ch 8. three-phase systems (kolmivaihejärjestelmä) · • three phase generator produce more power...
TRANSCRIPT
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Anouar Belahcen
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Ch 8. Three-phase systems (kolmivaihejärjestelmä)
• Lecture outcomes (what you are supposed to learn):
– Generation of three-phase voltages
– Connection of three-phase circuits
– Wye-Delta transformation
– Power of three-phase connected loads
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• High power equipments are built as three-phase systems.
• Three-phase systems can produce rotating field without special control.
• Three phase generator produce more power than single phase one with thesame volume.
• Three-phase systems are more reliable. They can deliver power even if onephase fails.
Introduction
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Schematic structure of Power systems
Power plants
Load centers
SubstationsandTransformer
Transmission lines
Industrial and Residential loads
International links
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a
a 0 0.01 0.02 0.03 0.04 0.05 0.06-400-300
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Time (s)in
duce
d vo
ltage
(V)
ea
0 0.01 0.02 0.03 0.04 0.05 0.06-400
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Time (s)in
duce
d vo
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(V)
eaeb
0 0.01 0.02 0.03 0.04 0.05 0.06-400
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Time (s)in
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(V)
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Generation of three-phase voltages
NS
w=e nBl• Simple three-phase generator
tq w=
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Generation of three-phase voltages
NS
Z
Z
Z
´ max cos( )aa av e V tw= =
´ max cos( 120 )bb bv e V tw= = - °
´ max
max
cos( 240 )
cos( 120 )cc cv e V t
V t
ww
= = - °= + °
• 3 single-phase circuits at different phase angle!
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• The voltage of each phase are called phase voltages• The phase voltages are written in complex form
Generation of three-phase voltages
max 0 02
aa
VV V¢ = Ð ° = Ð °
max 120 1202
bb
VV V¢ = Ð- ° = Ð- °
max 120 1202
cc
VV V¢ = Ð ° = Ð °
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Connecting the 3-phase voltages
• The potential difference is known but not the potentials !
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Connecting the 3-phase voltages
Line-to-line voltage=
Pääjännitte
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• Only 3 wires are needed to connect the source and load
Connecting the source and load
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• Three similar terminal of each coil connected to the same point calledneutral or N
Wye connection (Y- tai tähtikytkentä)
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• For balanced symmetrical three phase system:
Wye connection (Y- tai tähtikytkentä)
an bn cn phV V V V= = =
0an phV V= Ð °
120bn phV V= Ð- °
120cn phV V= Ð °
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• Magnitude of line-to-line voltage is larger than the magnitude of phasevoltages by a factor of
• Line-to-line voltage leads by
Line-to-line voltages in Wye connection0an phV V= Ð °
120bn phV V= Ð- °
120cn phV V= Ð °
ab an bnV V V= -
0 120
3 30ab ph ph
ph
V V V
V
= Ð °- Ð- °
= Ð °
abV
anV 3
abV anV 30°
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Line-to-line voltages in Wye connection
bc bn cnV V V= -
120 120
3 90bc ph ph
ph
V V V
V
= Ð- °- Ð °
= Ð- °
ca cn anV V V= -
120 0
3 150ca ph ph
ph
V V V
V
= Ð °- Ð °
= Ð °
ab an bnV V V= -
0 120
3 30ab ph ph
ph
V V V
V
= Ð °- Ð- °
= Ð °
3ll phV V=
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• The entrance terminal of one coil is connected to the end terminal of thenext coil
Delta connection (kolmiokytkentä)
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• Absence of a neural point i.e. floating potentials• Phase voltages are identical with line-to-line voltages
Delta connection
aa abV V¢ =
bb bcV V¢ =
cc caV V¢ =
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• Residential loads are usually single phase loads (230 V)• Industrial and commercial loads are mostly three phases loads (400 V)
• Clustered residential areas are powered by three phases
• Single houses might be powered by single phase
• Neutral point is grounded to ensure that all loads are powered regardless offluctuations in current
Single and three phases loads
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• Load impedances connected to a common neutral point from one terminal
• The load is powered by a three phases source
Wye connected load
Connection
an bn cnZ Z Z Z= = =
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• Phase currents
• Equal magnitudes, 120 phase shifts
Wye connected load
( )ph phanaV VV
IZ Z Z
qq j
j
Ð= = = Ð -
Ð
( )( )
120120ph phbnb
V VVI
Z Z Z
qq j
j
Ð -= = = Ð - -
Ð
( )( )
120120ph phcnc
V VVI
Z Z Z
qq j
j
Ð += = = Ð - +
Ð
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• Neutral current
• If source and loads are balancedthe neutral current is zero
• In transmission this means noneed for a neutral line
Wye connected load
n a b cI I I I= + +
120 120 0n a a aI I I I= + Ð- + Ð =
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• Loads connected between two transmission lines• Voltage across the single load is the line-to-line voltage
• Balanced load and source balanced currents
Delta-connected load
ab a caI I I= +
bc b abI I I= +
ca c bcI I I= +
abab
VI
Z=
bcbc
VI
Z=
caca
VI
Z=
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• If we choose as reference
Delta-connected load
0abI I= Ð °
120bcI I= Ð- °
120caI I= Ð °
abI
3 30 3 30a abI I I= Ð- ° = Ð- °
3 150 3 30b bcI I I= Ð- ° = Ð- °
90 3 30c caI I I= Ð ° = Ð- °
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• In general circuits can be so that the source or the load or both areconnected in Y-, Delta-, or any combination
Circuits with mixed connections
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• Such circuits requires the load and source to be in the same connectionY-Delta transformation
Circuits with mixed connections
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• Consider the impedance seen by the source terminals
• Transformation valid in both directions
Y-Delta transformation
(2 ) 23 3ab
Z ZZ Z
ZD D
DD
= = 2ab YZ Z=
3YZ
Z D=
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• The power of a three phase load is the sum of the powers of each load(each phase)
• Phases related quantities are called phase quantities (phase current, phasevoltage, phase power)
Power of three phases system
cos( )ph ph phP V I q=
sin( )ph ph phQ V I q=
3 3 cos( )ph ph phP P V I q= =
3 3 sin( )ph ph phQ Q V I q= =
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• Phase current equal to line current• Phase voltage different
Power of Y-connected three phases load
3ll
ph
VV =3 3 cos( )
3 cos( )
ph ph ph
ll l
P P V I
V I
q
q
= =
=
3 3 sin( )
3 sin( )
ph ph ph
ll l
Q Q V I
V I
q
q
= =
=
ph lI I=
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• Phase voltage equal to line-to-line voltage• Phase current different
Power of Delta-connected load
3l
ph
II =
3 3 cos( )
3 cos( )
ph ph ph
ll l
P P V I
V I
q
q
= =
=
3 3 sin( )
3 sin( )
ph ph ph
ll l
Q Q V I
V I
q
q
= =
=
ph llV V=
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• Three coils shifted by 120 deg in space generate balanced three voltages• The coils can be connected in Y or Delta• Loads also can be connected in Y or Delta• Basic equations for single phase system holds also for three phases system
• In Y-connection
• In Delta-connection
Summary of the lecture
3 3 cos( )ph ll lP P V I q= =
3 3 sin( )ph ll lQ Q V I q= =
3ll
ph
VV =ph lI I=
3l
ph
II =ph llV V=