Magnetically Coupled Circuits XIII.Frequency Response2. XIV.The Laplace Transform XV..[r]
(1)Electric Circuit Theory
(2)AC Power Analysis - sites.google.com/site/ncpdhbkhn
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
(3)AC Power Analysis
1 Instantaneous and Average Power 2 Maximum Average Power Transfer 3 RMS Value
4 Apparent Power and Power Factor 5 Complex Power
(4)Instantaneous Power (1)
AC Power Analysis - sites.google.com/site/ncpdhbkhn ( ) ( ) ( )
p t = v t i t ( ) m sin( v ) v t =V ω φt +
( ) m sin( i ) i t = I ω φt +
( ) m m sin( v) sin( i) p t V I ω φt ω φt
→ = + +
[cos( ) cos(2 )]
2
m m
v i v i
V I
t
φ φ ω φ φ
= − − + +
cos( ) cos(2 )
2 2
m m m m
v i v i
V I V I
t
φ φ ω φ φ
(5)Instantaneous Power (2)
( ) cos( ) cos(2 )
2 2
m m m m
v i v i
V I V I
p t = φ φ− − ω φ φt + +
cos( ) 2
m m
v i
V I
φ φ−
t
p(t)
0
2
m m
(6)Average Power (1)
AC Power Analysis - sites.google.com/site/ncpdhbkhn 0
1
( )
T
P p t dt T
= ∫
( ) cos( ) cos(2 )
2 2
m m m m
v i v i
V I V I
p t = φ φ− − ω φ φt + +
0
1 1 1 1
cos( ) cos(2 )
2 2
T T
m m v i m m v i
P V I dt V I t dt
T T
φ φ ω φ φ
→ = − ∫ − ∫ + +
The average of a sinusoid over its period is zero
1
cos( ) 2 m m v i
P V I φ φ
(7)Average Power (2)
m
V
=
V φv
*
m m
V I
=
VI φ φv − =i V Im m cos(φ φv − i) + jV Im m sin(φ φv − i )
1
cos( )
2 m m v i
P = V I φ φ−
m
I
=
I φi → =I* Im −φi
*
m m
V I
→ VI = φ φv − i
*
1
Re( ) 2
P
(8)Average Power (3)
AC Power Analysis - sites.google.com/site/ncpdhbkhn 2
1 1 1
cos(0)
2 m m 2 m m 2 m
P = V I = V I = I R
*
1 1
Re( ) cos( )
2 2 m m v i
P = VI = V I φ φ−
o 1
cos(90 ) 0 2 m m
P = V I =
:
v i
φ φ=
o 90 :
v i
(9)Average Power (4)
• Ex.:
(10)AC 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