EEE 302
Electrical Networks II
Dr. Keith E. Holbert
Summer 2001
Lecture 10
1
Source/Load Connections
• The equivalent load may be in an equivalent delta
() or wye (Y) configuration
– the delta load configuration has no neutral line
– the current is zero in the neutral line for a balanced wye
load configuration
• Source/Load connections can be connected in any
of the possible combinations:
Ysource-Yload
source-Yload
Ysource-load
source- load
– Analysis prefers the first connection (Y-Y)
Lecture 10
2
Balanced Wye-Wye Connection
a
Van
+
–
b
Vbn
+
–
c
Vcn
ZY
ZY
ZY
+
–
n
Lecture 10
Load
3
Balanced Wye-Wye Connection
• The line-to-line voltages (or line voltages) are
Vab = VP3 30°
Vbc = Vab -120°
Vca = Vab -240°
where VP is the magnitude of the phasor voltage between
any two lines
• The magnitude of the line voltage is
VL = VP3
Lecture 10
4
Balanced Wye-Wye Connection
• The line current for phase a is
Ia = Van / ZY = Vp 0° / ZY
– In a Y-Y connection the magnitude of the line current
(IL) equals the magnitude of the load current (IY)
• The neutral current In is
In = Ia + Ib + Ic = 0
• Balanced Y-Y three-phase ac circuits may be
analyzed on a per phase basis
Lecture 10
5
Balanced Wye-Delta Connection
Van
+
–
Vbn
+
–
n
Vcn
a
Z
b
Z
Z
+
–
c
Load
Lecture 10
6
Summarizing
• A very good summary appears on pages
568-9 of the textbook including a figure and
table for explanation
Lecture 10
7
Class Examples
• Extension Exercise E10.1
• Extension Exercise E10.2
Lecture 10
8
Three-Phase Power Relationships
• The real and reactive power per phase are
PP  VP I L cos  
QP  VP I L sin   
VL I L
3
VL I L
3
cos 
sin  
• The total real, reactive, and complex powers are
PT  3 PP  3 VL I L cos 
QT  3 QP  3 VL I L sin  
S T  3 VL I L 
Lecture 10
9
Class Examples
• Extension Exercise E10.8
• Extension Exercise E10.10
Lecture 10
10