Magnetically Coupled Circuits XIII.Frequency Response2. XIV.The Laplace Transform XV..[r]
Trang 1Electric Circuit Theory
AC Power Analysis
Trang 2AC Power Analysis - sites.google.com/site/ncpdhbkhn 2
Contents
I Basic Elements Of Electrical Circuits
II Basic Laws
III Electrical Circuit Analysis
IV Circuit Theorems
V Active Circuits
VI Capacitor And Inductor
VII First Order Circuits
VIII.Second Order Circuits
IX Sinusoidal Steady State Analysis
X AC Power Analysis
XI Three-phase Circuits
XII Magnetically Coupled Circuits
XIII.Frequency Response
XIV.The Laplace Transform
XV Two-port Networks
Trang 3AC Power Analysis
1 Instantaneous and Average Power
2 Maximum Average Power Transfer
3 RMS Value
4 Apparent Power and Power Factor
5 Complex Power
6 Power Factor Improvement
Trang 4Instantaneous Power (1)
AC Power Analysis - sites.google.com/site/ncpdhbkhn 4
( ) ( ) ( )
p t = v t i t
( ) m sin( v )
v t = V ω φ t + ( ) m sin( i )
i t = I ω φ t + ( ) m m sin( v ) sin( i )
p t V I ω φ t ω φ t
2
m m
V I
t
t
Trang 5Instantaneous Power (2)
cos( ) 2
m m
V I
φ φ −
t
p(t)
0
2
m m
V I
Trang 6Average Power (1)
AC Power Analysis - sites.google.com/site/ncpdhbkhn 6
0
1
( )
T
P p t dt
T
= ∫
p t = φ φ − − ω φ φ t + +
The average of a sinusoid over its period is zero
1
cos( )
2 m m v i
Trang 7Average Power (2)
m
V
=
*
m m
V I
=
VI φ φ v − = i V I m m cos( φ φ v − i ) + jV I m m sin( φ φ v − i )
1
cos( )
2 m m v i
P = V I φ φ −
m
I
=
m
I
*
m m
V I
*
1
2
P
Trang 8Average Power (3)
AC Power Analysis - sites.google.com/site/ncpdhbkhn 8
2
cos(0)
2 m m 2 m m 2 m
P = V I = V I = I R
*
o
1
cos(90 ) 0
2 m m
:
φ φ =
o
90 :
v i
φ φ − = ±
Trang 9Average Power (4)
• Ex.:
v(t) = 150sin(314t – 30 o ) V
i(t) = 10sin(314t + 45 o ) A
Find P?
Trang 10AC Power Analysis
1 Instantaneous and Average Power
2 Maximum Average Power Transfer
3 RMS Value
4 Apparent Power and Power Factor
5 Complex Power
6 Power Factor Improvement
AC Power Analysis - sites.google.com/site/ncpdhbkhn 10