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Copyright © “Compania-Dekart” S.R.L (www.dekart.com ) – 2002
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<A4=9=G=A EGA@6 F5G5@A9GD 87A9734=E EDI;?9 H5 FGA;AJD 9GAC=E5<3I
895<;5G95. ?;6 F= E8A@?, 8JA;=E5J= CD H54=<=;59AJ:<= =FGA;AJ39: 9GAC=E5<36,
>5G5<93G?kQ3A ?G=EA<: <5;AB<=893 3 457A89E5. FD9 GAMA<36 FG=CJA@,
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;<3@ 3H =8<=E<DO 8F=8=C=E =CA8FA7A<36 <5;AB<=893 3 457A89E5
FG=;?4N33 6EJ6A986 8=H;5<3A <5 FGA;FG36936O 8389A@ =CA8FA7A<36 457A89E5 3
8AG93K345N36 3O <5 8==9EA989E3A 9GAC=E5<36@ @AB;?<5G=;<=>= 895<;5G95
9001 3J3 G=883I84=>= 9001.
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3J3 ?;=C89E FG3 =FJ59A RJA49G=R<AG>33.
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CAHC=JAH<A<<=>= FAGAO=;5 <5 JkCDA 93FD 95G3K=E F?9A@
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<5FG3@AG, ?7A9 J:>=9 ? G5H<DO 459A>=G3I F=9GAC39AJAI. kC=I 3H E5G35<9=E
@<=>=95G3K<=>= ?7A95 F=9GAC?A9 FAGA=8<5QA<36 J3C= ;==8<5QA<36 F5G45
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954 <5HDE5A@DO RJA49G=<<DO "smart meters" - "?@<DO 87A9734=E", 3@AkQ3O E
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;<54= 8F=8=C<=89: G5C=959: E 8389A@5O - FGAG=>593E5 <A 9=J:4=
RJA49G=<<DO 87A9734=E. G6;A 89G5< GA5J3H=E5<5 3;A6 38F=J:H=E5<36 <5G6;? 8
RJA49G=<<D@3 954BA 3 3<;?4N3=<<DO RJA49G=87A9734=E E 457A89EA ;59734=E
85@DO 8=EGA@A<<DO 8389A@ ?7A95, E 9=@ 738JA @<=>=95G3K<DO 3 8
E=H@=B<=89:k FGA;=FJ59D. 95 E=H@=B<=89: F=6EJ6A986 E GAH?J:959A
E89G53E5<36 E 3<;?4N3=<<DI 87A9734 9AJA@A9G37A84=>= ;597345.
G3>3<5J:<D@ 9AO<37A843@ GAMA<3A@ 6EJ6A986 <=EDI 3<;?4N3=<<DI
RJA49G=87A9734 8 E<AM<3@ 9AJA@A9G37A843@ ?89G=I89E=@ -505 , 4=9=GDI
EDO=;39 <5 GD<=4 F=; H5GA>389G3G=E5<<=I 9=G>=E=I @5G4=I " S- ".
7A9734 FGA;895EJ6A9 8=C=I 3<9A>G3G=E5<<DA E =;<=@ FG3C=GA ;E5 =9;AJ:<DO
?89G=I89E5: 8=C89EA<<= RJA49G=87A9734, E ;5<<=@ 8J?75A R9= 3<;?4N3=<<DI
87A9734 -505, <= 8= 8FAN35J:<D@ E5G35<9=@ "4=B?O5", 3 FG3895E45 8
RJA49G=<<D@ K=9=5;5F9AG=@. SG3895E45 BA894= 4GAF3986 <5 "4=B?OA"
F=8GA;89E=@ <5FG5EJ6kQ3O, 5 7AGAH FG=HG57<=A =4<= E <3B<AI 75893 "4=B?O5"
FG=38O=;39 8739DE5<3A @A943 8 ;3845 87A97345.
X5G549AG<=I =8=CA<<=89:k R9=>= GAMA<36 6EJ6A986 9=, 79= E<?9G:
87A97345 <A ?895<5EJ3E5k986 <34543A RJA49G=<<DA ?89G=I89E5, 79= F=HE=J6A9
3<;?4N3=<<=@? 87A9734? =CA8FA739: F=J<=NA<<DI @ABF=EAG=7<DI 3<9AGE5J,
4=9=GDI G5EA< E R9=@ 8J?75A 16 >=;5@.
