FAULT LOCATION ESTIMATION FOR DISTRIBUTION SYSTEM USING SIMULATED VOLTAGE SAGS DATA
|
|
- Maximillian Hancock
- 3 years ago
- Views:
Transcription
1 FAULT LOCATION ESTIMATION FOR DISTRIBUTION SYSTEM USING SIMULATED VOLTAGE SAGS DATA H. Mokhlis (1), H.Y.Li (1) (1) The University of Mnchester ABSTRACT This pper presents new method for locting short-circuit fult in electricl distriution system. The method works y mtching the ctul voltge mgnitude nd phse ngle with the simulted ones from fult nlysis tht stored in dtse. The mtching will give the possile fulty section/sections. A mtching mesurement lgorithm is then pplied to quntify the mtching ccurcy nd to estimte fulty distnce from prticulr us on the section. In cse more thn one possile fulty section ville, rnking procedure is conducted to rnk down the sections ccording to the degree of mtching ccurcy. A simultion test of the proposed method showed stisfctory result. Keywords: Voltge Sgs, Dtse, Fult Loction, Distriution Networks. 1 INTRODUCTION Short-circuit fult in distriution system often cusing enormous losses to utility nd customer. Such losses cn e reduced if the loction of fult cn e locted s quickly s possile. A common technique to locte fult in distriution system (prticulrly in 11 kv systems) is using tril nd error technique. In this technique, the fult loction is serch y ptrolling long the feeder. The loction usully is guessed y n experience opertor efore sending the repiring crews. This technique is time consuming, costly, nd exposed the crew to dnger. Due to such prolems, vrious utomted fult loction techniques hve een proposed for distriution system. In generl, fult loction techniques cn e divided into three ctegories, which re impednce-sed method, knowledge-sed method nd trvelling wve method. The impednce-sed method estimtes the distnce of fult from the primry distriution us to the fult loction. This method requires voltge nd current vlues mesured t one end or two ends of the line. This method used mthemticl eqution to estimte the fult loction. Most of the method work for rdil system only nd require other informtion such s fult current wveforms, circuit reker sttus, nd fult indictor sttus for non-rdil system [1, ]. However, limited sttus informtion ville on distriution networks, in prticulr on 11kV networks, mkes this pproch very difficult, if not impossile, to estlish relile sttisticl estimtes. Some of this method lso time consuming due to itertive process nd need to know the fult type efore specific eqution cn e pplied. The second ctegory is knowledge-sed method for exmples Artificil Neurl network (ANN), Fuzzy Logic (FL), Expert System (ES) nd Genetic Algorithm (GA) [3] [6]. The ccurcy of the result using this method is highly depending to the given set of informtion such s short-circuit current nd informtion from fult detection devices t the min feeders. Unfortuntely, some of the informtion is not ville in mny distriution systems since mesurement is usully locted t the primry distriution us. This method such s ANN lso requires trining process tht consumes time nd need to e repeted whenever there re chnges in the system. Another type of knowledge-sed technique is y mtching mesured dt with historicl fult dt [6]. Whenever fult occurs in the distriution network, the wveform of voltge sgs mesured t the susttion is recorded into the dtse together with the known fult type nd loction. This dtse is updted whenever fult occurs in the system. When ctul fult occurs, the mesured voltge sgs wveforms t the susttion re compred to ll the voltge sgs wveforms in the dtse. The most mtching wveform in the dtse will give the type of fult nd the loction. The drwck of this method is tht it will not work if the ctul fult never hppens t prticulr loction, or not recorded in the dtse. The lst ctegory is using trvelling wve method to locte fult loction [7]. The principle of this method is sed on the reflection nd trnsmission of the fult generted trvelling wves on the fulted power network. Although this technique cn locte fult with high ccurcy, the implementtion is complex nd expensive. Tken into considertion the limittion of ville informtion in distriution system, the proposed method in this pper uses single mesurement t the primry distriution us to estimte fult loction. The mesured voltge sgs will e mtched with the voltge sg dt nd voltge eqution stored in the dtse. These dt re otined from fult nlysis. The mtch will give the UPEC 7-4
