1 Assad AbuJasser Ph D Electric Power Engineering

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1 Assad Abu-Jasser, Ph. D Electric Power Engineering The Islamic University of Gaza ajasser@iugaza.

1 Assad Abu-Jasser, Ph. D Electric Power Engineering The Islamic University of Gaza [email protected] edu. ps site. iugaza. edu. ps/ajasser Dr. Assad Abu-Jasser - EE Department - IUGaza

2 Review of AC Circuits Dr. Assad Abu-Jasser - EE Department - IUGaza

2 Review of AC Circuits Dr. Assad Abu-Jasser - EE Department - IUGaza

3 The Sinusoidal Waveform Dr. Assad Abu-Jasser - EE Department - IUGaza

3 The Sinusoidal Waveform Dr. Assad Abu-Jasser - EE Department - IUGaza

4 Example 1 A sinusoidal current has a maximum amplitude of 20 A. The

4 Example 1 A sinusoidal current has a maximum amplitude of 20 A. The current passes through one complete cycle in 1 ms. The magnitude of the current at zero time is 10 A. a) What is the frequency of the current in hertz? b) What is the frequency in radians per second? c) Write the expression for i(t) using the cosine function. Express Φ in degrees. d) What is the rms value of the current? Dr. Assad Abu-Jasser - EE Department - IUGaza

5 Example 2 A sinusoidal voltage is given by the expression υ=300 cos(120πt+30). a)

5 Example 2 A sinusoidal voltage is given by the expression υ=300 cos(120πt+30). a) What is the period of the voltage in ms? b) What is the frequency in hertz? c) Write the magnitude of the voltage at t=2. 778 ms? d) What is the rms value of the voltage? Dr. Assad Abu-Jasser - EE Department - IUGaza

6 Passive Circuit Elements in f-Domain V-I Relationship for a Resistor Dr. Assad Abu-Jasser

6 Passive Circuit Elements in f-Domain V-I Relationship for a Resistor Dr. Assad Abu-Jasser - EE Department - IUGaza

7 Passive Circuit Elements in f-Domain V-I Relationship for an Inductor Dr. Assad Abu-Jasser

7 Passive Circuit Elements in f-Domain V-I Relationship for an Inductor Dr. Assad Abu-Jasser - EE Department - IUGaza

8 Passive Circuit Elements in f-Domain V-I Relationship for a Capacitor Dr. Assad Abu-Jasser

8 Passive Circuit Elements in f-Domain V-I Relationship for a Capacitor Dr. Assad Abu-Jasser - EE Department - IUGaza

9 Impedance and Reactance Dr. Assad Abu-Jasser - EE Department - IUGaza

9 Impedance and Reactance Dr. Assad Abu-Jasser - EE Department - IUGaza

10 Example 3 A 90Ω resistor, a 32 m. H inductor, and a 5

10 Example 3 A 90Ω resistor, a 32 m. H inductor, and a 5 μF capacitor are connected in series across the terminals of a sinusoidal voltage source. The steady-state expression for the source voltage υs is 750 cos(5000 t+30 o) V. a) Construct the frequency-domain equivalent circuit b) Calculate the steady-state current i by the phasor method Dr. Assad Abu-Jasser - EE Department - IUGaza

11 The Instantaneous Power Dr. Assad Abu-Jasser - EE Department - IUGaza

11 The Instantaneous Power Dr. Assad Abu-Jasser - EE Department - IUGaza

12 Active and Reactive Power Dr. Assad Abu-Jasser - EE Department - IUGaza

12 Active and Reactive Power Dr. Assad Abu-Jasser - EE Department - IUGaza

13 Power for Purely Resistive Circuit Dr. Assad Abu-Jasser - EE Department - IUGaza

13 Power for Purely Resistive Circuit Dr. Assad Abu-Jasser - EE Department - IUGaza

14 Power for Purely Inductive Circuit Dr. Assad Abu-Jasser - EE Department - IUGaza

14 Power for Purely Inductive Circuit Dr. Assad Abu-Jasser - EE Department - IUGaza

15 Power for Purely Capacitive Circuit Dr. Assad Abu-Jasser - EE Department - IUGaza

15 Power for Purely Capacitive Circuit Dr. Assad Abu-Jasser - EE Department - IUGaza

16 The Power Factor Dr. Assad Abu-Jasser - EE Department - IUGaza

16 The Power Factor Dr. Assad Abu-Jasser - EE Department - IUGaza

17 The rms Value & Power Calculation Dr. Assad Abu-Jasser - EE Department -

17 The rms Value & Power Calculation Dr. Assad Abu-Jasser - EE Department - IUGaza

18 Example 4 a) A sinusoidal voltage having a maximum amplitude of 625 V

18 Example 4 a) A sinusoidal voltage having a maximum amplitude of 625 V is applied to the terminals of a 50 Ω resistor. Find the average power delivered to the resistor. b) Repeat (a) by first finding the current in the resistor Dr. Assad Abu-Jasser - EE Department - IUGaza

19 Complex Power Dr. Assad Abu-Jasser - EE Department - IUGaza

19 Complex Power Dr. Assad Abu-Jasser - EE Department - IUGaza

20 Example 5 An electric load operates at 240 V rms. The load absorbs

20 Example 5 An electric load operates at 240 V rms. The load absorbs an average power of 8 k. W at 0. 8 lagging power factor. a) Calculate the complex power of the load b) Calculate the impedance of the load Dr. Assad Abu-Jasser - EE Department - IUGaza

21 Balanced Three-Phase Voltages Dr. Assad Abu-Jasser - EE Department - IUGaza

21 Balanced Three-Phase Voltages Dr. Assad Abu-Jasser - EE Department - IUGaza

22 Three-Phase Voltage Sources Source Y Y ∆ ∆ Dr. Assad Abu-Jasser - EE

22 Three-Phase Voltage Sources Source Y Y ∆ ∆ Dr. Assad Abu-Jasser - EE Department - IUGaza Load Y ∆

23 Analysis of the Wye-Wye Circuit Va’n = Vb’n= Vc’n Zga=Zgb=Zgc Z 1 a=Z

23 Analysis of the Wye-Wye Circuit Va’n = Vb’n= Vc’n Zga=Zgb=Zgc Z 1 a=Z 1 b=Z 1 c ZA=ZB=ZC Dr. Assad Abu-Jasser - EE Department - IUGaza

24 Example 6 A balanced three-phase Y-connected generator with positive sequence has an impedance

24 Example 6 A balanced three-phase Y-connected generator with positive sequence has an impedance of 0. 2+j 0. 5 Ω/Φ and an internal voltage of 120 V/Φ. The generator feeds a balanced three-phase Y-connected load having an impedance of 39+j 28 Ω/Φ. The impedance of the line connecting the generator to the load is 0. 8+j 1. 5 Ω/Φ. The aphase internal voltage of the generator is specified as the reference phasor. a) Construct the a-phase equivalent circuit of the system b) Calculate three line currents Ia. A, Ib. B, and Ic. C c) Calculate three phase voltages at the load, VAN, VBN, and VCN d) Calculate the line voltages , VAB, VBC, and VCA at the terminals of the load e) Calculate the phase voltages at the generator terminals, V an, Vbn, and Vcn f) Calculate the line voltages at the generator terminals, V ab, Vbc, and Vca Dr. Assad Abu-Jasser - EE Department - IUGaza

25 End Dr. Assad Abu-Jasser - EE Department - IUGaza

25 End Dr. Assad Abu-Jasser - EE Department - IUGaza