3-Lesson_Notes_Lecture_26 - EE 204 Lecture 26 The Complex...

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EE 204 Lecture 26 The Complex Power & the Power Triangle The Complex Power: The complex power S can be defined using the following relation: SPj Q =+ [VA] Where: 0.5 cos PI V θ = (the average power) & 0.5 sin QI V = (the reactive power) The average power P equals the real part of the complex power S : Re( ) P S = The reactive power Q equals the imaginary part of the complex power S : Im( ) QS = Therefore: We know S We know both P & Q The Complex Power in Terms of the Voltage and Current Phasors: The complex power expression: 0.5 cos 0.5 sin Q I V jI V =+ = + [rectangular form of S ] 0.5 0.5 j SI V e I V == [exponential form of S ] The above equation can be rewritten as: 0.5 0.5 0.5 ( ) ( ) 0.5 vi i v V I V I V I V θθ = × × = Where I is the complex conjugate of I [since i II = i = ] The relation: 0.5 V =
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can be used to calculate the complex power from the current and voltage phasors. i II θ = v VV = Figure 1 The Relationship between the Complex and the Apparent Powers: The magnitude of the complex power 0.5 0.5 SI VI V == is given by: 0.5 SS I V S (the magnitude of the complex power) = the apparent power (0.5 IV ) As a summary, the complex power S and its magnitude S can be expressed as: 0.5 0.5 SPj Q I V I
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3-Lesson_Notes_Lecture_26 - EE 204 Lecture 26 The Complex...

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