Download - Week 1 Chapter 1 Review Single Phase System
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
1/47
Chapter 1
Three Phase System
Week 1 - 4
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
2/47
objectives
understand the relationship between line and
phase value in star connection
This chapter will help you to:
Understand the generation of three phase emf
Familiar with the delta and star connection ofthree phases
Be able to calculate voltages and currents in the
star connection
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
3/47
objectives
understand the relationship between line and
phase value in delta connection
Understand power measurement in three phase
system
Be able to calculate power in a three phase
system
Be able to calculate voltages and currents in the
delta connection
This chapter will help you to: (cont)
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
4/47
Week 1 Contents
Review of single phase system
Introduction to 3 phase system Generation of three phase
system
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
5/47
Power Plant
Power station prevailing in many
Commonwealth countries and especially in
the United Kingdom.
conversion of other forms of energy,
like chemical energy, gravitational
potential energy or heat energy into
electrical energy
At the center of nearly all power stations is a
generator, a rotating machine that converts
mechanical energy into electrical energy by
creating relative motion between a magnetic
field and a conductor
ENERGY CENTRE
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
6/47
6
Due to the large amount of power
involved, transmission normally takes
place at high voltage (110 kV or above).
Electricity is usually transmitted over
long distance through overhead power
transmission lines.
Electrical Power Transmission
Electric power transmission, a process in the delivery of electricity to
consumers. Typically, power transmission is between the power plant and a
substation near a populated area
http://upload.wikimedia.org/wikipedia/commons/6/66/Electric_transmission_lines.jpg -
7/29/2019 Week 1 Chapter 1 Review Single Phase System
7/47
7
A typical distribution system
consist of:
Substations
Distribution Feeder CircuitsSwitches
Protective Equipment
Primary Circuits
Distribution Transformers
Secondaries and Services
Electrical Power Distribution
A distribution system consists of all the facilities and equipment
connecting a transmission system to the customer's equipment.
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
8/47
8
Basic AC GenerationIf a conductor is placed in a magnetic field, and either the
field or the conductor moves, an electromotive force (emf) is
induced in the conductor. This effect is called
electromagnetic induction.
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
9/47
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
10/47
v(t) = Vm sin wt
Review of Single-Phase System
Equation of alternating 1-phase system, in term ofSinusoidal voltage
where
Vm = the amplitude of the sinusoid
w= the angular frequency in radian/st = time
v(t)
Vm
-Vm
wt
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
11/47
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
12/47
v(t)
Vm
-Vm
t
w
2
TT
1
f
f2w
The angular frequency in radians per second
1 cycle
Generation in one cycle
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
13/47
Graphical Method to Finding the AverageVoltage
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
14/47
Analytic Method to Finding the Average Voltage
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
15/47
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
16/47
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
17/47
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
18/47
v(t) = Vm sin (wt + q)
v(t)
Vm
-Vm
wtq
V1= V
msin wt
V2= V
msin wt + q)
Reference waveform
A more general expression for the sinusoid
(as shown in the figure):
where q is the phase
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
19/47
A sinusoid can be expressed in eithersine orcosine form. When
comparing two sinusoids, it is expedient to express both as
either sine or cosine with positive amplitudes.
sin (t 180o) = - sin t
cos (t 180o) = - cos t
sin (t 90o) = cos t
cos (t 90o) = + sin t
We can transform a sinusoid from sine to cosine form or vice
versa using this relationship:
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
20/47
v(t) = Vm cos (t + )
Time domain Phasor domain
Time domain
qrmsV
VPhasor domain
)cos( qwtVm qmV
)sin( qwtVmo
m 90V q
)cos( qwtmI qmI
)sin( qwtmIo
m 90I q
Sinusoids are easily expressed in terms of phasor.
A phasor is a complex number that represents the
amplitude and phase of a sinusoid.
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
21/47
21
Impedance, Z have two component:
Real component : Resistance, R
Imaginary Component : Reactance, X
Z can be written as:
Z = R + jX ()
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
22/47
22
Impedance for resistance, R
For resistance, impedance Z is represent by
ZR = R
0
= R
Voltage is in phase with current
I VR
Ref
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
23/47
23
Impedance for inductor, L
For ZL :jXL
Voltage leading current with 90
VL
I
Ref
fLjLjZL
w
2
L-VI
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
24/47
24
Impedance for capacitor, C
ZC : - jXc
Current leading Voltage with 90
Cj
CjZc
w
w
/1
/
fC
CXC
w
2/1
/1
IC
VC
Ref
C-IV
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
25/47
25
Some applications
RMS Current and Voltage Problem
I0 = V0 / R P0 = I0 V0= 34 / 8 = 144.5 W
= 4.25 A = peak power
= peak current
Vrms = V0 / 1.414
= 34 / 1.414
= 24 V--------------------
Irms = Io / 1.414
= 4.25 / 1.414
= 3 A
Parallel RLC Circuits
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
26/47
26
Two Speakers in Parallel
1 / Rp = 1 / 4 + 1 / 12 Rp = 12 / 4 = 3
= 3 / 12 + 1 / 12 (Note: less than the least.)
