Transcript Slide 1

AC Power
1
AC Power
As in the case with DC power, the instantaneous electric
power in an AC circuit is given by P = VI, but these quantities
are continuously varying. Almost always the desired power in
an AC circuit is the average power, which is given by
Pavg = V I cos 
where  is the phase angle between the current and the
voltage and V and I are understood to be the effective or rms
values of the voltage and current. The term cos  is called
the "power factor" for the circuit.
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Instantaneous Power
As in DC circuits, the instantaneous electric power in an AC circuit is given by
P=VI where V and I are the instantaneous voltage and current.
Since
then the instantaneous power at any time t can be expressed as
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the power becomes:
Averaging this power over a complete cycle gives the average power.
Average Power
Normally the average power is the power of interest in AC circuits. Since the
expression for the instantaneous power is a continuously varying one with time,
the average must be obtained by integration. Averaging over one period T of the
sinusoidal function will give the average power. The second term in the power
expression above averages to zero since it is an odd function of t. The average of
the first term is given by
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Since the rms voltage and current are given by
and
the average power can be expressed as
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Average Power Integral
Finding the value of the average power for sinusoidal voltages involves the integral
The period T of the sinusoid is related to the angular frequency
and angle
by
Using these relationships, the integral above can be recast in the form:
Which can be shown using the trig identity:
which reduces the integral to the value 1/2 since the
second term on the right has an integral of zero over
the full period.
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RLC Series Circuit
The RLC series circuit is a very important example of a resonant circuit.
It has a minimum of impedance Z=R at the resonant frequency, and the
phase angle is equal to zero at resonance.
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Single-phase System
The Sinusoidal voltage
v(t) = Vm sin wt
where
Vm = the amplitude of the sinusoid
w = the angular frequency in radian/s
t = time
v(t)
Vm




wt
-Vm
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v(t)
Vm




t
-Vm
2
T
w
1
f 
T
w  2f
The angular frequency in radians per second
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Single-phase System
A more general expression for the sinusoid (as shown in
the figure):
v(t) = Vm sin (wt + q)
where q is the phase angle
v(t)
Vm
q
V1 = Vm sin wt




wt
-Vm
V2 = Vm sin wt + q)
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Single-phase System
A sinusoid can be expressed in either sine or cosine
form. When comparing two sinusoids, it is expedient to
express both as either sine or cosine with positive
amplitudes. We can transform a sinusoid from sine to
cosine form or vice versa using this relationship:
sin (ωt ± 180o) = - sin ωt
cos (ωt ± 180o) = - cos ωt
sin (ωt ± 90o) = ± cos ωt
cos (ωt ± 90o) = + sin ωt
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Single-phase System
Apparent Power, Reactive Power and Power Factor
The apparent power is the product of the rms values of
voltage and current.
S  VrmsIrms
The reactive power is a measure of the energy
exchange between the source and the load reactive part.
Q  VrmsIrms sin( qv  qi )
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Single-phase System
The power factor is the cosine of the phase difference
between voltage and current.
P
Power factor 
 cos( qv  qi )
S
The complex power:
 P  jQ
 Vrms I rms qv  qi
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Three-phase System
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Generation of Three-phase
In a three phase system the source consists of three
sinusoidal voltages. For a balanced source, the three
sources have equal magnitudes and are phase displaced
from one another by 120 electrical degrees.
A three-phase system is superior economically and
advantage, and for an operating of view, to a singlephase system. In a balanced three phase system the
power delivered to the load is constant at all times,
whereas in a single-phase system the power pulsates
with time.
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Generation of Three-phase
Suppose three similar loops of wire with terminals R-R’,
Y-Y’ and B-B’ are fixed to one another at angles of 120o
and rotating in a magnetic field.
R
B1
Y1
N
S
Y
B
R1
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Generation of Three-phase
v(t)
vR

vY

vB
wt
The instantaneous e.m.f. generated in phase R, Y and B:
vR = VR sin wt
vY = VY sin (wt -120o)
vB = VB sin (wt -240o) = VBsin (wt +120o)
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Generation of Three-phase
Phase sequences:
(a) RYB or positive sequence
VB
VR  VR ( rms) 0o
w
VY  VY( rms)   120o
120o
120o
VR
-120o
VB  VB ( rms)   240o
 VB ( rms) 120o
VY
VR leads VY, which in turn leads VB
This sequence is produced when the rotor rotates in
the counterclockwise direction
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Generation of Three-phase
(b) RBY or negative sequence
VY
VR  VR ( rms) 0o
w
VB  VB( rms)   120o
120o
120o
VR
-120o
VY  VY ( rms)   240o
 VY ( rms) 120o
VB
VR leads VB, which in turn leads VY
This sequence is produced when the rotor rotates in
the clockwise direction
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Star and Delta Connection
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Star Connection
Three wire system
R
ZR
ZY
Z
B
Y
B
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Four wire system
R
VRN
V BN
ZR
V YN
ZY
Z
B
Y
N
B
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Wye connection of Load
R
R
Z1
Y
Z1
Z2
Y
Load
Z3
B
B
N
N
Z2
Z3
Load
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Delta Connection
R
R
Y
Y
B
B
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Delta connection of load
R
Load
R
Zc
Z
c
Zb
Y
B
Za
Y
Zb
Za
B
Load
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Wye Connection
IR
R
I phase  I line
VRN
VRY
N
Vphase  Vline
V YN
IY
VBR
Y
VBN
VRN  Vphase 0
VYB
IB
B
# Reference: VRN
Line-to-neutral voltages:
VYN  Vphase   120
VBN  Vphase   240
# Positive sequence
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VRY  VRN  VYN
 Vphase 0  Vphase   120

