Lecture Notes14_AcPower

Motor modelled as 57j v i v zl 46 j 329 a 565

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Unformatted text preview: Tellegen’s Theorem 14: Power in AC Circuits • Average Power • Cosine Wave RMS • Power Factor • Complex Power • Power in R, L, C • Tellegen’s Theorem • Power Factor Correction • Ideal Transformer • Transformer Applications • Summary Tellegen’s Theorem: The complex power, S , dissipated in any circuit’s components sums to zero. xn = voltage at node n Vb , Ib = voltage/current in branch b (obeying passive sign convention) abn −1 if Vb starts from node n = +1 if Vb ends at node n 0 else e.g. branch 4 goes from 2 to 3 ⇒ a4∗ = [0, −1, 1] Branch voltages: Vb = KCL @ node n: Tellegen: b E1.1 Analysis of Circuits (2013-3867) b abn xn (e.g. V4 = x3 − x2 ) abn Ib = 0 ⇒ ∗ V b Ib = = Note: b n n Sb = 0 ⇒ b b n ∗ abn Ib = 0 ∗ abn xn Ib ∗ abn Ib xn = b b Pb = 0 n xn b and also ∗ abn Ib = b n xn × 0 Qb = 0. AC Power: 14 – 7 / 11 Power Factor Correction 14: Power in AC Circuits • Average Power • Cosine Wave RMS • Power Factor • Complex Power • Power in R, L, C • Tellegen’s Theorem • Power Factor Correction • Ideal Transformer • Transformer Applications • Summary V = 230. Motor modelled as 5||7j Ω. V I = V + ZL R E1.1 Analysis of Circuits (2013-3867) AC Power: 14 – 8 / 11 Power Factor Correction 14: Power in AC Circuits • Average Power • Cosine Wave RMS • Power Factor • Complex Power • Power in R, L, C • Tellegen’s Theorem • Power Factor Correction • Ideal Transformer • Transformer Applications • Summary V = 230. Motor modelled as 5||7j Ω. V I = V + ZL = 46 − j 32.9 A R E1.1 Analysis of Circuits (2013-3867) AC Power: 14 – 8 / 11 Power Factor Correction 14: Power in AC Circuits • Average Power • Cosine Wave RMS • Power Factor • Complex Power • Power in R, L, C • Tellegen’s Theorem • Power Factor Correction • Ideal Transformer • Transformer Applications • Summary V = 230. Motor modelled as 5||7j Ω. V I = V + ZL = 46 − j 32.9 A = 56.5∠ − 36◦ R E1.1 Analysis of Circuits (2013-38...
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This document was uploaded on 02/20/2014 for the course EE 101 at WVU.

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