ELE B7 Power Systems Engineering. Power System Components Modeling

Size: px
Start display at page:

Download "ELE B7 Power Systems Engineering. Power System Components Modeling"

Transcription

1 Power Systems Engineering Power System Components Modeling

2 Section III : Trnsformer Model

3 Power Trnsformers- CONSTRUCTION Primry windings, connected to the lternting voltge source; Secondry windings, connected to the lod; Iron core, which link the flux in both windings; The primry nd secondry voltges re denoted by V 1 nd V 2 respectively. The current entering the primry terminls is I 1. Symbols Slide # 2

4 Power Trnsformers- IDEAL TRANSFORMER Idel trnsformer is chrcterized by: No rel power loss; No linkge flux; Mgnetic core hs infinite permebility (μ). d v1 e1 N 1 dt d v2 e2 N 2 dt Therefore v v N N where, is the turns rtio of the trnsformer Slide # 3

5 Power Trnsformers- IDEAL TRANSFORMER With no power loss: Pin P out v 1 i1 v2i2 Therefore i1 N2 1 i N 2 1 Slide # 4

6 Power Trnsformers- REAL TRANSFORMER Rel trnsformers hve losses hve lekge flux hve finite permebility of mgnetic core 1. Rel power losses resistnce in windings (i 2 R) core losses due to eddy currents nd hysteresis Slide # 5

7 Power Trnsformers- REAL TRANSFORMER The single-phse equivlent circuit of rel trnsformer is shown below. The lekge inductnces of the trnsformer is denoted by l1 & l1 nd R 1 & R 2 re the trnsformer s winding resistnces The core loss component is represented by R c while the mgnetizing rectnce is denoted by m. Slide # 6

8 Power Trnsformers- Approximte Circuits Neglecting the voltge drop cross the primry nd secondry windings due to the excittion current. Therefore, the mgnetiztion brnch cn be moved to either the primry or secondry terminls. The pproximte equivlent circuit of the trnsformer referred to the primry side is shown below. R eq R 1 2 R 2 eq l 1 2 l 2 Slide # 7

9 Power Trnsformers- Approximte Circuits The impednce of the shunt brnch is much lrger compred to tht of the series brnch. Therefore we neglect R c nd m. R eq is much smller thn eq. We cn therefore neglect the series resistnce. Therefore the trnsformer cn be represented by the lekge rectnce eq. = N 1 / N 2 Simplified equivlent circuit of single-phse trnsformer: () when referred to the primry side nd (b) when referred to the secondry side. Slide # 8

10 Power Trnsformers- EAMPLE 1 Slide # 9

11 Power Trnsformers- EAMPLE 1, Sol. Slide # 10

12 Power Trnsformers- EAMPLE 1, Sol. Slide # 11

13 Power Trnsformers- EAMPLE 1, Sol. Thus, the primry current nd voltge re: Slide # 12

14 Power Trnsformers- EAMPLE 2 Solution: Slide # 13

15 Power Trnsformers- EAMPLE 2, Sol. Slide # 14

16 Power Trnsformers- EAMPLE 2, Sol. Slide # 15

17 Per Unit Clcultions A key problem in nlyzing power systems is the lrge number of trnsformers. It would be very difficult to continully hve to refer impednces to the different sides of the trnsformers This problem is voided by normliztion of ll vribles. This normliztion is known s per unit nlysis. quntity in per unit ctul quntity bse vlue of quntity Slide # 16

18 Per Unit Conversion Procedure, 1 1. Pick 1 VA bse for the entire system, S B 2. Pick voltge bse for ech different voltge level, V B. Voltge bses re relted by trnsformer turns rtios. Voltges re line to neutrl. 3. Clculte the impednce bse, Z B = (V B ) 2 /S B 4. Clculte the current bse, I B = V B /Z B 5. Convert ctul vlues to per unit Note, per unit conversion on ffects mgnitudes, not the ngles. Also, per unit quntities no longer hve units (i.e., voltge is 1.0 p.u., not 1 p.u. volts) Slide # 17

19 Three Phse Per Unit Procedure is very similr to 1 except we use 3 VA bse, nd use line to line voltge bses 1. Pick 3 VA bse for the entire system, 2. Pick voltge bse for ech different voltge level, V B. Voltges re line to line. 3. Clculte the impednce bse Z B BLL, ( 3 BLN, ) BLN, B 3 B B V V V S S S 3 S B Exctly the sme impednce bses s with single phse! Slide # 18

20 Three Phse Per Unit, cont'd 4. Clculte the current bse, I B I SB 3 SB SB 1 B IB 3VBLL, 3 3VBLN, VBLN, Exctly the sme current bses s with single phse! 5. Convert ctul vlues to per unit Slide # 19

21 Section IV: Synchronous Mchine Model

22 Synchronous Genertor- CONSTRUCTION Round Rotor Mchine The sttor is ring shped lminted iron-core with slots. Three phse windings re plced in the slots. Round solid iron rotor with slots. A single winding is plced in the slots. DC current is supplied through slip rings. Chrcteristics: High speed pplictions; High power rtings (100s of MW) Driving system: e.g., Stem turbines. Slide # 21

23 Synchronous Genertor- CONSTRUCTION Slient Rotor Mchine The sttor hs lminted iron-core with slots nd three phse windings plced in the slots. The rotor hs slient poles excited by dc current. DC current is supplied to the rotor through slip-rings nd brushes. Chrcteristics: Low speed pplictions; Low rtings (10s of MW) Driving system: e.g., Hydro turbines. Slide # 22

