ELECTRICAL TECHNOLOGY ET 201

1. ELECTRICAL TECHNOLOGY ET 201 Explain and calculate average power, apparent power, reactive power Calculate the total P, Q and S and sketch the power triangle.

2. Power in AC Circuit • Power is distributed into the resistance and reactance in AC circuit. • The power delivered to a load at any instant is defined by the product of the applied voltage and the resulting current: • Since v and i are sinusoidal quantities

3. Power in AC Circuit The chosen v and i include all possibilities because • If the load is purely resistive:  = 0° • If the load is purely inductive:  = 90° • If the load is purely capacitive:  = - 90° • For a network that is primarily inductive,  is positive (v leads i ori lags v) • For a network that is primarily capacitive,  is negative (i leads v)

4. Power in AC Circuit • Positive power means that power has been distributed from supply into circuit. • Negative power means that the power has been distributed from circuit into supply. • There are three type of power in AC circuit: i) Average power, P ii) Apparent Power, S iii) Reactive Power, Q

5. Power in AC Circuit Average Power, P • The average power (real power) is the power delivered to the load and dissipated by the load. [watt, W] Where, θ : phase angle between Vrms and Irms OR ; [watt, W]

6. 14.5 Power Factor (Review) Average Power, P • For a purely resistive load; Hence; • For purely inductiveorpurely capacitive load; Hence;

7. Power in AC Circuit Apparent Power, S • From analysis of DC networks (and resistive elements above), it would seem apparent that the power delivered to the load is simply determined by P = VI, with no concern for the components of the load. • However, in Chapter 14 (Lecture 10) the power factor (cos θ) of the load has a pronounced effect on the power dissipated, less pronounced for more reactive loads. • Therefore P = VI is called apparent power, S. [volt-amperes, VA]

8. Power in AC Circuit Apparent Power, S OR ; [volt-amperes, VA] • The average power to the load is; However; Therefore • The power factor of a system Fp is

9. Power in AC Circuit Reactive Power, Q • In general, the reactive power associated with any circuit is defined to be [volt-ampere reactive, VAR] Where, θ : phase angle between Vrms and Irms OR [volt-ampere reactive, VAR] • For the resistor,

10. Power in AC Circuit Reactive Power, Q • For a purely inductive circuit, OR ; Since the apparent power, S = VI , and the average power for inductor, P = 0 vL leads iL by 90°

11. Power in AC Circuit Reactive Power, Q • For a purely capacitive circuit, OR ; Since the apparent power, S = VI , and the average power for capacitor, P = 0 iC leads vC by 90°

12. 19.7 Power Triangle • The three quantities average power P, apparent power S and reactive power Q can be related in the vector domain by with

13. 19.7 Power Triangle For an inductive load, the phasor power S, as it is often called, is defined by S = P + jQL For a capacitive load, the phasor powerSis defined by S = P - jQC

14. 19.7 Power Triangle • If a network has both capacitive and inductive elements, the reactive component of the power triangle will be determined by thedifference between the reactive power delivered to each. • If QL  QC, the resultant power triangle will be similar to the inductive load power diagram. • If QC  QL, the resultant power triangle will be similar to the capacitive load power diagram. • That the total reactive power is the difference between the reactive powers of the inductive and capacitive elements.

15. 19.7 The Total P, Q, and S The total number of watts PT, volt-amperes reactive QT, and volt-amperes ST, and the power factor Fp of any system can be found using the following procedure: • Find the real (average) power and reactive power for each branch of the circuit. • The total real power of the system (PT) is the sum of the average power delivered to each branch • The total reactive power (QT ) is the difference between the reactive power of the inductive loads and that of the capacitive loads. • The total apparent power is ST2 = PT2 + QT2. • The total power factor is PT /ST.

16. 19.7 The Total P, Q, and S There are two important points in the previous slide: • First, the total apparent power, ST must be determined from the total average PT and total reactive powers QT and cannot be determined from the apparent powers of each branch. • Second, and more important, it is not necessary to consider the series-parallel arrangement of branches. In other words, the total real PT , total reactive QT , or total apparent power ST is independent of whether the loads are in series, parallel, or series-parallel.

17. 19.7 The Total P, Q, and S Example 19.3 • Find the total number of watts PT, volt-amperes reactive QT, • and volt-amperes ST and draw the power triangle. • Find the power factor Fp • Find the current in phasor form.

18. 19.7 The Total P, Q, and S Example 19.3 – Solution 1. Load 1

19. 19.7 The Total P, Q, and S Example 19.3 – solution (cont’d) Load 2

20. 19.7 The Total P, Q, and S Example 19.3 – solution (cont’d) Load 3

21. 19.7 The Total P, Q, and S Example 19.3 – solution (cont’d) Total

22. 19.7 The Total P, Q, and S Example 19.3 – solution (cont’d) Total

23. 19.7 The Total P, Q, and S Example 19.3 – solution (cont’d) The power triangle; Total Note: ST is NOT equal to sum of each branch!!

24. 19.7 The Total P, Q, and S Example 19.3 – solution (cont’d) 2. The power factor FP

25. 19.7 The Total P, Q, and S Example 19.3 – solution (cont’d) 3. The current Since Fp is leading I leads E, predominantly capacitive circuit.