ࡱ> "$!e7 bjbjUU .07|7| Sl 4 $3J JJJJ%#%#%#/3131313131313$4 6U3%#"|%#%#%#U3%JJ_j3%%%%#6JJ/3%%#/3%R%+V]2@!3J> `j [$62 /33032x7%7!3%ETH curs V Puteri electrice in regim permanent sinusoidal  EMBED Equation.3  Vom determina puterea instantanee schimbata de dipol cu exteriorul pe la bornele sale aplicand unei suprafete inchise care contine in interior dipolul si trece prin bornele sale, th energiei electromagnetice care spune ca puterea instantanee este P=ui ; P=2Uisin((t+(u)sin((t+(i) 2sin(sin(=cos((-()-cos((+()=>P=Uicos((t+(u-(t-(i)-UIcos((t+(u+(t+(i) P=UIcos((u-(i)-UIcos(2(t+(u+(i) ; y=(u-(I P=valoarea medie pe o perioada a puterii instantanee (puterea activa P)  EMBED Equation.3  [P]si=W(reprez un aport mediu de putere la bornele dipolului, reprezentand totodata viteza generata de transferul energiei electromagnetice in alte forme de energie) P=UaI=IaV=RI2=U2/R(0 Puterea aparenta (S) reprezinta valoarea maxima a puterii active atunci cand tensiunea si curentul nu se modifica S=UI-caracterizeaza performantele aparatelor ; [S]si=VA Factorul de putere (K)-un coeficient adimensional subunitar care reprezinta raportul intre P si S: K=P/S=cos( Puterea reactiva P=UIcos( -Uicos(2(t+w(I+() P=UIcos([1-cos2((t+(I)]+ UIsin(sin2[1-cos2((t+(I)] ;P=puterea instantanee de pulsatie (Pp)+Puterea instantanee de oscilatie (Po) Puterea reactiva (Q)-maximul puterii instantanee de oscilatie Q=maxPo=UIsin( ; [Q]si=VAr(reactiv) Q=VrI=Uir=XI2=U2/x><0 poate fi + sau pt ca reactanta x poate fi + sau din cauza dipolului. Puterile pot fi definite si in domeniul complex (unde nu se poate reprezenta puterea instantanee)  EMBED Equation.3  Elemente ideale de circuit in regim permanent sinusoidal a)Rezistor ideal   EMBED Equation.3  Rezistorul ideal nu consuma si nu debiteaza putere relativa  EMBED Equation.3   EMBED Equation.3  Puterea aparenta complexa:  EMBED Equation.3  b)Bobina ideala in regim permanent sinusoidal  EMBED Equation.3  La bornele unei bobine ideale tensiunea este defazata inaintea curentului cu un sfert de perioada. P=UIcos( ; Q=UIsin(=UI=XlI2=(LI2=U2/XL=U2/(L(0 Bobina ideala consuma putere reactiva: S=UI=Q  EMBED Equation.3  Cele doua semnale sunt in cuadratura (curentul este in urma cu (/2 fata de tensiune)  EMBED Equation.3  Condensatorul in regim permanent sinusoidal  EMBED Equation.3  La bornele unui condensator ideal curentul este defazat inaintea tensiunii cu (/2 sau cu un sfert de perioada  EMBED Equation.3   EMBED Equation.3  Puterea aparenta complexa:  EMBED Equation.3  C u(t) i(t) u(t) i(t) i(t) R u(t) i(t) u(t) D.L.   ;<OPQRSbu_`bcdijlmntuxy~ʾʤ~t~t~t jbCJOJQJ jaCJOJQJCJH*OJQJ jgCJOJQJ jwCJOJQJ CJOJQJ$jCJEHOJQJUmHnHuj> CJUVaJCJOJQJmHnHu5CJOJQJ\mHnHu jCJOJQJUmHnHu5CJOJQJ\- ;STKp*BoD )  ; L N O P $`a$$a$$a$ *+>?@AEG'01:;>?ƹ5CJOJQJ\ jtCJOJQJ jCJOJQJCJH*OJQJjCJEHOJQJUj> CJUVaJjCJOJQJU jwCJOJQJCJH*OJQJ jgCJOJQJ CJOJQJ:?@ABKLTUWXYbcoprst  , - 1 2 5 6 8 9  ; = K L M P Q d e 𼲦znjT> CJUVaJjCJOJQJU jCJOJQJUmHnHuj&5CJEHOJQJU\jn> CJUVaJ5CJOJQJ\j5CJOJQJU\CJH*OJQJ jgCJOJQJ jwCJOJQJ jtCJOJQJ CJOJQJCJH*OJQJ*e f g      6 : ; N O P Q ໮࢕znaWW jtCJOJQJjCJEH~OJQJUj=> CJUVaJ5CJOJQJ\ jCJOJQJUmHnHujCJEHOJQJUj>> CJUVaJjCJEHOJQJUj> CJUVaJjKCJEHOJQJUjI> CJUVaJ CJOJQJjCJOJQJUjF CJEHOJQJU"P h  7 8 9 : R  - Q i $a$   ) * + , l m }sgjR> CJUVaJ5CJOJQJ\ jCJOJQJUmHnHuj#CJEHOJQJUj> CJUVaJ jpCJOJQJjICJEHOJQJUjR> CJUVaJjCJOJQJU jCJOJQJ jwCJOJQJCJH*OJQJCJH*OJQJ CJOJQJ' 1 2 Q R e f g h i j } ~  ʽ౤mH sH j4CJEHOJQJUj|> CJUVaJj0CJEHOJQJUj]> CJUVaJj,CJEHOJQJUjx> CJUVaJ jpCJOJQJ CJOJQJjCJOJQJUj;'CJEH@OJQJU/  $a$ ,1h. 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"2g6G`#xdRC `!;6G`#xdRp  xڕMhANnZ[-F`{WUhԢT 6д$ԢP1`xz##Iy<f:ja'$HP^'Yjs&Gʣ)b-xm9tdI0 % /s+1b"& }>Y\7WHFz}?bҿ"g?\w8!}ݱf֕_xfSRL~*(̊`=jGs'P*KEuZtE͝㊫%ڹ&9Tl1>$9O2Q*^tGX {+2rZ(?@ACFDEGHIJKLMcbOPQRSTUVWXYZ[\]^_`adghijklmnopqrstuvwxyz{|}~Root EntryK F`j%1Data 7WordDocumentJ.0ObjectPoolMj`j_1054327324FjjOle CompObjfObjInfo  !"#$%&'()*+,-.1456789:;>ADGHIJKNQRSTWZ[\]^_`abcdehklmnopqrsvyz{|}~ FMicrosoft Equation 3.0 DS Equation Equation.39qmIyI u(t)= 2  Usin(t+ u )i(t)= 2  Isin(t+ i )Equation Native _1054334462 FjjOle CompObj f FMicrosoft Equation 3.0 DS Equation Equation.39q@mIyI P=1TPdt 0T +" =1TUIcosdt 0T +" "1TUIcos(2t+, uObjInfo Equation Native  \_1054337390FjjOle  +, i )dt=UIcos 0T +" FMicrosoft Equation 3.0 DS Equation Equation.39qmIyI U=Ue j u I=Ie jCompObjfObjInfoEquation Native _1054338132 'Fj#j i S=I * "UI * =Ie "j i S=Ue j u Ie "j i =UIe j( u " i ) S=Se j =Scos+jsinS=P+jQS=Se j =UI(cos+jsin)=I(U a +jU r )=U(I a +I r )Z=UI!U=Z"IS=Z"I 2 S=Z"I"I * =Z"I 2 =(R+jx)I 2 =RI 2 +jxI 2 =P+jQS=U(y"U) * =Uy ** U * =(G+jB)U 2 =GU 2 +jBU 2 =P+jQy=IU!