Understanding Instantaneous, Average, and Reactive Power in Electrical Engineering, Slides of Electrical Circuit Analysis

Download Understanding Instantaneous, Average, and Reactive Power in Electrical Engineering and more Slides Electrical Circuit Analysis in PDF only on Docsity! Introduction to Power Calculations  Electrical Energy supplied in the form of Sinusoidal current and voltage  Sinusoidal Steady-State Power Calculations  Instantaneous Power  Average Power  Reactive Power  Complex Power  Apparent Power  Power Factor docsity.com Instantaneous Power  p = vi  p instantaneous power  v instantaneous voltage = Vmcos(ωt + θv)  i instantaneous current = Imcos(ωt + θi)  Any convenient reference selected for t=0  t=0 corresponds to i = Im  i = Imcos(ωt)  v = Vmcos(ωt + θv - θi) docsity.com Instantaneous Power   Instantaneous power has twice the frequency of the current and voltage  Instantaneous power is negative for a portion of its cycle  energy stored in capacitors and inductors is being extracted tIV tIVIVp iv mm iv mm iv mm   2sin)sin( 2 2cos)cos( 2 )cos( 2   docsity.com Instantaneous Power  Instantaneous power varies with time  Power delivered to motor varies with time  Torque produced is proportional to power  Variable Torque causes motor to vibrate  Motor driven appliances (refrigerators) vibrate docsity.com Average Power   average (real) power  reactive power  Average Power t2sinQt2cosPPp  )cos( 2 IVP ivmm  )sin( 2 IVQ ivmm  Pdt)t2sinQt2cosPP( T 1pdt T 1 Tt t Tt t 0 0 0 0    docsity.com Power for Purely Capacitive Circuits  In an capacitive circuit voltage and current lag by 900  θv = θi – 900   Average Power = 0  Energy continuously exchanged between circuit and source t2sinQp  -200.000 -150.000 -100.000 -50.000 0.000 50.000 100.000 150.000 200.000 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 time t p docsity.com Power Factor  Calculating Average (unit: W) & Reactive Power (unit: VAR)  and  Power Factor Angle (θv – θi)  Power Factor, pf = cos (θv – θi)  cos (θv – θi) = cos (θi – θv)  Leading power factor (current leads voltage)  pfa is –ve.  Lagging power factor (current lags voltage)  pfa is +ve.  Reactive Factor, rf = sin(θv – θi) )cos( 2 IVP ivmm  )sin(2 IVQ ivmm  docsity.com Example  At the terminals of a machine  v = 100cos(ωt + 150)  i = 4sin(ωt - 150)  Average & Reactive Power at the terminals?  Machine absorbing or delivering average power?  Machine absorbing or delivering reactive power? docsity.com