1. Balanced 3-phase systems Unbalanced 3-phase systems
Three-phase Circuits
Balanced 3-phase systems
Unbalanced 3-phase systems
SKEE 1043 Circuit Theory
Dr. Nik Rumzi Nik Idris

2. Balanced 3-phase systems
Single-phase two-wire system:
Single source connected to a load using two-wire system
Single-phase three-wire system:
Two sources connected to two loads using three-wire system
Sources have EQUAL magnitude and are IN PHASE

3. Balanced 3-phase systems
Balanced Two-phase three-wire system:
Two sources connected to two loads using three-wire system
Sources have EQUAL frequency but DIFFFERENT phases
Balanced Three-phase four-wire system:
Three sources connected to 3 loads using four-wire system
Sources have EQUAL frequency but DIFFFERENT phases

4. Balanced 3-phase systems
WHY THREE PHASE SYSTEM ?
ALL electric power system in the world used 3-phase system to GENERATE, TRANSMIT and DISTRIBUTE
Instantaneous power is constant – thus smoother rotation of electrical machines
More economical than single phase – less wire for the same power transfer
To pass SKEE 1043 – to be able to graduate !

5. Balanced 3-phase systems
SEE VIDEO
Generation of 3-phase voltage: Generator

6. Balanced 3-phase systems
Generation, Transmission and Distribution

7. Balanced 3-phase systems
Generation, Transmission and Distribution

8. Balanced 3-phase systems
Y and  connections
Balanced 3-phase systems can be considered as 3 equal single phase voltage sources connected either as Y or Delta () to 3 single three loads connected as either Y or 
SOURCE CONNECTIONS
LOAD CONNECTIONS
Y connected source
Y connected load
 connected source
 connected load
Y-Y
Y-
-Y
-

9. Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection + 
Van
Vbn
Vcn a n b c 
RMS phasors !
120o
240o
Vbn
Van
Vcn

10. Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection + 
Van
Vbn
Vcn a n b c
120o
Phase sequence : Van leads Vbn by 120o and Vbn leads Vcn by 120o
This is a known as abc sequence or positive sequence

11. Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection + 
Van
Vbn
Vcn a n b c 
RMS phasors !
Vbn
Van
Vcn
120o
240o

12. Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection
120o + 
Van
Vbn
Vcn a n b c
Phase sequence : Van leads Vcn by 120o and Vcn leads Vbn by 120o
This is a known as acb sequence or negative sequence

13. Balanced 3-phase systems
SOURCE CONNECTIONS
Source :  connection  + 
Vab
Vbc
Vca a b c  
RMS phasors !
120o
240o
Vab
Vbc
Vca

14. Balanced 3-phase systems
LOAD CONNECTIONS
Y connection
 connection a n b c a Zb Z1 Zc b Z2 Z3 Za c
Balanced load:
Z1= Z2 = Z3 = ZY
Za= Zb = Zc = Z
Unbalanced load: each phase load may not be the same.

15. Balanced 3-phase systems
Balanced Y-Y Connection Ia ZY + 
Van
Vbn
Vcn n b c a In Ib Ic N A C B
Phase voltages
line currents
line-line voltages OR
Line voltages
The wire connecting n and N can be removed !

16. Balanced 3-phase systems
Balanced Y-Y Connection

17. Balanced 3-phase systems
Balanced Y-Y Connection

18. Balanced 3-phase systems
Balanced Y-Y Connection

19. Balanced 3-phase systems
Balanced Y-Y Connection

20. Balanced 3-phase systems
Balanced Y-Y Connection

21. Balanced 3-phase systems
Balanced Y-Y Connection
where
and
Line voltage LEADS phase voltage by 30o

22. Balanced 3-phase systems
Balanced Y-Y Connection
For a balanced Y-Y connection, analysis can be performed using an equivalent per-phase circuit: e.g. for phase A: Ia A a
Van +  ZY
In=0 n N
Vcn  +  + Ib ZY ZY c C
Vbn b B Ic

23. Balanced 3-phase systems
Balanced Y-Y Connection
For a balanced Y-Y connection, analysis can be performed using an equivalent per-phase circuit: e.g. for phase A: Ia A a
Van +  ZY n N
Based on the sequence, the other line currents can be obtained from:

24. Balanced 3-phase systems
Balanced Y- Connection Ia Z + 
Van
Vbn
Vcn n b c a Ib Ic A B C
Using KCL,
Phase currents

25. Balanced 3-phase systems
Balanced Y- Connection
Phase current LEADS line current by 30o
where
and

26. Balanced 3-phase systems
Balanced - Connection Ia a A
Vca
Vab  + Z Z +  Ib Z +  B c C
Vbc b Ic
Using KCL,
line currents
Phase currents

27. Balanced 3-phase systems
Balanced - Connection Ia a A
Vca
Vab  + Z Z +  Ib Z +  B c C
Vbc b Ic
Alternatively, by transforming the  connections to the equivalent Y connections per phase equivalent circuit analysis can be performed.

28. Balanced 3-phase systems
Balanced -Y Connection Ia A a
Loop1 ZY
Vca
Vab  + +  N Ib +  ZY ZY c C
Vbc B b Ic
How to find Ia ?
Loop1
Since circuit is balanced, Ib = Ia-120o
Therefore

29. Balanced 3-phase systems
Balanced -Y Connection Ia A a ZY
Vca
Vab  + +  N Ib +  ZY ZY c C
Vbc B b Ic
How to find Ia ? (Alternative)
Transform the delta source connection to an equivalent Y and then perform the per phase circuit analysis