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Polyphase Systems
Introduction
An ac generator designed to develop a single sinusoidal voltage for each rotation of the shaft (rotor) is referred to as a single-phase ac generator. If the number of coils on the rotor is
increase in a specified manner, the result is a Polyphase ac generator, which develops more
than one ac phase voltage per rotation of the rotor.
In general, three-phase systems are preferred over single-phase systems for the transmission of
power for many reasons, including the following:
- Thinner conductor can be used to transmit the same kVA at the same voltage, which reduces the amount of copper required (typically about 25% less) and in turn reduces construction maintenance costs.
- The lighter lines are easier to install, and the supporting structure can be less massive and farther apart.
- Three-phase equipment and motors have preferred running and starting characteristics compared to single-phase systems because of a more even flow of power to the transducer than can be delivered with a single-phase supply.
- In general, larger motors are three phase because they are essentially self-starting and do not require a special design or additional starting circuitry.
e AN Em ( AN )sin t
sin ( 120 )
0 e (^) BN Em ( BN ) t
sin ( 240 )
0
eCN Em ( CN ) t
0 EAN Erms ( AN ) 0
0 EBN Erms ( BN ) 120
0 ECN Erms ( CN ) 240
EAN EBN ECN 0
cos( 30 )
2 0 AN
AB
E
E
2
3
2
AN
AB
E
E
E (^) AB 3 E AN
E (^) AB 3 Erms ( AN )( j
0 0 ( )
0 EAB 3 Erms ( AN ) 30 EAB 3 Erms AN 0 30
………………………………………………………………………………………………
EBC ECN E BN
E BC EBN E CN
0 0 EBC Erms ( BN ) 120 Erms ( CN ) 240
(cos 120 sin 120 ) (cos 240 sin 240 )
0 0 ( )
0 0 E (^) BC Erms ( BN ) j ErmsCN j
( )(^ ( )
E (^) BC ErmsBN j ErmsCN j
( )(^ ( )
E (^) BC ErmsBN j ErmsBN j
[ Erms (^) ( BN ) Erms ( CN ) ]
E (^) BC Erms ( BN )( j
E (^) BC 3 Erms ( BN )( j )
0 EBC 3 Erms ( BN ) 90
0 0 ( )
0 EBC 3 Erms ( BN ) 90 EBC 3 ErmsBN 120 30
………………………………………………………………………………………………
ECA EAN E CN
ECA ECN E AN
0 0 ECA Erms ( CN ) 240 Erms ( AN ) 0
0 ( )
0 0 ECA Erms ( CN )(cos 240 j sin 240 ) Erms AN 0
( ) ) ( ) 2
3
2
1 ECA ErmsCN ( j Erms AN
) 2
3
2
3 E (^) CA Erms ( CN )( j
[ Erms (^) ( AN ) Erms ( CN ) ]
) 2
1
2
3 E (^) CA 3 Erms ( CN )( j
0 0 ( )
0 ECA 3 Erms ( CN ) 210 ECA 3 ErmsCN 240 30
………………………………………………………………………………………………
0 EAB 3 Erms ( AN ) 30
0 EAB Erms ( AB ) 30
Erms (^) ( AB ) 3 Erms ( AN )
2 sin( 30 ) sin( 30 )
0 ( )
0 e (^) AB Erms ( AB ) t EmAB t
………………………………………………………………………………………………
0 EBC 3 Erms ( BN ) 90
0 EBC Erms ( BC ) 90
Erms (^) ( BC ) 3 Erms ( BN )
2 sin( 90 ) sin( 90 )
0 ( )
0 e (^) BC Erms ( BC ) t EmBC t
………………………………………………………………………………………………
0 ECA 3 Erms ( CN ) 210
0 ECA Erms ( CA ) 210
E (^) rms ( CA ) 3 Erms ( CN )
2 sin( 210 ) sin( 210 )
0 ( )
0 e (^) CA Erms ( CA ) t EmCA t
……………………………………………………………………………………………....
