Calculation of Complex Power and Instantaneous Power in Electrical Engineering - Prof. N. , Assignments of Electrical and Electronics Engineering

Download Calculation of Complex Power and Instantaneous Power in Electrical Engineering - Prof. N. and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! CONCEPTUAL TOOLS By: Neil E. Cotter ECE 2260 F 08 HW 7 probs 1, 2 solution EX: a b 80 Ω 4cos(ωt)A 200 µF 5 mF 3 H Note: ω = 10 r/s. Do the following for the impedance to the right of the a, b terminals: a) Calculate complex power S = P + jQ. b) Calculate average (or DC) power. c) Calculate maximum instantaneous power. d) Sketch the power waveform, p(t). SOL'N: a) We first create an s-domain model. We have the following impedance values: € 1 jωC1 = 1 j10r/s ⋅ 200µF = − j500 Ω € 1 jωC2 = 1 j10r/s ⋅ 5mF = − j20 Ω € jωL = j10r/s ⋅ 3H = j30 Ω Our s-domain model: a b 80 Ω 4A∠0° j30 Ω –j20 Ω –j500 Ω CONCEPTUAL TOOLS By: Neil E. Cotter Now we calculate the impedance to the right of a, b. € z = − j500 || (80 + − j20 || j30) Ω or € z =10 ⋅ (− j50 || (8 + − j2 || j3)) Ω or € z =10 ⋅ (− j50 || (8 + 6 j )) Ω or € z =10 ⋅ (− j50 || (8 − j6)) Ω or € z = 20 ⋅ (− j25 || (4 − j3)) Ω or € z = 20 ⋅ 25 ⋅ −3− j4 4 − j28       Ω or € z = 5 ⋅ 25 ⋅ −3− j4 1− j7 ⋅ 1+ j7 1+ j7       Ω or € z = 5 ⋅ 25 ⋅ 25 − j25 50       Ω or € z = 125 − j125 2 Ω One formula for complex power involves only current and impedance: € S = 1 2 VI* = 1 2 Iz ⋅ I* = 1 2 I 2z Using values from the problem, we find the numerical value of S: € S = 1 2 42 125 − j125 2 VA = 500 − j500 VA