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lecture2

lecture2 - EE 740 Professor Ali Keyhani Lecture#2 Balanced...

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1 EE 740 Professor Ali Keyhani Lecture #2 Balanced three phase circuits

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2 Balanced three phase Circuits: A three phase four wire system Balanced means: 1) Xa=Xb=Xc=Xs 2) Zaa=Zbb=Zcc=Zline 3) Z Y a=Z Y b=Z Y c=Zload 4) Saa=Sbb=Scc=P L +jQ L And the source is balanced: Ean=E 0 Ebn=E -120 =E 240 Note:E=Line-neutral Ecn=E 120=E -240 Therefore a balanced three phase system consists of balanced three phase generators, transmission lines and loads. jXc jXb jXa Ebn Ean Ecn Zbb Zaa Zcc Z Y b Z Y a Z Y c N n Ean Ecn Ebn 120 120 120
3 Suppose the loads are pure resistors, i.e. Z Y =R L or S L = P L , the transmission line impedance Z Line = R Line + jX Line . Internal generator reactance is neglected. Ean = Ia(Z Line + R L ) Ebn = Ib(Z Line + R L ) Ecn = Ic(Z Line + R L ) / Ia / = / Ib / = / Ic / = /Ean / = / Ean / / Z Line + R L / / Z ∠θ / Z = R Line + jX Line + R L = (R + jX) = / Z / ∠θ θ = tan-1 (X/R) where R = R Line + R and X Line = X Ia = E - θ and Ib = E -120- θ and Ic = E 120- θ / Z / / Z / / Z / Note: For a balanced three phase system the currents are also balanced. Ebn Ean Ecn Zline Zline Zline R L R L R L N n

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4 Note that: Ean + Ebn + Ecn = 0 or E 0 + E -120 + E 120 = 0 or E + j0 + E(-.5-j.866) + E(-.5+j.866) = 0
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