To do this we shall split the current into 2 components i t 2 I cos ωt φ i 2I

# To do this we shall split the current into 2

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while oscillating power flow is associated with inductor or capacitor. To do this, we shall split the current into 2 components, i ( t ) = 2 I cos( ωt + φ i ) = 2 I cos[( ωt + φ v ) ( φ v φ i )] = 2 I cos( φ v φ i ) cos( ωt + φ v ) + 2 I sin( φ v φ i ) sin( ωt + φ v ) . (1.11) The instantaneous power expression that follows comprises two terms, p ( t ) = V I cos( φ v φ i )[2 cos 2 ( ωt + φ v )] + V I sin( φ v φ i )[2 sin( ωt + φ v ) cos( ωt + φ v )] = V I cos( φ v φ i )[1 + cos(2 ωt + φ v )] + V I sin( φ v φ i )[sin(2 ωt + φ v )] = P [1 + cos(2 ωt + φ v )] + Q sin(2 ωt + φ v ) (1.12) The average ( P ) and oscillating ( Q ) power definitions thus exactly match the active and reactive power definitions of (1.9). Thus, S = V I = P + jQ = V I cos( φ v φ i ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright P + j V I sin( φ v φ i ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright Q (1.13) c circlecopyrt Dr. P. Sensarma, Department of Electrical Engg, IIT-Kanpur, India. 7

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• Spring '16
• Sandeep Anand

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