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1
Ch 8. Three-phase systems
• 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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Ch 8. Three-phase systems, Study notes of Electrical and Electronics Engineering
Three-phase systems can produce rotating field without special control. • Three phase generator produce more power than single phase one with the same volume. • ...
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Anouar Belahcen
Ch 8. Three-phase systems
• 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 the
same volume.
• Three-phase systems are more reliable. They can deliver power even if one
phase fails.
Introduction
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a
a -400 0 0.01 0.02 0.03 0.04 0.05 0.
0
100
200
300
400
Time (s)
induced voltage (V)
ea
-400 0 0.01 0.02 0.03 0.04 0.05 0.
0
100
200
300
400
Time (s)
induced voltage (V)
e ea b
-400 0 0.01 0.02 0.03 0.04 0.05 0.
0
100
200
300
400
Time (s)
induced voltage (V)
e ea ebc
Generation of three-phase voltages
(kolmivaihejärjestelmä)
S N
• Simple three-phase generator e^ < nBl^ ϖ
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Generation of three-phase voltages
N S ݁
Z
Z
Z
vaa (^) ´ < ea <Vmax cos( ϖ t)
vbb (^) ´ < eb < Vmax cos( ϖ t, 120 )↓
´ max max
cos( 240 ) cc c cos( 120 ) v e V t V t
ϖ ϖ
• 3 single-phase circuits at different phase angle!
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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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• Three similar terminal of each coil connected to the same point called
neutral or N
Wye connection (Y- tai tähtikytkentä)
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• For balanced symmetrical three phase system:
Wye connection (Y- tai tähtikytkentä)
V an < Vbn < Vcn <Vph
Van < Vph∉ ↓ 0 Vbn < Vph∉ , 120 ↓ Vcn < Vph∉ 120 ↓
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Line-to-line voltages in Wye connection
V bc < Vbn ,Vcn 120 120 3 90
bc ph ph ph
V V V
V
V ca < Vcn ,Van 120 0 3 150
ca ph ph ph
V V V
V
V ab < Van ,Vbn 0 120 3 30
ab ph ph ph
V V V
V
Vll < 3 Vph
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• The entrance terminal of one coil is connected to the end terminal of the
next coil
Delta connection (kolmiokytkentä)
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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 of
fluctuations 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
Z an < Zbn < Zcn <Z
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• Neutral current
• If source and loads are balanced
the neutral current is zero
• In transmission this means no
need for a neutral line
Wye connected load
I n < Ia ∗ I b ∗Ic
I n < I a ∗ I a ∉ , 120 ∗ Ia∉ 120 < 0
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