2 loction of the fult in term of distnce from prticulr us in the section. Since the method depends on the simulted dtse, ny chnges such s lod vrition in the system cn e ddressed y updting the dtse. The method lso not costly for implementtion since it requires only single mesurement t the min susttion BACKGROUND OF THE METHOD Consider 11 kv distriution system with mesurement point is locted t us s depicted in Figure 1. identity of the person. The sme concept is pplied in the proposed method, ut with different pproch of mtching process 3 DESCRIPTION OF THE METHOD 3.1 Simulted Dt Two types of dtses re developed nd used for this method. The first type is to store voltge mgnitude nd phse ngle monitored t the mesured us when fult is simulted t ll uses. The stored voltge mgnitude is the lowest mgnitude mong the three phses. The second type is to store generl eqution of voltge mgnitude nd phse ngle s function of distnce. The equtions re considering the voltge mgnitude nd phse ngle s mesured t the monitored us. Different type of fult hs different dtses. (i) Simulted Voltge Sgs t Buses The dt for this type of dtse is rrnged s depicted in Figure. The first column is the fulted us, second column is the voltge mgnitude nd the third column is the corresponding phse ngle. M M M x Figure 1 Study cse Typicl 11 kv distriution system If the ove system experienced short-circuit fult t ny loction in the system, the mesured us will experience voltge chnges. The chnges cuse voltge mgnitude t us to drop nd chnge the corresponding phse ngle, which is referred s voltge sg phenomen. The severity of the sg depends on the distnce of fult occurrence from us. The nerest the fult to us the severe the sg will e experienced t us. Different type of fult lso produce different sg chrcteristic t the monitored us. Bsed on this chrcteristic, fult loction cn e estimted y compring the mesured voltge t the monitored us with voltge sg dt nd its known loction where it occurred. The dt cn e collection of prcticl mesurement or from simultion nlysis. However, it is lmost impossile to otin complete set of dt from prcticl experience since short-circuit not lwys occurs nd the loction my vry nd not necessry cover the whole system. Due to this prolem, simulted voltge sgs dt re used in this study to estimte the fulty loction. The sic ide of the proposed method comes from finger print identifiction concept. In this technique, n unknown finger print is mtch with finger prints tht hve een stored in dtse. The mtch will give the Figure Dt rrngement for fult t uses (ii) Simulted Sgs Equtions From the preliminry study, it ws found out tht there re three different types of chnges for voltge mgnitude nd phse ngle over distnce. The types re liner, non-liner nd constnt. Ech section hs its own eqution nd the type of chnges my differ depends on the vlue of the section impednce. The lrger the impednce, the more non-liner the chnges will e. On the other hnd, smll impednce will produce liner nd lmost constnts chnges if the impednce is too smll. In this study, the eqution is ssumed to e polynomil type with the degree of two. The generl equtions re s follow: V i = d + d + (1) where, V i d,, 1,, 1 1 = d + d + i 1 () voltge mgnitude phse shift section where the eqution cn e pplied distnce coefficients of the voltge mgnitude eqution coefficients of the phse ngle eqution The existing of the coefficient will depend on the type of the eqution s follows: UPEC 7-43
3 ) Non-liner type - ll the coefficients hve vlue ) Liner type - nd is zero nd the rest hs vlue c) Constnt type only nd hs vlue, the rest is zero The following is the rrngement of the dt for second type of the dtse. Figure 3 Dt rrngement for voltge mgnitude nd phse ngle equtions The first column nd second column of the dtse re two djcent uses. The third, forth nd fifth column is the coefficient of the eqution s shown in equtions (1) nd () 3. Mtching Algorithm The serch of the est mtching dt using the developed dtses is sed on the following steps: possiility of overlpping oundry. The overlpping will cuse more thn one section selected s possile fulty section. The region cn e lso presented in the form of equtions s follows: V < V < V etween us nd us (3) fult fult < < etween us nd us (4) V fult V < α nd fult < α t us (5) V fult V < α nd fult < α t us (6) Where α is the specified threshold to determine the mtching etween the ctul nd the simulted