WIND ENERGY SYSTEMS - Cd3wd

Chapter 5—Electrical Network 5–12
+
♠
✏ ✏✏ ✏
E a
n
♠✏✏ ✏✏ +
E b
+
E ab
−
+
b
−
E ca
a
♠E c
E bc
+
− +
c
Figure 6: Balanced three-phase source.
The symbol V will be used for other types of voltages in the circuit. This will become more
evident after a few examples.
The line to line voltage E ab is given by
E ab = E a − E b = |E a |(1/0 o − 1/ − 120 o )
= |E a |[1 − (−0.5 − j0.866)] = |Ea|(1.5+j0.866)
In a similar fashion,
= |Ea| √ 3/30 o V (21)
E bc = √ 3|E a |/ − 90 o V
These voltages are shown in the phasor diagram of Fig. 7.
E ca = √ 3|Ea|/ − 210 o V (22)
When this three-phase source is connected to a balanced three-phase wye-connected load,
we have the circuit shown in Fig. 8.
The current I a is given by
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001