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PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
C
C H
H A
A P
P T E
E R
7
AC Power
McGraw-Hill
1
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.1 Circuit for illustration of AC power
i(t)
v ( t)
+
~
–
AC circuit
v (t) = V cos(
t+
i (t) = I cos( t +
= Ie j
= Ve
V
I
)
)
1
–j V
+
~
–
V
I
e j( )
Z =
AC circuit
in phasor form
McGraw-Hill
2
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.11 The complex power triangle
S
Q
Z
Pav
|S|=
2
Pav
~~
Pav = VI cos
~~
Q = VI
sin
McGraw-Hill
+ Q
2
~. ~
= V I
3
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.18
~
IS
+
R
+
~
–
~
VS
~
VL
jX
L
–
McGraw-Hill
4
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.19
Im
Q = 119 VAR
60
P = 68.4 W
McGraw-Hill
5
GIORGIO RIZZONI
Re
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.20 Power factor correction
~
IS
Im
+
50
~
VS
+
~
–
~
VL
C
Q L = 119 VAR
j86.7
–
Parallel
capacitor
for power factor
correction
McGraw-Hill
P=
68.4 W
6
GIORGIO RIZZONI
Re
QC = –119 VAR
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.22
~
I
+
+ Current –
+
LV
–
+
~
V
–
–
External connections
McGraw-Hill
LI
+
Voltage
–
Wattmeter coils (inside)
7
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.23
~
I
ZS
LI
+
–
+
~
VS ~
LV
~
V
Load
–
McGraw-Hill
8
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.38 Ideal transformer
~
I1
+
~
V1
_
Primary
McGraw-Hill
~
I2
n1: n2
or
1:N
+
~
V2
_
Secondary
9
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.39 Center-tapped transformer
~
I1
+
~
V1
_
McGraw-Hill
n1
n2
n3
+
~
V2
_
n2 ~
~
V2 =
V1
n1
+
~
V3
_
n3 ~
~
V3 =
V1
n1
10
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.40 Operation of an ideal
transformer
~
I1
Z
~
VS
S
+
~
_
1: N
+
~
V1
+
~
V2
_
~
I2 =
McGraw-Hill
~
I2
Z
L
_
~
I1
N
~
~
V 2 == N V
11
GIORGIO RIZZONI
1
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.41 Impedance reflection across a
transformer
ZS
ZS
1:N
~ ~
_
VS +
1:N
~ _
ZL VS +~
ZL
Z
Z
N 2ZS = Z
ZS
~
VS _+~
Z =
Reflected load
impedance circuit
McGraw-Hill
ZL
N2
~
N VS +
_~
ZL
Reflected source
impedance circuit
12
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.46 Balanced three-phase AC circuit
a
a
+
~
_
~
Ia
~
Van
Za
In
n
~
Vcn
c
McGraw-Hill
+
~
_
n
+
~
_
~
Vbn
b
Zb
b
13
GIORGIO RIZZONI
~
Ic
Zc
~
Ib
c
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.47 Positive, or abc, sequence for
balanced three-phase voltages
Im
~
Vcn
~
V an
Re
~
Vbn
McGraw-Hill
14
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.48 Balanced three-phase AC circuit
(redrawn)
~
V an
_
~
_
~
V
_
~
c
~
Ic
b
+
cn
~
b
~
Ib
a
+
~
V bn
n
a
~
Ia
c
+
Za
Zb
n
Zc
~
In
McGraw-Hill
15
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.49 Delta-connected generators
a
+
~
V
ab
_
+
~_
b
c
_
+
~
V bc
_
~
V ca
+
A delta-connected
three-phase generator
with line voltages
V ab , V bc , V ca
McGraw-Hill
16
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.52 Balanced wye generators with
balanced delta load
Ia
a
Van
b
I ca
ZD
Vca
Ic
+
_~
Vcn
+
_
c¢
ZD
c
V bc
Ib
McGraw-Hill
+
+
_~
n
Vbn ~+_
a¢
_
+
17
GIORGIO RIZZONI
ZD
Vab
I ab
I bc
b¢
_
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.56 Line voltage convention for
residential circuits
Hot
+
~
V
~
B
_
Neutral
_
~
V
~
R
+
Hot
~
V
~
V
~
V
or
McGraw-Hill
W
B
R
=0
0
(Neutral)
= 120
0
(Hot)
= 120
180 (Hot)
~
~
V R = – VB
18
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 7.64 Structure of an AC power
distribution network
18 kV
3
345 kV
step-down
transformer
140 kV
Generator
Generating plant
46 kV
3
step-down
transformer
(sub-station)
4,800 V
4,800 V
3
step-down
transformer
3
step-down
transformer to
industrial or
commercial
customer
Center-tap
transformer
120/240 Volt
Three-wire service
McGraw-Hill
19
GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000