Line Voltages (ABC Sequence)
0 ( )
0 E (^) AB Erms ( AB ) reference
0 EBC Erms ( BC ) 120
0 ECA Erms ( CA ) 240
Determining the phase sequence from the line voltages of a three-phase generator
ACB Phase Sequence (Y-Connected Generator)
Phase Voltages (ACB Sequence)
0 ( )
0 E (^) AN Erms ( AN ) reference
0 ECN Erms ( CN ) 120
0 EBN Erms ( BN ) 240
Determining the phase sequence from the phase voltages of a three-phase generator
Line Voltages (ACB Sequence)
0 ( )
0 E (^) AB Erms ( AB ) reference
0 ECA Erms ( CA ) 120
0 EBC Erms ( BC ) 240
The ^ -Connected Generator
Phase Sequence ABC
E AB EAN and eAN 2 EAN sin t
2 sin( 120 )
0
E BC EBN and eBN EBN t
2 sin( 240 )
0
E CA ECN and eCN ECN t
EL E g
I (^) BA IAa I AC
I (^) Aa IBA I AC
0 0 IAa Irms ( BA ) 0 Irms ( AC ) 240
(cos 240 sin 240 )
0 0 I (^) Aa Irms ( BA ) Irms ( AC ) j
I (^) Aa Irms BA Irms AC j
I (^) Aa Irms ( BA ) Irms ( BA )( j
[ I (^) rms ( BA ) Irms ( AC ) ]
I (^) Aa Irms ( BA )( j
I (^) Aa 3 Irms ( BA )( j
0 0 ( )
0 IAa 3 Erms ( BA ) 30 IAa 3 IrmsBA 0 30
………………………………………………………………………………………………
I (^) CB IBb I BA
I (^) Bb ICB I BA
0 0 IBb Irms ( CB ) 120 Irms ( BA ) 0
( )
0 0 I (^) Bb Irms ( CB )(cos 120 j sin 120 ) IrmsBA
I (^) Bb IrmsCB ( j IrmsBA
I (^) Bb IrmsCB ( j IrmsCB
[ I (^) rms ( CB ) Irms ( BA ) ]
I (^) Bb Irms ( CB )( j
I (^) Bb 3 Irms ( CB )( j
0 0 ( )
0 IBb 3 Irms ( CB ) 150 IBb 3 IrmsCb 120 30
………………………………………………………………………………………………
I (^) AC ICc I CB
I (^) Cc IAC I CB
0 ICc 3 Irms ( AC ) 270
0 ICc Irms ( Cc ) 270
I (^) rms ( Cc ) 3 Irms ( AC )
2 sin( 270 ) sin( 270 )
0 ( )
0 i (^) Cc Irms ( Cc ) t ImCc t
…………………………………………………………………………………………....
cos( 30 ) 2 0 BA
Aa
I
I
2
3
2
BA
Aa
I
I
I (^) Aa 3 I BA
0 0 ( )
0 EAB 3 Erms ( AN ) 30 EAB 3 Erms AN 0 30
…………………………………………………………………………………………………….
EBC ECN E BN
E BC EBN E CN
0 0 EBC Erms ( BN ) 240 Erms ( CN ) 120
(cos 240 sin 240 ) (cos 120 sin 120 )
0 0 ( )
0 0 E (^) BC Erms ( BN ) j ErmsCN j
E (^) BC Erms ( BN )( j Erms ( CN ) j
E (^) BC Erms ( BN )( j Erms ( BN ) j
[ Erms (^) ( BN ) Erms ( CN ) ]
E (^) BC Erms ( BN )( j
E (^) BC 3 Erms ( BN )( j )
0 EBC 3 Erms ( BN ) 270
0 0 ( )
0 EBC 3 Erms ( BN ) 270 EBC 3 ErmsBN 240 30
………………………………………………………………………………………………
ECA EAN E CN
ECA ECN E AN
0 0 ECA Erms ( CN ) 120 Erms ( AN ) 0
0 ( )
0 0 ECA Erms ( CN )(cos 120 j sin 120 ) Erms AN 0
( ) ) ( ) 2
3
2
1 E (^) CA ErmsCN ( j Erms AN
) 2
3
2
3 E (^) CA Erms ( CN )( j
[ Erms (^) ( AN ) Erms ( CN ) ]
) 2
1
2
3 E (^) CA 3 Erms ( CN )( j
0 0 ( )
0 ECA 3 Erms ( CN ) 150 ECA 3 ErmsCN 120 30
………………………………………………………………………………………………
ACB Phase sequence
I (^) BA IAa I AC
I (^) Aa IBA I AC
0 0 IAa Irms ( BA ) 0 Irms ( AC ) 120
(cos 120 sin 120 )
0 0 I (^) Aa Irms ( BA ) Irms ( AC ) j
I (^) Aa Irms ( BA ) Irms ( AC )( j
I (^) Aa Irms ( BA ) Irms ( BA )( j
[ I (^) rms ( BA ) Irms ( AC ) ]
I (^) Aa Irms ( BA )( j
I (^) Aa 3 Irms ( BA )( j
0 0 ( )
0 IAa 3 Erms ( BA ) 30 IAa 3 IrmsBA 0 30
………………………………………………………………………………………………
