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Expressões elementares ( ) ( )tRitv = ( ) ( )tv R ti 1= ( ) ( ) ( )titvtp = ( ) ( ) ( )0 0 WdptW t += ∫ ττ ( ) ( ) ( )01 0 vdi C tv t += ∫ ττ ( ) ( )tvdtdCti = ( ) ( ) ( )titvtp = ( ) ( ) = 2 2 tvCtWC ( ) ( )ti dt dLtv = ( ) ( ) ( )01 0 idv L ti t += ∫ ττ ( ) ( ) ( )titvtp = ( ) ( ) = 2 2 tiLtWL ( ) ( )tq C tv 1= ( ) ( )tCvtq = ( ) ( )tLit =Ψ ( ) ( )t L ti Ψ= 1 ( ) ( ) ( )0 0 qditq t += ∫ ττ ( ) ( )tqdtdti = ( ) ( )tdtdtv Ψ= ( ) ( ) ( )0 0 Ψ+=Ψ ∫ t dvt ττ [ ]θcos12 −=∆ YZZ n o360=θ 4444 84444 76 K 444 8444 76 K SC n nNNN NORTON n ON I Z V Z V Z V Z ZZZ V +++ +++ = 2 2 1 1 21 111 1 ( ) ( ) ( ) ( )θφω φω −+= += tIti tVtv cos cos max max ( ) ( )[ ] ( )φωθφωθ 22sensen 2 22cos1cos 2 maxmaxmaxmax ++++= tIVtIVtp φφφ nn n nnn jQPIVIVIVS +=⋅++⋅+⋅= 44444 344444 21 K termos * 2 * 21 * 1 S PFP == ϕcos 22 2 2 jXZ X Z M ref += ( ) ( ) ( ) ( ) ( ) 444444444 3444444444 21 K termos1 111222111 coscoscosRe − −−−+++== n nnnnnnnn IVIVIVSP γγγφφ 21LLkM = ( ) ( ) ( ) ( ) ( ) 4444444444 34444444444 21 K termos1 111222111 sensensenIm − −−−+++== n nnnnnnnn IVIVIVSQ γγγφφ 21XXkXM = ( ) ( ) 2 1 2 1 N N tv tv ±= ( ) ( ) 1 2 2 1 N N ti ti ±= 2 1 2 1 N N V V ±= 1 2 2 1 N N I I ±= ( )∑∞ = −+= 1 CCCC cos2n i n v n nnivivP θθ [ ]∫= TRMS dttfTF 0 2)(1 ∑ ∞ = += 1 2 2 0 2n n RMS AaF %100 2 22 %100 2 2 % 1 2 3 2 2 1 2 2 × + + =× = ∑∞ = V VV V V DHT n n v K %1001 2 %100 2 2% 2 1 2 1 2 12 ×− =× − = V V V VV DHT RMS RMS v %100 2 22%100 2 2 % 1 2 3 2 2 1 2 2 × + + =× = ∑∞ = I II I I DHT n n i K %1001 2 %100 2 2% 2 1 2 1 2 12 ×− =× − = I I I II DHT RMS RMS i 1Z 3Z 2Z BZ AZ CZ CBA BA ZZZ ZZZ ++=1 CBA CA ZZZ ZZZ ++=2 CBA CB ZZZ ZZZ ++=3 3 323121 Z ZZZZZZZ A ++= 2 323121 Z ZZZZZZZ B ++= 1 323121 Z ZZZZZZZC ++= Circuitos Elétricos B – SHaffner/LAPereira Versão: 12/4/2005 Página 1 de 1
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