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Instantaneous Power

# Instantaneous Power - Power in Single Phase 2-Phase and...

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0 5 10 15 20 25 30 200 0 200 400 600 Single Phase Power Time Power P a t ( ) 10 watt 2 V rms volt sin ω t θ v + ( ) 2 I rms sin ω t θ i + ( ) amp t ms 1 0 5 10 15 20 25 30 2 0 2 4 6 Single Phase Power Time Power P a t ( ) kW V rms I rms cos θ v θ i ( ) kW t ms 1 P c t ( ) 2 V rms sin ω t θ v + ( ) 120 deg + 2 I rms sin ω t θ i + ( ) 120 deg + := P b t ( ) 2 V rms sin ω t θ v + ( ) 120 deg 2 I rms sin ω t θ i + ( ) 120 deg := P a t ( ) 2 V rms sin ω t θ v + ( ) 2 I rms sin ω t θ i + ( ) := kVAR kW kVA kW ms 10 3 sec ω 2 π freq := t 0 ms 0.05 ms , 30 ms .. := θ i 40 deg := θ v 0 deg := I rms 20 amp := V rms 120 volt := freq 60 Hz := Instantaneous Power: January-17-2008, by Dr. M. Giesselmann Power in Single Phase, 2-Phase and 3-Phase Systems:

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0 5 10 15 20 25 30 2 0 2 4 6 Single Phase and 3-Phase Power Time Power P a t ( ) P b t ( ) + P c t ( ) + kW P a t ( ) kW P b t ( ) kW P c t ( ) kW t ms 1
3 V rms I rms cos θ v θ i ( ) 5.516 kW = Total 3-phase Real Power P a t ( ) P b t ( ) + P c t ( ) + P tot = 3 V rms I rms cos θ v θ i ( ) = Therefore we get: V rms I rms cos 2 ω t θ v + 120 deg θ i + ( ) V rms I rms cos 2 ω t θ v + 240 deg θ i + ( ) V rms I rms cos 2 ω t θ v + θ i + ( )

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