S=;4?F5A9 E3;3@56 FG=89=95 GAMA<36. ;<54= R95 FG=89=95 ;=893><?95
H5 87A9 8J=B<=893 RJA49G=<<=I 75893 FG3C=G5. JA49G=<<DI K=9=5;5F9AG a-
06 - ?<345J:<DI 3<KG54G58<DI =F937A843I FG3C=G,4=9=GDI H54GAFJ6A986 <5
87A9734A EH5@A< 4JA@@<=I 4GDM43.
H54Jk7A<3A <5;= =9@A939: 8JA;?kQAA: <5 8A>=;<6M<A@ GD<4A
FG3C=G=E ;J6 ?7A95 F=9GACJA<<=I RJA49G=R<AG>33 @=>?9 <5I93 @A89= JkCDA
RJA49G=87A97343, 454 3<;?4N3=<<DA, 954 3 RJA49G=<<DA. ;<54= 45B;DI
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8GA;89E5@3 CAH F38:@A<<=>= G5HGAMA<36 EJ5;AJ:N5 5E9=G843O FG5E.
, - . / 0 .
9. F=9GAC39AJ: ;=JBA< 3@A9: ;=89=EAG<?k 3<K=G@5N3k =C 3O 457A89EA,
@A9G=J=>37A84=I 9=7<=893 3 <5;AB<=893, ;J6 9=>= 79=CD 8;AJ59: FG5E3J:<DI
EDC=G.
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8GA;89E5@3 CAH F38:@A<<=>= G5HGAMA<36 EJ5;AJ:N5 5E9=G843O FG5E.
, - . / 0 .
10. 3 ? ]. 5- /. - W W _ . _ ./ 5 /
54 CDJ= 845H5<= EDMA, E <589=6QAA EGA@6 E=FG=8D 4=<9G=J6
F=9GACJA<36 3 R4=<=@33 RJA49G=R<AG>33 895<=E6986 E8A C=JAA <58?Q<D@3 3
549?5J:<D@3. SG3 R9=@ E @588=E=@ F=J:H=E5<33 E8A AQA =895A986 =>G=@<=A
4=J37A89E= @=G5J:<= ?895GAEM3O RJA49G=@AO5<37A843O 87A9734=E. PJ6 9=>=
79=CD G6;=E=I F=9GAC39AJ: =8=H<5J ;J6 8AC6 <A=CO=;3@=89: FG3=CGA9A<36
C=JAA 8=EGA@A<<DO 3 ?;=C<DO E 38F=J:H=E5<33 RJA49G=<<DO 87A9734=E,
<A=CO=;3@= 79=CD 9543A 87A97343 FG3 C=JAA ED8=43O F=9GAC39AJ:843O
E=H@=B<=896O, =CJ5;5J3 FG3EJA459AJ:<=I NA<=I, 3 =CA8FA73E5J3 E=H@=B<=89:
R4=<=@33 RJA49G=R<AG>33. J5E<D@ ?8J=E3A@ ;J6 R9=>= 6EJ6A986 38F=J:H=E5<3A
8=EGA@A<<=I RJA@A<9<=I C5HD, F=HE=J6kQAI EDF?8459: 8=EGA@A<<DA 8389A@D
3H@AGA<36 RJA49G=R<AG>33 FG3 <53J?7MA@ 8==9<=MA<33 NA<5/E=H@=B<=893.
53C=JAA 9G5;3N3=<<D@3 87A97345@3 RJA49G=R<AG>33 ;= <589=6QA>=
EGA@A<3 6EJ6J38: RJA49G=@AO5<37A843A 87A97343, FG3<N3F ;AI89E36 4=9=GDO
=8<=E5< <5 F=;87A9A H5 FG=@AB?9=4 EGA@A<3 4=J37A89E5 =C=G=9=E ;3845,
84=G=89: EG5QA<36 4=9=G=>= FG=F=GN3=<5J:<5 F=9GACJ6A@=I @=Q<=893.
