How To Balance Power In A Distribution System

Size: px
Start display at page:

Download "How To Balance Power In A Distribution System"

Transcription

1 NTERNATONA JOURNA OF ENERG, ssue 3, ol., 7 A dynmilly S bsed ompt ontrol lgorithm for lod blning in distribution systems A. Kzemi, A. Mordi Koohi nd R. Rezeipour Abstrt An lgorithm for pplying fixed pitor-thyristorontrolled retor F-TR type of stti vr ompenstor S for dynmilly blning system is introdued. With developed individul phse ontrol sheme, n S n redue negtivesequene urrent used by the lod to improve system blning. n ddition, the power ftor n be improved simultneously by seleting n pproprite mount of pitive/indutive ompenstion. A ompt ontrol lgorithm for retive power ompenstion nd lod blning with the stti vr ompenstor S in three-phse systems is used in this pper. Eh phse suseptne of the S n be obtined from very simple funtion of voltge nd power signls whih re mesured by three-phse voltge trnsduer nd two single-phse tive nd retive power P-Q trnsduers t the lod bus. The lultion of ompenstion suseptnes is bsed on the riterion of unity power ftor nd zero sequene urrents fter ompenstion. This Method is simulted on the EEE 3 node system blning nd totl hrmoni distortion THD is studied in unblned lod node nd Substtion bus nd results is presented. Keywords Distribution system, Negtive-sequene urrent, Stti vr ompenstor, od blning.. NTRODUTON HE lod is lwys hnging nd is normlly unblned T in distribution system. mblne loding ondition uses negtive sequene urrent. Negtive sequene urrent will inrese the resistive losses in field winding nd dmper winding of genertor []. esides it my use overheting nd instility problems. n distribution system, unblned loding inreses power loss in the line nd prevent using the whole pity of line. Furthermore it uses voltge symmetry t utility ends. oltge symmetry of n order of only 3.5% my results in 5% inrese in motor temperturerise [], Power eletronis devies pper to be Mnusript reeived April, 7; Revised version reeived Sept.6, 7. A. Kzemi is with the Deprtment of Eletril Engineering, rn University of Siene nd Tehnology, Tehrn, rn, phone: ; fx: ; e-mil: kzemi@iust..ir. A. Mordi Koohi, is with the Deprtment of Eletril Engineering, rn University of Siene nd Tehnology, Tehrn, rn, e-mil: Arshmordi@ee.iust..ir. R. Rezeipour is with the the Deprtment of Eletril Engineering, rn University of Siene nd Tehnology, Tehrn, rn, e-mil: r.rezeipour@yhoo.om. 7 sensitive to voltge symmetry too. Nmely supply symmetry my use generting urrent hrmonis of nonhrteristi orders suh s third order hrmoni [3]-[4]. There is lso mehnism in systems with indution motors tht mgnify the voltge symmetry. onsidering these problems in three-phse system, it is neessry to blne the lod so tht tive powers in three phses re equl. Presently, feeder swithing through mnul or utomti ontrol to redue the unblne of the lod is used mong industry. Sine this is performed in disrete mnner, it nnot dynmilly nd effetively blne the system lod. n priniple, the urrent of n unblned lod n be divided into zero, positive, nd negtive-sequene omponents. The zero-sequene urrent only influenes the viinity of the lod nd n be bloked by delt-wye grounded trnsformer. f devie ould be found to orret the negtive-sequene urrent in onjuntion with the zero-sequene urrent bloking in the distribution system, one ould obtin blned system, s viewed from the trnsmission level. n this pper, the bk ground of lod blning with S nd different onfigurtion of S is Reviewed, n prt. n prt, theory of S ompenstion is summrized. n prt, ompenstion suseptne is ome nd the formultion is given. n prt, se study is presented nd simultion re done. n prt, the results of simultion re presented.. AK GROUNG Thyristor-ontrolled suseptne TS iruits, or ommonly lled stti vr ompenstors Ss, hve been undergoing development sine the 97's [5]-[6]. The very first bsi struture developed ws just like the one presented in the ove pper, nmely, TS nd pitor in prllel [7]. However, the pplitions of suh TS's hve been limited to minly blned systems. t hs been well known tht thyristor swithed indutor is gret soure of urrent hrmonis, in prtiulr, the third hrmoni. A single-phse TS with bsi struture my hve urrent hrmoni distortion HD of the order of 5% t some firing ngles [7]. When three of suh TS's re onneted in delt onfigurtion, with symmetril ontrolling of firing ngles, this ompenstor is very effetive for ompensting the retive power of the lod without the injetion of third

