1 Eeng 224 Chapter 11 AC Power Analysis Huseyin Bilgekul Eeng224 Circuit Theory II Department of Electrical and Electronic Engineering Eastern Mediterranean University 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

2 Eeng 224 Instantenous AC Power  Instantenous Power p(t) is the power at any instant of time.

3 Eeng 224 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 Eeng 224 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 Eeng 224 Instantenous and Average Power

6 Eeng 224 Average Power  The average power P is the average of the instantaneous power over one period.

7 Eeng 224 Average Power  The average power P, is the average of the instantaneous power over one period.  A resistor has (θ v -θ i )=0º so the average power becomes: 1.P is not time dependent. 2.When θ v = θ i, it is a purely resistive load case. 3.When θ v – θ i = ±90 o, it is a purely reactive load case. 4.P = 0 means that the circuit absorbs no average power.

8 Eeng 224 Instantenous and Average Power  Example 1 Calculate the instantaneous power and average power absorbed by a passive linear network if:

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10 Eeng 224 Average Power Problem  Practice Problem 11.4: Calculate the average power absorbed by each of the five elements in the circuit given.

11 Eeng 224 Average Power Problem

12 Eeng 224 Maximum Average Power Transfer a) Circuit with a loadb) Thevenin Equivalent circuit  Finding the maximum average power which can be transferred from a linear circuit to a Load connected. Represent the circuit to the left of the load by its Thevenin equiv. Load Z L represents any element that is absorbing the power generated by the circuit. Find the load Z L that will absorb the Maximum Average Power from the circuit to which it is connected.

13 Eeng 224 Maximum Average Power Transfer Condition Write the expression for average power associated with Z L : P(Z L ). Z Th = R Th + jX Th Z L = R L + jX L

14 Eeng 224 Maximum Average Power Transfer Condition  For Maximum average power transfer to a load impedance Z L we must choose Z L as the complex conjugate of the Thevenin impedance Z Th. Therefore: Z L = R Th - X Th = Z Th will generate the maximum power transfer. Maximum power P max

15 Eeng 224 Maximum Average Power Transfer  Practice Problem 11.5: Calculate the load impedance for maximum power transfer and the maximum average power.

16 Eeng 224 Maximum Average Power Transfer

17 Eeng 224 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 P max formula given before.  Maximum power can be calculated by finding the power of R L when X L =0. ● ● RESISTIVE LOAD

18 Eeng 224 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 Eeng 224 Maximum Average Power for Resistive Load  Notice the way that the maximum power is calculated using the Thevenin Equivalent circuit. RLRL

20 Eeng 224 a) AC circuit 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. b) DC circuit

21 Eeng 224 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 Eeng 224 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. 4t4t 8-4t

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