# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

3 Pages

### lecture23

Course: EEL 4213, Fall 2011
School: FSU
Rating:

Word Count: 473

#### Document Preview

Systems Each Multi-machine synchronous machine is represented by a constant voltage source behind the direct axis transient reactance The input powers are assumed to remain constant Using the pre-fault voltage, all loads are converted to equivalent admittances to ground and are assumed to remain constant Damping or asynchronous powers are ignored The mechanical rotor angle of each machine coincides with...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Florida >> FSU >> EEL 4213

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Systems Each Multi-machine synchronous machine is represented by a constant voltage source behind the direct axis transient reactance The input powers are assumed to remain constant Using the pre-fault voltage, all loads are converted to equivalent admittances to ground and are assumed to remain constant Damping or asynchronous powers are ignored The mechanical rotor angle of each machine coincides with the electrical angle of the excitation voltage source Power Systems I Modeling Steps Solve the initial load flow and obtain the initial bus voltage magnitude and phase angle Calculate the machine currents prior to the disturbance I mach i * Smach i =* Vmach i Obtain the voltages behind the transient reactances + + Emach i = Vmach i + j X d I mach i Convert all loads to equivalent admittances yi 0 = Power Systems I Si* Vi 2 = Pi j Qi Vi 2 Modeling Steps Combine the generator models with the networks bus admittance matrix with converted loads 0 Ynn I = YT mach n mach Yn mach Vn E+ Ymach mach mach Use kron reduction (matrix form) to remove the network buses from the matrix 1 reduced Ybus = Ymach mach YnTmach [Ynn ] Yn mach reduced I mach = Ybus E+ mach Power Systems I Modeling Steps Express in terms of the machines excitation voltages, the power output * +* Smach i = Emach i I mach i [ +* Pmach i = Emach i I mach i ] m + I mach i = Emach jYij j =1 m + + Pmach i = Emach i Emach j Yij cos( ij i + j ) j =1 Power Systems I Multi-Machine Transient Stability Set conditions m + + P initial mach i = Emach i Emach j Y1ij cos( ij i + j ) 1 j =1 Pei ( ) = P1machi Pm i = Pei ( ) t =0 Set machine inertia constants on a common system power base SG i Hi = H G mach i SB Power Systems I Multi-Machine Transient Stability Solve the system of ODEs of the faulted network m H i d 2 i = Pmi Ei+ E +j Y2 ij cos( 2ij i + j ) 2 f 0 dt j =1 Solve the system of ODEs of the post-fault network m H i d 2 i = Pmi Ei+ E +j Y3ij cos( 3ij i + j ) 2 f 0 dt j =1 Power Systems I Example Consider the 3 machine system below select generator #1 as the swing machine with a constant angle of 0 degrees determine the system stability when a fault on the line 5-6 near bus 6 is cleared in 0.4 and 0.5 seconds H = 20 Xd = j0.2 1 4 5 6 H=5 Xd = j0.25 3 Power Systems I 2 H=4 Xd = j0.15 Example Load Data 1 2 3 4 5 6 P 0 0 0 1.0 0.9 1.6 Q 0 0 0 0.7 0.3 1.1 Generator Data 1 2 3 V 1.06 1.04 1.03 Power Systems I P --1.5 1.0 Line Data 1 1 1 2 3 4 5 4 5 6 4 5 6 6 R 0.035 0.025 0.040 0.000 0.000 0.028 0.026 X 0.225 0.105 0.215 0.035 0.042 0.125 0.175 B 0.0065 0.0045 0.0055 0.0000 0.0000 0.0035 0.0300 Example Phase angle difference (fault cleared at 0.4s) 150 Delta, degree Power angle / time fault clearing in 0.4 s 100 50 0 -50 -100 Power Systems I 0 0.5 1 t, sec 1.5 Example Phase angle difference (fault cleared at 0.5s) 1400 Power angle / time 1200 fault clearing in 0.5 s Delta, degree 1000 800 600 400 200 0 -200 Power Systems I 0 0.5 1 t, sec 1.5
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 2CHAPTER 1.8 and 21. A three phase wye-connected unbalanced load is supplied by a balanced three-phasedelta connected source. The three source voltages and two of the line currents are:Vab = 13.2 kV 90
