The line voltages (E1,2, E2,3, and E3,1) are the

between lines 1 and 2 equals the voltage drop across the

diagonals of three parallelograms whose sides are the

voltmeter connected to these lines.

phase voltages Ea, Eb, and Ec. From this vector

If the direction of the path traced through the

diagram, the following facts are observed:

generator is the same as that of the arrow, the sign of the

1. The line voltages are equal and 120° apart.

voltage is plus; if the direction of the trace is opposite to

the arrow, the sign of the voltage is minus. If the

2. The line currents are equal and 120° apart.

direction of the path traced through the voltmeter is the

3. The line currents are 30° out of phase with&

same as that of the arrow, the sign of the voltage is

line voltages when the power factor of the load

minus; if the direction of the trace is opposite to that of

is 100%.

the arrow, the sign of the voltage is plus.

4. The line voltage is the product of the phase

The following equations for voltage are based on

voltage and the

the preceding explanation:

E a + (-Eb) = E1,2, or E1,2 = Ea - Eb

E b + (-Ec) = E2,3, or E2,3 = Eb- Ec

by accompanying arrows in the generator phases in

E c + (Ea) = E3,1, or E3,1 = Ec - Ea

figure 3-22. These arrows point in the direction of the

The signs + and mean vector addition and vector

positive current and voltage of each phase. The three

subtraction, respective y. One vector is subtracted from

voltmeters connected across lines 1 and 2, 2 and 3, and

another by reversing the position of the vector to be

3 and 1, respectively, indicate effective values of line

subtraced through an angle of 180° and constructing a

and phase voltage. Line current 11 is supplied by phases

parallelogram, the sides of which are the reversed vector

a and c, which are connected to line 1. Line current is

and the other vector. The diagonal of the parallelogram

greater than phase current, but it is not twice as great

is the difference vector.

because the phase currents are not in phase with each

other. The relationship between line currents and phase

These equations are applied to the vector diagram

currents is shown in figure 3-28.

of figure 3-26. They are used, to derive the line voltages.

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