Chapter 11 AC Power Analysis

1. Chapter 11AC 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 Powerp(t) is the power at any instant of time.

3. Instantenous AC Power • Instantenous Powerp(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 • 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. Example 1Calculate the instantaneous power and average power absorbed by a passive linear network if: Instantenous and Average Power

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 ZLrepresents any element that is absorbing the power generated by the circuit. • Find the load ZL that will absorb the Maximum Average Powerfrom 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+ jXThZL= RL+ jXL

14. Maximum Average Power Transfer Condition • Therefore: ZL= RTh - XTh = ZThwill 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 Load RL • 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