(y=G"jB)Ole /CompObj0fObjInfo2Equation Native 3 FMicrosoft Equation 3.0 DS Equation Equation.39qmIyI u(t)= 2  Usin(t+ u )(1)i(t)= 2  Isin(t+ i )(2)i=UR; i = u ,= u " i =0P=UIcos=UI=RI 2 =U 2 Re"0Q=UIsin=0 FMicrosoft Equation 3.0 DS Equation Equation.39q_1054338377F#j#jOle <CompObj=fObjInfo?Equation Native @t_1054338450"F#j#jOle BCompObj CfXIdI S= P 2 +Q 2 =UI=P FMicrosoft Equation 3.0 DS Equation Equation.39qPyI~I U=Ue j u (3)I=IeObjInfo!EEquation Native Fl_1054338622$F#jKjOle L j i (4)I=UR=Ue j u RI=UR, u = i (=0) FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj#%MfObjInfo&OEquation Native P<_1054338877,)FKjKj IDI S=U"I * =Ue j u "j i =UIe j( u " i ) =UIe j 0 =UI=P+jQ FMicrosoft Equation 3.0 DS Equation Equation.39qOle UCompObj(*VfObjInfo+XEquation Native Y< mIyI u=Ldidt!i=1Ludt  +" i=1L 2  Usin(t+ u )dt= 2  UI  +" ["cos(t+ u )]= 2  ULsin(t+ u "2)I=ULX L =L(reactanta_inductiva)}I=UX L ; i = u "2;= u " i =2 FMicrosoft Equation 3.0 DS Eq_10543412021@.FKjKjOle fCompObj-/gfObjInfo0iuation Equation.39q` ImI I=1L1jU=1jLUe j u =("j)LUe  u =e "j2 LUe j u =ULe j(Equation Native j|_1054340082;3FjjOle tCompObj24uf u "2) I=UL=UX L  i = u "2!= u " i =2 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo5wEquation Native x_10543414588FjjOle ڐII S=U"I * =UIe j( u " i ) =UIe j2 =UIcos2+jUIsin2S=jUI=P+jQP=0Q=UI=LT 2 e"0CompObj79fObjInfo:Equation Native _1054340984=Fjj FMicrosoft Equation 3.0 DS Equation Equation.39qduII u(t)= 2  Usin(t+ u )i(t)= 2  Isin(t+ i )=Cdudt=Cddt( 2  Usin(t+ u ))= 2  CUcos(t+ u )= 2  CUsin(t+ u +2)I=CU1C=X c }I=UXcundeXc=reactantacapacitiva i = u +2!= u " i ="2 FMicrosoft Equation 3.0 DS Equation Equation.39qII P=UIcos=0!un_condensator_ideal_nu_conOle CompObj<>fObjInfo?Equation Native  suma_putere_activaQ=UIsin="UI="XcI 2 <0!cond_id_debiteaza_putere_reactivaS=UI="Q FMicrosoft Equation 3.0 DS Eq_10543414696EBFjjOle CompObjACfObjInfoDuation Equation.39q ĀIT:J U=Ue j u I=Ie j i I=jCU=e j2 CUe j u =CUe j( u +2) =CU=UEquation Native (_1054341500GFjjOle CompObjFHfX c  i = u +2!= u " i ="2 FMicrosoft Equation 3.0 DS Equation Equation.39qXdJLI S=ObjInfoIEquation Native 1Tablef7SummaryInformation(LU"I * =Ue j u Ie "j i =UIe j( u " i ) =UIe "j2 =UIcos("2)+jUIsin("2)="jUIS=P+jQ}!P=0;Q="UIV3U:/1}/18]21TLzDҹ~lfBO&M3v*ay.3& <9b=6W{7 ^_)=5j~\W|5yW|9O.&7dJ==֭˽n|31{χ|8'(;rRbv͐WsaOpIBź)p@UF)ex'I;eޓ@]܉;WtB 9-!Sӥrkݴ7pcDd` J  C A? 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