2 NTERNATONA JOURNA OF ENERG, ssue 3, ol., 7 hrmoni urrent to the system. However, it my not be dequte for use in n unblned system, sine it requires, most likely, n symmetri ontrolling of firing ngles. When this ours, the third hrmoni urrents generted by three TS brnhes re in phse, but different in their mgnitudes, nd therefore, tremendous mount of HD is introdued minly, the third hrmoni into the system. There is nother potentil problem worth mentioning when using TS with suh struture, nmely, resonne between the shunt pitor nd the system indutne my our. All of these ove-mentioned drwbks redue the ppliility of suh TS. To overome the resonnt problem between the shunt pitor nd the system indutne, series indutor n be inserted. To eliminte the third hrmoni urrent generted by TS, hrmoni filter tuned to the third hrmoni frequeny n be employed. A number of TS's with vrious strutures, s shown in Fig., hve been developed, studied, nd presented [6],[8]. With the onsidertions of minimizing hrmoni injetion to the system nd voiding the resonne between the ompenstor's pitor nd system indutor with minimum inrese of iruit omplexity, it ws onluded tht TS_S_PF, hving firly simple struture, ould possibly redue the HD to the order of %. A ompenstor with three TS_S_PF's in delt onfigurtion, ould be used to blne n unblned system dynmilly nd, therefore, ws termed n "dptive blning ompenstor" A [6], [9].. THEOR OF S OMPENSATON To void the omplition of other zero-sequene-relted problems, delt-onneted S is used in the development., every brnh hs fixed pitor nd thyristor-ontrolled retor. Eqution is the equivlent suseptne or dmittne of eh brnh by ontrolling the firing dely ngles α of thyristors. A bidiretionl symmetril ontrol is normlly dopted to void even-order hrmonis. π α sin α α = πω whee is the suseptne of the fixed pitors nd is the originl indutne of the thyristor ontrolled retor. As shown in Fig., the zero-sequene urrent n be bloked by the delt-onneted trnsformer, but the negtivesequene urrent n still pss through the trnsformer nd go into the trnsmission system to deteriorte the performne of genertors or other mhines. Therefore, the purpose of this pper is to derive n lgorithm to blok the negtive-sequene omponent by djusting the suseptne of the S. Theoretilly, omplete ompenstion n be obtined nd the negtive-sequene urrent n be ompensted by n S. This ide is illustrted in + + A A [ ] + + = j where is the symmetril omponent opertor e nd the dmittne of the S is j, j nd j. Eqution n be divided into rel nd imginry prts nd will hve three vriles nd two equtions. An dditionl onstrint hs to be dded to obtin unique solution. From the prtil point of view, the following onstrint is seleted: + + K 3 = Where nd b, is suseptne of ompenstor between phses is suseptne of ompenstor between phses b nd, is suseptne of ompenstor between phses nd. f the power ftor of the lod needs to be improved t the sme time, the right side of eqution 3 n be hnged to the required vlue. For simpliity, K is set to zero in the following derivtion. ombining equtions nd 3, one n get ll suseptnes of the S from mesured phse voltges nd urrents t the primry of the trnsformer[]. Fig. rious iruit onfigurtion of TS,s Fig. rious instlltion of S to blne the distribution lod 73

3 . OMPENSATON SUSEPTANE The digrm of the studied system is shown in Fig. 3, where substtion feeds eletri power to n unblned lod through three-phse system. t is ssumed tht both the substtion bus voltges nd trnsmission line impednes re blned. The supersripts S, T,, nd, used in this pper, represent the substtion, trnsmission line, ompenstor, nd lod, respetively. For the purpose of the S is to redue the negtive sequene urrents nd imginry prt of positive sequene urrents, hene, the usul trnsformtion mtrix [] is defined t first to relte the phse nd sequene quntities s shown in Eq. 4. = = [ T ] Where is voltge between phses nd b, Where is voltge between phses b nd, Where is voltge between phses nd, is zero sequene vlue of voltge, is positive sequene vlue of voltge, is positive sequene vlue of voltge. n Fig. 3, it is ssumed tht the lod is liner, nd then the lod urrent n be expressed s b = Applying the symmetril omponent trnsform in Eq. 4 to both side of Eq. 6, we hve = + = + 6 The negtive sequene voltge is introdued by unequl voltge drops on the trnsmission lines with unblned urrents flowing. n generl, the negtive sequene voltge is smller thn its positive sequene ounterprt. To simplify the nlysis proedure, the negtive sequene voltge is negleted, tht is = = NTERNATONA JOURNA OF ENERG, ssue 3, ol., 7 = 7 n order to redue the negtive sequene urrents nd imginry prt of the positive sequene urrents, it is required tht 4 5 m = m = = m = α euse n idel S ontins no power-onsuming element, it n be obtined from Eq. 6 tht =. Hene, the ompenstion suseptnes of the S n be desribed by nd s: = m = m = m = m 9 = m = m Substituting Eq. 6 into Eq. 9, the ompenstion suseptnes n be expressed in terms of symmetril omponents of the lod urrents. [ ] + [ + ] = m 8 3v = m 3v Four vriles, mgnitudes nd ngles of nd, re required to obtin the urrent informtion in Eq.. euse the sum of three-phse urrents is zero, the distribution ondition of three-phse urrents n be obtined by mesuring only two line urrents. Hene, only two single phse P-Q meters, with voltge-oils onneted to phse nd b nd urrent-oils onneted to phse nd s tht shown in Fig. 3, the so lled two-wttmeter onnetion method, re used to quire the four urrent vriles in Eq.. n prtil implementtion, the voltge signl in Eq. is the verge of three line to line voltges mesured by three-phse voltge trnsduer. Sine the lod bus voltge is ssumed blned, the omplex form of the signls mesured by the P-Q trnsduers n be desribed s: Fig. 3 A three phse system with n S t the lod bus = + 74

