Faculty of Electrical Engineering Universiti Teknologi Malaysia
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Transcript of Faculty of Electrical Engineering Universiti Teknologi Malaysia
Faculty of Electrical EngineeringUniversiti Teknologi Malaysia
Mechanical and Electrical Systems SKAA 2032
Power Supply (AC and DC)
Alternating voltage and current
• Electricity is produced by generators at power station.
• Electricity is then distributed by a vast network of transmission lines called National Grid System.
• It is easier and cheaper to generate AC than DC.• It is more convenient to distribute AC than DC
since the voltage can be readily altered using transformer.
• Whenever DC is needed, devices called rectifiers are used for conversion.
Alternating voltage and current
Power socket
Rectifier
Generation of Single Phase
• An electric current can be induced in a circuit by a changing magnetic field – Faraday’s Law
• The direction of the induced current is such that the induced magnetic field always opposes the change in the flux – Len’z Law
• Direction of current for generator – Fleming’s right hand rule.
Single phase
• Single phase electricity is generated by rotating a single turn coil through a magnetic field.
• The shape of the waveform produced by a generator (i.e. the alternator) is in the form of sine wave.
• Wires used:– Live conductor (yellow)– Neutral conductor (blue)– Earth conductor (green) –connected from neutral via a
protective gear to earth
Single phase
Single phase system
A general expression for the sinusoid is given by: v(t) = Vm sin (wt + q)
whereVm is the amplitude or peak valueω is the angular frequency radian/s given by ω=2πftf is the frequency in hertz (Hz)t is the time in second (s)T is the period in second, given by T=1/f θ is the phase angle in degree
Single phase system
v(t)Vm
-Vm
t
w
2T
T1f
f2wThe angular frequency in radians/second
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:
cos ωt = sin (ωt + 90o)
sin ωt = cos (ωt - 90o)
Single phase system
Example 1.1
Find the amplitude, phase angle, angular frequency, period and frequency of the sinusoidal waveform
(a) v(t) = 12 cos (50t + 10o)
(b) v(t) = 5 sin (4πt - 60o)
(a) (12V, 10o, 50rads/sec, 0.126 sec., 7.937 Hz)
(a) (5V, -60o, 4π rads/sec, 0.5 sec., 2 Hz)
Single phase system
• Sinusoids are easily expressed in terms of phasors. • A phasor is a complex number that represents the
amplitude and phase of a sinusoid. v(t) = Vm cos (ωt + θ)
q mVV
Time domain
Phasor domain
Time domain Phasor domain)cos( qwtVm qmV
om 90V q)sin( qwtVm
)cos( qwtmI qmIo
m 90I q)sin( qwtmI
Single phase system
Instantaneous and Average Power• The instantaneous power is the power at any
instant of time: p(t) = v(t) i(t)
• Where v(t) = Vm cos (ωt + θv) i(t) = Im cos (ωt + θi)
• Using the trigonometric identity, gives )2cos(
21)cos(
21)( ivmmivmm tIVIVtp qqwqq
Single phase system
The average power is the average of the instantaneous power over one period.
T
0dtt
T1 )(pP
)cos( ivmmIV21
qqP
p(t)
t
)cos( ivmmIV21
mmIV21
Single phase system
• The effective value is the root mean square (rms) of the periodic signal.
• The average power in terms of the rms values is given by
Where
)cos( ivP qq rmsrmsIV
2V
V mrms
2I
I mrms
Single phase system
Example 1.2An ac voltage of a sinusoidal waveform has a peak value of 300 V. What is the rms value of this voltage?(212.1 V)
Example 1.3What is the peak voltage of 120 V rms?(169.7)
Single phase system
Example 1.4An alternating current of sinusoidal waveform has a r.m.s value of 10A. What are the peak values of this current over one cycle?
(14.14A & -14.14A)
Single phase system
Example 1.5An alternating voltage can be represented by v=141.4 sin 377t. Determine: (a) r.m.s. voltage (b) frequency (c) the instantaneous voltage when t = 3 ms
(100V, 60Hz, 127.8V)
Single phase system
Apparent Power, Reactive Power and Power Factor
The apparent power is the product of the rms values of voltage and current.
The reactive power is a measure of the energy exchange between the source and the load reactive part.
rmsrmsIVS
)sin( ivQ qq rmsrmsIV
Single phase system
The power factor is the cosine of the phase difference between voltage and current.
The complex power:
)cos( ivfactor Power qqSP
iv
jQPqq
rmsrms IV
Single phase system
rmsrmsIVS
)sin( ivQ qq rmsrmsIV
)cos( ivrmsrmsIVP qq True or active power:
Apparent power:
Watts (W)
reactive volt·amperes (var)
Reactive power:
S Q
Pθv–θi
volt·amperes (VA)
Three phase system
Three phase system
• A three-phase electricity is generated when three coils are placed 120° apart, and the whole rotated in a magnetic field.
• The result is three independent supplies of equal phase voltage - distinguished by 120° phase angle.
• The convention adopted to identify the phase voltages: R-red, Y-yellow, B-blue.
• The standard phase sequence is R, Y, B.
