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# ECE 316

ECE 316. Introduction to Electric Energy Systems Fall 2014 Mark Patterson TTh 4:30-5:45, KL-351G. Today’s Quote: Agree to walk away when a discussion becomes too heated. “A gentle answer turns away wrath, but a harsh word stirs up anger.” Proverbs 15:1. Major Points from Lecture 3.

## ECE 316

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1. ECE 316 Introduction to Electric Energy Systems Fall 2014 Mark Patterson TTh 4:30-5:45, KL-351G

2. Today’s Quote: Agree to walk away when a discussion becomes too heated. “A gentle answer turns away wrath, but a harsh word stirs up anger.” Proverbs 15:1

3. Major Points from Lecture 3 • Transmission lines are not cheap. • The utility companies have over a trillion dollars invested in the US power grids. • Blackouts are bad! • The smart grid is coming gradually. • AC isn’t necessarily everywhere. • Technology is changing the power field to be more electronic. • Most countries uses a different voltage/frequency standard.

4. AC Nomenclature

5. Fundamental Assumptions: Steady State AC Circuit Analysis • ALL sources are sinusoidal…..and are often of the same frequency. • ALL transient phenomena have decayed to zero. • ALL circuit elements are linear…..or are approximately so. • ALL currents and voltages are sinusoidal and have the same frequency as the source. • Superposition is VALID. • The MAGNITUDE and PHASE of all voltages and currents completely define the circuit state. • The instantaneous POWER associated with any circuit element IS the product of a sinusoidal voltage and a sinusoidal current. • A COMPLEX NUMBER (or PHASOR) can be chosen to represent a sinusoidal voltage or current where the magnitude or absolute value of the number represents the MAGNITUDE of the voltage or current, and the angle of the number represents the PHASE of the voltage or current relative to an arbitrary reference. • The selection of the reference PHASOR is purely arbitrary. Any reference phasor will yield the SAME circuit solution. • Sometimes, appropriate selection of the reference phasor makes a problem solution more tractable. • Kirchoff’s Voltage and Current Laws and Ohm’s Law can be shown to be valid in AC steady-state. Consequently node and mesh analysis can be applied.

6. Voltage Waveforms

7. Alternating Current Waveform A sinusoidal voltage signal is described by: v(t) = Vmaxsin(ωt) or v(t) = Vmaxcos(ωt) where ω= 2f and f is frequency (i.e., 60 Hz).

8. Root Mean Square Average Voltage of AC signal = 0 120VAC * = 169.7 VAC

9. Phase Shift Current in a resistor Current in an inductor Current in a capacitor

10. Phase Shift

11. Phase Shift

12. Phase Shift

13. Phase Shift

14. Phase Shift

15. Phasors & Complex Numbers

16. Impedance Impedance of a passive component Impedance of a resistor Impedance of a capacitor Impedance of an inductor

17. Complex Impedance

18. Complex Impedance

19. Complex Impedance

20. Complex Admittance G = Conductance (0 deg) BL = Inductive Susceptance(-90 deg) BC= Capacitive Susceptance(+90 deg)

21. Complex Impedance Table

22. Sample Problem 1 V(t) = 10cos(400t) What is the maximum value of current in the capacitor?

23. Sample Problem 2 V(t) = 120 VAC R = 4, XC = -j8, XL = j6 (all in series) What is the value of total current in the circuit?

24. Sample Problem 3 V(t) = 100 VAC R = 5, XC = -j20, XL = j10 (all in parallel) What is the value of total current in the circuit?

25. Sample Problem 4 What is Vout?

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