4 NTERNATONA JOURNA OF ENERG, ssue 3, ol., 7 = + = + b From Eq., the positive nd negtive sequene urrents n be expressed in terms of tive nd retive powers. = b Define four outputs of P-Q trnsduers s: = P jq b = P jqb b 3 where P + P nd Q + Qd re the tive nd retive powers onsumed by lods, respetively. Substituting Eq. 3 nd Eq. into Eq., we get the online ompenstion formuls for the S. The ompenstion formul shown in Eq. 4 is very ompt nd need only two single phse P-Q trnsduers, so tht it is very suitle for on-line ontrol. = 3Q 3P b 3 = 3P + 3Q 4 b 3 = 3P + 3P b 3 σ = P Q, TR S, 5 F The reltionship between ondution ngles nd orresponding suseptnes of the TR is shown in Eq... SMUATON RESUTS Equtions, 5 nd re used to blne lod urrents of node 675, while Ss re onneted to this node. THD, urrent wveforms, nd RMS urrent of nodes 675 nd 65 Substtion bus re studied before nd fter Ss onnetion presented in fig. 5 nd 6. THDs before nd fter S onnetion is shown in tle. t n lso be observed tht the S genertes hrmoni urrents. The indued hrmoni urrents from n S would flow to the power distribution system nd hrm the power qulity. Hrmonis mitigtion tehniques suh s hrmoni filters should be employed in the design of S Fig. 4 EEE 3 node network ASE STUD The implemented S is instlled in distribution system simultor s shown in Fig.4. EEE 3 node distribution system represents the distribution system simultor. An unblned lod is dded to node 675. The S tht onsists of Δ - onneted thyristor ontrolled retors nd fixed pitors TR-F is instlled t the lod node node no 675. The trnsduer modules whih onsist of line-to-line tive power P, retive power Q, nd voltge trnsduers re instlled ner the unblned lod. A triggering signl is sent to eh thyristor to ontrol the ondution ngle of the TR in order to give the required ompenstion suseptnes. The tul vlues of retive powers nd voltges n be obtined similrly. These tul vlues re used to lulte ompenstion suseptnes of the S using Eq. 4. The needed suseptne of eh phse of the TR is given by the following. Fig. 5 Unblned lod urrent without S. 75

5 NTERNATONA JOURNA OF ENERG, ssue 3, ol., 7. ONUSON An lgorithm for pplying fixed pitor-thyristorontrolled retor F-TR type of stti vr ompenstor S for dynmilly blning system is proposed in this pper. Sine the phse suseptne of the S n be obtined from very simple funtion of voltge nd power signls, the lgorithm is very suitle for on-line ontrol. The required mesurement equipments re two single-phse P-Q trnsduers nd three-phse voltge trnsduer whih re ommerilly ville. Simultion results show tht, with the S, THD is gretly redued. The ontrol pproh n be esily dopted to other types of S. Tle.RMS,THD,st, nd & 3rd Hrmoni of urrent in phse A Fig. 5 Unblned lod urrent without S. Fig. 6 od urrent with S. REFERENES [] Dniel Kuy-hyn hen, Design of n On-line Miroproessor sed ndividul Phse ontrol of Stti r ompenstor", EEE nt. onf. On dvnes in power system ontrol, opertion, nd mngement, Nov. 99 Hong. [] EPR report No. EM-37, "Tehniques for Energy onservtion in A Motor-driven Systems". [3] vmini, R., nd Smith, W.J, "Third Hrmoni urrent from Unblned A/D onverters", Pro. EE,983,3,3,pp [4] ude,., nd Shrf, A.M., "Unhrteristi Hrmonis used by A System mblne nd the Effet of Smoothing Retors", Pro. of the 3rd nt. onf. On Hrmonis in Power Systems, Nshville,USA, 988. [5]. Gyugyi, "Priniples nd pplitions of stti, thyristor-ontrolled shunt ompenstors," EEE Trns. Power App. Syst., vol. PAS-97, Sept./Ot. 978, pp [6]. S. zrneki, G. hen, Z. Stroszzyk, nd S. M. Hsu, "ompenstors with thyristor swithed indutors operted under degrded power qulity: Performne nd its improvement," in Pro. PQA 4th nt. onf. Power Qulity, Applitions nd Perspetives, My 9-, 995. [7] Shih-Min Hsu, "Disussion of Using A Stti r ompenstor to lne A Distribution System", EEE Trns. ol. 35, No. 5, 999, pp [8]. S. zrneki nd S. M. Hsu, "Thyristor ontrol suseptnes for blning ompenstors operted under nonsinusoidl onditions," Pro. [9] nst. Elet. Eng. Elet. Power Applit., vol. 4, no. 4,July 994, pp []. S. zrneki, S. M. Hsu, nd G. hen, "Adptive blning ompenstor," EEE Trns. Power Delivery, vol., July 995, pp [] J.H.hen,W.J.ee,M.S.hen,"Using A Stti s ompenstor To lning A Distribution System", EEE Trns. ol35,no.,999, pp []. J. Wu,. M. iw, nd S.. ee, "Miroproessor-sed Stti Retive Power ompenstors for Unblned lods," Eletri Power Systems Reserh, ol. 3, No., 994, pp

Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur

Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur Module 5 Three-hse A iruits Version EE IIT, Khrgur esson 8 Three-hse Blned Suly Version EE IIT, Khrgur In the module, ontining six lessons (-7), the study of iruits, onsisting of the liner elements resistne,

More information

p-q Theory Power Components Calculations

p-q Theory Power Components Calculations ISIE 23 - IEEE Interntionl Symposium on Industril Eletronis Rio de Jneiro, Brsil, 9-11 Junho de 23, ISBN: -783-7912-8 p-q Theory Power Components Clultions João L. Afonso, Memer, IEEE, M. J. Sepúlved Freits,

