AC POWER CALCULATION

1
AC POWER CALCULATION Instantaneous, average and
reactive power Apparent Power and Power
Factor Complex Power
SEE 1023 Circuit Theory
Dr. Nik Rumzi Nik Idris
2
Instantaneous, Average and Reactive Power
v(t) ?
Instantaneous power absorbed by the network is,
p v(t).i(t)
Let v(t) Vm cos (?t ?v) and i(t)
Imcos(?t ?i)
Which can be written as
v(t) Vm cos (?t ?v ? ?i) and i(t)
Imcos(?t)
3
v(t) Vm cos (?t ?v ? ?i) and i(t)
Imcos(?t)
p Vm cos(?t ?v ?i ) . Im cos(?t)
Example when ?v ? ?i 45o
45o
positive p power transferred from source to
network
Instantaneous Power (p)
negative p power transferred from network to
source
4
v(t) Vm cos (?t ?v ? ?i) and i(t)
Imcos(?t)
p Vm cos(?t ?v ?i ) . Im cos(?t)
Using trigonometry functions, it can be shown
that
Which can be written as
p P Pcos(2?t) ? Qsin(2?t)
5
(No Transcript)
6
Example for ?v-?i 45o
7
p P P cos(2?t) ? Q sin(2?t)
P average power
Q reactive power
8
p P P cos(2?t) ? Q sin(2?t)
P AVERAGE POWER

• Useful power also known as ACTIVE POWER

• Converted to other useful form of energy heat,
  light, sound, etc

• Power charged by TNB

Q REACTIVE POWER

• Power that is being transferred back and forth
  between load and source

• Associated with L or C energy storage element
  no losses

• Is not charged by TNB

• Inductive load Q positive, Capacitive load Q
  negative

9
Power for a resistor
Q reactive power 0
10
Power for an inductor
P average power 0
11
Power for a capacitor
P average power 0
12
Apparent Power and Power Factor
Consider v(t) Vm cos (?t ?v) and i(t)
Imcos(?t ?i)
We have seen,
Is known as the APPARENT POWER
VA
13
Apparent Power and Power Factor
We can now write,
is known as the POWER FACTOR
The term
For inductive load, (?v ? ?i) is positive ?
current lags voltage ? lagging pf
For capacitive load, (?v ? ?i) is negative ?
current leads voltage ? leading pf
14
Apparent Power and Power Factor
15
Apparent Power and Power Factor
(lagging)
Power factor of the load cos (10-(-40)) cos
(50o) 0.6428
Apparent power, S 1250 VA
Active power absorbed by the load is 250(5) cos
(50o) 1250(0.6428) 803.5 watt
Reactive power absorbed by load is 250(5) sin
(50o) 1250(0.6428) 957.56 var
16
Complex Power
Defined as
(VA)
?
Where,
and
and
If we let
(VA)
17
Complex Power
(VA)
Where,
18
Complex Power
The complex power contains all information about
the load
We have seen before
Apparent power, S 1250 VA
Active power, P 803.5 watt
Reactive power, Q 957.56 var
With complex power,
S 250?10o (5?-40o) VA
S 1250 ?50o VA
S (803.5 j957.56) VA
S S Apparent power
1250 VA
19
Complex Power
Other useful forms of complex power
P
Q
20
Complex Power
Other useful forms of complex power
21
Conservation of AC Power
Complex, real, and reactive powers of the sources
equal the respective sums of the complex, real
and reactive powers of the individual loads
22
Conservation of AC Power
Complex, real, and reactive powers of the sources
equal the respective sums of the complex, real
and reactive powers of the individual loads
Ss Ps jQs (P1 P2 P3) j (Q1 Q2 Q3)
23
Maximum Average Power Transfer
Max power transfer in DC circuit can be applied
to AC circuit analysis
What is the value of ZL so that maximum average
power is transferred to it?
24
Maximum Average Power Transfer
What is the value of ZL so that maximum average
power is transferred to it?
25
Maximum Average Power Transfer
What is the value of ZL so that maximum average
power is transferred to it?
ZTh RTh jXTh
ZL RL jXL
and
P max when
26
Maximum Average Power Transfer
What is the value of ZL so that maximum average
power is transferred to it?
XL ?XTh , RL RTh