24 Synchronous Genertor- OPERATION Principle of Opertion 1) From n externl source, the field winding is supplied with DC current -> excittion. 2) Rotor (field) winding is mechniclly turned (rotted) t synchronous speed. 3) The rotting mgnetic field produced by the field current induces voltges in the outer sttor (rmture) winding. The frequency of these voltges is in synchronism with the rotor speed. Slide # 23

25 Synchronous Genertor- CHARACTERESTICS Opertion Chrcteristics The frequency - speed reltion is f = (p / 120) n = p n /120 where: p is the number of poles. Typicl rotor speeds re 3600 rpm for 2-pole, 1800 rpm for 4 pole nd 450 rpm for 16 poles. The RMS vlue of the induced voltges of phse A is: E = 4.44 N BA f, (BA = ) where: N = number of turns, B= flux density, A = cross sectionl re of the mgnetic circuit, f = frequency, nd = flux per pole Slide # 24

26 Synchronous Genertor- Equivlent Circuit Round Rotor Type 1) DC current in the field winding produces the min flux, f. 2) f induces n emf, E, in the rmture winding. 3) Depending on the lod condition, the rmture current I A is estblished. In the following discussions, it is ssumed to be lgging power fctor. 4) I A produces its own flux due to rmture rection, E AR is the induced emf by AR. 5) The resulting phsor, E resultnt = E + E AR is the true induced emf tht is vilble. Slide # 25

27 Synchronous Genertor- Equivlent Circuit The per phse equivlent circuit for round rotor genertor where, ( AR + A ) = synchronous rectnce, s. Slide # 26

28 Synchronous Genertor- Equivlent Circuit The phsor digrm of round rotor genertor: V E I ( R j s ) where R A : Armture winding resistnce; s : Synchronous rectnce; δ: Power ngle of the synchronous genertor. Slide # 27

29 Synchronous Genertor- EAMPLE 3 A 60-Hz, three-phse synchronous genertor is observed to hve terminl voltge of 460 V (line-line) nd terminl current of 120 A t power fctor of 0.95 lgging. The field-current under this operting condition is 47 A. The mchine synchronous rectnce is equl to 1.68 Ω. Assume the rmture resistnce to be negligible. Clculte: ) the generted voltge E in volts, b) the mechnicl power input to the genertor in kw Slide # 28

30 Synchronous Genertor- EAMPLE 3-Sol. Using the motor reference direction for the current nd neglecting the rmture resistnce, the generted voltge cn be found from the equivlent circuit: E V V ji s A lgging power fctor of 0.95 corresponds to power fctor ngle 18.2 o I Slide # 29

31 Synchronous Genertor- EAMPLE 3-Sol. Solution (cont.): E V ji s b) The mechnicl power input to the genertor Pin cn be found s three times the power input to phse : P in 3 E I KW V cos( ) cos( ) Slide # 30

32 Synchronous Genertor- Equivlent Circuit Slient Rotor Type The per phse equivlent circuit for slient rotor genertor: E V I R ji d d ji q q Slide # 31

33 Synchronous Genertor- Equivlent Circuit Slient Rotor Type The phsor digrm of slient rotor genertor (neglecting the rmture resistnce): E V ji d d ji q q where d : Direct xis rectnce; q : Qudrture xis rectnce; Slide # 32

34 Slide # 33 Synchronous Genertor- Equivlent Circuit ) ( ) ( but, ) ( ' ' q d d q d d E q q d q d q d q q d d ji E E ji ji V E I I I ji ji ji ji V E Slient Rotor Type The expression for E my be written s follows: The phse ngle of E = the phse ngle of E

35 Synchronous Genertor- EAMPLE 4 Slide # 34

36 Synchronous Genertor- EAMPLE 4-Sol. Slide # 35

37 Synchronous Genertor- EAMPLE 4-Sol. Slide # 36

38 Synchronous Genertor- Power-Angle Cc s Power-Angle chrcteristics of synchronous mchine: The mximum power tht synchronous mchine cn deliver is determined by the mximum torque tht cn be pplied without loosing synchronism. The expression of the power supplied will be expressed in terms of the mchine prmeters nd the system tht is connected o it. Slide # 37

39 Slide # 38 Synchronous Genertor- Power-Angle Cc s Round rotor synchronous mchine: Neglecting R nd tking V s reference phsor, s j V E I E E V V & 0

40 Slide # 39 Synchronous Genertor- Power-Angle Cc s Round rotor synchronous mchine: The complex power is given by: nd s s s s s s V V E Q V E P V j V E j V E V I V jq P S 2 2 * cos 3 sin

41 Synchronous Genertor- Power-Angle Cc s Power ngle Chrcteristics The P(δ) curve shows tht the increse of power increses the ngle between the induced voltge nd the terminl voltge. The power is mximum when δ =90 o The further increse of input power forces the genertor out of synchronism. This genertes lrge current nd mechnicl forces. The mximum power is the sttic stbility limit of the system. P( ) Round Rotor Mchine P mx Slide # 40

42 Synchronous Genertor- Power-Angle Cc s Slient rotor synchronous mchine: Neglecting R nd tking E s reference phsor, o o V V & E E 0 Slide # 41

43 Synchronous Genertor- Power-Angle Cc s Slient rotor synchronous mchine: Using the bove phsor digrm nd tking E s reference: I q V sin E V cos & Id q d Slide # 42

44 Slide # 43 Synchronous Genertor- Power-Angle Cc s Slient rotor synchronous mchine: The complex power is given by: d q d d q d d q d q d q V V E Q V V E P simplify nd I I for substitute I I V ji I V I V jq P S * * cos sin cos 3 sin sin 3 &