More information

Simulation of a large electric distribution system having intensive harmonics in the industrial zone of Konya

Simulation of a large electric distribution system having intensive harmonics in the industrial zone of Konya Turkish Journl of Eletril Engineering & omputer Sienes http:// journls. tuitk. gov. tr/ elektrik/ Reserh rtile Turk J Ele Eng & omp Si (2013) 21: 934 944 TÜİTK doi:10.3906/elk-1201-55 Simultion of lrge

More information

Calculating Principal Strains using a Rectangular Strain Gage Rosette

Calculating Principal Strains using a Rectangular Strain Gage Rosette Clulting Prinipl Strins using Retngulr Strin Gge Rosette Strin gge rosettes re used often in engineering prtie to determine strin sttes t speifi points on struture. Figure illustrtes three ommonly used

More information

THE LONGITUDINAL FIELD IN THE GTEM 1750 AND THE NATURE OF THE TERMINATION.

THE LONGITUDINAL FIELD IN THE GTEM 1750 AND THE NATURE OF THE TERMINATION. THE LONGITUDINAL FIELD IN THE GTEM 175 AND THE NATURE OF THE TERMINATION. Benjmin Guy Loder Ntionl Physil Lbortory, Queens Rod, Teddington, Middlesex, Englnd. TW11 LW Mrtin Alexnder Ntionl Physil Lbortory,

More information

OUTLINE SYSTEM-ON-CHIP DESIGN. GETTING STARTED WITH VHDL August 31, 2015 GAJSKI S Y-CHART (1983) TOP-DOWN DESIGN (1)

OUTLINE SYSTEM-ON-CHIP DESIGN. GETTING STARTED WITH VHDL August 31, 2015 GAJSKI S Y-CHART (1983) TOP-DOWN DESIGN (1) August 31, 2015 GETTING STARTED WITH VHDL 2 Top-down design VHDL history Min elements of VHDL Entities nd rhitetures Signls nd proesses Dt types Configurtions Simultor sis The testenh onept OUTLINE 3 GAJSKI

More information

CHAPTER 31 CAPACITOR

CHAPTER 31 CAPACITOR . Given tht Numer of eletron HPTER PITOR Net hrge Q.6 9.6 7 The net potentil ifferene L..6 pitne v 7.6 8 F.. r 5 m. m 8.854 5.4 6.95 5 F... Let the rius of the is R re R D mm m 8.85 r r 8.85 4. 5 m.5 m

More information

MODELLING AND SIMULATION OF TWO-LEVEL SPACE VECTOR PWM INVERTER USING PHOTOVOLTAIC CELLS AS DC SOURCE

MODELLING AND SIMULATION OF TWO-LEVEL SPACE VECTOR PWM INVERTER USING PHOTOVOLTAIC CELLS AS DC SOURCE INTERNATIONAL JOURNAL OF ELECTRONICS; MECHANICAL nd MECHATRONICS ENGINEERING ol. Num.4 pp.(3-37) MODELLING AND SIMULATION OF TWO-LEEL SPACE ECTOR PWM INERTER USING PHOTOOLTAIC CELLS AS DC SOURCE Ayse KOCALMIS

More information

COMPENSAZIONE DEI DEAD TIMES NEGLI INVERTER DI TENSIONE. M.Zigliotto Università di Udine

COMPENSAZIONE DEI DEAD TIMES NEGLI INVERTER DI TENSIONE. M.Zigliotto Università di Udine 14/04/2004 COMPENSAZIONE DEI DEAD TIMES NEGLI INVERTER DI TENSIONE M.Zigliotto Università di Udine INTRODUCTION The vilbility of powerful nd reltively inexpensive fst digitl signl proessors (DSP) is the

More information

Clause Trees: a Tool for Understanding and Implementing Resolution in Automated Reasoning

Clause Trees: a Tool for Understanding and Implementing Resolution in Automated Reasoning Cluse Trees: Tool for Understnding nd Implementing Resolution in Automted Resoning J. D. Horton nd Brue Spener University of New Brunswik, Frederiton, New Brunswik, Cnd E3B 5A3 emil : jdh@un. nd spener@un.

More information

Equivalence Checking. Sean Weaver

Equivalence Checking. Sean Weaver Equivlene Cheking Sen Wever Equivlene Cheking Given two Boolen funtions, prove whether or not two they re funtionlly equivlent This tlk fouses speifilly on the mehnis of heking the equivlene of pirs of

More information

1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.

1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5. . Definition, Bsi onepts, Types. Addition nd Sutrtion of Mtries. Slr Multiplition. Assignment nd nswer key. Mtrix Multiplition. Assignment nd nswer key. Determinnt x x (digonl, minors, properties) summry

More information

How To Find The Re Of Tringle

How To Find The Re Of Tringle Heron s Formul for Tringulr Are y Christy Willims, Crystl Holom, nd Kyl Gifford Heron of Alexndri Physiist, mthemtiin, nd engineer Tught t the museum in Alexndri Interests were more prtil (mehnis, engineering,

More information

Maximum area of polygon

Maximum area of polygon Mimum re of polygon Suppose I give you n stiks. They might e of ifferent lengths, or the sme length, or some the sme s others, et. Now there re lots of polygons you n form with those stiks. Your jo is

