week 1 chapter 1 review single phase system

7/29/2019 Week 1 Chapter 1 Review Single Phase System

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Chapter 1

Three Phase System

Week 1 - 4


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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


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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)


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Week 1 Contents

Review of single phase system

Introduction to 3 phase system Generation of three phase

system


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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


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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


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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.


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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.


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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


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v(t)

Vm

-Vm

t

w

2

TT

1

f

f2w

The angular frequency in radians per second

1 cycle

Generation in one cycle


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Graphical Method to Finding the AverageVoltage


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Analytic Method to Finding the Average Voltage


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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


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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:


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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.


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21

Impedance, Z have two component:

Real component : Resistance, R

Imaginary Component : Reactance, X

Z can be written as:

Z = R + jX ()


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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


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23

Impedance for inductor, L

For ZL :jXL

Voltage leading current with 90

VL

I

Ref

fLjLjZL

w

2

L-VI


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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


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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


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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


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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


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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


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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


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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.


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Total Power

MVA

Real Power

MW

Reactive Power MVAr


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The complex power:

)cos( ivS

PfactorPower qq

)( ivrmsrms IV

jQP

qq

The powerfactoris the cosine of the phase

difference between voltage and current.


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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


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Power Factor (p.f.) is the ratio of real power (kW) to apparent power(kVA) in a circuit


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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?


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v(t)

Vm

-Vm

wt

Phasor

diagram

Which one is:

Vm = ?

Vinst = ?

q = ?

+V

-V


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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.


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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-


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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


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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.


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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)


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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


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(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


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Simulation of current flow in 3 phase system


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3 phase generator
http://localhost/var/www/apps/conversion/tmp/scratch_3/alternator1.swfhttp://localhost/var/www/apps/conversion/tmp/scratch_3/3phase.swf


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Second week continue

Thursday

September 20, 2012

15.00 15.50

Tutorial

16.00 16.50


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THANK YOU

week 1 chapter 1 review single phase system

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