45 Synchronous Genertor- Power-Angle Cc s Power ngle curve of slient-pole synchronous genertor P(δ) E 3 V d sin Reluctnce power Slide # 44

46 Synchronous Genertor- Power-Angle Cc s Slient rotor synchronous mchine: Observtions: The first term of the ctive power is identicl to the power delivered by round rotor synchronous genertor; The second term represents the effect of genertor sliency, nd it is clled reluctnce power; In slient pole mchine, d > q. When slient mchine pproches round rotor, the vlues of d & q will both pproch s nd P &Q of slient pole mchine re reduced to tht of round rotor mchine. Slide # 45

47 Synchronous Genertor- EAMPLE 5 A 25 kva, 230 V three phse, four pole, 60 Hz, Y-connected synchronous genertor hs synchronous rectnce of 1.5 /phse nd negligible rmture resistnce. The genertor is connected to n infinite bus of constnt voltge (230 V) nd frequency (60 Hz), find:. The generted EMF (E ) when the mchine is delivering rted kva t 0.8 power fctor lgging. b. If the field current I f is incresed by 20 % without chnging the power input find the sttor current I. c. With the field excittion current I f s in prt (), the input power from prime mover is incresed very slowly. Wht is the stedy stte limit? Determine the sttor current I, power fctor, nd rective power Slide # 46

48 Synchronous Genertor- EAMPLE 5-Sol. Slide # 47

49 Synchronous Genertor- EAMPLE 5-Sol. Slide # 48

50 Synchronous Genertor- EAMPLE 5-Sol. Slide # 49

51 Synchronous Genertor- EAMPLE 5-Sol. Slide # 50

52 Synchronous Genertor- EAMPLE 5-Sol. From the previous phsor digrm, Slide # 51

53 Synchronous Genertor- EAMPLE 6 Slide # 52

54 Synchronous Genertor- EAMPLE 7 Slide # 53

Lec 3: Power System Components

Lec 3: Power System Components Lec 3: Power System Components Dr. Mlbik Bsu 8/0/2009 Lesson pln 3 nd L.O. Sequence nlysis exmple ( detil fult nlysis next sem) Trnsformer model recp, tp chnge nd phse chnge, 3-phse Modeling of Synchronous

More information

WELCOME TO THE LECTURE

WELCOME TO THE LECTURE WELCOME TO THE LECTURE ON DC MOTOR Force on conductor If conductor is plced in mgnetic field nd current is llowed to flow through the conductor, the conductor will experience mechnicl force. N S Electric

More information

POLYPHASE CIRCUITS. Introduction:

POLYPHASE CIRCUITS. Introduction: POLYPHASE CIRCUITS Introduction: Three-phse systems re commonly used in genertion, trnsmission nd distribution of electric power. Power in three-phse system is constnt rther thn pulsting nd three-phse

More information

The University of New South Wales FINAL EXAMINATION. Session ELEC4613 ELECTRIC DRIVE SYSTEMS. 1. Time allowed 3 hours

The University of New South Wales FINAL EXAMINATION. Session ELEC4613 ELECTRIC DRIVE SYSTEMS. 1. Time allowed 3 hours The University of New South Wles FINAL EXAMINATION Session 010 ELEC4613 ELECTRIC DRIVE SYSTEMS 1. Tie llowed 3 hours. Reding tie: 10 inutes 3. Totl nuber of questions in this pper = SIX 4. Answer ny FOUR

More information

ELE B7 Power System Engineering. Unbalanced Fault Analysis

ELE B7 Power System Engineering. Unbalanced Fault Analysis Power System Engineering Unblnced Fult Anlysis Anlysis of Unblnced Systems Except for the blnced three-phse fult, fults result in n unblnced system. The most common types of fults re single lineground

More information

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses

More information

DIRECT CURRENT CIRCUITS

DIRECT CURRENT CIRCUITS DRECT CURRENT CUTS ELECTRC POWER Consider the circuit shown in the Figure where bttery is connected to resistor R. A positive chrge dq will gin potentil energy s it moves from point to point b through

More information

In the diagram below, the rotation continues until N-S alignment, resulting in lock-up that is, if nothing is done to prevent it.

In the diagram below, the rotation continues until N-S alignment, resulting in lock-up that is, if nothing is done to prevent it. 25-1 DC motors DC motors re importnt in mny pplictions. In portble pplictions using bttery power, DC motors re nturl choice. DC mchines re lso used in pplictions where high strting torque nd ccurte speed

More information

Solution of Tutorial 2 Converter driven DC motor drive

Solution of Tutorial 2 Converter driven DC motor drive chool of Electricl Engineering & Telecommunictions, UNW olution of Tutoril Converter driven DC motor drive Question 1. T V s D V I L E V 50 V,.5, I 0 A rted rted f 400 Hz, 0 rev/ min s rted (i) 0 6.8 rd

More information

A New Method for Estimating Permanent Magnet Synchronous Machine Parameters

A New Method for Estimating Permanent Magnet Synchronous Machine Parameters J. Bsic. Appl. Sci. Res., (9)9145-9151, 01 01, TextRod Publiction ISSN 090-4304 Journl o Bsic nd Applied Scientiic Reserch www.textrod.com A New Method or Estimting Permnent Mgnet Synchronous Mchine Prmeters