one. The threshold is required ecuse it is not possile to otin exctly the sme vlue of oth the simultion nd ctul mesurement. (ii) Mtching mesurement The mtching mesurement is sed on the mismtch etween the distnce otined from voltge mgnitude eqution nd distnce otined from phse ngle eqution. Figure 6 shows how the distnce is otined using oth types of equtions. In the figure, the function ( V, d) represents n eqution of voltge mgnitude f V over distnce nd the function f (, d) represents phse ngle over distnce. Both functions re representing voltge sg profile long the two djcent uses, which is us nd us. The eqution cn e ny type s discussed in section A nd not necessry nonliner s presented in Figure 6. Figure 4 Flow chrt showing the generl steps of the proposed method (i) Glol Serch The im of glol serch is to find ll the section tht ounds the mesured voltge V, ). This section is ( f f considered s the possile fulty section. The oundry cn e presented in the form of grph s follows: d V d Figure 6 Equtions of voltge mgnitude nd phse ngle for section - Figure 5 Fulty region for section - The region represents the oundry of voltge mgnitude nd phse ngle vlues when fult occurs t ny loction on section -. A given voltge mgnitude nd its corresponding phse ngle tht fll inside this region will e considered cused y fult t this section. Ech section hs its own oundry ut there is lso The mtching vlue is given y the following eqution: σ = d V d (7) where, σ mtching vlue or the mismtch of the distnce d distnce otined from voltge mgnitude eqution V d distnce otined from phse ngle eqution UPEC 7-44
4 The mtching is considered 1 % mth if σ.. The lower the vlue of σ, the higher the mtching ccurcy will e. This mesurement lso provides n estimtion of the fulty distnce in the section from us in the section -, which is given y d nd d V. (iii) Rnking of the possile fulty section In the sitution if more thn one possile fulty section selected from glol serch, the sections need to e rnked ccording to its degree of mtching. The cndidte with the highest degree of similrity will e selected s the most likely fulty section. However, the other cndidtes re lso considered in cse the first choice is incorrect upon visul inspection. Due to this reson, rnking procedure is developed to ssign the section ccording to the priority for inspection. The process cn e simplified in the following steps: ) Find the minimum vlue from the clss group, σ min = min{ σ, σ L σ }, (1 < i < n) where n is 1 i the numer of sections selected from the glol serch. ) The section i corresponding to lowest vlue of σ is considered s the most mtching pir nd ssigned s the first possile section. c) The steps re repeted to find the next most mtching pir of dt. This step is repeted until ll the sections hve een rnked. The finl result is the list of possile fulty section/sections thn hs een rnked ccording to it degree of mtching. At the sme time, the lgorithm lso provides the estimtion of fult distnce in the section. 4 EVALUATION OF THE METHOD Due to the sence of rel mesurement, the proposed method is tested using simulted ones. A distriution networks in Figure 1 is used to study the ility of the proposed method to locte fult. The network consists of 33kV equivlent network source, 33/11kV trnsformer nd n 11kV feeder with 1 nodes i.e. 19 sections nd rnches. In this pper only Single Line to Ground Fult (SLGF) result will e presented. The short-circuit fult in this test is considered olted fult. 4.1 Dtse Development In this study, the dtse is estlished from the fult nlysis simultion s discussed in section 3. Tle 1 shows smple of dtse contins voltge mgnitude nd phse ngle of the lowest voltge mgnitude t the monitored us when SLGF is simulted t ll uses in the system. Tle 1: Simulted Voltge Sgs t Bus Fulted Bus Voltge Mgnitude (pu) Phse Angle (rdin) M M M Tle nd Tle 3 re the coefficient vlues of the voltge mgnitude versus distnce nd phse ngle versus distnce equtions respectively. Tle : Voltge Mgnitude s Function of distnce Coefficients Section M M M M Tle 3: Phse Angle s Function of distnce Coefficients Section M M M M The grphs in Figure 7 nd Figure 8 show two exmples of the eqution for section 3-4 nd section 4-5 of SLGF respectively. The equtions represent the vlue of voltge mgnitude nd phse ngle t monitored us when fult occur t ny loction etween the two djcent uses. The loction is considered from us 3 towrds us 4 nd us 4 towrds us 5 