1. Lecture 71 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

2. Lecture 72 The First of Many Definitions Today average power, P = V rms I rms cos(  v -  i ) apparent power = V rms I rms –apparent power is expressed in volt-amperes (VA) or kilovolt-amperes (kVA) to distinguish it from average power

3. Lecture 73 Power Factor (pf) Derivation of power factor (0  pf  1) a low power factor requires more rms current for the same load power which results in greater utility transmission losses in the power lines, therefore utilities penalize customers with a low pf

4. Lecture 74 Power Factor Angle (  Z L ) power factor angle is  v -  i =  Z L (the phase angle of the load impedance) power factor (pf) special cases –purely resistive load:  Z L = 0°  pf=1 –purely reactive load:  Z L = ±90°  pf=0

5. Lecture 75 Class Example Extension Exercise E9.11

6. Lecture 76 Complex Power (S) Definition of complex power, S –P is the real or average power –Q is the reactive or quadrature power, which indicates temporary energy storage rather than any real power loss in the element; and Q is measured in units of volt- amperes reactive, or var

7. Lecture 77 Complex Power (S) This is really a return to phasor use of voltage and current rather than just the recent use of magnitude and rms values Complex power is expressed in units of volt-amperes like apparent power Complex power has no physical significance; it is a purely mathematical concept Note relationships to apparent power and power factor of last section |S| = V rms I rms = apparent power  S =  (  v -  i ) =  Z L = power factor angle

8. Lecture 78 From a Load Perspective Recall phasor relationships between current, voltage, and load impedance The load impedance also has several alternate expressions

9. Lecture 79 Real Power (P) Alternate expressions for the real or average power (P)

10. Lecture 710 Reactive Power (Q) Alternate expressions for the reactive or quadrature power (Q)

11. Lecture 711 Power Triangle The power triangle relates pf angle to P and Q –the phasor current that is in phase with the phasor voltage produces the real (average) power –the phasor current that is out of phase with the phasor voltage produces the reactive (quadrature) power Re Im P=I 2 rms Re(Z) Q=I 2 rms Im(Z) S=I 2 rms Z  v -  i

12. Lecture 712 Summarizing Complex Power (S) Complex power (like energy) is conserved, that is, the total complex power supplied equals the total complex power absorbed,  S i =0

13. Lecture 713 Class Examples Extension Exercise E9.12 Extension Exercise E9.13