Lecture Notes14_AcPower

Xn voltage at node n vb ib voltagecurrent in branch

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Unformatted text preview: • 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 n abn xn (e.g. V4 = x3 − x2 ) abn Ib = 0 ⇒ ∗ V b Ib = = E1.1 Analysis of Circuits (2013-3867) b n b b n b ∗ abn Ib = 0 ∗ abn xn Ib ∗ abn Ib xn AC Power: 14 – 7 / 11 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 n abn xn (e.g. V4 = x3 − x2 ) abn Ib = 0 ⇒ ∗ V b Ib = = E1.1 Analysis of Circuits (2013-3867) b n b b n b ∗ abn Ib = 0 ∗ abn xn Ib ∗ abn Ib xn = n xn b ∗ abn Ib AC Power: 14 – 7 / 11 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 n abn xn (e.g. V4 = x3 − x2 ) abn Ib = 0 ⇒ ∗ V b Ib = = E1.1 Analysis of Circuits (2013-3867) b n b b n b ∗ abn Ib = 0 ∗ abn xn Ib ∗ abn Ib xn = n xn b ∗ abn Ib = n xn × 0 AC Power: 14 – 7 / 11...
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This document was uploaded on 02/20/2014 for the course EE 101 at WVU.

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