Example 2: A three-phase, delta-connected ac

Effective values of line and phase voltages are

generator has a terminal voltage of 450 volts, and the

indicated in figure 3-28 by vectors Ea, Eb, and Ec. Note

current in each phase is 200 amperes. The power factor

that the vector sum of Ea, Eb, and Ec is zero. The phase

of the load is 75 percent. Find (a) the line voltage, (b)

currents are equal to each other because the loads are

the line current, (c) the apparent power, and (d) the true

balanced. The line currents are equal to each other for

power.

the same reason. At unity-power-factor loads, the phase

current and phase voltage have a 0-degree angle

between them.

The power delivered by a balanced, three-phase,

delta-connected system is also three times the power

delivered by each phase. Mathematically, you can

prove this as follows:

Because

the total true power is

The wattmeter connections for measuring the true

power in a three-phase system are shown in figure 3-29.

The method shown in figure 3-29, view A, uses three

wattmeters with their current coils inserted in series with

Thus, the expression for three-phase power delivered by

the line wires and their potential coils connected

a balanced delta-connected system is the same as the

between line and neutral wires. The total true power is

expression for three-phase power delivered by a

equal to the arithmetic sum of the three wattmeter

balanced wye-connected system. Two examples are

readings.

given to illustrate the phase relations between current,

voltage, and power in (1) a three-phase, wye-connected

The method shown in figure 3-29, view B, uses two

system and (2) a three-phase, delta-connected system.

wattmeters with their current coils connected in series

Example 1: A three-phase, wye-connected ac

generator has a terminal voltage of 450 volts and

delivers a full-load current of 300 amperes per terminal

at a power factor of 80 percent. Find (a) the phase

voltage, (b) the full-load current per phase, (c) the

kilovolt-ampere, or apparent power, rating, and (d) the

true power output.

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