to rotate in a direction that three-phase voltages are
generated in the following order: Ea, Eb, and Ec.
The voltage in phase b, or Eb, lags the voltage in
phase a, or Ea, by 120. Likewise, Ec lags Eb by 120,
and Ea lags Ec by 120. In figure 3-26, the arrows, Ea,
Eb, and Ec, represent the positive direction of generated
voltage in the wye-connected ac generator. The arrows,
I1, I2, and I3, represent the positive direction of phase
and line currents supplied to balance unit power-factor
connected between lines 1 and 2, 2 and 3, and 3 and 1
indicate effective values of line voltage. The line
voltage is greater than the voltage of a phase in the
w ye-connected circuit because there are two phases
Figure 3-25.--Waves and vectors of alternating current and
connected in series between each pair of line leads, and
their voltages combine. However, line voltage is not
twice the value of phase voltage because the phase
can remember this by the memory hint ELI --voltage
voltages are out of phase with each other.
leads current in an inductive circuit). Since voltage
is leading current, the vector diagram shows voltage in
The relationship between the phase and the line
a counterclockwise or positive direction from current.
voltages is shown in the vector diagram (fig. 3-27).
Effective values of phase voltage are indicated by
Now, look at figure 3-25, which shows the current
vectors Ea, Eb, and Ec. Effective values of line and
(I) leading the voltage (E) by degrees. Using the
phase current are indicated by vectors Ia, Ib, and Ic.
memory hint ICE-- current leads voltage in a
Because there is only one path for the current between
capacitive circuit --you can remember this vector.
any given phase and the line lead to which it is
Since current leads voltage by degrees, the vector
connected, the phase current is equal to the line current.
representing voltage is in a clockwise or negative
The respective phase currents have equal values because
direction from the vector representing current.
the load is assumed to be balanced. For the same reason,
Analysis of Wye Connected Stators
the respective line currents have equal values. When the
load has unity power factor, the phase currents are in
The phase relationships in a three- wire, three-phase,
phase with their respective phase voltages.
wye-connected system are shown in figure 3-26. In
constructing vector diagrams of three-phase circuits, a
In combining ac voltages, it is important to know
counterclockwise rotation is assumed in order to
the direction in which the positive maximum values of
maintain the correct phase relation between line
the voltages act in the circuit as well as the magnitudes
voltages and currents. Thus, the ac generator is assumed
of the voltages. (NOTE: As you read this section, look
Figure 3-26.--Three-phase, wye-connected system.