Three-phase Circuits
Balanced 3-phase systems
Unbalanced 3-phase systems
SKEE 1043 Circuit Theory
Dr. Nik Rumzi Nik Idris
1
Unbalanced 3-phase systems
What is unbalanced 3-phase system?
• Sources that are unbalanced: unequal magnitude and unequal
difference in phase angles
• Unequal load impedance  only this will be considered in SKEE1043
This will result in unbalanced currents (even though
the sources are balanced)  hence for Y connected
load, with 4 wire, IN  0
The line or phase currents have to be calculated individually
2
Unbalanced 3-phase systems
Ia
A
ZA
In
N
C
Ib
Ic
Ia 
VAN
ZA
VBN
Ib 
ZB
ZB
B
Ic 
VCN
ZC
ZC
C
Ia  Ib  Ic  In
What if the system is a 3-wire system (i.e.  or Y)?
Ia  Ib  Ic  0
For Y connected load with 3 wire system, mesh analysis can be used
3
Unbalanced 3-phase systems
A
a
IAB
Z1
Z3
ICA
b
B
Z2
IBC
C
c
VAB
IAB 
Z1
V
IBC  BC
Z2
VCA
ICA 
Z3
4
Unbalanced 3-phase systems
Power measurement for unbalanced system
• Two-wattmeter method is still applicable. However only
PT=P1+P2 is true. Reactive power CANNOT be obtained
from √3(P2-P1)
• For a Y connected, 4 wire system, three wattmeters
(instead of two) are needed since In  0
• Again, the line (or phase) currents has to be calculated
individually
5