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 3CHAPTER 3(Problems 3-1, 3-2, 3-3, 3-4, 3-6, 3-7, 3-8, pp 154-157 in Textbook)1. The secondary winding of a transformer has a terminal voltage ofvs(t) = 282.8 sin 377t V. The turns ratio of the transfo
FSU - EEL - 3216
Life Long LearningProfessional development: seminars, workshops, conferences,summer courses, PE licenseLiterature resourcesReference books, i.e. McGraw Hill Standard Handbook for ElectricalEngineersMagazines, i.e. IEEE Power &amp; Energy, CIGRE Electra
FSU - EEL - 3216
Transmission LinesOverhead ConductorOverhead Spacer CableUnderground CableThree-Conductor CableService CablesFundamentals of Power SystemsLecture 141Overhead ConductorsACSRAluminum Conductor withinner Steel ReinforcedstrandsACARAluminum Con
FSU - EEL - 3216
Induced Voltage in Stator Coil P-PolesFor a P-pole machine the flux per pole remains the same(integrating d =rlBmcos(P/2 )d over one pole pitch - /P to + /P )2rlBMThe electrical frequency becomesP2elmTherefore, the induced voltage per pole-pair (
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 1SOLUTIONS1. In the 60Hz circuit shown in Figure 1, VS = 240.0VR1 = 2.530 and I1 = 38.8A-36.2.L1 = 0.015 Ha) Determine the phasor currents, IS and I2, and the impedance Z2.b) Calculate the apparent
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 2SOLUTIONS1. A three phase wye-connected unbalanced load is supplied by a balanced three-phasedelta connected source. The source voltages and load impedances are:Vab = 13.2 kV 90Vbc = 13.2 kV 210Vca
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 3SolutionsCHAPTER 3(Problems 3-1, 3-2, 3-3, 3-4, 3-6, 3-7, 3-8, pp 154-157 in Textbook)1. The secondary winding of a transformer has a terminal voltage ofvs(t) = 282.8 sin 377t V. The turns ratio of t
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 4SOLUTIONS1. A Y-connected bank of three identical 100-kVA, 7967/480-V transformers is suppliedwith power directly from a large constant-voltage bus. In the short-circuit test, therecorded values on th
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 5, SOLUTIONS4-2. A three-phase four-pole winding is installed in 12 slots on a stator. There are 40turns of wire in each slot of the windings. All coils in each phase are connected inseries, and the thr
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 6SOLUTIONS4-6. The flux density distribution over the surface of a two-pole stator of radius r andlength l is given by)B BM cos( m tProve that the flux density under each pole face is2rlBMSolve fir
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 7 Solution1. A 3-phase, 4-pole synchronous machine rotates CCW with 1500 rpm and produces arated torque of 668.45 Nm at the shaft in CW direction. The total rated losses are5 kW and the rated stator (co
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 8A balanced 3-phase impedance type load is rated 3 MVA at 4.16 kV, with a laggingpower factor of 0.75. It is supplied by a generator via a 2 km long overhead transmissionline. The GMD of the conductors
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 8A balanced 3-phase impedance type load is rated 3 MVA at 4.16 kV, with a laggingpower factor of 0.75. It is supplied by a generator via a 2 km long overhead transmissionline. The GMD of the conductors
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 9Problems from book 9-6, 9-11, and 9-15 as shown below.Problem 9-6 refers to a single-phase, 8 kV, 50 Hz, 50 km long transmission line consisting of twoaluminum conductors with a 3 cm diameter separated
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 9Problems from book 9-6, 9-11, and 9-15 as shown below.Problem 9-6 refers to a single-phase, 8 kV, 50 Hz, 50 km long transmission line consisting of twoaluminum conductors with a 3 cm diameter separated
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 10Problem from book 5-29 as shown below.
