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ECE 355 - Electromechanical Energy Conversion

Assignment 1

Review of Phasors, Power and Reactive Power

and

Introduction toThree Phase Systems

Objectives:

1. Sharpen phasor computational skills.

2. Appreciate the properties underlying the evolution of the modern interconnected sinusoidal AC power

system.

3. Understand and be able to calculate average power, reactive power and rms values.

4. Sharpen Fourier Series theoretical background and computational skills.5 Understand advantages of three phase systems and be able to calculate performance using single line

to ground model.

Reading:

Review1) Chapter on Phasors in your Circuits Book

2) Chapter on Power and Reactive Power in your Circuits Book

3) Phasor Review Problems (with answers) - not required to be turned in.

Text: "Electrical Machinery -6th Edition" Fitzgerald, Kingsley and Umans, McGraw Hill, 2002.

1) Notes on Periodic Waves and Electric Power2) Appendix A: Three Phase Circuits -- pp 628 643

Major Emphasis A2, A.3(Ex A.2, Ex A.3), A4

Secondary Emphasis A.1, A.3(Ex A.1)

Additional Reading (if you feel the need for another viewpoint or more examples):

"Electrical Machinery Fundamentals-3rd Edition" Stephen J. Chapman, WCB/McGraw Hill,1998. (worked examples are presented).

Trouble Spots:

1. Phase angles - assuming everything is in phase.

2. Power factor - assuming P = VI (actually same as #1).

3. 3 factor in line to phase conversion in three phase systems.

4. Failure to sketch a phasor diagram - especially in three phase problems.

5. General lack of skill manipulating sine waves via complex numbers.

6. Lack of familiarity with concept of Fourier series and computations using harmonics.

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Tapes:

1) Course organization, importance of Assignment Sheet, review of phasor concept, phasor as atransformation, identity for product of sine waves, application to calculation of average of a sine product,average equal to 1/2 product of amplitudes times cos , concept of Fourier series, example of square waveFourier series, calculation of Fourier series coefficients using sine wave averages.

2) Example of power calculation and phasor analysis, magnitude-angle form of Fourier series, Fourierseries examples, rms value calculation, calculation of rms value from Fourier series components, exampleusing harmonics to approximate the rms value, example calculation of 5th harmonic response of circuit,discussion of model selection to represent the load, introduction of concept of displacement and distortionpower factors.

3) Introduction of reactive power concept based on circuit considerations, time domain illustration ofinstantaneous power in non-sinusoidal and sinusoidal situations, illustration of time domain properties ofaverage power and reactive power, review of basis for structure of modern electric power system includinganswers to: 1) why electric power? 2) why AC? 3) why sinusoidal? 4) why 60 hz? 5) Why three phase?

4) Control of power and reactive power in large power systems, the power angle curve, discussion of powerlimits in AC systems, complex power, example of power and reactive power computations, power factorcorrection, reactive power in non-sinusoidal systems, three phase Y-Y systems, relation between line andphase voltage,

5) Description of variable frequency electrical system proposed for next generation aircraft, illustration of Pand Q when harmonics are present in the current, advantages of three phase systems, analysis using singleline circuit diagrams, relation between line and phase voltage, -connected systems, replacing a -connectedload with an equivalent Y, power expressed with line voltage and current.

6) Relation between line and phase current in a connection, example of three phase system calculation,power factor correction in three phase systems, power measurement in three phase systems, the twowattmeter method, harmonic behavior of three phase systems, special properties (zero sequence) of thetriplen harmonics in three phase systems.

7) Reasons for grounding in AC systems, the single phase, four wire grounded electrical utilization system,purpose of equipment ground, polarized plug, GFI and arcing ground protection, advantage of magneticover electrostatic energy storage, the ultracapacitor as an improved electrostatic energy storage, Bli andB2/20 forces in magnetic systems, illustration of real devices operating on one or the other of theseprinciples,

Required Homework:

Required HW1 - Instantaneous and Average Power With Periodic Waveforms - work after Lecture 3

Required HW2 - Three Phase Systems - Importance of Phasor Diagrams - work after Lecture 5

Team HW1 - Harmonics in Single and Three Phase Systems - work after Lecture 7

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Worked Examples:

Example Problem 1 - Three Phase Systems

Practice Problems on Three Phase Systems (to help build your confidence):

1) A balanced three phase load dissipates 15 kW at a power factor of 0.8 leading from a balanced threephase 208 volt (line to line) 60 hz source. For a Y connected load find the equivalent per phase seriesconnected load impedance. Repeat for a -connected load.

Answers: ZY = (1.84 j1.38) Z = (5.52 j4.14)

2) The load on abalanced three phase 460 volt (line to line) 60 hz source consists of three equalimpedances of 100 + j100 ohms connected in Y and three equal impedances of 300 j300 ohms connectedin . Find the line current, the power and the power factor at the source.

Answers: IS = 2.66 A PS = 2110 W cos = 1.0

3) A balanced three phase 230 volt (line to line) 60 hz source supplies 600 W to a Y-connected load at apower factor of 0.7 lagging. Three equal capacitors connected in Y are placed in parallel with the load toimprove the power factor. What must be the size of each capacitor to yield a power factor of 0.85 lagging?What would be the required capacitor size if the caps were -connected?

Answers: CY = 12.1 f CD = 4.03

4) The total power delivered to a balanced Y-connected load is 720 kW at a lagging power factor of 0.80.The line to line voltage at the load is 3464 V. If the load is fed through a transmission line with a lineimpedance of 1.0 + j3.0 , find the line current, the line voltage at the sending end of the line, the averagepower dissipated in the line and the total power and reactive power supplied by the source.

Answers: I = 150 A VS = 4166 V PL = 67.5 kW PS = 788 kW QS = 742 kvar

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355-as1-05s05sm