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

c b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00

c b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00 Chter 19, exmle rolems: (19.06) A gs undergoes two roesses. First: onstnt volume @ 0.200 m 3, isohori. Pressure inreses from 2.00 10 5 P to 5.00 10 5 P. Seond: Constnt ressure @ 5.00 10 5 P, isori. olume

More information

Measurement of Reactive Power in Three-Phase Electric Power Systems by Use of Walsh Functions

Measurement of Reactive Power in Three-Phase Electric Power Systems by Use of Walsh Functions 87 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER 2 Mesurement of Retive Power in hree-phse Eletri Power Systems y Use of Wlsh Funtions Adlet Aiyev Memer IEEE Girne Amerin University/Dertment of Eletril nd

More information

Vectors 2. 1. Recap of vectors

Vectors 2. 1. Recap of vectors Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms

More information

Active Directory Service

Active Directory Service In order to lern whih questions hve een nswered orretly: 1. Print these pges. 2. Answer the questions. 3. Send this ssessment with the nswers vi:. FAX to (212) 967-3498. Or. Mil the nswers to the following

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

The remaining two sides of the right triangle are called the legs of the right triangle.

The remaining two sides of the right triangle are called the legs of the right triangle. 10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right

More information

Fundamentals of Cellular Networks

Fundamentals of Cellular Networks Fundmentls of ellulr Networks Dvid Tipper Assoite Professor Grdute Progrm in Teleommunitions nd Networking University of Pittsburgh Slides 4 Telom 2720 ellulr onept Proposed by ell Lbs 97 Geogrphi Servie

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives

More information

Words Symbols Diagram. abcde. a + b + c + d + e

Words Symbols Diagram. abcde. a + b + c + d + e Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To

More information

Arc-Consistency for Non-Binary Dynamic CSPs

Arc-Consistency for Non-Binary Dynamic CSPs Ar-Consisteny for Non-Binry Dynmi CSPs Christin Bessière LIRMM (UMR C 9928 CNRS / Université Montpellier II) 860, rue de Sint Priest 34090 Montpellier, Frne Emil: essiere@rim.fr Astrt. Constrint stisftion

More information

Chapter. Contents: A Constructing decimal numbers

Chapter. Contents: A Constructing decimal numbers Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting

More information

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?

More information

Lecture 3: orientation. Computer Animation

Lecture 3: orientation. Computer Animation Leture 3: orienttion Computer Animtion Mop tutoril sessions Next Thursdy (Feb ) Tem distribution: : - :3 - Tems 7, 8, 9 :3 - : - Tems nd : - :3 - Tems 5 nd 6 :3 - : - Tems 3 nd 4 Pper ssignments Pper ssignment

More information

Ratio and Proportion

Ratio and Proportion Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty

More information

Neural network-based Load Balancing and Reactive Power Control by Static VAR Compensator

Neural network-based Load Balancing and Reactive Power Control by Static VAR Compensator nternational Journal of Computer and Eletrial Engineering, Vol. 1, No. 1, April 2009 Neural network-based Load Balaning and Reative Power Control by Stati VAR Compensator smail K. Said and Marouf Pirouti

More information

UNIVERSITY AND WORK-STUDY EMPLOYERS WEBSITE USER S GUIDE

UNIVERSITY AND WORK-STUDY EMPLOYERS WEBSITE USER S GUIDE UNIVERSITY AND WORK-STUDY EMPLOYERS WEBSITE USER S GUIDE Tble of Contents 1 Home Pge 1 2 Pge 2 3 Your Control Pnel 3 4 Add New Job (Three-Step Form) 4-6 5 Mnging Job Postings (Mnge Job Pge) 7-8 6 Additionl

More information

J. Q. Mou, Fukun Lai, I. B. L. See, and W. Z. Lin Data Storage Institute, 5 Engineering Drive 1, Singapore 117608

J. Q. Mou, Fukun Lai, I. B. L. See, and W. Z. Lin Data Storage Institute, 5 Engineering Drive 1, Singapore 117608 Anlysis of Noteook Computer Cssis Design for rd Disk Drive nd Speker Mounting J. Q. Mou, Fukun Li, I. B. L. See, nd W. Z. Lin Dt Storge Institute, 5 Engineering Drive 1, Singpore 117608 Astrt - Cssis design

More information

Cell Breathing Techniques for Load Balancing in Wireless LANs

Cell Breathing Techniques for Load Balancing in Wireless LANs 1 Cell rething Tehniques for Lod lning in Wireless LANs Yigl ejerno nd Seung-Je Hn ell Lortories, Luent Tehnologies Astrt: Mximizing the network throughput while providing firness is one of the key hllenges

More information

Density Curve. Continuous Distributions. Continuous Distribution. Density Curve. Meaning of Area Under Curve. Meaning of Area Under Curve

Density Curve. Continuous Distributions. Continuous Distribution. Density Curve. Meaning of Area Under Curve. Meaning of Area Under Curve Continuous Distributions Rndom Vribles of the Continuous Tye Density Curve Perent Density funtion f () f() A smooth urve tht fit the distribution 6 7 9 Test sores Density Curve Perent Probbility Density

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Inter-domain Routing

Inter-domain Routing COMP 631: COMPUTER NETWORKS Inter-domin Routing Jsleen Kur Fll 2014 1 Internet-sle Routing: Approhes DV nd link-stte protools do not sle to glol Internet How to mke routing slle? Exploit the notion of

