chapter 7 lecture powerpoint

7/23/2019 Chapter 7 Lecture PowerPoint

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Chapter 7Chapter 7

Copyright The McGraw-Hill Companies, Inc. Permission required or reproduction or display.


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Learning Objectives

!. "nderstand the meaning o instantaneous and a#erage power,

master $C power notation, and compute a#erage power or $C

circuits. Compute the power actor o a comple% load.


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The most general e%pressions or the

#oltage and current deli#ered to anaritrary load are as ollows/

0here Vand Iare the pea1 amplitudes o

the sinusoidal #oltage and current,

respecti#ely, and yand Iare their phaseangles.


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2ince the instantaneous power

dissipated y a circuit element is gi#en y

the product o the instantaneous #oltage

and current, it is possile to otain a

general e%pression or the power

dissipated y an $C circuit element/


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$#erage power


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Impedance triangle


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Throughout the remainder o this

chapter, the symols and will

denote the rms #alue o a

#oltage or a current, and thesymols and will denote rms

phasor #oltages and currents.


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The term cos3)is reerred to as thepowerfactor (pf).The power actor is

equal to 4 or a purely inducti#e orcapaciti#e load and equal to ! or a purely

resisti#e load.


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!. $n a#erage component, which is constant( this

is called the average power and is denoted y thesymol

where R 5 6e Z.

&. $ time-#arying 3sinusoidal7 component with *ero

a#erage #alue that is contriuted y the power

luctuations in the resisti#e component o the load

and is denoted y


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+. $ time-#arying 3sinusoidal7 component with

*ero a#erage #alue, due to the power

luctuation in the reacti#e component o the

load and denoted ypx(t)/

whereX 5 Im Z and Q is called the reactive

power. Note that since reactive eleents can

only store energy and not dissipate it! there isno net average power a"sor"ed "y X#


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The units o Qare volt amperes

reactive, or VAR. Qrepresents e%change

o energy etween the source and the

reacti#e part o the load( no net power isgained or lost in the process.


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The magnitude o 8$8, is measured in

units o volt amperes (VA)and iscalled the apparent power.


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FOCU O! "#$%O&OLO'

CO"L#* O+#R CALCULA$,O! FOR A ,!'L# LOA&

!. Compute the load #oltage and current in rms phasor orm, usingthe $C circuit analysis methods presented in Chapter and

con#erting pea1 amplitude to rms #alues.

&. Compute the comple% power and set

+. )raw the power triangle, as shown in 9igure :.!!.

. I Q is negati#e, the load is capaciti#e( i positi#e, the load isreacti#e.

. Compute the apparent power 8$8 in #olt amperes.


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Insert ;%ample :.

Comple% Power Calculations


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$ power actor close to unity signiies an eicienttranser o energy rom the $C source to the load.

I the load has an inducti#e reactance, then is

positi#e and the current lags 3or %ollows7 the

#oltage. Thus, when and Q are positi#e, the

corresponding power actor is termed lagging#

Con#ersely, a capaciti#e load will ha#e a negati#eQ and hence a negati#e . This corresponds to a

leading power actor, meaning that the load current

leads the load #oltage.


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FOCU O! "#$%O&OLO'CO"L#* O+#R CALCULA$,O! FOR O+#R

FAC$OR CORR#C$,O!

!. Compute the load #oltage and current in rms phasor orm, using

the $C circuit analysis methods presented in Chapter and

con#erting pea1 amplitude to rms #alues.

&. Compute the comple% power and set

+. )raw the power triangle, or e%ample, as shown in 9igure :.!:.

. Compute the power actor o the load p 5 cos()#

. I the reacti#e power o the original load is positi#e 3inducti#e

load7, then the power actor can e rought to unity y connecting a

parallel capacitor across the load, such that QC 5


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Power 9actor Correction


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The ideal transormer consists o two coils that arecoupled to each other y some magnetic medium. There

is no electrical connection etween the coils. The coil on

the input side is termed the primar-and that on the

$ transormer is a de#ice that couples two $C circuits

magnetically rather than through any direct conducti#e

connection and permits a =transormation> o the#oltage and current etween one circuit and the other.

Transormers

The Ideal Tranormer


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Ideal transormer


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$n ideal transormer multiplies a

sinusoidal input #oltage y a actor o N

and di#ides a sinusoidal input current y aactor o N.


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It should e apparent that e%pressing the

circuit in phasor orm does not alter the asic

properties o the ideal transormer, as

illustrated y the ollowing equations/


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Impedance relection across a transormer


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0hen the load impedance is equal to the

comple% con?ugate o the source

impedance, the load and source

impedances are matched and ma%imum


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Ma%imum Power Transer Through a Transormer


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Most o the $C power used today is

generated and distriuted as three-phasepower, y means o an arrangement in

which three sinusoidal #oltages are

generated out o phase with one another.

@alanced three-phase $C circuit


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Positi#e, or a"c, sequence or alanced three-phase

#oltages

The line #oltages may e computed relati#e to the

phase #oltages as ollows/


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The total power deli#ered to the alanced

load y the three-phase generator is

constant.

@alanced three-phase $C circuit 3redrawn7


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)elta-connected generators


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