Lecture Notes14_AcPower

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Unformatted text preview: on • 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 S = V I ∗ = 10.6 + j 7.6 kVA = 13∠36◦ kVA cos φ = |P | = cos 36◦ = 0.81 S Add parallel capacitor of 300 µF: ZC = 1 jωC = −10.6j Ω ⇒ IC = 21.7j A I = 46 − j 11.2 A = 47∠ − 14◦ A ∗ SC = V IC = −j 5 kVA S = V I ∗ = 10.6 + j 2.6 kVA = 10.9∠14◦ kVA cos φ = |P | = cos 14◦ = 0.97 S Average power to motor, P , is 10.6 kW in both cases. I , reduced from 56.5 47 A (−16%) ⇒ lower losses. Effect of C : VARs = 7.6 2.6 kVAR 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 S = V I ∗ = 10.6 + j 7.6 kVA = 13∠36◦ kVA cos φ = |P | = cos 36◦ = 0.81 S Add parallel capacitor of 300 µF: ZC = 1 jωC = −10.6j Ω ⇒ IC = 21.7j A I = 46 − j 11.2 A = 47∠ − 14◦ A ∗ SC = V IC = −j 5 kVA S = V I ∗ = 10.6 + j 2.6 kVA = 10.9∠14◦ kVA cos φ = |P | = cos 14◦ = 0.97 S Average power to motor, P , is 10.6 kW in both cases. I , reduced from 56.5 47 A (−16%) ⇒ lower losses. Effect of C : VARs = 7.6 2.6 kVAR , power factor = 0.81 E1.1 Analysis of Circuits (2013-3867) 0.97. AC Power: 14 – 8 / 11 Ideal Transformer 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 A transformer has ≥ 2 windings on the same magnetic core. E1.1 Analysis of Circuits (2013-3867) AC Power: 14 – 9 / 11 Ideal Transformer 14: Power in AC Circuits • Average Powe...
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