24-AC Power w corrections

24-AC Power w corrections - AC Power AC Power I Fred Terry...

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C Power I AC Power I © Fred Terry all, 008 Fall, 2008 1
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Understanding AC Power • Power Delivery (Detroit Edison) ommunications Electronics ) ()() t vtit Communications Electronics • Dynamic Power Dissipation in Logic Circuits () pt • Everything in This Area Rests on the Fact that Instantaneous ower Given by: i(t) + Power Is Given by: Circuit Element v(t) = • p(t) is NOT A LINEAR FUNCTION _ 2 – Superposition does not apply
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stantaneous Power for Instantaneous Power for Sinusoids () cos ( ) cos mv i vt V t it I t ω θ =+ ()() cos( )cos( ) mi mm v i pt vtit VI t t ωθ = + [] 1 cos( )cos( ) cos( ) cos( ) 2 AB A B A B =− + + Constantin time ACwith2 ω oscillation 1 ( ) cos (2 ) 2 v i v i t θω ⎡⎤ + + + ± ²³ ² ´± ² ² ²³ ² ²²´ 3 ⎣⎦
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Example θ v =0, θ i = π /4 1.5 v/Vm Normalized Voltage Phase 0 i/Im Normalized Current Phase pi/4 Normalized Power p/(Vm*Im) Average Power/(Vm*Im) 0.5 1 age Phase 0 -0.5 0 rmalized Volt a 5 -1 v/Vm No r 4 -1.5 -1 -0.5 0 0.5 1 time
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Average Power ⎡⎤ Constantin time ACwith2 ω oscillation 1 () cos ( ) cos (2 ) 2 ) mm v i v i pt VI t verage Power Givenby IntegrationOver OneCyc Period θ θω ⎢⎥ =− + + + ⎣⎦ ±²³² ´± ² ² ²³ ² ²²´ 21 Average Power Givenby IntegrationOver OneCycle Period T f π ω == 0 1 T ave Pp t d t T = Constantin t 11 cos( ) 2 ave m m v i PV I T θθ 00 ime ω oscillation cos(2 ) TT vi dt t dt ωθθ ++ + ∫∫ ² ² 5 1 cos( ) 2 ave m m v i I
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Phasors & Average Power i N V v j jt m phasor VV ee θ ω = N I i j j t m phasor II e e Notethat = ± () * VI c o s s i n mm v i v i v i j so θθ ⋅= = + [] ** * 11 Re V I Re V I Re S 22 ave P ⎡⎤ =⋅ = = ⎣⎦ rms rms 1 S V I Complex Power 2 Complex PowerisConserved ≡⋅ = 6 [ ] 1 Re V I 2 ave P
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24-AC Power w corrections - AC Power AC Power I Fred Terry...

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