 Vphase (cos0o  j sin0o )  (cos(120o )  j sin (120o )

IR
 3 Vphase  30
R
VRN
The two other can be
calculated similarly.
VRY
N
V YN
IY
VBR
Y
VBN
VYB
IB
B
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The line to line voltages
VRY  VRN  VYN
VYB  VYN  VBN
VBR  VBN  VBN
VRY  3 Vphase  30
VYB  3 Vphase   90
VBR  3 Vphase   210
 3 Vphase 150
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Delta Connection
R
V
V
RY
BR
Y
V
V
B
RY
V
Vphase  Vline
BR
I phase  I line
YB
Line-to-line currents:
V
YB
I RY  I phase 0
# Reference: IRY
I YB  I phase   120
# Positive sequence.
I BR  I phase   240
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I R  I RY  I BR
 I phase 0  I phase 120

 I phase (cos0o  j si n0o )  (cos120o  j si n120o

 3 I phase   30
The two other can be
calculated similarly.
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The line currents:
I R  I RY  I B R
I Y  I YB  I RY
I B  I B R  I YB
I R  3 I phase   30
I Y  3 I phase   150
I B  3 I phase   270
 3 I phase  90
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Vector diagram
• Phasor diagram is used to
visualize the system voltages
• Wye system has two type of
voltages: Line-to-neutral, and
line-to-line
• The line-to-neutral voltages are
shifted with 120 degrees
• The line-to-line voltage leads
the line to neutral voltage with
30 degrees
• The line-to-line voltage is times
the line-to-neutral voltage
VBR
VBN
VRY
30°
-120°
-VYN
VRN
VYN
VYB
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TNB SUPPLY SYSTEM
Voltage 3 phase, 50 Hz
The main transmission and substation network are:
- 275 kV
- 132 kV
- 66 kV
The distribution are:
- 33 kV
- 22 kV
- 11 kV
- 6.6 kV
- 415 volts
- 240 volts (single phase) drawn from 415 volts 3 phase
(phase voltage), between line (R, Y, B) and Neutral (N)
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SYSTEM
The low voltage system (415/240 V) is 3-phase four wire.
The low voltage system is a mixture of overhead lines and
under ground cables.
The high voltage and extra high voltage system is 3-phase three wire
Configuration. Overhead line and under ground cable system are used.
Supply Method (two types of premises)
1. Single consumer such as private dwelling house, workshop, factory, etc
a. Single phase, two wire, 240 V, up to 12 kVA max demand
b. Three phase, four wire, 415 V, up to 45 kVA max demand
c. Three phase, four wire, C. T. metered 415 V, up to 1,500 kVA max
demand
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2. Multi tenanted premises, such as high rises flats, commercial,
office blocks, etc
- Low Voltage
Three phase, four wire, C.T. metered 415 V, up to 1,500 kVA max
demand
- High Voltage and Extra High Voltage
a. Three phase, three wires, 6,600 and 11,000 V for load of 1, 500 kVA
max demand and above, whichever voltage is available
b. Three phase, three wires, 22,000 and 33,000 V for load of 5,000 kVA
max demand and above, whichever voltage is available
c. Three phase, three wires, 66,000 V, 132,000 V and 275,000 for
exceptionally large load of above 20 MVA max demand
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Standby Supply
Standby generator(s) to be used by the consumer in his premises, in
accordance with the relevant by-laws, may be provided by the consumer
The generator(s) shall remain a separate system from the TNB’s
Distribution system and should be certified and registered by
Suruhanjaya Tenaga (formerly JBE)
This may be used in place of the TNB’s supply source through a suitable,
Approved change over facility under emergency conditions.
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Beban
Berubah setiap masa, hari, minggu dan bulan.
Beban mempengaruhi penjanaan tenaga.
Penjanaan tenaga berdasarkan permintaan beban yang
lepas.
Lengkuk beban berubah dalam sehari.
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