1. Lecture 07
AC POWER
&
POWER FACTOR

2. Lesson Objectives
Compute and define apparent, reactive, and average power for capacitors, inductors, and resistors.
Compute and draw the power triangle for RC, RL, and RLC circuits.
Define and compute the power factor for RC, RL, and RLC circuits.
Summarize the basic steps to compute AC power in all or part of a circuit.

3. COMPLEX POWER

4. COMPLEX POWER
The frequency domain representations of the current and voltage of an element
and

5. Definition of Complex Power

6. The magnitude of S is called the Apparent Power:

7. Converting the complex power from polar to rectangular form:

8. Real & Imaginary part of S

9. AVERAGE POWER, P
The real part of S is called Average Power, P. The unit is Watts.

10. REACTIVE POWER, Q
The imaginary part of S is called Reactive Power, Q. The unit is Var.

11. The complex power may be expressed in terms of the load impedance, Z:

12. S in terms of Z

13. AVERAGE POWER

14. AC AVERAGE POWER where;
Average power is independent of whether v leads i, or i leads v.

15. Average Power in RESISTOR
Since ||=0o and cos (0o) =1

16. Average Power in L and C PAV in a capacitor and inductor is 0, since;
|C|= |L|= 90o and cos (90o) =0.

17. REACTIVE POWER

18. REACTIVE POWER, Q
The reactive power, Q is given by:

19. Reactive power repeatedly stored and returned to a circuit in either a capacitor or an inductor.

20. Q For Various Load Q = 0 for resistive load
Q > 0 for inductive load
Q < 0 for capacitive load

21. POWER FACTOR

22. POWER FACTOR
The factor that has the significant control over the delivered power level is the cos (), where:
No matter what level I and V are, if:
cos ()=0, >> the power delivered is zero. cos ()=1, >> the power delivered is max.

23. POWER FACTOR
Power Factor equation:
where,

24. Power Factor Leading or Lagging?
Inductive circuits have lagging power factors.
Capacitive circuits have leading power factors.
Power factors follow the current.
Remember ELI and ICE

25. Ex. Find power factor if, Sinusoidal shift to the right
Sinusoidal shift to the left

26. Solution
Lagging because current is lagging and ELI.

27. POWER TRIANGLE

28. Power Triangle and Apparent Power
The impedance triangle with R, X, and Z may be shown to be similar to the power triangle with P, Q, and S, respectively as components.
Apparent power – A useful quantity combining the vector sum of P and Q.

29. Recall the Impedance TriangleXL Z q R

30. The Power Phasor
I2XL
I2Z q
I2R

31. The Power Triangle S QL q P

32. S P
+QL (lagging) Re Im
-QC (leading)

33. SUMMARY OF POWER

34. IMPORTANCE OF S S contains all power of a load.
The real part of S is the real power, P
Its imaginary part is the reactive power, Q.
Its magnitude is the apparent power
The cosine of its phase angle is the power factor, pf.

36. Review Quiz Name the three types of power. Q has units of … ?
P has units of … ?
S has units of … ?
Formula for P,Q,S… ?
Power factor is … ?
T/F: Power factor can never be greater than one or less than zero.