1. Electric Power
Lecture 1

2. EFFECTIVE OR RMS VALUES
If the current is sinusoidal the average
power is known to be
The effective value is the equivalent DC
value that supplies the same average power
Definition is valid for ANY periodic
signal with period T

3. Labview Application Open Waveform Generator.vi
Run the vi using 3 different sine waves (change the amplitude, frequency, and phase shift).
Check that the RMS and average values are correct for both the sine wave and the rectified wave. (you can use Mathematica or Matlab to check)
Repeat 1 and 2 for square waveform
Repeat 1 and 2 for the triangle waveform
Put your results for Labview and your calculations in an excel sheet and save it on the google drive.

4. Harmonic Distortions
Harmonic: A component frequency of the signal that is an integer multiple of the fundamental frequency
Due to:
Nonlinear loads
Magnetic saturation in transformer cores
Switching devices and power supplies
Rectification process
Distorted nonsinusoidal waveforms can be represented by a series of harmonics (a Fourier series)
Harmonics can cause
Unwanted rotation of an induction motor
Harmonic power that does no useful work
In motors, torque ripple, noise, vibration,etc
To eliminate harmonics:
Add harmonic filters at the source of the harmonic
Programmed switching

5. Labview Application Open the Waveform and Harmonics Analysis.vi
Do questions 1-7 on page 22 of Labview for Electric Circuits…
You may want to use Mathematica or Matlab for this assignment
Put your results for Labview and your calculations in an excel sheet and save it on the google drive.

6. Read pp of LECMDL
Do self study exercises on page 50
Take screen shots of your results and explain them in a report.
Upload your report to the google drive

7. COMPLEX POWER The units of apparent and reactive power are Volt-Ampere
inductive
capacitive
Active Power
Reactive Power
Another useful form

8. Fundamental Definitions
With distortion (which is assumed to be small, with Irms1=Fourier Fundamental component of current Irms

9. How much phase delay is too much? Had Cleveland been shed in 2003,
it might have saved the day.

10. Per-Unit Values Dimensionless system
Quantities such as voltages are currents are normalized by a per-unit base so that they have no units
Used to display multiple quantities like voltages and currents on the same scale
Calculations are simplified because quantities do not change when they are referred from one side of transformer to the other
An advantage in power system analysis with its large numbers of transformers

11. Power Triangles
Do Exercises 1-4 on page Note that the answers given in problem 3 are a bit off

12. COMPLEX POWER The units of apparent and reactive power are Volt-Ampere
inductive
capacitive
Active Power
Reactive Power
Another useful form

14. POWER FACTOR CORRECTION
Low power factors increase
losses and are penalized by
energy companies
Typical industrial loads
are inductive
Simple approach to power factor correction

17. LEARNING EXAMPLE
Roto-molding
process

18. Power Factor correction
Do Questions on pages 57. Show that you answer for #5 is correct.
For problem of previous slide, find ZL and Use Labview 11 with Single Phase Power Factor Correction to check response (You must change the precision of RL and XL to extended precision)

19. THREE PHASE CIRCUITS Theorem
For a balanced three phase circuit the instantaneous power is constant

20. THREE-PHASE CONNECTIONS
Positive sequence
a-b-c
Y-connected
loads
Delta connected loads

21. Line-phase current
relationship
LEARNING EXTENSION

22. Do self-study questions on page 67 Wye vs Delta
Delta systems have four wires—three hot and one ground. Wye systems have five wires—three hot, one neutral and one ground. While both Delta and Wye systems measure 208VAC between any two hot wires, Wye systems also measure 120VAC between any hot wire and neutral. In other words, it’s the neutral wire of the Wye system that allows for providing two different voltages and powering both 3-phase and single-phase devices in the data center.
That’s not to say that Delta doesn’t have its place—we mainly see Delta used for any large motors or heaters that don’t need a neutral. Delta is also used in power transmission because it’s expensive to run a fourth neutral wire all those miles. That’s why distribution transformers are wired as Delta-Wye. This creates the neutral that allows the transformer to deliver power for single-phase loads.

23. REPLACE IN THE THIRD AND SOLVE FOR R1
Labview VI
Labview VI
REPLACE IN THE THIRD AND SOLVE FOR R1
SUBTRACT THE FIRST TWO THEN ADD
TO THE THIRD TO GET Ra

24. Modified from "Wye-delta bridge simplification" by SlothMcCarty - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons -

25. RAB = 6Ω R1 = R12R31 / (R12+R23+R31) R1 = (3*6)/ (3+6+9) R1 = 1Ω
R1 = (3*6)/ (3+6+9)
R1 = 1Ω
R2 = R23R12 / (R12+R23+R31)
R2 = (9*3)/18
R2 = 1.5Ω
R3 = R31R23 / (R12+R23+R31)
R3 = (6*9)/18
R3 = 3Ω
RAB = 6Ω

26. rp[r1_,r2_ :=r1⁢ r2 r1+r2
r=rp[rp[rab,r2]+rp[rbc,r3],r1] 6.
Do exercises on page 60.
Do Exercise 2 using wye (star)-delta and delta-star. Use 60 ohms for the unknown resistor.
Do exercises on page 64-66

27. Power Measurements

28. Two-Wattmeter Method for Power Measurements
P1: reading in Wattmeter 1
P2: reading in Wattmeter 2
Total real
power ->
Total reactive power/31/2 ->

29. Three-Wattmeter Method for Power Measurements

30. Do self-study questions on p 73