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Three-Phase AC Systems
Lecture 26 August 2003
MMME2104Design & Selection of Mining Equipment
Electrical Component
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 3-
phase 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 SystemsElectrical 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
N
S
a
1
Va1
-400
-300
-200
-100
0
100
200
300
400
0.000 0.005 0.010 0.015 0.020
time (s)
Volta
ge (V
), C
urre
nt (A
)
Va1
Single-Phase System
N
S
a
1
Va1
R
0
10000
20000
30000
40000
50000
60000
0.000 0.005 0.010 0.015 0.020
time (s)
Pow
er (W
)
Pow er
-400
-300
-200
-100
0
100
200
300
400
0.000 0.005 0.010 0.015 0.020
time (s)
Volta
ge (V
), C
urre
nt (A
)
Va1
Ia1
Ia1
Three-Phase System
N
S
a
2
31
bc RR
R
Three-Phase System3-Phase Voltages and Currents
-400
-300
-200
-100
0
100
200
300
400
0.000 0.005 0.010 0.015 0.020
time (s)
volta
ge (V
), cu
rren
t (A) Va1
Ia1
Vb2
Ib2
Vc3
Ic3
Three-Phase System
Va1
Ib2
Vb2
Vc3
Ic3
Ia1
Phasor Diagram
120º
120º
120º
Three-Phase System3 Phase Pow ers
0
10000
20000
30000
40000
50000
60000
70000
80000
0.000 0.005 0.010 0.015 0.020
time (s)
pow
er (W
) Phase a1
Phase b2
Phase c3
Total
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
• Each phase is electrically independent• Therefore, the 3 return conductors can be
combined into 1 to create a 3-phase, 4-wire system
a
2
31
bc ZZ
Z
Three-Phase System: 4-wire
• 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
a
n
bc ZZ
Z
neutral conductor
Three-Phase System: 3-wire
• Loads (impedances) must be identical• Otherwise unbalanced voltages are produced
across the 3 loads
a
n
bc ZZ
Z
Balanced Three-Phase System
• 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.)
a
n
bc ZZ
Z
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
• For balanced loads (3-wire system)• Most applicable to transformers and machines• Different voltage/current relationships
a
n
bc
a
bc
Star (Wye) Connection
Line-to-neutral voltages:VLn: Van, Vbn, Vcn
Line-to-line (line) voltages:VL: Vab, Vbc, Vca
|VL| = 2 x |VLn| cos30º= √3 |VLn|
Van
Vcn
Vbn
-Vbn
-Vcn
-Van
Vca
Vab
Vbc
30º
30º
30º
Delta Connection
Branch currents:IB: Iab, Ibc, Ica
Line currents:IL: Ia, Ib, Ic
|IL| = 2 x |IB| cos30º= √3 |IB|
Iab
Ica
Ibc
-Ica
-Iab
-Ibc
Ic
Ia
Ib
30º
30º
30º
Three Phase Power: Star (Wye) and Delta Connections
Star…Power in each branch:PB = VLn x IL
= 1/√3 x VL x IL
Total power:Ptot = 3PB
= √3VLIL
Delta…Power in each branch:PB = VL x IB
= 1/√3 x VL x IL
Total power:Ptot = 3PB
= √3VLILThe 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 / SWhere:S = total 3-phase apparent power (VA)P = total 3-phase active power (W)Q = total 3-phase reactive power (VAr)cosφ = power factorφ = phase angle between line current and line-
to-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.