More information

5 Equivalent Circuits and Parameters of Power System Plant

5 Equivalent Circuits and Parameters of Power System Plant Equivlent Circuits nd Prmeters of Power System Plnt Introduction 5.1 Synchronous mchines 5. Armture rection 5. Stedy stte theory 5.4 Slient pole rotor 5.5 Trnsient nlysis 5.6 Asymmetry 5.7 Mchine rectnces

More information

Cross-section section of DC motor. How does a DC Motor work? 2 Commutator Bars N X. DC Motors 26.1

Cross-section section of DC motor. How does a DC Motor work? 2 Commutator Bars N X. DC Motors 26.1 DC Motors 26.1 How does DC Motor work? Crosssection section of DC motor Mgnetic field vector, B oft Iron Core (otor) Wire length vector, dl Force vector, df Current, i Permnent Mgnet (ttor) Crosssection

More information

Chapter 10: Symmetrical Components and Unbalanced Faults, Part II

Chapter 10: Symmetrical Components and Unbalanced Faults, Part II Chpter : Symmetricl Components nd Unblnced Fults, Prt.4 Sequence Networks o Loded Genertor n the igure to the right is genertor supplying threephse lod with neutrl connected through impednce n to ground.

More information

Industrial Electrical Engineering and Automation

Industrial Electrical Engineering and Automation CODEN:LUTEDX/(TEIE-719)/1-7/(7) Industril Electricl Engineering nd Automtion Estimtion of the Zero Sequence oltge on the D- side of Dy Trnsformer y Using One oltge Trnsformer on the D-side Frncesco Sull

More information

Electrical Drive 4 th Class

Electrical Drive 4 th Class University Of Technology Electricl nd Electronics Deprtment Dr Nofl ohmmed Ther Al Kyt A drive consist of three min prts : prime mover; energy trnsmitting device nd ctul pprtus (lod), hich perform the

More information

DC Machines. Introduction - commutation. Commutation. I. Introduction Electrical Energy Technology

DC Machines. Introduction - commutation. Commutation. I. Introduction Electrical Energy Technology UNVERSTY OF TECHNOLOGY, SYDNEY FACULTY OF ENGNEERNG 48550 Electricl Enery Technoloy DC Mchines Topics to cover: 1. ntroduction 2. EMF & Torque 3. Equivlent Circuit 4. Perornce. ntroduction Principle o

More information

Examination Electrical Machines and Drives Et4-117 Thursday, October 30, 2003 from 9.00 to 12.00

Examination Electrical Machines and Drives Et4-117 Thursday, October 30, 2003 from 9.00 to 12.00 Exmintion Electricl Mchine nd Drive Et4-117 Thurdy, Octoer 30, 003 from 900 to 100 Thi exmintion conit of 6 prolem The numer efore prolem indicte how mny point cn e erned with thi prolem 15 Prolem 1 c

More information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3 2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is

More information

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write

More information

196 Circuit Analysis with PSpice: A Simplified Approach

196 Circuit Analysis with PSpice: A Simplified Approach 196 Circuit Anlysis with PSpice: A Simplified Approch i, A v L t, min i SRC 5 μf v C FIGURE P7.3 () the energy stored in the inductor, nd (c) the instntneous power input to the inductor. (Dul of Prolem

More information

8 THREE PHASE A.C. CIRCUITS

8 THREE PHASE A.C. CIRCUITS 8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),

More information

Electrical Motors/Generator Technology

Electrical Motors/Generator Technology John Driesen, Ronnie Belmns K.U.Leuven, Deprtment Electricl Engineering (ESAT) Div. ESAT/ELECTA Ksteelprk Arenberg 0 B-300 Leuven BELGUM http://www.est.kuleuven.c.be/elect.0 NTRODUCTON Devices, trnsforming

More information

Sample Exam 5 - Skip Problems 1-3

Sample Exam 5 - Skip Problems 1-3 Smple Exm 5 - Skip Problems 1-3 Physics 121 Common Exm 2: Fll 2010 Nme (Print): 4 igit I: Section: Honors Code Pledge: As n NJIT student I, pledge to comply with the provisions of the NJIT Acdemic Honor

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

Electrical Machines. 1. Transformers 800 V. As the slope is uniform the induced voltage is a square wave. 01. Ans: (b) Sol: 400/200 V 50 Hz

Electrical Machines. 1. Transformers 800 V. As the slope is uniform the induced voltage is a square wave. 01. Ans: (b) Sol: 400/200 V 50 Hz lectricl Mchine. Trnformer 0. An: (b) Sol: 400/00 50 Hz B mx. T 800, 50 Hz liner dimenion ll double B mx? l l b b A l b A 4A B 800 B 400. mx B mx mx 4A A A A f f. B mx. T 4 0. An: (c) 40 Sol: b c.m 40

More information

LECTURE 23 SYNCHRONOUS MACHINES (3)

LECTURE 23 SYNCHRONOUS MACHINES (3) ECE 330 POWER CIRCUITS AND ELECTROMECHANICS LECTURE 3 SYNCHRONOUS MACHINES (3) Acknowledgent-Thee hndout nd lecture note given in cl re bed on teril fro Prof. Peter Suer ECE 330 lecture note. Soe lide

More information

Chapter E - Problems

Chapter E - Problems Chpter E - Prolems Blinn College - Physics 2426 - Terry Honn Prolem E.1 A wire with dimeter d feeds current to cpcitor. The chrge on the cpcitor vries with time s QHtL = Q 0 sin w t. Wht re the current

More information

Potential Changes Around a Circuit. You must be able to calculate potential changes around a closed loop.