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 10SOLUTION
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 11Problem from book 7-5, 7-7, 7-11 as shown below.7-57-77-11
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 11 SOLUTIONSProblem from book 7-5, 7-7, 7-11 as shown below.7-5Attention: this solution, as provided by the author of the book, is inconsistent with the text of thebook. The core losses are supplied by
FSU - EEL - 3216
EEL 3216 Fundamentals of Power SystemsHomework # 12You are encouraged to solve the two problems below in a group effort. Therefore, amaximum of 5 students may submit one assignment together. If you do so, clearly writethe names of the 5 students who h
FSU - EEL - 3216
Electric MotorsThree basic types of motorsSynchronous, SMInduction (asynchronous), IMDC motorsIn the past: preferred for variable speed applicationsDecreasing in popularity; replaced by combination of IM and powerelectronic variable speed drive (VS
FSU - EEL - 3216
U.S. Electric Power Industry ExistingNet Summer Capacity by State, 2003Fundamentals of Power SystemsLecture 11U.S. Electric Power TransmissionSystem in 2000Fundamentals of Power SystemsLecture 1Page 12Power Systems ComponentsPrimary power sour
FSU - EEL - 3216
Electric Powersingle-phase (1~) systemsOne sourceTwo energy-carrying wiresPulsating instantaneous power (2f)three-phase (3~) systemsThree sources, 120 phase shiftedLecture 2Fundamentals of Power Systems1Single Phase Powerptv, i, pPVvtptDe
FSU - EEL - 3216
Notes on Phasor Notation andDiagramsMathematically correctComplex quantity(underlined)VmMagnitudeV Vm e jvttVm cos( t )Re(V) Vm cosvtorjVm sin( t )tIm(V) Vm sintPractical notation and usageComplex quantity, butI = 10 Aunderlining omitt
FSU - EEL - 3216
Ideal 1~ Transformer ModelFlux linkages (winding flux)Ideali1i2N1N1 ,1N22N2SourceV2av1e1 , v2e2aV1N1N2e1e2ZLN1N2Loadv1v2i2i1Dot conventionCurrent into doted end produces positive MMF (NI) orampere-turnsTherefore, orientat
FSU - EEL - 3216
FSU - EEL - 3216
Three-phase transformersCore arrangementsTransformer bank =&gt; three 1~ transformers (core typeor shell type)3~ transformer (3, 4, 5 legged core-type)Winding arrangementsY-Y-YYWith tertiaryFundamentals of Power SystemsLecture 61Core Type vs. She
FSU - EEL - 3216
Changing BasesThe impedances of generators, transformers,transmission lines, and loads are supplied by themanufacturers in per unit based on theequipments own rating.When placing the equipment into a system, theimpedance must be converted to the sy
FSU - EEL - 3216
AC Machine FundamentalsGeneratorsMotors3-phase1-phaseSynchronousInductionFundamentals of Power SystemsLecture 91AC Machines SystematicFundamentalsPrinciple of generating a rotating magnetic fieldMagnetomotive force and induced voltagePrincip
FSU - EEL - 3216
SM No-Load CharacteristicRotor flux magnitudeInduced stator voltage magnitudeEAkCharacteristic of theiron (stator and rotor)Rotor field currentRotor field currentEffect of saturation: for large field currents the no-loadarmature voltage magnitud
FSU - EEL - 3216
AmpacityLecture 15Fundamentals of Power Systems1Geometric Mean Radius (GMR)'L102r4lnDr02Inductance of conductorup to a distance of 1 unit(e.g. 1 foot)'L102lnDGMRr4L'GMR1Dlnr110lnGMR2lnInductance of conductor in Hpe
FSU - EEL - 3216
ExampleM1TST = 1.5 MVAX = 3%NH/NL = 5.4586BusV = 4.16 kVM2M150 Hz, 6 pole, Y-connectedPR = 75 kW, Xm = 7.2R1 = 0.082 , R2 = 0.07X1 = 0.19 , X2 = 0.18Friction and windage losses 1.3 kWCore losses 1.4 kWMiscellaneous losses 150 WM2Rated 10
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 1CHAPTER 1.8 and 21. In the 60Hz circuit shown in Figure 1, VS = 240.0VR1 = 2.530 and IS = 35 A15.L1 = 0.015 Ha) Determine the phasor currents, I1 and I2, and the impedance Z2.b) Calculate the appa
