determining voltage drop for 1-phase lines
determining voltage drop for 1-phase lines
(OP)
Gang:
I'm a "lurker" on this board and have found many helpful tips and knowledge. Thanks to all who make these boards so interesting and helpful.
Now for my question: I'm an agricultural engineer who is quite rusty on my elementary electricity. Could somebody refresh me on the proper calculations to properly determine voltage drop along a supply wire for a 1-phase motor.
As I understand, the equation for a 3-phase drop is:
dV = 1.732 * I * K (conductor materials) * L/CM (cir mil)
For 1-phase, is the 1.732 factor simply removed? Please advise on the correct formula so that I can sharpen my electrical pencil.
Thank you.
I'm a "lurker" on this board and have found many helpful tips and knowledge. Thanks to all who make these boards so interesting and helpful.
Now for my question: I'm an agricultural engineer who is quite rusty on my elementary electricity. Could somebody refresh me on the proper calculations to properly determine voltage drop along a supply wire for a 1-phase motor.
As I understand, the equation for a 3-phase drop is:
dV = 1.732 * I * K (conductor materials) * L/CM (cir mil)
For 1-phase, is the 1.732 factor simply removed? Please advise on the correct formula so that I can sharpen my electrical pencil.
Thank you.





RE: determining voltage drop for 1-phase lines
A simole rule for wiring resistance is
10 ga. wire has a resistance of one Ohm per 1000 ft. Every three gages the resistance doubles (or halves). So
13 ga. is 2 Ohms/1000 ft.
16 ga. is 4 Ohms/1000 ft.
7 ga. is 0.5 Ohms/1000 ft.
Remember that there are two wires in the circuit. For example; 500 ft. from source to load with ten ga. wire carrying ten amps.
Resistance (R) = 1 Ohm/1000 ft. x 500 ft x 2/1000 = 1 Ohms
E = IR = 10 x 1 = 10 Volts drop.
RE: determining voltage drop for 1-phase lines
Note that a key difference between 3-phase and 1-phase circuits, which sreid alluded to, is that you often have very low neutral current on 3-phase (or maybe no neutral at all), and therefore you don't get voltage drop on the neutral. That means that a 3-phase circuit, given the same conductor size and current, will have less voltage drop than a single-phase circuit.
RE: determining voltage drop for 1-phase lines
RE: determining voltage drop for 1-phase lines
1. Approximately:
Vo=Esending,end-Ereceiving,end=Eo'-Eo=IxZx2xL/1000, in Volts
where
I is conductor loop current
Z=R+jX, in Ohms/1000ft, e.g. from NEC
L is Length of Line
2. Accurately:
Vo=Esending,end-Ereceiving,end=Eo'-Eo={sqrt[(Eo x cos(theta)+IxR)^2 + (Eo x sin(theta) + IxX)^2] - Eo}
Where:
theta is power factor angle of the load
X is 60cycle Reactance of line in Ohms/1000ft per conductor
R is AC resistance of line in Ohms/1000ft per conductor
I line current in Amps
Eo', Eo sending and receiving end voltages to neutral in Volts
RE: determining voltage drop for 1-phase lines
Using line-to-line voltage, §3.11.1 in IEEE Std 141-1993 …Electric Power Distribution for Industrial Plants mentions a mutliplier of 1.732 for 3ø circuits and 2 for 1ø circuits.
RE: determining voltage drop for 1-phase lines
namely:
2. Accurately:
Vo=Esending,end-Ereceiving,end=Eo'-Eo={sqrt[(Eo x cos(theta)+IxR)^2 + (Eo x sin(theta) + IxX)^2] - Eo}x 2xL/1000ft
RE: determining voltage drop for 1-phase lines
Voltage drop = 2 x K x I x L divided by circular mil
cir mil = 2 x K x I x L divided by desired volts dropped
max lengeth = cmils x desired volt dropped divided 2 x k x L
max current= cmils x desired volt dropped divided2 x k x L
Three Phase voltage drop:
Volt drop = 1.73 x K x I x L diveded by circular mils
circular mils = 1.73 x K x I x L divide by desired volt drop
max length= cir mils x desired volt drop divde 1.73 X K x I
max current= cirmils x desired volt drop divide 1.73 x K x L
I = current in conductor
K = is approximately 12 for copper and 18 for aluminum
L = length of circuit from supply point to load
cir mils = circular mil area of condutor from table 8 of NEC
1.73 = square root of 3
you multiply single phase loads by 2 because you have the wire out to the load and power coming back
you only use the 1.73 for three phase and you DO NOT multiply by 2
NEC wants no more than 3% volt drop for branch circuits and 3% for feeder but not more than 5% combind branch and feeder total
sample problem: single phase
150 amp load, 240 volt, 120 feet from source, desired voltage drop is 3% using copper conductors
2 x K X I x L divide by desired volt drop
2 x 12(for copper) x 150 amps x 120 feet
divide by 7.2 volts (3% of 240volts)
equals 60,000 cirmils
table 8 copper conductor THHN = #2 copper
Good luck with your problem
RE: determining voltage drop for 1-phase lines
Thanks for all the great answers. I feel more confident in my ability to ensure that I'm recommending the proper wire size.