Potential Changes Around a Circuit. You must be able to calculate potential changes around a closed loop. Tody s gend: Potentil Chnges Around Circuit. You must e le to clculte potentil chnges round closed loop. Electromotive force (EMF), Terminl Voltge, nd Internl Resistnce. You must e le to incorporte ll

More information

Fundamentals of magnetic field

Fundamentals of magnetic field Fundmentls of mgnetic field The forces between sttic electric chrges re trnsmitted vi electric field (ccording to the Coulomb's lw). Forces between moving chrges (e.g. in current crrying conductors) lso

More information

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph. nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $

More information

Section 4.2 Analysis of synchronous machines Part II

Section 4.2 Analysis of synchronous machines Part II Section 4. Anlyi of ynchronou mchine Prt 4.. Sttor flux linkge in non-lient pole ynchronou motor due to rotor The ir-gp field produced by the rotor produce flux linkge with individul phe winding. Thee

More information

PHYSICS ASSIGNMENT-9

PHYSICS ASSIGNMENT-9 MPS/PHY-XII-11/A9 PHYSICS ASSIGNMENT-9 *********************************************************************************************************** 1. A wire kept long the north-south direction is llowed

More information

Unique Solutions R. All about Electromagnetism. C h a p t e r. G l a n c e

Unique Solutions R. All about Electromagnetism. C h a p t e r. G l a n c e 5. C h p t e r t G l n c e When electric current is pssed through conductor, it produces mgnetic field round it. The first discovery of the connection between electricity nd mgnetism ws mde by H. C. Oersted.

More information

Fundamentals of Electrical Circuits - Chapter 3

Fundamentals of Electrical Circuits - Chapter 3 Fundmentls of Electricl Circuits Chpter 3 1S. For the circuits shown elow, ) identify the resistors connected in prllel ) Simplify the circuit y replcing prllel connect resistors with equivlent resistor.

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information

1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon

1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon 2001 1. ) Describe the principle chrcteristics nd uses of the following types of PV cell: Single Crystl Silicon Poly Crystl Silicon Amorphous Silicon CIS/CIGS Gllium Arsenide Multijunction (12 mrks) b)

More information

#6A&B Magnetic Field Mapping

#6A&B Magnetic Field Mapping #6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by

More information

I Current waveform required for constant torque

I Current waveform required for constant torque AN INVESTIGATION INTO THE TORQUE BEHAVIOR OF A BRUSHLESS DC MOTOR DRIVE. illy Deprtment of Electricl nd Electronic Engineering University of Newcstle upon Tyne NE 7RU, Englnd R.Krishnn Electricl Engineering

More information

Stepping Motor Driver IC IK6502N TECHNICAL DATA. General Description

Stepping Motor Driver IC IK6502N TECHNICAL DATA. General Description TECHNICAL DATA Stepping Motor Driver IC IK6502 Generl Description IK6502 is stepping motor driver ICs with MOS output trnsistors. The ICs cn control two-phse stepping motor forwrd nd reverse by bipolr

More information

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials:

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials: Summry of equtions chpters 7. To mke current flow you hve to push on the chrges. For most mterils: J E E [] The resistivity is prmeter tht vries more thn 4 orders of mgnitude between silver (.6E-8 Ohm.m)

More information

DESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM

DESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM Interntionl Journl of Automotive Technology, Vol. 18, No. 3, pp. 499 504 (2017) DOI 10.1007/s12239 017 0049 x Copyright 2017 KSAE/ 096 13 pissn 1229 9138/ eissn 1976 3832 DESIGN OF FERRITE MAGNET CFSM

More information

Scientific notation is a way of expressing really big numbers or really small numbers.

Scientific notation is a way of expressing really big numbers or really small numbers. Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific

More information

10. DC Drives. Prof. A. Binder : Electrical Machines and Drives 10/1. Institut für Elektrische Energiewandlung FB 18. Source: Siemens AG

10. DC Drives. Prof. A. Binder : Electrical Machines and Drives 10/1. Institut für Elektrische Energiewandlung FB 18. Source: Siemens AG 10. DC Drives Source: Siemens AG 10/1 10.1 Principles of Opertion of DC Mchines Source: H. Kleinrth, Studientext 10/2 Bsic function of DC mchine Rotor coil rottes in sttor DC mgnetic field; voltge is induced

More information

EMF Notes 9; Electromagnetic Induction ELECTROMAGNETIC INDUCTION

EMF Notes 9; Electromagnetic Induction ELECTROMAGNETIC INDUCTION EMF Notes 9; Electromgnetic nduction EECTOMAGNETC NDUCTON (Y&F Chpters 3, 3; Ohnin Chpter 3) These notes cover: Motionl emf nd the electric genertor Electromgnetic nduction nd Frdy s w enz s w nduced electric

More information

Magnetically Coupled Coil

Magnetically Coupled Coil Mgnetilly Coupled Ciruits Overview Mutul Indutne Energy in Coupled Coils Liner Trnsformers Idel Trnsformers Portlnd Stte University ECE 22 Mgnetilly Coupled Ciruits Ver..3 Mgnetilly Coupled Coil i v L

More information

Physics 202, Lecture 10. Basic Circuit Components

Physics 202, Lecture 10. Basic Circuit Components Physics 202, Lecture 10 Tody s Topics DC Circuits (Chpter 26) Circuit components Kirchhoff s Rules RC Circuits Bsic Circuit Components Component del ttery, emf Resistor Relistic Bttery (del) wire Cpcitor

More information

Measuring Electron Work Function in Metal

Measuring Electron Work Function in Metal n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd

More information

Maejo International Journal of Science and Technology

Maejo International Journal of Science and Technology Mejo nt. J. Sci. Technol. 4, 8(), 9- Full Pper Mejo nterntionl Journl of Science nd Technology SSN 95-787 vilble online t www.mijst.mju.c.th Protective coordintion of min nd bckup overcurrent relys with

More information

Physics 2135 Exam 1 February 14, 2017

Physics 2135 Exam 1 February 14, 2017 Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted

More information

A method for studying sequential faults on a three phase distribution transformer

A method for studying sequential faults on a three phase distribution transformer Scholrs' Mine Msters Theses Student Reserch & Cretive Works 1971 A method for studying sequentil fults on three phse distribution trnsformer Shshi Knt Pndey Follow this nd dditionl works t: http://scholrsmine.mst.edu/msters_theses

More information

Applications of Bernoulli s theorem. Lecture - 7

Applications of Bernoulli s theorem. Lecture - 7 Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.

More information

BME 207 Introduction to Biomechanics Spring 2018

BME 207 Introduction to Biomechanics Spring 2018 April 6, 28 UNIVERSITY O RHODE ISAND Deprtment of Electricl, Computer nd Biomedicl Engineering BME 27 Introduction to Biomechnics Spring 28 Homework 8 Prolem 14.6 in the textook. In ddition to prts -e,

More information

CBSE Sample Paper 2. Question 6 The maximum KE of the electrons emitted in a photocell is 10eV. What is the stopping potential?

CBSE Sample Paper 2. Question 6 The maximum KE of the electrons emitted in a photocell is 10eV. What is the stopping potential? CBSE Smle Per 2 Generl Instruction:. Answer ll questions 2. Internl choices re rovided for some questions 3. Question numbers to 8 re very short nswer questions nd crry mrk ech. 4. Question numbers 8 to

More information

THREE DIMENSIONAL MAGNETOSTATIC ANALYSIS OF A 3-PHASE, 12/8 POLE 250 W SWITCHED RELUCTANCE MOTOR USED IN A WASHING MACHINE DRIVE

THREE DIMENSIONAL MAGNETOSTATIC ANALYSIS OF A 3-PHASE, 12/8 POLE 250 W SWITCHED RELUCTANCE MOTOR USED IN A WASHING MACHINE DRIVE THREE DIMENSIONAL MAGNETOSTATIC ANALYSIS OF A 3-PHASE, /8 POLE 50 W SWITCHED RELUCTANCE MOTOR USED IN A WASHING MACHINE DRIVE Ahmet FENERCİOĞLU Ünl KURT Gziosmnpş University, Turhl Higher Voctionl School,

More information

Numerical Analysis: Trapezoidal and Simpson s Rule

Numerical Analysis: Trapezoidal and Simpson s Rule nd Simpson s Mthemticl question we re interested in numericlly nswering How to we evlute I = f (x) dx? Clculus tells us tht if F(x) is the ntiderivtive of function f (x) on the intervl [, b], then I =

More information

INTRODUCTION. The three general approaches to the solution of kinetics problems are:

INTRODUCTION. The three general approaches to the solution of kinetics problems are: INTRODUCTION According to Newton s lw, prticle will ccelerte when it is subjected to unblnced forces. Kinetics is the study of the reltions between unblnced forces nd the resulting chnges in motion. The

More information

Problem Solving 7: Faraday s Law Solution

Problem Solving 7: Faraday s Law Solution MASSACHUSETTS NSTTUTE OF TECHNOLOGY Deprtment of Physics: 8.02 Prolem Solving 7: Frdy s Lw Solution Ojectives 1. To explore prticulr sitution tht cn led to chnging mgnetic flux through the open surfce

More information

Section 2 - DC Motor Drives

Section 2 - DC Motor Drives Section 2 - DC Motor Drives eview of DC motors nd chrcteristics Switched mode PWM converters. Single nd three phse thyristor converter circuits. Anlysis of converter nd DC motor circuits. Effects of discontinuous

More information

Read section 3.3, 3.4 Announcements:

Read section 3.3, 3.4 Announcements: Dte: 3/1/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: 1. f x = 3x 6, find the inverse, f 1 x., Using your grphing clcultor, Grph 1. f x,f

More information

332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006

332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006 2:221 Principles of Electricl Engineering I Fll 2006 Nme of the student nd ID numer: Hourly Exm 2 Novemer 6, 2006 This is closed-ook closed-notes exm. Do ll your work on these sheets. If more spce is required,

More information

ANALYTICAL CALCULATION OF PARALLEL DOU- BLE EXCITATION AND SPOKE-TYPE PERMANENT- MAGNET MOTORS; SIMPLIFIED VERSUS EXACT MODEL

ANALYTICAL CALCULATION OF PARALLEL DOU- BLE EXCITATION AND SPOKE-TYPE PERMANENT- MAGNET MOTORS; SIMPLIFIED VERSUS EXACT MODEL Progress In Electromgnetics Reserch B, Vol. 47, 145 178, 13 ANALYTICAL CALCULATION OF PARALLEL DOU- BLE EXCITATION AND SPOKE-TYPE PERMANENT- MAGNET MOTORS; SIMPLIFIED VERSUS EXACT MODEL Kmel Boughrr 1,

More information

13: Diffusion in 2 Energy Groups

13: Diffusion in 2 Energy Groups 3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups

More information

Analysis of Abnormal Modes of Hoisting DC Electric Drive System

Analysis of Abnormal Modes of Hoisting DC Electric Drive System Americn Journl of Applied Sciences 7 (4): 527-54, 2010 ISSN 154-929 2010Science Publictions Anlysis of Abnorml Modes of Hoisting DC Electric Drive System Kosms Zdrozis Deprtment of Automtion, Technologicl

More information

Designing Information Devices and Systems I Anant Sahai, Ali Niknejad. This homework is due October 19, 2015, at Noon.

