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
MEASUREMENT OF POWER
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.
Figure 3-29.--Wattmeters.
3-21