J5E<D@3 ;=89=3<89E5@3 9543O 87A9734=E 6EJ6J38: FG=89=95, <5;AB<=89:, 3
<AED8=456 89=3@=89:. A;=895945@3 6EJ6k986 <AED8=456 9=7<=89: 3 =98?989E3A
;=F=J<39AJ:<DO K?<4N3=<5J:<DO E=H@=B<=89AI. 9= 4585A986 454 =;<=K5H<DO
CD9=EDO, 954 3 9GAOK5H<DO FG=@DMJA<<DO 87A9734=E.
F=8JA;<AA EGA@6 E 8E6H3 8 C?G<D@ G5HE393A@ @34G=RJA49G=<343 3
F=6EJA<3A@ <A;=G=>3O @34G=4=<9G=JJAG=E 3 N3KG=EDO FG=NA88=G=E =CG5C=943
83><5J=E (DSP) 895J3 F=6EJ69:86 C=JAA 9=7<DA 3 8=EGA@A<<DA 8GA;89E5
3H@AGA<36 RJA49G=R<AG>33. ?QA89E?A9 <A84=J:4= 895<;5G9<DO F=;O=;=E F=
F=89G=A<3k 87A9734=E RJA49G=R<AG>33 8 38F=J:H=E5<3A@ @34G=FG=NA88=G=E.
SGA;895EJA<<56 <5 G38. 1 89G?49?G<56 8OA@5 F=89G=A<36 87A97345
F=HE=J6A9 =CA8FA739: <53C=J:M?k >3C4=89:, 3 FG3 ?8J=E33 38F=J:H=E5<36
ED8=4=9=7<DO 5<5J=>=-N3KG=EDO FGA=CG5H=E59AJAI 3 DSP =7A<: ED8=4?k
9=7<=89: 3H@AGA<36 F5G5@A9G=E RJA49G37A84=I 8A93. P384GA9<DA @><=EA<<DA
H<57A<36 9=45 3 <5FG6BA<36 (Ii 3 Ui) =CG5C59DE5k986 8 38F=J:H=E5<3A@ DSP ;J6
F=J?7A<36 H<57A<3I P, Q, S. AJ373<5 5493E<=I @=Q<=893 P ED738J6A986, F=
K=G@?JA 454 8GA;<A5G3K@A937A84=A FG=3HEA;A<3A ;384GA9<DO H<57A<3I 9=45
(Ii) 3 <5FG6BA<36 (Ui) E F=8JA;=E59AJ:<=I EDC=G4A F= FAG3=;? 3H@AG6A@=>=
83><5J5:
1 N
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>;A N — 4=J37A89E= =987q9=E E =;<=@ FAG3=;A 83><5J5.
SG3 ?8J=E33 83<?8=3;5J:<DO K=G@ 9=45 3 <5FG6BA<36 E 8A93 @=Q<=89:
ED738J6A986 F= 8JA;?kQAI =CQAI K=G@?JA:
p(t) = u(t) * i(t) = Umsin t * Imsin( t + ) = UIcos – UIcos(2 t + ),
>;A u(t) 3 i(t) — @><=EA<<DA H<57A<36, 8==9EA989EA<<=, <5FG6BA<36 3 9=45 E
8A93;
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8GA;89E5@3 CAH F38:@A<<=>= G5HGAMA<36 EJ5;AJ:N5 5E9=G843O FG5E.
, - . / 0 .
11. Um 3 Im — @><=EA<<DA H<57A<36 <5FG6BA<36 3 9=45;
U 3 I — ;AI89E?kQ3A H<57A<36 <5FG6BA<36 3 9=45 (U = Um/ 2; I = Im/ 2);
— ?>=J 8;E3>5 K5H @AB;? 9=4=@ 3 <5FG6BA<3A@.
SG3 R9=@ H<57A<3A 5493E<=I F=9GACJ6A@=I @=Q<=893:
P = UIcos = Scos [ ],
>;A S = UI — F=J<56 @=Q<=89: F=9GACJA<36 [ ].
AJ373<5 GA5493E<=I @=Q<=893 E R9=@ 8J?75A =FGA;AJ6A986 F= K=G@?JA
Q = UIsin = Ssin [ ].