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 through a magnetic field.
R
R1
B
B1
Y
Y1
N S
Three phase system
• Three conductors (lines) to carry the three phase supply, colored red, yellow and blue.
• A fourth conductors called the neutral, connected through protective device to earth.
• The three phase system is usually connected using: – star connection (sources i.e. alternators)– delta connection (transformers, motors and other
loads)
Generation of Three-phase
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)
v(t)
wt
vR
vY vB
Generation of Three-phase
Phase sequences:(a) RYB or positive sequence
120o
-120o
120o VR
VY
VB
w
o)rms(YY 120VV
o)rms(RR 0VV
o)rms(B
o)rms(BB
120V
240VV
VR leads VY, which in turn leads VB.This sequence is produced when the rotor rotates in the counterclockwise direction.
Generation of Three-phase
(b) RBY or negative sequence
o)rms(BB 120VV
o)rms(RR 0VV
o)rms(Y
o)rms(YY
120V
240VV
120o
-120o
120o VR
VB
VY
w
VR leads VB, which in turn leads VY.This sequence is produced when the rotor rotates in the clockwise direction.
Star Connection
Three wire systemR
Y
B
ZR
Y B
Star Connection
Four wire system
VRN
VBN VYN
ZR
R
BN
Y
Star Connection of Load
Z1
Z3
Z2
R
B
Y
NLoad
Z3
R
Y
B
Load
N
Delta Connection
R
Y
B
Y
B
R
Delta Connection of Load
Zc
Za
Zb
R
B
Y
Load
Za
R
Y
B
Load
Star Connection
N
R
Y
B
VRY
VYB
VBR
VYN
VBN
VRN
IR
IY
IB
Phase voltages (line-to-neutral voltages):
240
120
0
phaseBN
phaseYN
phaseRN
V
V
V
V
V
V
# Reference: VRN
# Positive sequence.
Line voltages (line-to-line voltages):
RNBNBR
BNYNYB
YNRNRY
VVVVVVVVV
Star Connection
N
R
Y
B
VRY
VYB
VBR
VYN
VBN
VRN
IR
IY
IB
Line currents, Iline:
BYR III ,,
Phase currents are equal to their line currents:
linephase II
linephase
linephase
V
II
V
Star Connection – Line Voltages
N
R
Y
B
VRY
VYB
VBR
VYN
VBN
VRN
IR
IY
IB
303
120j1200j0
1200
seph
oooophase
phasephase
YNRNRY
aV
V
VVVVV
)sin()(cos()sin(cos
The two other can be calculated using similar method.
Star Connection - Line voltages
RNBNBR VVV
1503
2103
903
303
phase
phaseBR
phaseYB
phaseRY
V
VV
VV
VV
BNYNYB VVV
YNRNRY VVV
Star connection - Vector diagram
30°
-120°
VBR VRY
VYB
VYN
VRN
VBN
-VYN
• Phasor diagram is used to visualize the system voltages• Star system has two type of voltages: Line-to-neutral, and line-to-line.• The line-to-neutral voltages are shifted with 120o
• The line-to-line voltage leads the line to neutral voltage with 30o
• The line-to-line voltage is times the line-to-neutral voltage
Star connection - Distribution
Typical distribution voltage of 415/240V, 3 phase 4 wires system
Delta Connection
VRY
VBR
VYB
VRY
R
Y
BV
YB
VBR
Phase voltages are equal to the line voltages# Reference: IRY
# Positive sequence. linephase VV
Delta Connection
Phase currents:
240II
120II
0II
phaseBR
phaseYB
phaseRY
linephase
linephase
II
VV
VRY
VBR
VYB
VRY
R
Y
B
VYB
VBR
R
YB
Delta Connection – Line Currents
30I3
120j1200j0I
120I0IIII
seph
oooophase
phasephase
BRRYR
a
sin(cos)sin(cos
The two other can be calculated using similar method.
Delta Connection – Line Currents
BRRYR III
RYYBY III
YBBRB III
90I3
270I3I
1503I
30I3I
phase
phaseB
phaseY
phaseR
V
Delta Connection – Vector Diagram
-30°
120°
IY I R
IB
I YB
IRY
I BR
-I BR
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)
TNB Supply 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 demandb. Three phase, four wire, 415 V, up to 45 kVA max demandc. Three phase, four wire, C. T. metered 415 V, up to 1,500 kVA max demand
TNB Supply System2. Multi tenanted premises, such as high rises flats, commercial, office blocks, etc
- Low 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
Three phase, four wire, C.T. metered 415 V, up to 1,500 kVA maxdemand
- High Voltage and Extra High Voltage
Standby Supply
• Standby generator(s) may be used by the applicant at their premises, subject to compliance with the relevant laws.
• The generators shall remain a separate system from TNB distribution system and the applicant shall declare to TNB on the safe installation of the generator(s).
• This may be used in place of TNB’s supply source through a suitable, approved changeover facility.
• The Energy Commission and other relevant authorities govern the usage of generators and standby supply.
• This may be used in place of the TNB’s supply source through a suitable, approved change over facility under emergency conditions.