§ 12-5 Power measurement in three-phase system
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A
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Three watt-meters method P=PA+PB+PC
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AZ BZ
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dtiiiT cCCxbBBxT aAAx )(1 0 ??? ??? ?
dtiTdtpTP T aAAxT AA ?? ?? 00 11 ?
CBA PPPP ???
The readings of three watt-meters
NxCNCxNxBNBxNxANAx VVVVVVVVV
????????? ??????
dtiiiTdtiiiTP cCbBT aANxcCCNbBBNT aAAN )((1)(1 00 ?????? ?? ????
dtiiiT cCCNbBBNT aAAN )(1 0 ??? ??? ?
The sum of the average powers taking by the three-phase loads.
?? ?? l o a dm e t e rw a t t PP
Let us now consider
the effect of placing point
x directly on the one of
three lines.(x=>B)
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x
00 ???? BBx PV
dtiTdtiTPPP T cCCBaAT ABCA ?? ???? 00 11 ??
dtiTdtiT T cCBNCNaABNT AN ?? ???? 00 )(1)(1 ????
dtiidtidtiT cCaABNcCCNT aAAN )(1 0 ???? ? ???
dtiiiT cCCNbBBNT aAAN )(1 0 ??? ??? ? bBi?
(The sum of the average powers taking by the three-phase loads.)
????? || ZZZZIf CBA
)30c o s ()c o s ( ?? ??? ?? VIIVIVP aAABaAABA
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)30c o s ()c o s ( ?? ??? ?? VIIVIVP cCCBcCCBC
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)30c os (
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PPPF 3t a nc o s 1
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Example,PD=2.5kW,PF=0.866(lagging),VL=380V,Find,WcWa
Solution:
AV PI
L
D
L 38 6.486 6.038 03
25 00
86 6.03 ?????
?? 30866.0c o s 1 ?? ?
VVL et an ?? 022003380 ?????
bnV?
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anV?
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AIVV aAab ?? 3038 6.43038 0 ?????? ??
AIVV cCcb ?? 90386.490380 ????? ??
Wa WP
a 8 3 160co s3 8 6.43 8 0 ???? ?
Wc WP
c 1 6 6 70co s3 8 6.43 8 0 ???? ?
WPPP caD 2 5 0 0???
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a
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c cW
aW