AC CIRCUIT
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Transcript of AC CIRCUIT
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Vishwakarma government engineering college
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THREE-PHASE POWER CIRCUITS
Prepared by: • Meet Patel 140170119056• Sindhi Parth 140170119057• Soni Kunjan 140170119058• Thakor Chetan 140170119059• Thakor Milan 140170119060
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INTRODUCTION
Almost all electric power generation and most of the power transmission in the world is in the form of three-phase AC circuits. A three-phase AC system consists of three-phase generators, transmission lines, and loads.
There are two major advantages of three-phase systems over a single-phase system:1) More power per kilogram of metal form a three-phase
machine;2) Power delivered to a three-phase load is constant at all
time, instead of pulsing as it does in a single-phase system.
The first three-phase electrical system was patented in 1882 by John Hopkinson - British physicist, electrical engineer, Fellow of the Royal Society.
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1. GENERATION OF THREE-PHASE VOLTAGES AND CURRENTS
A three-phase generator consists of three single-phase generators with voltages of equal amplitudes and phase differences of 1200.
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Each of three-phase generators can be connected to one of three identical loads.
This way the system would consist of three single-phase circuits differing in phase angle by 1200.
The current flowing to each load can be found as
VIZ
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1. Generation of three-phase voltages and currents
Therefore, the currents flowing in each phase are
0
0
0
0
120120
240240
A
B
A
VI I
Z
VI I
Z
VI I
Z
(3.5.1)
(3.5.2)
(3.5.3)
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We can connect the negative (ground) ends of the three single-phase generators and loads together, so they share the common return line (neutral).
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The current flowing through a neutral can be found as0 0
0 0 0 0
0 0 0 0
120 240
cos( ) sin( ) cos( 120 ) sin( 120 ) cos( 240 ) sin( 240 )
cos( ) cos( 120 ) cos( 240 ) sin( ) sin( 120 ) sin( 240 )
cos(
N A B CI I I I I I I
I jI I jI I jI
I jI
I
0 0 0 0
0 0 0 0
) cos( )cos(120 ) sin( )sin(120 ) cos( )cos(240 ) sin( )sin(240 )
sin( ) sin( )cos(120 ) cos( )sin(120 ) sin( )cos(240 ) cos( )sin(240 )jI
1 3 1 3cos( ) cos( ) sin( ) cos( ) sin( )
2 2 2 2
1 3 1 3sin( ) sin( ) cos( ) sin( ) cos( )
2 2 2 2
0
NI I
jI
Which is:
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As long as the three loads are equal, the return current in the neutral is zero!
Such three-phase power systems (equal magnitude, phase differences of 1200, identical loads) are called balanced.
In a balanced system, the neutral is unnecessary!
Phase Sequence is the order in which the voltages in the individual phases peak.
abc acb
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VOLTAGES AND CURRENTS
There are two types of connections in three-phase circuits: Y and .
Each generator and each load can be either Y- or -connected. Any number of Y- and -connected elements may be mixed in a power system.
Phase quantities - voltages and currents in a given phase.Line quantities – voltages between the lines and currents in the lines connected to the generators.
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VOLTAGES AND CURRENTS
1. Y-connection
Assuming a resistive load…
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VOLTAGES AND CURRENTS
1. Y-connection (cont)
0
0
0
0
120
240
an
bn
cn
V V
V V
V V
0
0
0
0
120
240
a
b
c
I I
I I
I I
Since we assume a resistive load:
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VOLTAGES AND CURRENTS
1. Y-connection (cont 2)
The current in any line is the same as the current in the corresponding phase.
LI I
Voltages are:
0
0
0 1 3 3 30 120
2 2 2 2
3 13
2 2303
aab bV V V V V V jV V j V
j V
V
V
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Voltages and currents
1. Y-connection (cont 3)
3LLV V
Magnitudes of the line-to-line voltages and the line-to-neutral voltages are related as:
In addition, the line voltages are shifted by 300 with respect to the phase voltages.
In a connection with abc sequence, the voltage of a line leads the phase voltage.
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Voltages and currents
1. -connection
0
0
0
0
120
240
ab
bc
ca
V V
V V
V V
0
0
0
0
120
240
ab
bc
ca
I I
I I
I I
assuming a resistive load:
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VOLTAGES AND CURRENTS
1. -connection (cont)
LLV V
The currents are:
0 0
0
1 30 240
2 2
3 3 3 13
2 2 2 23 30
ab caa I I I I I II
I
j I
I j I I j
3LI IThe magnitudes:
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VOLTAGES AND CURRENTS
For the connections with the abc phase sequences, the current of a line lags the corresponding phase current by 300 (see Figure below).
For the connections with the acb phase sequences, the line current leads the corresponding phase current by 300.
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POWER RELATIONSHIPS
The instantaneous power is:
( ) ( ) ( )p t v t i t
Therefore, the instantaneous power supplied to each phase is:
0 0
0 0
( ) ( ) ( ) 2 sin( )sin( )
( ) ( ) ( ) 2 sin( 120 )sin( 120 )
( ) ( ) ( ) 2 sin( 240 )sin( 240 )
a an a
b bn b
c cn c
p t v t i t VI t t
p t v t i t VI t t
p t v t i t VI t t
Since
1sin sin cos( ) cos( )
2
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POWER RELATIONSHIPS
Therefore
0
0
( ) cos cos(2 )
( ) cos cos(2 240 )
( ) cos cos(2 480 )
a
b
c
p t VI t
p t VI t
p t VI t
The total power on the load
( ) ( )( ) 3 cos( )tot a b cp t p tp t Vp t I
The pulsing components cancel each other because of 1200 phase shifts.
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Power relationships
The instantaneous power in phases.
The total power supplied to the load is constant.
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Power relationships
Phase quantities in each phase of a Y- or -connection.
23 cos 3 cosP V I I Z
23 sin 3 sinQ V I I Z
23 3S V I I Z
Real
Reactive
Apparent
Note: these equations are valid for balanced loads only.
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Power relationships
Line quantities: Y-connection.
Power consumed by a load: 3 cosP V I
Since for this load 3L LLI I and V V
Therefore: 3 cos3LL
L
VP I
Finally: 3 cosLL LP V I
Note: these equations are valid for balanced loads only.
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Power relationships
Line quantities: -connection.
Power consumed by a load: 3 cosP V I
Since for this load 3L LLI I and V V
Note: these equations were derived for a balanced load.
Therefore: 3 cos3L
LL
IP V
Finally: 3 cosLL LP V I
Same as for a Y-connected load!
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Power relationships
Line quantities: Y- and -connection.
3 sinLL LQ V I
3 LL LS V I
Reactive power
Apparent power
Note: is the angle between the phase voltage and the phase current – the impedance angle.
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