enee204Lectures_09_10_Gomez

enee204Lectures_09_10_Gomez - 1 1 Welcome to ENEE 204...

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Unformatted text preview: 1 10/3/2005 10/3/2005 1 Welcome to ENEE 204 Welcome to ENEE 204 Basic Circuit Theory Basic Circuit Theory Lecture 9 Lecture 9 Chapter 3: Chapter 3: Recap: POWER in AC Recap: POWER in AC Exponentially Dependent AC Exponentially Dependent AC Chapter 4: Chapter 4: Review of Connections Review of Connections REMINDER: Midterm I, Thursday Oct.6, 2005 REMINDER: Midterm I, Thursday Oct.6, 2005 10/3/2005 10/3/2005 2 Complex and average power Complex and average power We can define complex power, ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ = I ˆ * V ˆ 2 1 Re P ave I ˆ V ˆ 2 1 S ˆ * = { } S P ave ˆ Re = 10/3/2005 10/3/2005 3 Comparing with the previous Comparing with the previous formula for average power formula for average power ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = I ˆ * V ˆ 2 1 Re P ave e V ˆ j m φ V ≡ e I ˆ j m φ I ≡ v I ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ) I φ V-j( φ e m I m V P ave 2 1 Re ( ) ) I φ V ( φ j ) I φ V ( φ [ I V P m m ave − − − = sin cos Re 2 1 ) φ ( φ I V φ ( φ I V P I V RMS RMS I V m m ave − = − = cos ) cos 2 1 POWER FACTOR 10/3/2005 10/3/2005 4 Example: Power on Device R=10 Ω Z D I ˆ 5000 + − ( ) ( ) kV e e Z I V j j D D D 0.142j 464 . 322 . 3.54e 36 . 22 1 . 158 ˆ ˆ = = = ∴ − j D e j Z 464 . 36 . 22 10 20 = + = W x W A e kV I V j D D 5 5 322 . 0.142j- ave 10 5 . 2 ) 464 cos(. 2.8x10 ) 1 . 158 )( (3.54e 2 1 Re ˆ ˆ 2 1 Re P = = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ∴ − + A e j Z V I j T s D 322 . 1 . 158 10 30 5000 ˆ − = + = = 2 10/3/2005 10/3/2005 5 What is the Power Factor? What is the Power Factor? ) cos( I V PF φ φ − = Power factor: This is a measure of the efficiency that average power is dissipated in the device network. Note with care that z I V φ φ φ = − And: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − − resistance reactance tan tan 1 1 R X z φ Z + _ V ˆ I ˆ Z = R + jX PF = 1 is great. It simply means delivering the highest power with least current. 10/3/2005 10/3/2005 6 Problem: what is the optimal value of the Problem: what is the optimal value of the capacitor for increasing the power factor of capacitor for increasing the power factor of an electric motor? an electric motor? Electric motor is modeled as an inductor and resistor We will see that by adding a capacitor we can increase the power factor R L v s (t) C AC source at 60 Hz 10/3/2005 10/3/2005 7 Impedance of motor with an Impedance of motor with an added added capacitor capacitor R L C I ˆ V ˆ 1 I ˆ C RL eff Z Z Z || = ( ) 2 2 2 1 1 1 1 1 1 L R L j R C j L j R C j Z Z Z RL C eff ω ω ω ω ω + − + = + + = + = ( ) ( ) L j R C j L R L R ω ω ω ω − + + + = 2 2 2 2 2 2 ( ) R j L L C CR L R + − + + = ω ω ω ω ω 2 2 2 2 2 2 Looks complicated, but otherwise easy to get....
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This note was uploaded on 04/07/2008 for the course ENEE 204 taught by Professor Gomez during the Fall '04 term at Maryland.

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enee204Lectures_09_10_Gomez - 1 1 Welcome to ENEE 204...

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