Parallel RLC Circuits
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
27/47
Where v(t) = Vm cos (wt + qv)i(t) = Im cos (wt + qi)
)cos()cos()( ivmmivmm t2IV2
1IV
2
1t qqwqqp
Instantaneous and Average Power
The instantaneous power is the power at any instantof time.
p(t) = v(t) i(t)
Using the trigonometric identity, gives
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
28/47
The average power is the average of the
instantaneous power over one period.
T
dttpT
P0
)(1
)cos( ivmmIV2
1qqP
(t)
t
)cos( ivmmIV2
1qq
mmIV2
1
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
29/47
Where
)cos( ivP qq rmsrmsIV
2
V
V
m
rms
2
I
Im
rms
The effective value is the root mean square (rms) of
the periodic signal.
The average power in terms of the rms values is
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
30/47
The reactive poweris a measure of the energy
exchange between the source and the load reactivepart.
rmsrmsIVS
)sin( ivQ qq rmsrmsIV
Apparent Power, Reactive Power and
Power Factor
The apparent poweris the product of the rms
values of voltage and current.
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
31/47
Total Power
MVA
Real Power
MW
Reactive Power MVAr
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
32/47
The complex power:
)cos( ivS
PfactorPower qq
)( ivrmsrms IV
jQP
qq
The powerfactoris the cosine of the phase
difference between voltage and current.
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
33/47
Power types Formulas Unit
Average Power P = VeffIeffcosqP = Ieff
2 R
P = Veff2 /R
Watt
Reactive Power P = VeffIeffsinq
P = Ieff2 X
P = Veff2 /X
VAR
Apparent Power S = VeffIefS = I
eff
2 Z
S = (P2 + Q2)
VA
Complex Power S = V(I*) = S+/- q
S = P jQ
VA
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
34/47
Power Factor (p.f.) is the ratio of real power (kW) to apparent power(kVA) in a circuit
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
35/47
An alternating voltage has the
equation v=13.1 sin 314t; what are
the values of:a. r.m.s voltage;
b. Frequency;
c. The instantaneous voltage
when t = 2.5 ms
An alternating current of sinusoidal waveform has an r.m.s value of 10.0 A.
What are the peak values of this current over one cycle?
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
36/47
v(t)
Vm
-Vm
wt
Phasor
diagram
Which one is:
Vm = ?
Vinst = ?
q = ?
+V
-V
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
37/47
37
A three-phase system is superior economically and
advantage, and for an operating of view, to a single-
phase system. In a balanced three phase system thepower delivered to the load is constant at all times,
whereas in a single-phase system the power pulsates
with time.
Three-Phase System
In a three phase system the source consists of threesinusoidal voltages. For a balanced source, the three
sources have equal magnitudes and are phase
displaced from one another by 120 electrical degrees.
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
38/47
Advantages of 3- compared to 1- system
High efficiency
For same power at the transmission line,
less conductor and lighter Construction and maintenance, minimum
(cheaper)
Starting behavior and operation of 3-equipment better or more stable than 1-
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
39/47
39
Generation of Three-PhaseThree separate windings or coils with terminals R-R, Y-Y and B-B are
physically placed 120o apart around the stator.
Y
BY
B
Stator
Rotor
Y
R
B
R
R
N
S
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
40/47
40
It has 3 conductor loops
that is R (red), Y (yellow) and
B (blue). The conductor loop will
move in circle and then cut
off the magnetic flux.
It will produces the
electromagnetic force e.m.fin the conductor.
Maximum e.m.f is when the
conductor loop is 90 with
magnetic flux line.
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
41/47
41
v(t)
wt
vR
vY
vB
The instantaneous e.m.f. generated in phase R, Y and B:
vR= VRsin wtvY= VY sin (wt -120
o)
vB= VB sin (wt -240o)= VBsin (wt +120
o)
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
42/47
42
Phase sequences : RYB and RBY
120o
-120o
120o VR
VY
VB
w
o
)rms(RR0VV
o
)rms(YY120VV
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.
(a) RYB or positive sequence
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
43/47
43
(b) RBY or negative sequence
o
)rms(RR0VV
o
)rms(BB120VV
o
rmsY
ormsYY
V
V
120
240
)(
)(
V
VR leads VY, which in turn leads VB.This sequence is produced when the rotor rotates in
the clockwise direction.
V
120o
-120o
120o
VR
VB
Y
w
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
44/47
Simulation of current flow in 3 phase system
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
45/47
3 phase generator
http://localhost/var/www/apps/conversion/tmp/scratch_3/alternator1.swfhttp://localhost/var/www/apps/conversion/tmp/scratch_3/3phase.swf -
7/29/2019 Week 1 Chapter 1 Review Single Phase System
46/47
Second week continue
Thursday
September 20, 2012
15.00 15.50
Tutorial
16.00 16.50
-
7/29/2019 Week 1 Chapter 1 Review Single Phase System
47/47
THANK YOU