1. Lesson 26 AC Power and Power Factor

2. Learning Objectives
Perform AC power calculations using the complex form of Apparent Power
Define power factor.
Define unity, leading and lagging power factors.

3. Real and Reactive Power
Review
Real and Reactive Power
The power triangle shows the relationship between real (P), reactive (Q), and apparent (S) power.

4. 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.
NOTE!
The complex conjugate of Current is used to make the power angle the same as the impedance angle!

5. Example Problem 1
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.

6. 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%)

7. 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
NOTE: Ө is the phase angle of ZT, not the current or voltage.

8. 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.

9. Lagging power factor ( > 0º)
The load current lags load voltage ELI
Implies that the load looks inductive.

10. Leading power factor ( < 0º)
The load current leads load voltage ICE
Implies that the load looks capacitive.

11. 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?

12. 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?