Lecture 32
•Review: AC power analysis
• Average power, complex power, power
triangles
• RMS values
• Power factor
•Power factor correction
•Related educational modules:
–Section 2.9.1, 2.9.2
AC power analysis
• Average power:
• Average power in terms of RMS (or effective) values:
• Complex power:
Power triangles
• Complex power
(rectangular form):
• Real (average) and
reactive power:
• Presented graphically:
Power factor (pf)
• Power factor:
• Load impedance:
V
ZL 
I
Z L  V   I
Z L   v   i
Example 1
For the circuit below, determine:
(a) the complex power delivered by the source
(b) the average power delivered by the source
•
•
•
•
•
Outline problem on previous slide:
1. find equivalent impedance
2. find source current
3. complex power = VI*/2
4. Average power = (Vm*Im/2)*cos(thetavthetai)
(a) Determine the complex power delivered by the source
(b) Determine the average power delivered by the source
Effect of pf on power delivery
• If v - i  0, we have some
reactive power that is not
consumed by the load
– The current provided to the
load is higher than
necessary
– Results in additional power
dissipated during delivery
– Power companies don’t like
this!
Power factor correction
• Power companies may require that users maintain a
minimum power factor
– e.g. pf > 0.9
• Most large loads are inductive in nature
– e.g. inductive motors
• Power factor correction may be necessary
– The approach must be inexpensive & simple to implement
• Adding a capacitor in parallel with the inductive load
will increase the power factor
Power factor correction – continued
• We have an inductive
load with some power
factor cos1:
• The power triangle is
shown below:
Power factor correction – continued again
• We can increase the
power factor by adding
a capacitor in parallel
with the load:
• The power triangle then
becomes:
I
V
+
-
ZL
ZC
Example 2 – power factor correction
For the circuit below if
(a) Determine the power factor
(b) Re-design the circuit so that pf = 1
Example 2 – Determine pf
Example 2 – Re-design circuit so that pf = 1