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

2 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 Power in AC Circuit

3 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 or i lags v) For a network that is primarily capacitive,  is negative (i leads v) Power in AC Circuit

4 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 Power in AC Circuit

5 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 V rms and I rms OR; [watt, W] Power in AC Circuit

Power Factor (Review) Average Power, P For a purely resistive load; Hence; For purely inductive or purely capacitive load; Hence;

7 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] Power in AC Circuit

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

9 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 V rms and I rms OR [volt-ampere reactive, VAR] For the resistor, Power in AC Circuit

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

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

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

Power Triangle For an inductive load, the phasor power S, as it is often called, is defined by S = P + jQ L For a capacitive load, the phasor power S is defined by S = P - jQ C

14 If a network has both capacitive and inductive elements, the reactive component of the power triangle will be determined by the difference between the reactive power delivered to each. If Q L  Q C, the resultant power triangle will be similar to the inductive load power diagram. If Q C  Q L, 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 Power Triangle

The Total P, Q, and S The total number of watts P T, volt-amperes reactive Q T, and volt-amperes S T, and the power factor F p of any system can be found using the following procedure: 1.Find the real (average) power and reactive power for each branch of the circuit. 2.The total real power of the system (P T ) is the sum of the average power delivered to each branch 3.The total reactive power (Q T ) is the difference between the reactive power of the inductive loads and that of the capacitive loads. 4.The total apparent power is S T 2 = P T 2 + Q T 2. 5.The total power factor is P T / S T.

16 There are two important points in the previous slide: First, the total apparent power, S T must be determined from the total average P T and total reactive powers Q T 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 P T, total reactive Q T, or total apparent power S T is independent of whether the loads are in series, parallel, or series-parallel The Total P, Q, and S

17 Example Find the total number of watts P T, volt-amperes reactive Q T, and volt-amperes S T and draw the power triangle. 2.Find the power factor F p 3.Find the current in phasor form The Total P, Q, and S

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

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

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

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

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

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

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

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

26