More information

Towards Zero-Overhead Static and Adaptive Indexing in Hadoop

Towards Zero-Overhead Static and Adaptive Indexing in Hadoop Nonme mnusript No. (will e inserted y the editor) Towrds Zero-Overhed Stti nd Adptive Indexing in Hdoop Stefn Rihter Jorge-Arnulfo Quiné-Ruiz Stefn Shuh Jens Dittrih the dte of reeipt nd eptne should e

More information

VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR. A Thesis by. Hong-Tuan Nguyen Vu

VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR. A Thesis by. Hong-Tuan Nguyen Vu VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR A Thesis by Hong-Tuan Nguyen Vu Eletrial Engineer, Polytehni University of HCMC, 1993 Submitted to the College of

More information

McAfee Network Security Platform

McAfee Network Security Platform XC-240 Lod Blner Appline Quik Strt Guide Revision D MAfee Network Seurity Pltform This quik strt guide explins how to quikly set up nd tivte your MAfee Network Seurity Pltform XC-240 Lod Blner. The SFP+

More information

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

Quick Guide to Lisp Implementation

Quick Guide to Lisp Implementation isp Implementtion Hndout Pge 1 o 10 Quik Guide to isp Implementtion Representtion o si dt strutures isp dt strutures re lled S-epressions. The representtion o n S-epression n e roken into two piees, the

More information

GENERAL OPERATING PRINCIPLES

GENERAL OPERATING PRINCIPLES KEYSECUREPC USER MANUAL N.B.: PRIOR TO READING THIS MANUAL, YOU ARE ADVISED TO READ THE FOLLOWING MANUAL: GENERAL OPERATING PRINCIPLES Der Customer, KeySeurePC is n innovtive prout tht uses ptente tehnology:

More information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

More information

Fundamentals of transformer design

Fundamentals of transformer design Fundmentls of trnsformer design y H du Preez, onsultnt trnsformer is stti piee of equipment with omplited eletromgneti iruit. The eletril energy is trnsferred from one eletril iruit to nother through mgneti

More information

A System Context-Aware Approach for Battery Lifetime Prediction in Smart Phones

A System Context-Aware Approach for Battery Lifetime Prediction in Smart Phones A System Context-Awre Approh for Bttery Lifetime Predition in Smrt Phones Xi Zho, Yo Guo, Qing Feng, nd Xingqun Chen Key Lbortory of High Confidene Softwre Tehnologies (Ministry of Edution) Shool of Eletronis

More information

SE3BB4: Software Design III Concurrent System Design. Sample Solutions to Assignment 1

SE3BB4: Software Design III Concurrent System Design. Sample Solutions to Assignment 1 SE3BB4: Softwre Design III Conurrent System Design Winter 2011 Smple Solutions to Assignment 1 Eh question is worth 10pts. Totl of this ssignment is 70pts. Eh ssignment is worth 9%. If you think your solution

More information

Laboratory support for the didactic process of engineering processes automation at the Faculty of Mechanical Engineering

Laboratory support for the didactic process of engineering processes automation at the Faculty of Mechanical Engineering of Ahievements in Mterils nd Mnufturing Engineering VOLUME 15 ISSUE 1-2 Mrh-April 2006 Lortory support for the didti proess of engineering proesses utomtion t the Fulty of Mehnil Engineering J. Świder,

More information

INSTALLATION, OPERATION & MAINTENANCE

INSTALLATION, OPERATION & MAINTENANCE DIESEL PROTECTION SYSTEMS Exhust Temperture Vlves (Mehnil) INSTALLATION, OPERATION & MAINTENANCE Vlve Numer TSZ-135 TSZ-150 TSZ-200 TSZ-275 TSZ-392 DESCRIPTION Non-eletril temperture vlves mnuftured in

More information

Printer Disk. Modem. Computer. Mouse. Tape. Display. I/O Devices. Keyboard

Printer Disk. Modem. Computer. Mouse. Tape. Display. I/O Devices. Keyboard CS224 COMPUTER ARCHITECTURE & ORGANIZATION SPRING 204 LAYERED COMPUTER DESIGN. Introdution CS224 fouses on omputer design. It uses the top-down, lyered, pproh to design nd lso to improve omputers. A omputer

More information

REMO: Resource-Aware Application State Monitoring for Large-Scale Distributed Systems

REMO: Resource-Aware Application State Monitoring for Large-Scale Distributed Systems : Resoure-Awre Applition Stte Monitoring for Lrge-Sle Distriuted Systems Shiong Meng Srinivs R. Kshyp Chitr Venktrmni Ling Liu College of Computing, Georgi Institute of Tehnology, Atlnt, GA 332, USA {smeng,

More information

SOLVING EQUATIONS BY FACTORING

SOLVING EQUATIONS BY FACTORING 316 (5-60) Chpter 5 Exponents nd Polynomils 5.9 SOLVING EQUATIONS BY FACTORING In this setion The Zero Ftor Property Applitions helpful hint Note tht the zero ftor property is our seond exmple of getting

More information

Section 7-4 Translation of Axes

Section 7-4 Translation of Axes 62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the

More information

On Equivalence Between Network Topologies

On Equivalence Between Network Topologies On Equivlene Between Network Topologies Tre Ho Deprtment of Eletril Engineering Cliforni Institute of Tehnolog tho@lteh.eu; Mihelle Effros Deprtments of Eletril Engineering Cliforni Institute of Tehnolog

