1. Chapter 11 AC Power Analysis
Chapter Objectives:
Know the difference between instantaneous power and average power
Learn the AC version of maximum power transfer theorem
Learn about the concepts of effective or rms value
Learn about the complex power, apparent power and power factor
Understand the principle of conservation of AC power
Learn about power factor correction
Huseyin Bilgekul
Eeng224 Circuit Theory II
Department of Electrical and Electronic Engineering
Eastern Mediterranean University

2. Instantenous AC Power
Instantenous Power p(t) is the power at any instant of time.

3. Instantenous AC Power
Instantenous Power p(t) is the power at any instant of time.
The instantaneous power is composed of two parts.
A constant part.
The part which is a function of time.

4. Instantenous and Average Power
The instantaneous power p(t) is composed of a constant part (DC) and a time dependent part having frequency 2ω.
Instantenous Power p(t)

5. Instantenous and Average Power

6. Average Power
The average power P is the average of the instantaneous power over one period .

7. Average Power A resistor has (θv-θi)=0º so the average power becomes:
The average power P, is the average of the instantaneous power over one period .
A resistor has (θv-θi)=0º so the average power becomes:
P is not time dependent.
When θv = θi , it is a purely resistive load case.
When θv– θi = ±90o, it is a purely reactive load case.
P = 0 means that the circuit absorbs no average power.

8. Instantenous and Average Power
Example 1 Calculate the instantaneous power and average power absorbed by a passive linear network if:

10. Average Power Problem
Practice Problem 11.4: Calculate the average power absorbed by each of the five elements in the circuit given.

11. Average Power Problem

12. Maximum Average Power Transfer
Finding the maximum average power which can be transferred from a linear circuit to a Load connected.
a) Circuit with a load
b) Thevenin Equivalent circuit
Represent the circuit to the left of the load by its Thevenin equiv.
Load ZL represents any element that is absorbing the power generated by the circuit.
Find the load ZL that will absorb the Maximum Average Power from the circuit to which it is connected.

13. Maximum Average Power Transfer Condition
Write the expression for average power associated with ZL: P(ZL).
ZTh = RTh + jXTh ZL = RL + jXL

14. Maximum Average Power Transfer Condition
Therefore: ZL = RTh - XTh = ZTh will generate the maximum power transfer.
Maximum power Pmax
For Maximum average power transfer to a load impedance ZL we must choose ZL as the complex conjugate of the Thevenin impedance ZTh.

15. Maximum Average Power Transfer
Practice Problem 11.5: Calculate the load impedance for maximum power transfer and the maximum average power.

16. Maximum Average Power Transfer

17. Maximum Average Power for Resistive Load
When the load is PURELY RESISTIVE, the condition for maximum power transfer is:
Now the maximum power can not be obtained from the Pmax formula given before.
Maximum power can be calculated by finding the power of RL when XL=0. ●
RESISTIVE LOAD ●

18. Maximum Average Power for Resistive Load
Practice Problem 11.6: Calculate the resistive load needed for maximum power transfer and the maximum average power.

19. Maximum Average Power for Resistive LoadRL
Notice the way that the maximum power is calculated using the Thevenin Equivalent circuit.

20. Effective or RMS Value
The EFFECTIVE Value or the Root Mean Square (RMS) value of a periodic current is the DC value that delivers the same average power to a resistor as the periodic current.
a) AC circuit
b) DC circuit

21. Effective or RMS Value of a Sinusoidal
The Root Mean Square (RMS) value of a sinusoidal voltage or current is equal to the maximum value divided by square root of 2.
The average power for resistive loads using the (RMS) value is:

22. Effective or RMS Value
Practice Problem 11.7: Find the RMS value of the current waveform. Calculate the average power if the current is applied to a 9  resistor. 4t
8-4t