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 71. A 3-phase, 4-pole synchronous machine rotates CCW with 1500 rpm and produces arated torque of 668.45 Nm at the shaft in CW direction. The total rated losses are5 kW and the rated stator (copper) los
FSU - EEL - 3216
EEL 3216 Introduction to Power SystemsHomework # 3CHAPTER 31. (Problem 3-10 in Textbook)2. (Problem 3-22 in Textbook)3. In a certain single-phase system the per unit values of the impedance, current, voltage,and apparent power are:Z = 0.65 pu I = 1
FSU - EEL - 3216
Power Flow in a SM - GeneratorPout3V I A cos( )PoutReactive QoutpowerNote: is the phase anglebetween armature voltage V andarmature current IA. It is NOT theangle between VT and IL!Qout3 VT I L cos( )3V I A sin( )3 VT I L sin( )Lecture 13Fu
FSU - EEL - 3216
Magnetomotive Force and FluxDistributionThe magnetic fieldused to inducesinusoidal voltages(in the stator) has tobe distributedsinusoidal along thecircumference of thestator/rotor (air gap)Snapshot of oneinstantaneousvalue in timeThis spatial
FSU - EEL - 3216
T-Line Equivalent CircuitsThree general models for equivalent transmissionline circuitsChoice influenced by the line length, type (cable oroverhead line), and operating voltage levelChoice based on the analysis (e.g., short circuit orvoltage drop)M
Drexel - BLAW - 201
Milos RujevicEthics In BusinessMy approach to the topic ethics in business will start with the slogan on the wallof the main factory hall of the paper factory of Mr. Vapa in Belgrade in the years 1930-44.It read: Live, work and give the other to live
Drexel - BLAW - 201
Chapter 1: Terms of EndearmentDefining Information Technology12Chapter 1: Terms of EndearmentDefining Information TechnologyB. megabytesC. gigabytesD. terabytesChapter 1 Test BankTrue/False1.Most of the computers you would see in an airport term
Drexel - BLAW - 201
12Chapter 7 Test Bank True/False 1. Debugging means to solve IT problems. 2. The purpose of debugging is to improve systems. 3. Computers dont make mistakes. 4. 0 is not allowed in an email address. 5. 0 and 1 are allowed in URLs and email addresses. 6.
Drexel - BLAW - 201
CS 103, Fall 2008Midterm 2Prof. NakayamaFamily (or Last) Name_Given (or First) Name_Student ID_Instructions1. This exam has 7 pages in total, numbered 1 to 7. Make sure your copy has all the pages.2. Note the number written on the upper right -han
Drexel - BLAW - 201
Answer Key Testname: MT2-08F1) TRUE 2) FALSE 3) FALSE 4) TRUE 5) TRUE 6) C 7) A 8) 9) 10) FALSE 11) TRUE 12) FALSE 13) FALSE 14) TRUE 15) B 16) B 17) B 18) A 19) D 20) A 21) B 22) B 23) byte 24) nibble 25) 256 26) Hexadecimal 27) TRUE 28) FALSE 29) TRUE
Drexel - PSY - 101
Psychology 101 Dr. D. L. ChuteSample Quiz 11.The inability to recognize familiar faces as a result of brain damage is calledPROSOPAGNOSIA2. What are the primary functions of the frontal lobes?PLANING AND EXECUTIVE FUNCTIONS3.Damage to which lobe o
Drexel - PSY - 101
The principle reason, reduce anxietyThis potential long term effect of alcoholism is caused by a deficiency in thiamine and ischaracterized by encephalitis and psychosis: FETAL ALCOHOL SYNDROMEBlood Alcohol Content (BAC) depends on which of the followi
Drexel - PSY - 101
Psychology 101 Dr. D. L. ChuteSample Quiz 21. The therapeutic technique by which a phobicstimulus is conditioned to beassociated with relaxation rather than anxiety isknown as:c. systematic desensitization2. What strengthens the likelihood of a beh
Drexel - PSY - 101
Drexel - MUS - 130
In the Middle Ages, most important musicians were PRIESTS.When notating music for others to read, composers have traditionally used ITALIANwords to indicate dynamics.Not TTHE CATHOLIC CURCH WAS MORE POWERFUL DURING THE RANAISSANCETHE MEDIEVAL PERIOD.
