Voltage Regulation Formulas and Reactance of Conductors - Okonite Electrical Wire & Cable

Voltage regulation is often the limiting factor in the choice of either conductor or type of insulation. While the heat loss in the cable determines the maximum current it can safely carry without excessive deterioration, many circuits will be limited to currents lower than this in order to keep the voltage drop within permissible values. In this connection it should be remembered that the high voltage circuit should be carried as far as possible so that the secondary runs, where most of the voltage drop occurs, will be small.

The voltage drop of a feeder may be calculated from the following formulae:

V = 100 (VS — VL) / VL

V = Voltage regulation in percent

VL = Voltage across load

VS = Voltage at source

VS =VS = square root [(VL Cos theta + Rl)2 + (VL sin theta + Xl)2]

theta = is the angle by which the load current lags the voltage across the load

Cos theta = Power factor of load

R = Total a-c resistance of feeder

X = Total reactance of feeder

I = Load current

Approximate formula for voltage drop:

(VS — VL) = RI cos theta  +  XI sin theta

This above formula is satisfactory where the power factor angle is nearly the same as the impedance angle. It is exact when they are equal.

That is: tan theta = X / R

Above values apply directly for single phase lines when resistance and reactance are loop values and voltage is voltage between lines.

For 3-phase circuits, use voltage to neutral and resistance and reactance of each conductor to neutral. This gives voltage drop to neutral. To obtain voltage drop line-to-line, multiply voltage drop by square root of 3. (The percent voltage drop is of course the same between conductors as from conductor to ground and should not be multiplied by square root of 3).

Example: 3 single coated copper conductors 600 volt cables in non-metallic conduit.

Size conductor =4/0, Awg Copper .080 insulation, .045 jacket.

O.D. = .810”
Voltage = VS = 440 volts 3 phase
Current = I= 250 amperes
Power Factor = cos theta  = 0.8
Length = 750 ft.

Resistance

Per conductor = R

= .0525 ohms 1000 feet at 25°C

= .047 ohms for 750 feet at 75°C

Reactance

Per conductor = X

= .031 ohms 1000 feet (see table)

= .028 ohms for 750 feet
   (including 20% for random lay)

VS =VS = square root [(VL Cos theta + Rl)2 + (VL sin theta + Xl)2]

440 / square root 3 = square root [(.8VL + .047 x 250)2 + (.6VL + .028 x 250)2]

Solving for VL ; VL = 240.4

Line-to-line voltage = 240.4 square root of 3 = 417

Voltage drop = 440 — 417 = 23 volts

V = [(440 - 417) / 417 ] (100) = 5.52%

Approximate Formula:

Voltage drop = line to neutral

= Rl cos theta + Xl sin theta
= 0.047 X 250 X .08 + 0.028 X 250 X 0.6
= 9.4 + 4.2 = 13.6

Line-to-line voltage drop = 13.6 square root of 3  = 23.5 volts

Conductor Reactance

The following table shows a nomogram for determining the reactance of any solid or concentric stranded conductor. This covers spacings encountered for conduit wiring as well as for open wire circuits. Various modifications necessary for use under special conditions are covered in notes on the nomogram. The reactances shown are for 60-Hertz operation.

Where regulation is an important consideration several factors should be kept in mind in order to obtain the best operating conditions.

Open wire lines have a high reactance. This may be improved by using parallel circuits but is much further reduced by using insulated cable. Three conductors in the same conduit have a lower reactance than conductors in separate conduits.

Single conductors should not be installed in individual magnetic conduit because of the excessive reactance.

Three conductors in magnetic conduit will have a somewhat higher reactance than cables in non-magnetic conduit.

Reactance of conductors at 60Hz
(Series inductive reactance to neutral)
conductor reactance table at 60Hz