respectively. For oth section, it cn e oserved tht the chnges of voltge mgnitude over distnce is lmost liner. However, the phse ngle for oth section re nonliner. In the Figure 7() nd Figure 8 (), the severity of voltge sg reduces s fult occur further wy from the monitored us. This cn e seen y compring the voltge mgnitude t us 4 nd us 5 in the grphs of Figure 7() nd Figure 8(). At us 4, the voltge mgnitude is round.7 pu nd t us 5 it is round.17 pu. This chrcteristic is inline with the chrcteristic of voltge sg where the nerer the fult to the mesured point, the more the drop of voltge mgnitude will e. Figure 7(): Eqution of voltge mgnitude versus distnce for section 3-4 UPEC 7-45
5 Figure 7() Eqution of phse ngle versus distnce for section 3-4 The result is given in Tle 5, where the first column of the tle is the test no, the second column shows the selected fulty section/section from the lgorithm. The third nd forth column re the estimted distnce from voltge eqution nd phse ngle eqution respectively. The fifth column is the degree of mtching nd finlly the lst column represents the rnk of the selected fulty section. Tle 5: Testing Result Test No Selected fulty section d (pu) V d (pu) σ Rnk Figure 8() Eqution of voltge mgnitude versus distnce for section Fult loction (pu) Figure 8() Eqution of phse ngle versus distnce for section Simultion Test Tle 4 shows some testing point where Single Line to Ground fult is simulted. Tle 4: Testing Loction -SLGF Test No Simulted fulty section 1 Section -3,.5 pu of distnce from us Section 3-4,.75 pu of distnce from us 3 3 Section 4-5,.3 pu of distnce from us 4 4 Section 5-6,.75 pu of distnce from us 5 5 Section 6-7,.5 pu of distnce from us 6 6 Section 7-8,.5 pu of distnce from us 7 7 Section 8-9,.75 pu of distnce from us 8 8 Section 9-1,.5 pu of distnce from us 9 9 Section 7-11,.5 pu of distnce from us 7 1 Section -1,.75 pu of distnce from us The result in the ove tle shows some importnt oservtions. Firstly is on the possile fulty section. It cn e seen tht from us to us 6, the lgorithm only selected one possile fulty section. Wheres, strting from us 6, more thn one section is selected s the possile fulty section. This occurred ecuse of the prllel sections strting from us 6. Tken test no 5 s n exmple of this sitution, two possile sections re selected i.e. section 6 7 nd section Both sections re prllel line. The sme goes to other prllel sections strting from us 6. For prllel lines, there is loction t ech of the lines where the occurrence of fult will produce the sme voltge sg chrcteristic. This hppen ecuse t this loction, the electricl distnce is the sme s seen from the monitored us. If the system is in rdil form without ny rnches, the lgorithm will get only one possile fulty section. UPEC 7-46
6 The second oservtion is on the rnking of the possile fulty sections. The sections hve een rnked ccording to the vlue of mtching ccurcy. The most lower is set s the first choice for visul inspection nd followed y the other sections. In the tle, the most likely fulty section is in the grey ox. For exmple, for test no 9, three possile sections hve een selected. The sections hve een rnked in sequence, where section 7-11 is the first possile fulty section, followed y section 7-8 nd finlly section The first section will e checked first nd if this choice is incorrect, the second section will e inspected nd if still incorrect the third one cn e checked. The possiility of hving more thn one section cnnot e voided using this method, unless the rnch where the fult occurrence cn e identified. This cn e done y plcing fult indictor t the end of ech rnch. The third oservtion is on the estimtion of the fult distnce. For exmple, for test no 1, the fulty loction is estimted occur t section -3 with estimtion of loction t.498 pu or.4989 pu from us. These fulty distnce estimtion would help the repiring crew to hve resonle estimtion where to look first insted of guessing the loction sed on previous experienced tht might e wrong 5 FUTURE WORKS In the future, the proposed method will e improved to consider the effect of fult resistnce. A thorough study will lso e conducted to study the performnce of the method due to mesurement error nd how to overcome such prolem. The method lso will e tested using other distriution networks. 