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Power Systems
Chapter 2
Basic Principles
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©Woei-Luen Chen
Basic Principles
Ch2 - 1
Pvumjof!
z
z
z
z
z
3/2!Qibtps!Sfqsftfoubujpo!
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©Woei-Luen Chen
Basic Principles
Ch2 - 2
3/2!Qibtps!Sfqsftfoubujpo! … Steady-state Calculation
peak value:Ⲙῤ
angular frequency:奺柣䌯
Instantaneous
voltage
phase:䚠ỵ
Im
I
V
Re
Effective phasor:
|V |
Vmax
2
Rectangular form:
©Woei-Luen Chen
Z 2S f
2S u 60Hz 377rad / sec
T
1 / 60Hz 16.67ms
1/ f
Basic Principles
Ch2 - 3
3/3!Dpnqmfy!Qpxfs!Tvqqmjfe!up!b!Pof.Qpsu!
Instantaneous power:
Average power:
Power Factor:
©Woei-Luen Chen
90 o d I d 90 o
Basic Principles
Ch2 - 4
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Im
i(t)
v(t)
V
I lags V
Lagging
PF
I
2|I |
Zt
Re
2 |V |
I
I
Im
i(t)
I
I leads V
Leading
PF
I
v(t)
Zt
Re
V
©Woei-Luen Chen
I
Basic Principles
Ch2 - 5
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ख़ཥۓကႝࢬБӛ
Ex2:
Ex1:
Im
Im
Im
I
I
I
Re
Re
V
I
V
V
I
©Woei-Luen Chen
Basic Principles
Re
Ch2 - 6
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CASE-I: PF<1 lagging (N is Inductive)
p(t)
p
(t))
v(t)
Zt
p t v t u i t i(t)
CASE-III: PF=1 (N is Resistive)
CASE-II: PF<1 leading (N is Capacitive)
p(t)
(t))
p(t)
(t))
v(t)
v(t)
Zt
Zt
i(t)
i(t)
©Woei-Luen Chen
Basic Principles
Ch2 - 7
Bd!dvssfou!efdpnqptjujpo!
ian (t) =
iR (t) +
Out of phase,
reactive power
component
p
In phase,
Real power
component
p
Ian2
=
IR2
iX (t)
+
I
IX2
iR
I
©Woei-Luen Chen
iX
Basic Principles
Ch2 - 8
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Instantaneous power:
1
2
Vmax I max ª¬cos TV T I cos 2Zt 2TV TV T I º¼
1
2
Vmax I max ª¬cos I cos 2 Zt TV cos I sin 2 Zt TV sin I º¼
1
2
Vmax I max cos I ª¬1 cos 2 Zt TV º¼ ª¬ sin I sin 2 Zt TV º¼
^
`
90o d I d 90 o
|V || I | cos I ª¬1 cos 2 Zt TV º¼ |V || I | ª¬ sin I sin 2 Zt TV º¼
P ª¬1 cos 2 Zt TV º¼ Q sin 2 Zt TV Active power (Real power, average power):
P |V || I | cos I
Reactive power:
Q |V || I | sin I
©Woei-Luen Chen
Basic Principles
Ch2 - 9
Qptjujwf!0!Ofhbujwf!;!bdujwf!qpxfs!boe!sfbdujwf!qpxfs!
Active power (Real power, average power):
P |V || I | cos I
Reactive power:
Q |V || I | sin I
Ex1:
Q
90o d I d 90 o
Im
P
Ex2:
I
I
Q
Im
V
P
I
Re
V
I
I 0
I !0
P>0: N is a load
Q<0: N is Capacitive,
leading power factor
P>0: N is a load
Q>0: N is Inductive,
lagging power factor
©Woei-Luen Chen
Basic Principles
Re
Ch2 - 10
Qptjujwf!0!Ofhbujwf!;!bdujwf!qpxfs!boe!sfbdujwf!qpxfs!
Im
Ex3:
S
Re
V
I
Im
Q
P
I
I
S
Re
V
I 0
N is a power source
N is Inductive,
lagging power factor
P>0: S is a load
Q<0: S is Capacitive,
leading power factor
©Woei-Luen Chen
Basic Principles
Ch2 - 11
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Active power (Real power, average power):
P |V || I | cos I
S VI *
|V | TV | I | T I
jQ
II
|V || I | TV T I I
P
Reactive power:
Q |V || I | sin I
III
Complex power:
IV
|V || I | I
|V || I | cos I j |V || I | sin I
P jQ
ҷӼ
ґ
Ю
©Woei-Luen Chen
Basic Principles
Ch2 - 12
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