You may easily find the resistance in tables.
The impedance of a conductor is increased by the skin effect.
In Canada, table D3, voltage drop, is based on skin effect and may be used to calculate the effective resistance at various temperatures.
The effective resistance of a branch circuit or feeder is effected by the inductive reactance of the cable and the impedance varies.
Some factors:
In steel conduit or in in aluminum conduit.
Armour or sheath.
The spacing of the conductors.
Trefoil, flat, the arrangement of multiple conductors per phase.
Bill
-------------------- Ohm's law
Not just a good idea; It's the LAW!
The CEC gives the circuit length for a 1% voltage drop, based on effective resistance.
You will have to work backwards from there.
The table is in Appendix D, Tabulated General Information of the Canadian Electrical Code. Table D3
Distance to centre of distribution for a 1% drop in voltage on
nominal 120 V, 2-conductor copper circuits.
Calculated at 60 degrees C.
Bill
-------------------- Ohm's law
Not just a good idea; It's the LAW!
I don't think that adding or subtracting two feet from a one hundred foot run of #14 AWG cable will make much more than 2% difference in the fault current, if that much.
Bill
-------------------- Ohm's law
Not just a good idea; It's the LAW!
Nor are you taking into account of the impedance at connections or the how the cables are laid out (geometry) and how they couple with things around them will affect the impedance. Fussing about impedance differences at 30 and 75 C is like shuffling deck chairs on the Titanic. I suspect at best are only ever within 10% of actual impedance.
Well, when you look at it code making panels, software designers, and corporations like Eaton are very much fussing over 30*C vs 75*C in short circuit studies. You have to assume worse case in about half of everything in relation to short circuits.
Yes, in maximum disconnection times you assume 75*C, but when it comes to interrupting capacity you have to assume 30*C.
If you're pushing equipment ratings to the point that 30C vs. 75C matters, you're barking up the wrong tree. As I've said a number of times, if the inspector has to take out the tape measure to verify clearance distances you don't have enough clearance regardless of what's measured; here if 30C vs. 75C matters, the device is over dutied and needs to be replaced with a higher rating. Things change, numbers represent a single snapshot based on a gillion assumptions, many of which are unstated, all of which represent one instant in time. More than once when I was doing building systems, I had to specify expensive equipment change outs to raise interrupting ratings; maybe nothing had actually changed from the initial construction other than the utility got more conservative in how they gave out equipment rating fault levels, maybe there had been real changes, maybe the original engineer hadn't done it correctly, but in any case things had been shaved too close.
The last thing you should ever want to do in any design is build in the desire of future maintainers to want to make a voodoo doll of you and start sticking pins in it.
I’ll see your silver lining and raise you two black clouds. - Protection Operations
30*C increases fault current. Taking into account 50 feet of wire between a pad mount transformer and main disconnect makes all the difference in the world in terms of cost. While the infinite method gives 65,000 amps on the secondaries, a few feet knocks the current down to the point more economical equipment can be used. I see it as wise, practical design especially when code lets you do it that way.
I worked on a very large mine mill.
The 13kV switchboard lineup was 93 feet long.
There were a large number of transformers direct connected to 480V PDCs.
The spec called for a minimum of 100 feet of cable to feed each unit transformer/PDC. (The extra cable length to be run past and doubled back in the cable trays.)
Without the extra cable, the close in transformers would have needed higher interrupting rated local disconnects.
The length makes a lot more difference than the temperature.
FYI, the impedance voltage of a transformer is tested on transformers at working temperature.
Testing a cold transformer will show a noticeably lower impedance than the same test on a hot transformer. (First hand experience. Long story.)
If you are calculating the forces on the insulators due to a fully offset fault current it may be well to consider the temperature of both the transformer and of the conductors.
For the selection of distribution equipment ratings, the method of determining the Available Short Circuit Current is conservative enough to accommodate temperature changes.
If you are concerned, do some research and determine the X/R ratio that is used for ASSC ratings.
If your transformer X/R ratio is close to the assumed X/R ratio, then consider David Beach's excellent advice.
In the real world, the difference between the actual X/R ratio of the source transformer and the X/R ratio assumed for rating is great enough to more than compensate for temperature differences.
Bill
-------------------- Ohm's law
Not just a good idea; It's the LAW!
Google the Southwire Power Cable Manual. You will find temperature adjustment factor as well as ac/dc resistance ratio information. A useful resource. In some analysis software, the temperature adjustment is built into the cable model, as well as ac resistance at operating frequency.
@Waross: Never assume or anticipate the safety factor built in or conservatism will save you. When you calculate short circuit current you always assume cold system closing into a bolted fault. Chapter 9 Table 9 values assumes worse case hot conditions, not cold.
I know people are almost irritated that I would consider pushing anything to its limits but thats not my goal. My goal is having exact numbers and running real and hypothetical scenarios for all scenarios.
It still amazes (in a curious way) just how many detractors come out of the wood work when challenging NFPA-70 or the code making process itself. Ditto for North America's collective intransigence toward acknowledging earth fault loop impedance or disconnection times as being the central pillar to protection of life and property.
With that said
Proposing this change be made to 250.4 (A) 5, and that a new paragraph 250.4 (A) 6 be added after 250.4 (A) 5.
(5) Effective Ground-Fault Current Path. Electrical equipment
and wiring and other electrically conductive material
likely to become energized shall be installed in a manner that
creates a low-impedance circuit facilitating the operation of the
overcurrent device not exceeding the time specified in 250.4 (A) 6 or ground detector for high-impedance grounded systems. It shall be capable of safely carrying the maximum ground-fault current likely to be imposed on it from any point on the wiring system where a ground fault may occur to the electrical supply source. The earth shall not be considered as an effective ground-fault current path.
(6) Maximum Permitted Overcurrent Device Disconnection Time. The maximum total clearing time of an associated overcurrent device during a ground fault shall not exceed any of the following:
(a) 1 second for final branch circuits protected at 30 amps or less, operating over 50 volts to ground but not exceeding 150 volts to ground.
(b) 0.5 seconds for final branch circuits protected at 30 amps amps or less, operating over 150 volts to ground but not exceeding 300 volts to ground.
(c) 0.25 seconds for final branch circuits protected at 30 amps or less, operating over 300 volts to ground but not exceeding 600 volts to ground.
(d) 0.125 seconds for final branch circuits protected at 30 amps or less, operating at over 600 volts to ground.
(e) 5 seconds for feeders and branch circuits protected at 35 amps or more but not exceeding 350 amps, operating at over 50 volts to ground.
(f) 10 seconds for feeders and branch circuits protected at 400 amps or more, operating over 50 volts to ground.
FPN: Disconnection time is typically derived via
the minimum fault current as determined by the total
combined circuit impedance present at the furthest
point of a circuit's fixed wiring compared to a device's
published time current curve. See Chapter 9, Table 9
for specific impedance values.
FPN: Faster disconnection times than maximum
limits above greatly reduce incident energy
at the point of a ground fault.
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