7A9734 =CD7<= 8=89=39 3H 3H@AG39AJ:<DO ;59734=E 9=45 3 <5FG6BA<36 (
3J3 9G5<8K=G@59=G=E 8 ?J?7MA<<D@3 O5G549AG389345@3), 8OA@ 3H@AGA<36
( ZS - 5<5J=>=-N3KG=EDA FGA=CG5H=E59AJ3), @34G=4=<9G=JJAG5
=CG5C59DE5kQA>= N3KG=EDA 83><5JD, F5@693 ;J6 OG5<A<36 ;5<<DO 87A97345.
86 3<K=G@5N36 87A97345 EDE=;3986 <5 B3;4=4G3895JJ37A84=A 95CJ=.
S395k986 87A97343 =CD7<= =9 F=;4Jk7A<<DO 4 <3@ NAFAI <5FG6BA<36.
;=F=J<A<3A, O=G=M3@ 9=<=@ 6EJ6A986 ?895<=E45 GAHAGE<=>= F395<36 <5 87A9734
(E E3;A G5HJ37<DO 544?@?J69=G<DO C595GAI). <3 FGA;<5H<57A<D ;J6
F=;;AGB5<36 NAJ=89<=893 E5B<=I 3<K=G@5N33, 4=>;5 87A9734 =94Jk7A< =9
NAFAI F395<36. <57A<36 F=9GACJ6A@=>= 9=45 =FGA;AJ6A986 8 F=@=Q:k
9G5<8K=G@59=G=E 9=45. ;5J:<AIMA@ FG=38O=;39 FAGA@<=BA<3A 83><5J=E 9=45
3 <5FG6BA<36 (F= EDMA =F385<<D@ K=G@?J5@) 7AGAH ZS <5
ED8=4=FG=3HE=;39AJ:<=@ @34G=FG=NA88=GA 8 RISC-<5C=G=@ 4=@5<;. 86
F=J?7A<<56 3<K=G@5N36 H5F38DE5A986 E F5@69: 87A97345 3 F5G5JJAJ:<=
=9=CG5B5A986 <5 B3;4=4G3895JJ37A84=@ ;38FJAA.
9J3739AJ:<56 =8=CA<<=89: 9543O 87A9734=E - R9= E=H@=B<=89: ?7A95
RJA49G=R<AG>33 F= 95G3K5@. 9= =H<575A9, 79= D @=BA9A G588739DE59:86 H5
F=9GACJA<<?k RJA49G=R<AG>3k F=-G5H<=@?. 5FG3@AG(FG3@AG EH69 8 4G53<D):
A89: 3 95G3K5 G587A95 H5 RJA49G=R<AG>3k - F34=EDI (=CD7<= R9= ?9GA<<3A 3
EA7AG<3A 758D), F=J?F34=EDI (R9= FG54937A843 EA8: ;A<: 4G=@A ?9G5 3 EA7AG5) 3
<=7<=I. ZA<5 H5 F=9GACJA<<?k RJA49G=R<AG>3k @A<6A986 E H5E383@=893 =9
95G3K5. SG3 =;<=895E=7<=@ 95G3KA 1 4 9·7 89=39 0,1271 >G3E<D, A8J3 BA D
GAM3J3 G588739DE59:86 F= 95G3K5@ 9= 5@ <?B<= C?;A9 ?@<=B59: R9? NA<? <5
8JA;?kQ3A 4=RKK3N3A<9D:
• F34=EDI 95G3K - 1.8
• F=J?F34=EDI 95G3K - 1.02
• <=7<=I 95G3K - 0.2
7AE3;<=, 79= ED>=;<AA E8A>= G5C=959: FG3 <=7<=@ 95G3KA (NA<5 H5 1
4 9··7 @A<:MA E 4 G5H5). 895GDO 3<;?4N3=<<DO 87A97345O D <A @=>J3
?739DE59: FAGAO=;D <5 G5HJ37<DA EGA@A<<DA 95G3KD (;J6 R9=>= <5;= CDJ= CD
F=895E39: 7AJ=EA45 ? 87A97345, 4=9=GDI 8JA;3J, 4=>;5 <589?F39, <5FG3@AG,
F34=EDI 95G3K 3 H5F38DE5J F=45H5<36). 54 EDO=; @=B<= CDJ= CD
38F=J:H=E59: 4=@F:k9AG<?k 8389A@? 8C=G5 3<K=G@5N33 E GAB3@A GA5J:<=>=
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8GA;89E5@3 CAH F38:@A<<=>= G5HGAMA<36 EJ5;AJ:N5 5E9=G843O FG5E.