Designing Information Devices and Systems I Anant Sahai, Ali Niknejad. This homework is due October 19, 2015, at Noon. EECS 16A Designing Informtion Devices nd Systems I Fll 2015 Annt Shi, Ali Niknejd Homework 7 This homework is due Octoer 19, 2015, t Noon. 1. Circuits with cpcitors nd resistors () Find the voltges cross

More information

The momentum of a body of constant mass m moving with velocity u is, by definition, equal to the product of mass and velocity, that is

The momentum of a body of constant mass m moving with velocity u is, by definition, equal to the product of mass and velocity, that is Newtons Lws 1 Newton s Lws There re three lws which ber Newton s nme nd they re the fundmentls lws upon which the study of dynmics is bsed. The lws re set of sttements tht we believe to be true in most

More information

Name Class Date. Match each phrase with the correct term or terms. Terms may be used more than once.

Name Class Date. Match each phrase with the correct term or terms. Terms may be used more than once. Exercises 341 Flow of Chrge (pge 681) potentil difference 1 Chrge flows when there is between the ends of conductor 2 Explin wht would hppen if Vn de Grff genertor chrged to high potentil ws connected

More information

Designing Information Devices and Systems I Spring 2018 Homework 7

Designing Information Devices and Systems I Spring 2018 Homework 7 EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should

More information

4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve

4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve Dte: 3/14/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: Use your clcultor to solve 4 7x =250; 5 3x =500; HW Requests: Properties of Log Equtions

More information

Introduction to Synchronous. Machines. Kevin Gaughan

Introduction to Synchronous. Machines. Kevin Gaughan Introduction to Synchronous Machines Kevin Gaughan The Synchronous Machine An AC machine (generator or motor) with a stator winding (usually 3 phase) generating a rotating magnetic field and a rotor carrying

More information

Adaptive STATCOM Control for a Multi-machine Power System

Adaptive STATCOM Control for a Multi-machine Power System Adptive SACOM Control for Multi-mchine Power System AHMARhim nd MBer As King Fhd University of Petroleum & Minerls, Dhhrn, Sudi Ari; Sudi Electricity Compny, Dmmm, Sudi Ari Astrct Synchronous sttic compenstor

More information

Flexible Beam. Objectives

Flexible Beam. Objectives Flexile Bem Ojectives The ojective of this l is to lern out the chllenges posed y resonnces in feedck systems. An intuitive understnding will e gined through the mnul control of flexile em resemling lrge

More information

38 Riemann sums and existence of the definite integral.

38 Riemann sums and existence of the definite integral. 38 Riemnn sums nd existence of the definite integrl. In the clcultion of the re of the region X bounded by the grph of g(x) = x 2, the x-xis nd 0 x b, two sums ppered: ( n (k 1) 2) b 3 n 3 re(x) ( n These

More information

Physics 202, Lecture 14

Physics 202, Lecture 14 Physics 202, Lecture 14 Tody s Topics Sources of the Mgnetic Field (Ch. 28) Biot-Svrt Lw Ampere s Lw Mgnetism in Mtter Mxwell s Equtions Homework #7: due Tues 3/11 t 11 PM (4th problem optionl) Mgnetic

More information

On the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou

On the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou On the Uncertinty of Sensors Bsed on Mgnetic Effects E. ristoforou, E. Kyfs, A. Kten, DM Kepptsoglou Ntionl Technicl University of Athens, Zogrfou Cmpus, Athens 1578, Greece Tel: +3177178, Fx: +3177119,

More information

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,

More information

- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.

- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students. - 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting

More information

Synoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences?

Synoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences? Synoptic Meteorology I: Finite Differences 16-18 September 2014 Prtil Derivtives (or, Why Do We Cre About Finite Differences?) With the exception of the idel gs lw, the equtions tht govern the evolution

More information

Version 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T

Version 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T Version 001 HW#6 - lectromgnetic Induction rts (00224) 1 This print-out should hve 12 questions. Multiple-choice questions my continue on the next column or pge find ll choices efore nswering. AP 1998

More information

Lesson 8. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

Lesson 8. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER) Lesson 8 Thermomechnicl Mesurements for Energy Systems (MEN) Mesurements for Mechnicl Systems nd Production (MME) A.Y. 205-6 Zccri (ino ) Del Prete Mesurement of Mechnicl STAIN Strin mesurements re perhps

More information

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011 Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you

More information

Overview. Before beginning this module, you should be able to: After completing this module, you should be able to:

Overview. Before beginning this module, you should be able to: After completing this module, you should be able to: Module.: Differentil Equtions for First Order Electricl Circuits evision: My 26, 2007 Produced in coopertion with www.digilentinc.com Overview This module provides brief review of time domin nlysis of

More information

5.4 The Quarter-Wave Transformer

5.4 The Quarter-Wave Transformer 3/4/7 _4 The Qurter Wve Trnsformer /.4 The Qurter-Wve Trnsformer Redg Assignment: pp. 73-76, 4-43 By now you ve noticed tht qurter-wve length of trnsmission le ( = λ 4, β = π ) ppers often microwve engeerg

