IEEE Exact Voltage Drop
Formulae 



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NEC® Specifications Concerning
Voltage Drop 

NEC® Sections 21019(a) (FPN No.4)
and 2152(b) (FPN No.2) recommend sizing both feeders and
branch circuits to prevent a voltage drop exceeding 3 percent at the farthest
outlet, where the maximum total voltage drop of the feeders and branch circuits
does not exceed 5 percent. NEC® section 1103(b) requires
equipment to be installed in accordance with the equipment instructions.
Therefore, electrical equipment must be installed so that it operates within its
voltage rating as specified by the manufacturer. Additionally, NEC®
Section 31015(a) (FPN No.1) states that the ampacities provided in
it's Tables do not take voltage drop into consideration. 




Ground Conductors 

NEC® 250122(b) states that
where circuit conductors are increased in size to compensate for voltage drop,
the equipment grounding conductors, where installed, shall be adjusted
proportionately according to circular mil area. 





The following sections are the ANSI / IEEE Std
141 formulae used by Volts for voltage drop computations. 



AC Circuits 




For AC circuits, where AC resistance and
inductive reactance are considered, the following is the IEEE Std 141 exact
voltage drop formula. 


where: 
Vd = Voltage
drop (Line to Neutral) 
V = Voltage
(source) 
I = Current in
amperes (A) 
R = AC
Resistance from NEC® Chapter 9 Table 9 (Ohms to Neutral) 
X = AC Reactance
from NEC® Chapter 9 Table 9 (Ohms to Neutral) 
distance (L) is considered from the Resistance & Reactance Tables 
where Ohms per unit / 1000 * L in same unit = R or X 
θ = Angle of Phase Offset = Arc Cosine (device or circuit
Power Factor) Line to Line is computed by Line to
Neutral VD / Sqrt(3).







VOLTS™ automatically computes the correct
conductor, neutral and ground sizes based on the conductor / cable type,
voltage, raceway type, ambient and terminal temperature, distance, hertz (Hz)
and the user defined voltage drop limit. The resulting voltage drop information
is also automatically updated from the accumulation of resistance / impedance
from the entry of upstream panels and transformers.
Volts also features a very comprehensive
Voltage Drop Analysis with Graphing report. 



DC Circuits 





where: 
Vd = Voltage drop 
R = DC Resistance from NEC®
Chapter 9 Table 8 
L = Distance 
I = Current in amperes (A) 

K = Material Resistivity
constant  12.9 for Cu & 21.2 for Al 
CM = Circular mils of
conductor 





Ambient Temperature 




Additionally, ambient temperature is considered
with the following ratio of temperatures formula. This formula is used to adjust
the Chapter 9 Table 9 values from 75ºC to the installation ambient temperature
in Celsius (C). 


R2 = New Conductor
Resistance 
R1 = Original
Conductor Resistance 
α =
Material Resistivity 
T2 = Ambient Temperature in
Celsius (TA) 





Magnetic (Eddy) Currents 




Eddy currents are induced currents in surrounding magnetic or nonmagnetic
metal. These currents create heating in the metal and therefore act as an
energy loss that translates into an increase in resistance of the circuit.
NEC® Chapter 9, Table 9
segregates
conduits into three groups, PVC, Aluminum and Steel to account for the added
resistance with each of the three conduit group types. PVC, being
nonmetallic, does not produce any eddy currents and therefore has the least
resistance value of the three. Steel and Aluminum conduit, being metallic,
do produce eddy currents and their respective resistance values are reflective
of this. 




Volts utilizes these factors in determining
the correct conductor size and voltage drop computations along with the
accumulation of the impedance / resistance of all upstream conductors. 


VOLTS™ utilizes both ambient and
terminal temperatures separately to size the conductor and compute the resulting voltage
drop. 