Have a great weekend.
Jeremiah
RE: determining voltage drop for 1-phase lines
Feeders: 2% at full connected load
Branches: 3% at full connected load.
Also, if I remember correctly, NEC states their voltage drop limits as guidelines only (except in some special circumstances, such as fire pump starting). ASHRAE-90.1 states their limits as absolute mandatory maximums.
RE: determining voltage drop for 1-phase lines
RE: determining voltage drop for 1-phase lines
Note that ASHRAE-90.1 (which is well on its way to being adopted here and there and everywhere across the US as we speak) has tighter requirements for voltage drop than NEC:
Feeders: 2% at full connected load
Branches: 3% at full connected load.
///The overall voltage drop requirement is the same from both: ASHRAE and NEC, namely, 5% voltage drop maximum.\\\
RE: determining voltage drop for 1-phase lines
FPN No. 4: Conductors for branch circuits as defined in
Article 100, sized to prevent a voltage drop exceeding
3 percent at the farthest outlet of power, heating, and lighting loads, or combinations of such loads, and where the
maximum total voltage drop on both feeders and branch
circuits to the farthest outlet does not exceed 5 percent,
provide reasonable efficiency of operation. See 215.2 for
voltage drop on feeder conductors.
RE: determining voltage drop for 1-phase lines
Also, please note that NEC does not include any *requirement* for max voltage drop. It simply includes a helpful little footnote mentioning that 5% max provides for reasonable efficiency of operation, just in case you happen to care about such things.
In contrast, ASHRAE states that 2+3% is an absolute code-mandated maximum permissible drop, and that's the max allowable even if you think it would be pretty slick to heat your place with your wiring. Too bad for you, 5% is all the heat you'll ever get out of those puppies.
RE: determining voltage drop for 1-phase lines
RE: determining voltage drop for 1-phase lines
The ONLY place that I'm aware of NEC actually MANDATING a specific maximum permissible voltage drop is on FIRE PUMP STARTING. I admit, there may well be possible that there are other places where other wiring also is also specified by NEC. BUT -- GENERAL PURPOSE wiring is most definitely NOT limited to 5% drop by NEC.
Read those FPN's again and tell me I'm wrong.
RE: determining voltage drop for 1-phase lines
NEC "90.5(C) Explanatory Material. Explanatory material . . . is included in this Code in the form of fine print notes (FPNs). Fine print notes are informational only and are not enforceable as requiremetns of this Code."
So maybe they count, but they don't really count for all that much if they're not enforceable, do they?
RE: determining voltage drop for 1-phase lines
Really, one should be concerned with NEMA MG standard for this. Motors designed around their guidelines are derated starting at 1% VUB (as defined by NEMA).
RE: determining voltage drop for 1-phase lines
"""(D) Voltage Drop. The voltage drop on any branch circuit shall not exceed 1.5 percent. The combined voltage drop of feeder and branch-circuit conductors shall not exceed 2.5 percent.
(1) Fixed Equipment. The voltage drop on branch circuits supplying equipment connected using wiring methods in Chapter 3 shall not exceed 1.5 percent. The combined voltage drop of feeder and branch-circuit conductors shall not exceed 2.5 percent."""
RE: determining voltage drop for 1-phase lines
As I mentioned previously, "I admit, there may well be possible that there are other places" than FIRE PUMP STARTING where voltage drop is specified -- so we can add professional recording studios to this list now too.