AC Power V3

# AC Power V3 - AC Power DePiero EE 201 Learning Objec7ves •  Compute average power for AC circuits. Compute power factor. •

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Unformatted text preview: AC Power DePiero EE 201 Learning Objec7ves •  Compute average power for AC circuits. Compute power factor. •  Use complex power; Compute apparent, real and reac7ve power. •  Determine components for power factor correc7on. •  Note: These topics are geared towards improving eﬃciency of power delivery. Average Power Determines Ability To Do Real Work •  Instantaneous power includes both constant and oscilla7ng por7ons: p( t ) = v ( t )i( t ) = VI cos( wt ) cos( wt − θ ) VI VI p( t ) = cos(θ ) + cos(2 wt − θ ) 2 2 € •  Oscilla7ng component (2wt) averages to zero € •  Angle between V,I determines average power PAVG = € VI cos(θ ) 2 Power Calcula7ons Conveniently Done via RMS •  How might the intensity of sin() be described? –  Peak amplitude? Mean? RMS! •  RMS value for sin() , cos(): VRMS •  Thus P = V I cos(θ ) AVG RMS RMS € VRMS = 1 = T ∫ T 0 1 T ∫ T 0 v ( t ) 2 dt A ( A sin( wt )) dt = 2 2 –  And θ is the phase diﬀerence between VRMS , IRMS € 2 –  For DC: P = V DC / R For AC: PAVG = VR2MS / R € € € € € Power Calcula7ons Conveniently Done via RMS v ( t ) = A sin( wt + α ) ‘Time-Domain Signal’ ˜ V = A <α ‘Signal in Phasor Form’ VRMS A = <α 2 ‘Phasor with an RMS value’ € •  Don’t use a 130V Cap, across a ‘120 V AC’ line € –  Because ‘120 V’ is really 120 VRMS, peaks at ~170V Complex Power Fic77ous, But Useful •  Deﬁne ‘Complex Power’: S = V I * = PAVG + jQ –  Conjugate give phase change of voltage vs current € The ‘Power Triangle’ S θ jQ Real Power = PAVG (Watts) Reactive Power = Q (VAR) PAVG Volts Amps Reactive €ower factor describes efficiency pf = cosθ P € € Pf ‘lagging’ <-> Q>0 <-> inductive load €Pf ‘leading’ <-> Q<0 <-> capacitive load € € Current leads/lags voltage € Z L = jwL 1 ZC = − j wC Power Factor Correc7on Reduces V,I Requirements Motor Motor with Correction S θ jQC jQL S PAVG jQL PAVG € € •  Flacen triangle by adding Qc to neutralize reac7ve power € € € € € € ...
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## This note was uploaded on 10/24/2011 for the course EE 251 taught by Professor Arakaki during the Spring '08 term at Cal Poly.

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