Drexel - MUS - 130
Classical music 1740- 1820MOOD, classical composers will fluctuate in mood ( only masters where able to composewide emotional range )RHYTHM, flexibility of rhythm adds variety to classical music. A classical Compositionhas a wealth of rhythmic pattern
Drexel - ACCT - 116
9.2APRILMAY50,0007,50057,5005,00052,500Bugeted Sales in UnitsAdd ending inventoryTotal budgeted sales in unitsDeduct beginning inventoryRequired productionJUNEQuarter75,00090,000215,0009,0008,00024,50084,00098,000239,5007,5009,000
Drexel - MATH - MATH 101
Math 101 Review Quiz # 7Section _Name:_1. How much must you save each week in a 5.5% savings account to have \$26,000 for avacation home in 16 years?2. A Discover card statement shows a balance of \$945 at 15.7% compounded monthly.What monthly payment
Drexel - MATH - MATH 101
Math 101 Review Quiz # 2Section _Name:_1. Compute each of the following:a)c)416 =b) (4)3/2=(4) 3 =d)( 4)3=2. Evaluate each of the following functions at the given x-value:a)f ( x) =x 2 at x = 6b)f ( x) =x - 2 at x = 93. Factor the fun
Drexel - MATH - MATH 101
Math 101 Review Sheet Spring 2008-2009RoomMatheson 109CAT 61Sections011, 013, 016, 017009, 010Exam Coverage: 1.1-1.6Date: Friday, April, 24th 8-8:50 amRecap of section 1.1:Interval NotationInequalityInterval notation[ a, )( a, )( , a ]( ,
Drexel - MATH - MATH 101
Practice Exam 21. Solve the following equations for x.i. 16x+3 = 642x5ii. log2 (5x 2) log2 (x + 3) = 2iii. ln(x + 2) = 22. Use the properties of logs to combine each of the following into one log.i. (3x 4) ln y + ln (x + 2) ln (x3 x + 2)ii. 3 log4
Drexel - MATH - MATH 101
Exam I - Review1. Find the equation of the line perpendicular to the line 2x y = 7 andpassing through the point (2, 1).2. Find the equation of a horizontal line passing through the point (5, 2).3. Find the equation of a vertical line passing through t
Drexel - MATH - MATH 101
Drexel - FIN - 301
End of Chapter SolutionsEssentials of Corporate Finance 6th editionRoss, Westerfield, and JordanUpdated 08-01-2007CHAPTER 1INTRODUCTION TO CORPORATEFINANCEAnswers to Concepts Review and Critical Thinking Questions1.Capital budgeting (deciding on
Drexel - FIN - 301
CHAPTER 2WORKING WITH FINANCIALSTATEMENTSAnswers to Concepts Review and Critical Thinking Questions1.Liquidity measures how quickly and easily an asset can be converted to cash without significant lossin value. Its desirable for firms to have high l
Drexel - FIN - 301
CHAPTER 3WORKING WITH FINANCIALSTATEMENTSAnswers to Concepts Review and Critical Thinking Questions1.a. If inventory is purchased with cash, then there is no change in the current ratio. If inventory ispurchased on credit, then there is a decrease i
Drexel - FIN - 301
CHAPTER 4INTRODUCTION TO VALUATION: THETIME VALUE OF MONEYAnswers to Concepts Review and Critical Thinking Questions1.Compounding refers to the growth of a dollar amount through time via reinvestment of interestearned. It is also the process of dete