1
ECE201 Linear Circuit Analysis I
Lecture 38
Topic:
Complex Power: Reactive & Apparent Power; Conservation of Power
1. Real Power
P
ave
=
V
eff
⋅
I
eff
⋅
cos
θ
Z
=
V
rms
⋅
I
rms
⋅
cos
θ
Z
What are the meanings of P
ave
, V
eff
(V
rms
), I
eff
(I
rms
), and
θ
Z
?
What are their units?
P
ave
is also called the
Real Power
, its unit is
watts
, or
W
.
2. Apparent Power
The quantity V
eff
· I
eff
is called the
Apparent Power
, its unit is
volt-ampere
, or
VA
.

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2
3. Complex Power
(1) Complex power is a phasor:
eff
v
eff
V
V
=
∠θ
i
eff
eff
θ
I
I
∠
=
*
eff
eff
I
V
S
×
≡
(Definition of complex power)
(
)
eff
v
eff
i
eff
eff
v
i
eff eff
z
eff eff
z
S
V
I
V
I
V
I
cos
jV
I
sin
=
∠θ ×
∠ − θ
=
⋅
∠ θ
− θ
=
θ
+
θ
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P
ave
+
jQ
(2) complex
=
average
+ j
reactive
power
power
power
(
)
(
)
2
2
eff eff
z
eff eff
z
eff eff
S
S
V
I
cos
V
I
sin
V
I
=
=
θ
+
θ
=
Therefore, the magnitude of the complex power is the apparent power in unit
(VA).
The reactive power:
{ }
Q
Im S
=
(VAR)
volt
ampere
reactive
P
ave
=
Scos
θ
z
(
W
)
Q = Ssin
θ
z
=
P
ave
tan
θ
z