Download AC Power and Power Factor

Lesson 26
AC Power and
Power Factor
Learning Objectives

Perform AC power calculations using the complex
form of Apparent Power

Define power factor.

Define unity, leading and lagging power factors.
Review
Real and Reactive Power

The power triangle shows the relationship
between real (P), reactive (Q), and apparent (S)
power.
P  VI cos  S cos
Q  VI sin   S sin 
S  VI
(W)
(VAR)
(VA)
P

S
QL

P
QC
S
Use of complex numbers in Power calculations



AC power can be calculated using complex equations.
Apparent Power can be represented as a complex number
The resultant can be used to determine real and reactive power by
changing it to rectangular form.
I*is complex conjugate of I

S  VI  P  jQ
S
V
Z
P

2
QC
2

I Z
S
NOTE!
The complex conjugate of Current is used to make the power angle the same as
the impedance angle!
Example Problem 1
a.
Determine PT and QT by determining individual
component real and reactive powers and summing
them. Use PT and QT to find Apparent Power for the
circuit.
b. Determine the complex form of Apparent Power by
using the equation below. Change the complex S into
rectangular form to determine real and reactive total
powers.
S  VI

Power Factor


Power factor (FP) tells us what portion of the
apparent power (S) is actually real power (P).
Power factor is a ratio given by
FP = P / S

Power factor is expressed as a number
between 0 to 1.0 (or as a percent from 0% to
100%)
Power Factor

From the power triangle it can be seen that
FP = P / S = cos 

Power factor angle is thus given
 = cos-1(P / S)



For a pure resistance,  = 0º
For a pure inductance,  = 90º
For a pure capacitance,  = -90º
S
Q
NOTE: Ө is the phase angle of ZT, not the
current or voltage.

P
Unity power factor (FP = 1)




Implies that all of a load’s apparent power is
real power (S = P).
If FP = 1, then  = 0º.
It could also be said that the load looks purely
resistive.
Load current and voltage are in phase.

P,S
Q=0
Lagging power factor ( > 0º)

The load current lags load voltage

Implies that the load looks inductive.
S
Q

P
VARind
ELI
Leading power factor ( < 0º)

The load current leads load voltage ICE

Implies that the load looks capacitive.
P

Q
S
VARcap
Example Problem 2
a. Determine P,Q,S and the power factor for this circuit.
Draw the power triangle.
b. Is it a leading or lagging power factor?
c. Is the circuit inductive or capacitive?
Example Problem 3
a. Determine total current, apparent power, and the power
factor for this circuit. Is it a leading or lagging power
factor?
b. Determine total current, apparent power, and the power
factor if the capacitor reactance is decreased to 40
ohms. What kind of power factor does it have?