms per 1000 feet and a reactance of 0.039 ohms per 1000 feet. 3 gauge wire has a resistance of 0.25 ohms per 1000 feet and a reactance of 0.047ohms per 1000 feet.

My question is do these R and X values still hold true given the difference in size between each phase and ground? And if not how much variance should I anticipate?
 
The inductive reactance and the AC resistance are both functions of the wire diameter, and the inductive reactance assumes a single wire in free air.
The skin effect will not change when wires are bundled, but the effective inductive reactance will be reduced when the matching return current flows in a conductor very close to the conductor being measured. In effect a single or partial turn inductor approaches being a zero turn inductor because of the magnetic field cancellation. The relative sizes of the two wires is likely to be only a second order effect on the result.
 
GoldDigger said:
The inductive reactance and the AC resistance are both functions of the wire diameter, and the inductive reactance assumes a single wire in free air.
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Can I dispute this? My understanding, albeit thin and incomplete, is the chapter 9 table 9 is based on 3 wire in conduit. Not free air.

The skin effect will not change when wires are bundled, but the effective inductive reactance will be reduced when the matching return current flows in a conductor very close to the conductor being measured. In effect a single or partial turn inductor approaches being a zero turn inductor because of the magnetic field cancellation. The relative sizes of the two wires is likely to be only a second order effect on the result.
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Agree. But I'm left wondering how much of an impact differing sizes have.
 
mbrooke said:
Can I dispute this? My understanding, albeit thin and incomplete, is the chapter 9 table 9 is based on 3 wire in conduit. Not free air.



Agree. But I'm left wondering how much of an impact differing sizes have.
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1. I think you may be right on this.
2. The difference between DC and AC impedance is small enough already that I am completely comfortable ignoring the effect of differing diameters. Just use the impedance for each wire size for its part in the series impedance calculation. If the neutral does not carry any current (balanced three phase or split phase) then it does not contribute anything.
 
GoldDigger said:
1. I think you may be right on this.
2. The difference between DC and AC impedance is small enough already that I am completely comfortable ignoring the effect of differing diameters. Just use the impedance for each wire size for its part in the series impedance calculation. If the neutral does not carry any current (balanced three phase or split phase) then it does not contribute anything.
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Fair enough.
 
The resistance depends on temperature [it is always the insulation rated],
skin effect and proximity effect. Proximity effect depends on distance between phases.
The reactance depends also on this distance.
The maximum distance it is the distance between conductors’ centrelines in the extreme position in a conduit and this depends on conduit inner diameter and insulated core diameter.[see the sketch]
There are a lot of insulation thickness types and different conduit types. However, NEC takes an average distance.Distances in a conduit.jpg
Since the NEC reactances are based on average values for insulated core and inner conduit diameter [average stays unchanged] no change in resistance and reactance is expected.
 
mbrooke said:
What is proximity effect?
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Mutual inductance and phase to phase capacitance.

What you are getting close to is recognizing that the conductors are really transmission lines but when everything is electrically short we can treat it as a resistance (VD), a reactance (SCCR) dominates by self inductance, or at worst (arcing faults) a complex impedance rather than use a full transmission line model with distributed elements (series resistance and reactance, shunt reactance and capacitance). These only tend to become an issue for long overhead power lines, 409 Hz systems, and VFDs where the full transmission line model at least conceptually applies.
 
Skin effect it is produced by the alternative current itself when passing through the conductor. Depending on frequency the effective cross section area will be only a thin concentric tube close to the conductor edge [as a skin]. Doing this the cross-section area will be reduced and the conductor resistance increased.
When two or more conductors are placed near to each other, then their electromagnetic fields interact with each other. Due to this interaction, the current in each of them is redistributed such that the greater current density is concentrated in that part of the strand most remote from the interfering conductor.
If the conductors carry the current in the same direction, then the magnetic field of the halves of the conductors which are close to each other is cancelling each other and hence no current flow through that halves portion of the conductor. The current is crowded in the remote half portion of the conductor.
This phenomenon conduces to another resistance increasing.
The calculation may be done following Neher & McGrath theory[eq.24] or
IEC 60287-1-1 2.1.4 Proximity effect factor yp for three-core cables and for three single-core cables
Proximity effect.jpg
 
Julius Right said:
Skin effect it is produced by the alternative current itself when passing through the conductor. Depending on frequency the effective cross section area will be only a thin concentric tube close to the conductor edge [as a skin]. Doing this the cross-section area will be reduced and the conductor resistance increased.
When two or more conductors are placed near to each other, then their electromagnetic fields interact with each other. Due to this interaction, the current in each of them is redistributed such that the greater current density is concentrated in that part of the strand most remote from the interfering conductor.
If the conductors carry the current in the same direction, then the magnetic field of the halves of the conductors which are close to each other is cancelling each other and hence no current flow through that halves portion of the conductor. The current is crowded in the remote half portion of the conductor.
This phenomenon conduces to another resistance increasing.
The calculation may be done following Neher & McGrath theory[eq.24] or
IEC 60287-1-1 2.1.4 Proximity effect factor yp for three-core cables and for three single-core cables
View attachment 2553361
Click to expand...

So what is it like with 3 phase? What happens when a ground wire is next to or in between the conductors? Still the same or do things change?

I thank you for this, Mike's Books don't go this far in depth.
 
paulengr said:
Mutual inductance and phase to phase capacitance.

What you are getting close to is recognizing that the conductors are really transmission lines but when everything is electrically short we can treat it as a resistance (VD), a reactance (SCCR) dominates by self inductance, or at worst (arcing faults) a complex impedance rather than use a full transmission line model with distributed elements (series resistance and reactance, shunt reactance and capacitance). These only tend to become an issue for long overhead power lines, 409 Hz systems, and VFDs where the full transmission line model at least conceptually applies.
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I want to ask now... what is the surge impedance loading on NM cable and THHN in conduit?
 
mbrooke said:
A 50 mile line would still have surge impedance loading, would it not?
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If you just look at transmission line theory, the initial surge of current in the form of applied voltage divided by characteristic impedance, will only last until the voltage/current wave hits the far end of the line and reflects back (just under 1 ms.)
After that point with multiple reflections at each end you could probably get a quicker useful estimate by looking instead at the distributed capacitance of the line and ignoring the distributed inductance.
The surge loading exists for any length transmission line, but the duration of the surge will be directly proportional to the length of the line. And any impedance associated with the power source may affect the surge current significantly.
My comment about ignoring it was based on the initial subject of this thread involving lengths of NM and wire in conduit.
 
GoldDigger said:
If you just look at transmission line theory, the initial surge of current in the form of applied voltage divided by characteristic impedance, will only last until the voltage/current wave hits the far end of the line and reflects back (just under 1 ms.)
After that point with multiple reflections at each end you could probably get a quicker useful estimate by looking instead at the distributed capacitance of the line and ignoring the distributed inductance.
The surge loading exists for any length transmission line, but the duration of the surge will be directly proportional to the length of the line. And any impedance associated with the power source may affect the surge current significantly.
My comment about ignoring it was based on the initial subject of this thread involving lengths of NM and wire in conduit.
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I know, but I was referring to SIL in these terms:

If the load is less than the SIL, reactive volt-amperes are generated, and the voltage at the receiving end is greater than the sending end voltage. On the other hand, if the SIL is greater than the load, the voltage at receiving end is smaller because the line absorbs reactive power.
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Steady state application.

My apologies- I take responsibility for the confusion :)
 
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