chapter 12 three phase circuits
DESCRIPTION
Chapter 12 Three Phase Circuits. Chapter Objectives: Be familiar with different three-phase configurations and how to analyze them. Know the difference between balanced and unbalanced circuits Learn about power in a balanced three-phase system - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 12Three Phase Circuits
Huseyin BilgekulEeng224 Circuit Theory II
Department of Electrical and Electronic Engineering Eastern Mediterranean University
Chapter Objectives: Be familiar with different three-phase configurations and
how to analyze them. Know the difference between balanced and unbalanced
circuits Learn about power in a balanced three-phase system Know how to analyze unbalanced three-phase systems Be able to use PSpice to analyze three-phase circuits Apply what is learnt to three-phase measurement and
residential wiring
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Power in a Balanced System The total instantaneous power in a balanced three phase system is constant.
2 cos( ) 2 cos( 120 ) 2 cos( 120 )
2 cos( ) 2 cos( 120 ) 2 cos( 120 )
2 cos( )cos( ) cos( 120 )cos( 120 ) cos( 120 )co
AN p BN p CN p
a p b p b p
a b c AN a BN b CN c
p p
v V t v V t v V t
i I t i I t i I t
p p p p v i v i v i
p V I t t t t t
s( 120 )
1cos cos [cos( ) cos( )] Using the identity and simplif
The instantenous power is not function of time.
The total power behav
n2
e
yi g
3 cos p p
t
A B A B A B
p V I
s similar to DC power.
This result is true whether the load is Y or connected.
The average power per phase .3
cos 3
p p p
pp
pP I
P
V
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Power in a Balanced System
The complex power per phase is Sp. The total complex power for all phases is S.
p p
p p p p p
2p p p p
Complex power for each phas
3 cos
1 1= cos = sin
3 3
S V I
3 3 cos 3 cos
3 3 sin 3 sin
S=3S 3V
e
I 3
p p
p p p p p p p
a b c p p p L L
p p p L L
p
p V I
P p V I Q p V I S V I
P jQ
P P P P P V I V I
Q Q V I V I
I Z
p L
2p
p , , and are
Total
all rm
complex powe
s values, is the load impedance angl
3
3
r
eL
p
L L
V
Z
P jQ
I
V
V I
I
V
S
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Power in a Balanced System
Notice the values of Vp, VL, Ip, IL for different load connections.
2p2
p p p
p
p
p L, , and are all rms values, is the load impe
To
da
3S=3S 3V I 3
nce
al c
an
3
omplex ower
gle
p
L
pp
L L
V
VI Z
Z
P
V
V I
I
jQ
I
S
VLVL
VL
Vp Vp
VpIp
Ip Ip
VL
Vp
Ip
VL
VL Vp
Vp
Ip
Ip
Y connected load. Δ connected load.
3L p L pV V I I 3L p L pV V I I
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Power in a Balanced System
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Single versus Three phase systems Three phase systems uses lesser amount of wire than single phase systems for the same line voltage VL and same power delivered.
a) Single phase system b) Three phase system
2 2
'2 '2
Wire Material for Single phase 2( ) 2 2(2) 1.33
Wire Material for Three phase 3( ) 3 3
r l r
r l r
If same power loss is tolerated in both system, three-phase system use only 75% of materials of a single-phase system
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VL=840 V (Rms)
Capacitors for pf Correction
IL
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7365050.68A
3 3840
Without Pf Correction
L
L
SI
V
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Unbalanced Three Phase Systems An unbalanced system is due to unbalanced voltage sources or unbalanced load. In a unbalanced system the neutral current is NOT zero.
Unbalanced three phase Y connected load.
Line currents DO NOT add up to zero.
In= -(Ia+ Ib+ Ic) ≠ 0
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Three Phase Power Measurement Two-meter method for measuring three-phase power
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Residential Wiring
Single phase three-wire residential wiring