Electric Power Lecture 1

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

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.

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

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.

Read pp 48-49 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

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

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

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

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

Power Triangles Do Exercises 1-4 on page 53-54. Note that the answers given in problem 3 are a bit off

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

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

LEARNING EXAMPLE Roto-molding process

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)

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

THREE-PHASE CONNECTIONS Positive sequence a-b-c Y-connected loads Delta connected loads http://www.belden.com/blog/datacenters/3-Phase-Power-Wye-It-Matters.cfm

Line-phase current relationship LEARNING EXTENSION

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. http://www.belden.com/blog/datacenters/3-Phase-Power-Wye-It-Matters.cfm

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

Modified from "Wye-delta bridge simplification" by SlothMcCarty - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Wye-delta_bridge_simplification.svg#/media/File:Wye-delta_bridge_simplification.svg

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

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

Power Measurements

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

Three-Wattmeter Method for Power Measurements

Do self-study questions on p 73