Transcript EE212 Passive AC Circuits - University of Saskatchewan

EE212 Passive AC Circuits
Lecture Notes 5a
Three Phase Systems
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Three Phase Systems
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Three Phase Systems
Bulk power generation and transmission systems are three-phase
(3-f) systems. Generation and transmission of electrical power are
more efficient in 3-f systems than in 1-f systems.
Generation:
 steady power (1-f power is fluctuating)
 more efficient conversion of mechanical power to electrical
power (3 times power with additional armature windings and
slightly more torque)
Transmission:
 More efficient transmission of power (steady power)
 less conducting material required to transmit power (delta
transmission – no return conductor)
 3-f transformers are more efficient
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Single Phase Power Fluctuates with Time
v(t) = Vm sin wt volts
i(t) = Im sin(wt-θ) amperes
i(t)
v(t)
Instantaneous Power, p(t) = v(t) x i(t)
p(t) = Vm sin wt . Im sin(wt-θ)
p(t) =
2SinA.SinB = Cos(A-B) - Cos(A+B)
Vm I m
V I
cos θ – m m cos(2wt-θ)
2
2
1st term is constant (equal to the
average or real power)
2nd term is sinusoidal at twice the
excitation frequency.
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Three Phase Systems
Three phase power does not vary with time.
Consumption: 3-f machines start and run more efficiently.
Industrial loads, larger motors require 3- f supply.
Most lighting loads, heating loads and small motors require 1-f
supply.
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1-f Power Generation:
Vm
N
0
0
90
180
270
360
S
-Vm
3-f Power Generation:
Phase Sequence is
a-b-c
Phase Sequence:
the order in which the
voltages of the individual
phases reach their
maximum values
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Voltages in the three phases (1200 out of phase):
Phase a 
Phase b 
Phase c 
va = Vm sin wt
vb = Vm sin (wt – 1200)
vc = Vm sin (wt – 2400) = Vm sin (wt + 1200)
In Phasor Form,
Va =
Vc
Vm 0
/0
2
Vb =
Vm /-1200
2
Vc =
Vm /1200
2
1200
Va
-1200
Vb
3 Phases: a-b-c, R-Y-B, L1-L2-L3
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Types of Three Phase Systems
Balanced Systems:
- 3 phases (V & I) are equal in magnitude and 1200 out of
phase
Unbalanced Systems:
-3 phases (V or I) are unequal in magnitude
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Types of Three Phase Systems
(continued)
Three Phase Systems are connected either in:
- Y (wye or star) connection (3 phase 3 wire, or 3 phase 4 wire)
- D (delta) connection
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Line and Phase Parameters
D (delta) connection
Y (wye or star) connection
(3 phase 3 or 4 wire)
Phase parameters usually not easily accessible
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Balanced Y System
B
A
a
b
Za
n
Zc
C
Zb
Phase voltages, Vp:
|Van| = |Vbn| = |Vcn|
Phase currents, Ip:
|I an| = |I bn| = |I cn|
c
Phase sequence a-b-c
Vab = Van + Vnb = Van – Vbn
Vca
Vcn
Vab
-Vbn
300
Van
Vbn
Vbc
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Balanced D System
a
A
Zab
Zca
C
c
Zbc
b
Phase voltages, Vp:
|Vab| = |Vbc| = |Vca|
Line voltages, VL:
|Vab| = |Vbc| = |Vca|
Phase currents, Ip:
|I ab| = |I bc| = |I ca|
Line currents, IL:
|I a| = |I b| = |I c|
B
Ic
Phase sequence a-b-c
I a = Iab + Iac = Iab - Ica
Ica
From phasor diagram:
cos 300 = (½|Ia|) / |Iab|= 3/2
i.e. |Ia| = 3 |Iab| and Ia lags Iab by 300
Vline = Vphase
|Iline| = 3 |Iphase|
300
Ib
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Ibc
-Ica
Iab
Ia
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Balanced 3-Phase Systems
Y  |VL| = 3 |Vph|, IL = Iph,
D  VL = Vph,
|IL| = 3 |Iph|,
Vab(line) leads Van(ph) by 300
Ia(line) lags Iab(ph) by 300
Power Factor of a 3-f load  cos 
where,  is the angle between the phase current and the phase voltage
3-phase power = 3 x Per phase power
P (3- f)
= 3 |Vph|.|Iph|. cos 
= 3.|VL|.|IL|. cos 
Q (3- f) = 3 |Vph|.|Iph|.sin  = 3.|VL|. |IL|. sin 
S (3- f) = 3 |Vph|.|Iph|
= 3.|VL|. |IL|)
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