, - . / 0 .
12. EGA@A<3 8 F=8JA;?kQ3@ G?7<D@ G5HC3A<3A@ <5 3<9AGE5JD F= 95G3K5@. ;<54=
>=G5H;= FG=QA F=895E39: @34G=FG=NA88=G<DI 87A9734, E<?9GA<<66 FG=>G5@@5
4=9=G=>= 85@5 CD 8JA;3J5 H5 FAGAO=;=@ 3H =;<=I 95G3K<=I H=<D E ;G?>?k 3
H5F38DE5J5 G58O=; RJA49G=R<AG>33 =9;AJ:<= F= 45B;=@? 3<9AGE5J?.
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345456 7589: ;5<<=>= ;=4?@A<95 <A @=BA9 CD9: E=8FG=3HEA;A<5 E 454=I CD 9= <3 CDJ= K=G@A 3 4543@3 CD, 9= <3 CDJ=
8GA;89E5@3 CAH F38:@A<<=>= G5HGAMA<36 EJ5;AJ:N5 5E9=G843O FG5E.
, - . / 0 .
13. 38. 1. 9G?49?G<56 8OA@5 F=89G=A<36 87A97345
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345456 7589: ;5<<=>= ;=4?@A<95 <A @=BA9 CD9: E=8FG=3HEA;A<5 E 454=I CD 9= <3 CDJ= K=G@A 3 4543@3 CD, 9= <3 CDJ=
8GA;89E5@3 CAH F38:@A<<=>= G5HGAMA<36 EJ5;AJ:N5 5E9=G843O FG5E.
, - . / 0 .
14. G=@A 9=>=, ?739DE56 ED8=43I 4J588 9=7<=893 9543O 879A7345 (0,2 - 0,5)
3 =98?989E3A 85@=O=;5 (9.A. 85@=FG=HE=J:<=>= ;E3BA<36 ;3845, 454 E
3<;?4N3=<<=@ 87A9734A) @=B<= 845H59:, 79= <5 8A>=;<6M<3I ;A<: 9543A
87A97343 85@DI ?;=C<DI E5G35<9 ;J6 ?7A95 RJA49G=R<AG>33.
PJ6 9=>=, 79=CD 87A9734 @=> 873959: 3 F=45HDE59: ;5<<DA E <A>=
<A=CO=;3@= E<A893 FG=>G5@@?, 4=9=G56 C?;A9 "?45HDE59:" 87A9734?, 79= ;AJ59::
454 3H@AG69:, 79= 3H@AG69:, 4?;5 3 E 454=@ E3;A H5F38DE59:.( F=8JA;?kQ3O
>J5E5O @D G588@=9G3@ 3 FG=5<5J3H3G?A@ 8?QA89E?kQ3A 8389A@D ).
739DE56 F=9GAC<=893 GD<45 E <A;=G=>3O 87A97345O, 4=@F5<3AI Analog
Devices CDJ= G5HG5C=95<= <=E=A F=4=JA<3A N3KG=EDO 87A9734=E
RJA49G=R<AG>33 E 3<9A>G5J:<=@ 38F=J<A<33. 93 87A97343 F=J?73J3
<53C=J:MAA G58FG=89G5<A<3A H5 3O 457A89E=, ;=89?F<=893, FG3A@JA@=I NA<A 3,
79= =8=CA<<= E5B<=, 3 H5 <5J3736 O=G=M3O K3G@A<<DO =9J5;=7<DO 8GA;89E,
O=G=MAI 9AO<37A84=I ;=4?@A<95N33 (A89: <5 G?884=@ 6HD4A) 3 457A89EA<<=I
9AO<37A84=I F=;;AGB4A. 3BA FG3EA;A<D =8<=E<DA O5G549AG389343 3
4Jk7AEDA =9J3736 @34G=8OA@ R9=>= G6;5:
C 0 2 1
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