Hi tripp,
I use the IEEE Std 141 exact formulae:
Vd = V + IRcos(theta) + IXsin(theta) - sqrt(V^2 - (IXcos(theta) - IRsin(theta))^2)
where:
Vd = Voltage drop (Line to Neutral)
V = Voltage (source)
I = Current in amperes (A)
R = AC Resistance from NEC® Chapter 9 Table 9
X = AC Reactance from NEC® Chapter 9 Table 9
distance (L) is considered from the Resistance & Reactance Tables
where Ohms per unit / 1000 * L in same unit = R or X
theta = Arccos(device or circuit Power Factor) = angle of phase offset
Line to Line is computed by Line to Neutral VD / Sqrt(3) for 3 phase circuits.
You'll also have to get into some sin wave destruction formulae for power factor averaging when computing the Vd across a panel's bus bar. Total(kW) / Total(kVA) should be close enough for the bus bar PF average.
I forgot to mention that since resistance(impedance) is very sensative to temperature you must multiply the resistance value by the following factor:
R2 = R1[1 + a(T2 - 75)]
where:
R2 = Adjusted Conductor Resistance
R1 = Table Conductor Resistance @ 75ºC
a = Conductor Material Resistivity
a(cu) = 0.00323 and a(AL) = 0.00330
T2 = Ambient Temperature in Celsius (TA)
convert temperature in ºF to ºC with:
TºC = (TºF - 32) / 1.8
Also:
You would take the VD across the aluminum first. Then use the lessened voltage from the aluminum run to start the copper VD computation. Most engineers would compute the run as all aluminum to keep conservative.
And:
Regardless of the voltage drop formula you use, The fact that you take VD into consideration puts you in the top 1% of electrican's in my opinion!!!
The NEC only references VD in fine print notes. HOWEVER, all electrical devices used in the USA must have a UL label. United Labratories tests these device under "normal" conditions within a VD limit from its nameplate rated voltage. If you, the electrican, install a circuit that is not capable of supplying the correct voltage within the devices voltage range, the following will happen.
1. The UL approval is VOIDED.
2. The conductors will produce added heat. Heat, like raditation, is accumulative (just ask a fireman for verification). This means that a fire will eventually result in a given amount of time from not considering voltage drop.
3. When this happens who does the insurance company go after.......
Personally, as an engineer, I need to be as accurate as possible to not only ensure a problem free installation, but to also cover my butt in case there is a future problem. The IEEE Std 141 Exact Formula is the only VD formula that is recognized as correct both nationally and internationally.
Volts computes VD with all the necessary environmental and device considerations and sizes the conductors to the correct NEC ampacity table, the correct voltage drop and the correct terminal temperature of the device....in less time than you can write a single sentence.