More information

Radial blowers with AC motor

Radial blowers with AC motor Rdil lowers with AC motor Generl informtion Desription 32 Rdil lowers, motor diretly mounted RL, RLF, RLD, RLA, RLE, RLS 33 Rdil lowers with doule housing 37 Rdil lowers, motor deoupled mounted, high temperture

More information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

DiaGen: A Generator for Diagram Editors Based on a Hypergraph Model

DiaGen: A Generator for Diagram Editors Based on a Hypergraph Model DiGen: A Genertor for Digrm Eitors Bse on Hypergrph Moel G. Viehstet M. Mins Lehrstuhl für Progrmmiersprhen Universität Erlngen-Nürnerg Mrtensstr. 3, 91058 Erlngen, Germny Emil: fviehste,minsg@informtik.uni-erlngen.e

More information

control policies to be declared over by associating security

control policies to be declared over by associating security Seure XML Querying with Seurity Views Wenfei Fn University of Edinurgh & Bell Lortories wenfei@infeduk Chee-Yong Chn Ntionl University of Singpore hny@ompnusedusg Minos Groflkis Bell Lortories minos@reserhell-lsom

More information

SOLVING QUADRATIC EQUATIONS BY FACTORING

SOLVING QUADRATIC EQUATIONS BY FACTORING 6.6 Solving Qudrti Equtions y Ftoring (6 31) 307 In this setion The Zero Ftor Property Applitions 6.6 SOLVING QUADRATIC EQUATIONS BY FACTORING The tehniques of ftoring n e used to solve equtions involving

More information

Space Vector Pulse Width Modulation Based Induction Motor with V/F Control

Space Vector Pulse Width Modulation Based Induction Motor with V/F Control Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:

More information

Lesson 2.1 Inductive Reasoning

Lesson 2.1 Inductive Reasoning Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10,

More information

Active Load Balancing in a Three-Phase Network by Reactive Power Compensation

Active Load Balancing in a Three-Phase Network by Reactive Power Compensation Ative Load Balaning in a hree-phase Network by eative Power Compensation Adrian Pană Politehnia University of imisoara omania. ntrodution. Brief overview of the auses, effets and methods to redue voltage

More information

PLWAP Sequential Mining: Open Source Code

PLWAP Sequential Mining: Open Source Code PL Sequentil Mining: Open Soure Code C.I. Ezeife Shool of Computer Siene University of Windsor Windsor, Ontrio N9B 3P4 ezeife@uwindsor. Yi Lu Deprtment of Computer Siene Wyne Stte University Detroit, Mihign

More information

Binary Representation of Numbers Autar Kaw

Binary Representation of Numbers Autar Kaw Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy

More information

BUSINESS PROCESS MODEL TRANSFORMATION ISSUES The top 7 adversaries encountered at defining model transformations

BUSINESS PROCESS MODEL TRANSFORMATION ISSUES The top 7 adversaries encountered at defining model transformations USINESS PROCESS MODEL TRANSFORMATION ISSUES The top 7 dversries enountered t defining model trnsformtions Mrion Murzek Women s Postgrdute College for Internet Tehnologies (WIT), Institute of Softwre Tehnology

More information

Orthodontic marketing through social media networks: The patient and practitioner s perspective

Orthodontic marketing through social media networks: The patient and practitioner s perspective Originl rtile Orthodonti mrketing through soil medi networks: The ptient nd prtitioner s perspetive Kristin L. Nelson ; Bhvn Shroff ; l M. Best ; Steven J. Linduer d BSTRCT Ojetive: To (1) ssess orthodonti

More information

Student Access to Virtual Desktops from personally owned Windows computers

Student Access to Virtual Desktops from personally owned Windows computers Student Aess to Virtul Desktops from personlly owned Windows omputers Mdison College is plesed to nnoune the ility for students to ess nd use virtul desktops, vi Mdison College wireless, from personlly

More information

Thermosensing Ability of Trg and Tap Chemoreceptors in Escherichia coli

Thermosensing Ability of Trg and Tap Chemoreceptors in Escherichia coli JOURNAL OF BACTROLOGY, Feb. 99, p. 2-24 2-993/9/32-5$2./ Copyright C) 99, Amerin Soiety for Mirobiology Vol. 73, No. 3 Thermosensing Ability of Trg nd Tp Chemoreeptors in sherihi oli TOSHFUM NARA, LAN

More information

Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00

Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00 COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided

More information

Application of high-speed line scan camera for acoustic measurements of vibrating objects

Application of high-speed line scan camera for acoustic measurements of vibrating objects Applition of high-speed line sn mer for ousti mesurements of virting ojets Mirko Mustonen, Dmitri Krtofelev, Antoli Stulov Lortory of Nonliner Dynmis, Institute of Cyernetis t Tllinn University of Tehnology,

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chapter 40 Key Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

More information

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time

More information

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of

More information

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of

More information

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324 A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................