More information

FEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS

FEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS XIX IMEKO orld Congress Fundmentl nd Applied Metrology September 6 11, 2009, Lisbon, Portugl FEM ANALYSIS OF ROGOSKI COILS COUPLED ITH BAR CONDUCTORS Mirko Mrrcci, Bernrdo Tellini, Crmine Zppcost University

More information

Designing Information Devices and Systems I Spring 2018 Homework 8

Designing Information Devices and Systems I Spring 2018 Homework 8 EECS 16A Designing Informtion Devices nd Systems I Spring 2018 Homework 8 This homework is due Mrch 19, 2018, t 23:59. Self-grdes re due Mrch 22, 2018, t 23:59. Sumission Formt Your homework sumission

More information

Factors affecting the phonation threshold pressure and frequency

Factors affecting the phonation threshold pressure and frequency 3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch

More information

Chapter 3. Generator and Transformer Models; The Per-Unit System

Chapter 3. Generator and Transformer Models; The Per-Unit System 3.1 Introduction Chpter 3. Genertor nd Trnforer Model; The Per-Unit Syte 1. Ue of the "per phe" bi to repreent three-phe blnced yte.. Ue the π odel to decribe trniion line (ee Chpter 5). 3. Siple odel

More information

ME 141. Lecture 10: Kinetics of particles: Newton s 2 nd Law

ME 141. Lecture 10: Kinetics of particles: Newton s 2 nd Law ME 141 Engineering Mechnics Lecture 10: Kinetics of prticles: Newton s nd Lw Ahmd Shhedi Shkil Lecturer, Dept. of Mechnicl Engg, BUET E-mil: sshkil@me.buet.c.bd, shkil6791@gmil.com Website: techer.buet.c.bd/sshkil

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

More information

1 Bending of a beam with a rectangular section

1 Bending of a beam with a rectangular section 1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure

More information

Dynamics: Newton s Laws of Motion

Dynamics: Newton s Laws of Motion Lecture 7 Chpter 4 Physics I 09.25.2013 Dynmics: Newton s Lws of Motion Solving Problems using Newton s lws Course website: http://fculty.uml.edu/andriy_dnylov/teching/physicsi Lecture Cpture: http://echo360.uml.edu/dnylov2013/physics1fll.html

More information

Terminal Velocity and Raindrop Growth

Terminal Velocity and Raindrop Growth Terminl Velocity nd Rindrop Growth Terminl velocity for rindrop represents blnce in which weight mss times grvity is equl to drg force. F 3 π3 ρ L g in which is drop rdius, g is grvittionl ccelertion,

More information

The Predom module. Predom calculates and plots isothermal 1-, 2- and 3-metal predominance area diagrams. Predom accesses only compound databases.

The Predom module. Predom calculates and plots isothermal 1-, 2- and 3-metal predominance area diagrams. Predom accesses only compound databases. Section 1 Section 2 The module clcultes nd plots isotherml 1-, 2- nd 3-metl predominnce re digrms. ccesses only compound dtbses. Tble of Contents Tble of Contents Opening the module Section 3 Stoichiometric

More information

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction Lesson : Logrithmic Functions s Inverses Prerequisite Skills This lesson requires the use of the following skills: determining the dependent nd independent vribles in n exponentil function bsed on dt from

More information

Final Exam - Review MATH Spring 2017

Final Exam - Review MATH Spring 2017 Finl Exm - Review MATH 5 - Spring 7 Chpter, 3, nd Sections 5.-5.5, 5.7 Finl Exm: Tuesdy 5/9, :3-7:pm The following is list of importnt concepts from the sections which were not covered by Midterm Exm or.

More information

Nonlinear Least-Square Estimation (LSE)-based Parameter Identification of a Synchronous Generator

Nonlinear Least-Square Estimation (LSE)-based Parameter Identification of a Synchronous Generator Nonliner Lest-Squre Estimtion (LSE)-sed Prmeter Identifiction of Synchronous Genertor Yngkun Xu, Student Memer, IEEE, Yin Li, Student Memer, IEEE, Zhixin Mio, Senior Memer, IEEE Astrct The ojective of

More information

AP Calculus Multiple Choice: BC Edition Solutions

AP Calculus Multiple Choice: BC Edition Solutions AP Clculus Multiple Choice: BC Edition Solutions J. Slon Mrch 8, 04 ) 0 dx ( x) is A) B) C) D) E) Divergent This function inside the integrl hs verticl symptotes t x =, nd the integrl bounds contin this

More information

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source

More information

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA Hrris: Quntittive Chemicl Anlysis, Eight Edition CHAPTER 08: MONOPROTIC ACIDBASE EQUILIBRIA CHAPTER 08: Opener A CHAPTER 08: Opener B CHAPTER 08: Opener C CHAPTER 08: Opener D CHAPTER 08: Opener E Chpter

More information

Department of Mechanical Engineering MECE 551 Final examination Winter 2008 April 16, 9:00 11:30. Question Value Mark

Department of Mechanical Engineering MECE 551 Final examination Winter 2008 April 16, 9:00 11:30. Question Value Mark Deprtment of Mechnicl Engineering MECE 55 Finl exmintion Winter 8 April 6, 9: :3 Notes: You my hve your text book nd one pge formul sheet Electronic devices re not llowed except n pproved clcultor NAME:

More information

Physics 212. Faraday s Law

Physics 212. Faraday s Law Phsics 1 Lecture 17 Frd s Lw Phsics 1 Lecture 17, Slide 1 Motionl EMF Chnge Are of loop Chnge mgnetic field through loop Chnge orienttion of loop reltive to In ech cse the flu of the mgnetic field through

More information