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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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