dfang - Voltage drop is a function of impedance, not frequency. The frequency does affect the ac resistance of the conductor because of skin effect (the tendency for alternating current to crowd toward the surface of the conductor); proximity effect (the distortion of current distribution due to the magnetic effects of other nearby currents); and hysteresis and eddy current losses in nearby ferromagnetic materials and induced losses in short-circuited nearby non-ferromagnetic materials.
In addition to the ac resistance, note that the dominant factor in cable impedance is the cable reactance, which is of course directly proportional to frequency.
Good comment, Peter. I didn't word my response as well as I should have. Obviously inductive reactance varies with frequency (XL=2*pi*f*L). I concentrated on the frequency effects on the ac resistance only, as the effect of frequency on reactance is self-evident.
Suggestion to dfang (Electrical) Sep 10, 2001 marked ///\\\:
Is voltage drop a function of frequency?
///IEEE Std 141-1993 "IEEE Recommended Practice for Electric Power Distribution for Industrial Plants" Page 98 includes:
actual voltage drop=Es + IR cosfi + IX sinfi - [Es**2 - (IX cosfi - IR sinfi)**2]**0.5
which has some members dependent on frequency, e.g. X=2 x pi x f, therefore the voltage drop is generally dependent on the frequency.\\Suggestion to Chas (Electrical) Sep 10, 2001 marked ///\\\:
The values in Table 9 of the NEC are based on 60HZ. Where can I find tables that are based on 50HZ?
///Please, could you clarify that Table 9.\\\
A good approximation to estimate the voltage drop for 50 Hz application using AC resistance and reactance listed in Table 9 of the NEC for 60 Hz will be as follow:
Delta(V)= (R)*PF + 0.80(X)sin [arcos(PF)].
The above relation used by NEC is satisfactorily for values of PF greater than 85 %, the resistance value at 50 Hz do not change significantly and the reactance at 50 Hz is 20% lower than the one at 60 Hz.
The justification of the above statement could be supported as bellow.
RESISTANCE:
The ratio of cable AC resistance at 60 Hz divided by the resistance at 50 Hz could be estimated as follow.
R60/50=1+5*10^-6*kcmil+1.7*10^-8*kcmil^2.
For practical application the resistance at 60 and 50 Hz is the same for cable size up to 250 kcmil. Above 250 kcmil the resistance at 50 Hz is reduced gradually up to 2.5% for 1000 kcmil cable. This small variation is produced by the skin effect.
REACTANCE:
X(f)=2Pi (f) [0.1404 log(s/r) + 0.0153]kx10^-3 Ohms/1000 ft
Therefore the ratio of cable reactance at 60 Hz divided by the reactance at 50 Hz could be estimated as follow.
