MMME2104
Design & Selection of Mining Equipment
Electrical Component
Three-Phase AC Systems
Lecture 2
6 August 2003
Lecture Outline
• Polyphase systems
• 3-phase systems
– 3-phase power flow
– 3-phase circuit arrangements
– Star and Delta connections
– Active, reactive and apparent power in 3phase systems
– Analysing 3-phase circuits
Poly-Phase Systems
• “many phases”
• Multiple phases produces a smoother
electrical power input/output
• Piston-engine analogy
• Trade-offs in the number of phases
– Simplicity
– Cost
– Efficiency
Three-Phase Systems
Electrical power is generated, transmitted and
distributed as 3-phase power. Why?
Three-phase systems are generally considered
to be the best trade-off:
• 3-phase motors, generators and transformers
are simpler, cheaper and more efficient
• 3-phase transmission lines can deliver more
power for a given weight and cost
• The voltage regulation of 3-phase
transmission lines is inherently better
Single-Phase System
a
N
400
S
1
Voltage (V), Current (A)
300
200
100
0
0.000
-100
Va1
0.005
0.010
-200
-300
-400
time (s)
Va1
0.015
0.020
Single-Phase System
a
R
S
300
Voltage (V), Current (A)
N
400
200
100
0
0.000
-100
Va1
0.005
0.010
0.015
0.020
Ia1
-200
-300
-400
1
time (s)
60000
50000
Ia1
Va1
Power (W)
40000
Pow er
30000
20000
10000
0
0.000
0.005
0.010
time (s)
0.015
0.020
Three-Phase System
a
R
N
S
c
1
3
2
b
R
R
Three-Phase System
3-Phase Voltages and Currents
400
voltage (V), current (A)
300
200
Va1
100
Ia1
0
0.000
-100
Vb2
0.005
0.010
0.015
0.020
Ib2
Vc3
Ic3
-200
-300
-400
time (s)
Three-Phase System
Vb2
Phasor Diagram
Ib2
120º
120º
120º
Ic3
Vc3
Ia1
Va1
Three-Phase System
3 Phase Pow ers
80000
70000
power (W)
60000
Phase a1
50000
Phase b2
40000
Phase c3
30000
Total
20000
10000
0
0.000
0.005
0.010
time (s)
0.015
0.020
Three-Phase System
• The power flow in an ideal 3-phase system is
constant
• This has inherent advantages for an electrical
power system:
–
–
–
–
Components are not oversized or under-utilised
Losses are minimised
Vibration is minimised
Mechanical components connected to the
electrical system (motors or generators) have
smooth input/output
Three-Phase System: 6-wire
a
Z
1
3
c
2
b
Z
Z
• Each phase is electrically independent
• Therefore, the 3 return conductors can be
combined into 1 to create a 3-phase, 4-wire
system
Three-Phase System: 4-wire
a
Z
n
c
neutral conductor
b
Z
Z
• Neutral conductor carries the sum of the 3
phase currents (ideally zero)
• If balanced, we can remove the neutral
conductor to get a 3-phase, 3-wire system
Three-Phase System: 3-wire
a
Z
n
c
b
Z
Z
• Loads (impedances) must be identical
• Otherwise unbalanced voltages are produced
across the 3 loads
Balanced Three-Phase System
a
Z
n
c
b
Z
Z
• A 3-phase system is said to be balanced when the
impedances (Z) of each phase are equal.
• (Under these circumstances, all voltages, currents
and powers “balance” each other.)
Three-Phase Systems
• 3-phase, 4-wire systems are widely used to
supply electric power to commercial and
industrial users
• 3-phase, 3-wire systems most commonly
occur in motor/generator drives
Star (Wye) and Delta Connections
a
a
n
c
b
c
• For balanced loads (3-wire system)
• Most applicable to transformers and machines
• Different voltage/current relationships
b
Star (Wye) Connection
-Van
Vca
30º
Vab
Vcn
30º
Van
Vbn
-Vbn
Line-to-neutral voltages:
VLn: Van, Vbn, Vcn
Line-to-line (line) voltages:
VL: Vab, Vbc, Vca
30º
Vbc
-Vcn
|VL| = 2 x |VLn| cos30º
= √3 |VLn|
Delta Connection
-Ibc
Ica
Branch currents:
IB: Iab, Ibc, Ica
Ic
30º
Line currents:
IL: Ia, Ib, Ic
Iab
Ib
-Iab
30º
30º
Ibc
Ia
-Ica
|IL|
= 2 x |IB| cos30º
= √3 |IB|
Three Phase Power:
Star (Wye) and Delta Connections
Star…
Power in each branch:
PB = VLn x IL
= 1/√3 x VL x IL
Delta…
Power in each branch:
PB = VL x IB
= 1/√3 x VL x IL
Total power:
Ptot = 3PB
= √3VLIL
Total power:
Ptot = 3PB
= √3VLIL
The same!
Three-Phase Systems:
active, reactive and apparent power
The relationship between active power P,
reactive power Q, and apparent power
S is the same for balanced 3-phase
circuits as for single-phase circuits.
Three-Phase Systems:
active, reactive and apparent power
S2 = P2 + Q2
cosφ = P / S
Where:
S = total 3-phase apparent power (VA)
P = total 3-phase active power (W)
Q = total 3-phase reactive power (VAr)
cosφ = power factor
φ = phase angle between line current and lineto-neutral voltage
Three-Phase Systems:
active, reactive and apparent power
Q. But how do we find φ for delta connections
where there is no line-to-neutral voltage?
A. For analysis purposes, we simply assume
that our circuit is star-connected. The maths
still works!
Analysing 3-Phase Circuits
A balanced 3-phase load may be considered to
be composed of three identical single-phase
loads.
Consequently, the easiest way to analyse such
circuits is to consider only one phase.