More information

Adjustable Speed Drive Control Based on Random Pulse Width Modulation

Adjustable Speed Drive Control Based on Random Pulse Width Modulation Adjustle Speed Drive Control Bsed on Rndo Pulse Width Modultion Shin Ki, Eri Benedit, Fereshteh Ftehi, Niish Ptel, Adollh Hoifr, Thos A. Lipo Center for Power Eletronis Systes The Deprtent of Eletril Engineering

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

KEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001

KEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001 KEY SKILLS INFORMATION TECHNOLOGY Level 3 Question Pper 29 Jnury 9 Ferury 2001 WHAT YOU NEED This Question Pper An Answer Booklet Aess to omputer, softwre nd printer You my use ilingul ditionry Do NOT

More information

Pure C4. Revision Notes

Pure C4. Revision Notes Pure C4 Revision Notes Mrch 0 Contents Core 4 Alger Prtil frctions Coordinte Geometry 5 Prmetric equtions 5 Conversion from prmetric to Crtesin form 6 Are under curve given prmetriclly 7 Sequences nd

More information

MATH PLACEMENT REVIEW GUIDE

MATH PLACEMENT REVIEW GUIDE MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your

More information

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is so-clled becuse when the sclr product of two vectors

More information

and thus, they are similar. If k = 3 then the Jordan form of both matrices is

and thus, they are similar. If k = 3 then the Jordan form of both matrices is Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If

More information

Vectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m

Vectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m . Slr prout (ot prout): = osθ Vetors Summry Lws of ot prout: (i) = (ii) ( ) = = (iii) = (ngle etween two ientil vetors is egrees) (iv) = n re perpeniulr Applitions: (i) Projetion vetor: B Length of projetion

More information

To be able to perform analysis on power systems with regard to load flow, faults and system stability Outline Syllabus

To be able to perform analysis on power systems with regard to load flow, faults and system stability Outline Syllabus EE 4 ower yte Anlyi [etion ower yte Fult] Lerning Objetive To be ble to perfor nlyi on power yte with regrd to lod flow, fult nd yte tbility Outline yllbu. ower Flow Anlyi: (8 hr Anlogue ethod of power

More information

WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER

WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER Interntionl Journl of Computers nd Applictions, Vol. 9, No., 007 WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER Y.W. Bi nd Y.C. Wu Abstrct Bsed on our survey

More information

Volumes by Cylindrical Shells: the Shell Method

Volumes by Cylindrical Shells: the Shell Method olumes Clinril Shells: the Shell Metho Another metho of fin the volumes of solis of revolution is the shell metho. It n usull fin volumes tht re otherwise iffiult to evlute using the Dis / Wsher metho.

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

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999 Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

HW 9. Problem 14.5. a. To Find:

HW 9. Problem 14.5. a. To Find: HW 9 Problem 14.5. To Find: ( The number-verge moleulr weight (b The weight-verge moleulr weight ( The degree of polymeriztion for the given polypropylene mteril Moleulr Weight Rnge (g/mol x i w i 8,000

More information

REDUCTION FACTOR OF FEEDING LINES THAT HAVE A CABLE AND AN OVERHEAD SECTION

REDUCTION FACTOR OF FEEDING LINES THAT HAVE A CABLE AND AN OVERHEAD SECTION C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 EUCTION FACTO OF FEEING LINES THAT HAVE A CABLE AN AN OVEHEA SECTION Ljuivoje opovi J.. Elektrodistriuija - Belgrade -

More information

Innovation in Software Development Process by Introducing Toyota Production System

Innovation in Software Development Process by Introducing Toyota Production System Innovtion in Softwre Development Proess y Introduing Toyot Prodution System V Koihi Furugki V Tooru Tkgi V Akinori Skt V Disuke Okym (Mnusript reeived June 1, 2006) Fujitsu Softwre Tehnologies (formerly

More information

A Language-Neutral Representation of Temporal Information

A Language-Neutral Representation of Temporal Information A Lnguge-Neutrl Representtion of Temporl Informtion Rihrd Cmpell*, Tkko Aikw, Zixin Jing, Crmen Lozno, Mite Melero nd Andi Wu Mirosoft Reserh One Mirosoft Wy, Redmond, WA 98052 USA {rihmp, tkko, jingz,

More information

1 Fractions from an advanced point of view

1 Fractions from an advanced point of view 1 Frtions from n vne point of view We re going to stuy frtions from the viewpoint of moern lger, or strt lger. Our gol is to evelop eeper unerstning of wht n men. One onsequene of our eeper unerstning

More information

VMware Horizon FLEX Administration Guide

VMware Horizon FLEX Administration Guide VMwre Horizon FLEX Administrtion Guide Horizon FLEX 1.0 This doument supports the version of eh produt listed nd supports ll susequent versions until the doument is repled y new edition. To hek for more

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 David McIntyre 1 Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

More information

To the Graduate Council:

To the Graduate Council: o the Graduate Counil: I am submitting herewith a dissertation written by Yan Xu entitled A Generalized Instantaneous Nonative Power heory for Parallel Nonative Power Compensation. I have examined the

More information

output voltage and are known as non-zero switching states and the remaining two

output voltage and are known as non-zero switching states and the remaining two SPACE ECTOR MODULATION FOR THREE-LEG OLTAGE SOURCE INERTERS.1 THREE-LEG OLTAGE SOURCE INERTER The toology of three-leg voltge soure iverter is show i Fig..1. Beuse of the ostrit tht the iut lies must ever

More information

Microcontroller Based PWM Controlled Four Switch Three Phase Inverter Fed Induction Motor Drive

Microcontroller Based PWM Controlled Four Switch Three Phase Inverter Fed Induction Motor Drive SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 7, No., November 00, 95-04 UDK: 004.466 Miroontroller Based PWM Controlled Four Swith Three Phase Inverter Fed Indution Motor Drive Nalin Kant Mohanty, Ranganath

More information