6 CONCLUSIONS In this pper, new method to estimte fult loction for distriution system hs een presented. The test of the method shows promising result nd hence the method cn e further improved to ddress fult resistnce effect nd mesurement error. The method is simple nd inexpensive for implementtion since its only requires single mesurement t the monitored us. Any chnges such s lod vritions or network reconfigurtion cn e dpted y this method y updting the dtse.. E.C. Senger, G. Jr. Mnssero, C. Goldemerg, E.L. Pellini, Automted fult loction system for primry distriution networks, IEEE Trns on Power Delivery, Vol., No, pges , April Hong-Tzer Yng, Wen-Yeu Chng, Ching-Lien Hung, A new neurl networks pproch to on-line fult section estimtion using informtion of protective relys nd circuit rekers, IEEE Trns on Power Delivery, Vol. 9, No 1, pges -3, Jn P. Jrventust, P. Verho, J. Prtnen, Using fuzzy sets to model the uncertinty in the fult loction process of distriution networks, IEEE Trns on Power Delivery, Vol 9, No, pges , April Hsu Yun-Yih, Lu, F.-C., et. l, An expert system for locting distriution system fults, IEEE Trns. On Power Delivery, Vol. 6, Issue 1, pges , Jn M. Kezunovic, Y. Lio, Fult loction estimtion sed on mtching the simulted nd recorded wveforms using genetic lgorithms, Development in Power System Protection, Amsterdm, The Netherlnds, pges April Zeng Xingjun, Li, K.K., Liu Zhengyi, Yin Xinggen, Fult loction using trvelling wve for power networks, Industry Applictions Conference, Vol. 4, pges 46 49, 3-7 Oct. 4. AUTHOR'S ADDRESS The first uthor cn e contcted t School of Electricl & Electronic Engineering, University of Mnchester, A3, Ferrnti Building. Emil hzli@um.edu.my 7 ACKNOWLEDGEMENTS The first uthor grtefully cknowledges the studentship given y the University of Mly, Mlysi, for the PhD work in this re. 8 REFERENCES 1. Jun Zhu, D.L. Lukemn, A.A. Girgis, Automted fult loction nd dignosis on electric power distriution feeders, Trns on Power Delivery, Vol. 1, No, pges 81-88, April UPEC 7-47
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 informationEQUATIONS 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 informationRegular Sets and Expressions
Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite
More informationPolynomial 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 informationSection 5-4 Trigonometric Functions
5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationPentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful
Pentominoes Bruce Bguley Cscde Mth Systems, LLC Astrct. Pentominoes nd their reltives the polyominoes, polycues, nd polyhypercues will e used to explore nd pply vrious importnt mthemticl concepts. In this
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationReasoning 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 informationAntiSpyware Enterprise Module 8.5
AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility
More informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
More informationAppendix 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 informationMathematics. 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 informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationDlNBVRGH + 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 informationP.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
More informationEE247 Lecture 4. For simplicity, will start with all pole ladder type filters. Convert to integrator based form- example shown
EE247 Lecture 4 Ldder type filters For simplicity, will strt with ll pole ldder type filters Convert to integrtor bsed form exmple shown Then will ttend to high order ldder type filters incorporting zeros
More informationRotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
More informationA.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 informationOr 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 informationSimulation of operation modes of isochronous cyclotron by a new interative method
NUKLEONIKA 27;52(1):29 34 ORIGINAL PAPER Simultion of opertion modes of isochronous cyclotron y new intertive method Ryszrd Trszkiewicz, Mrek Tlch, Jcek Sulikowski, Henryk Doruch, Tdeusz Norys, Artur Srok,
More informationVectors 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 informationSpace 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 informationGraphs 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 informationEconomics 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 informationWarm-up for Differential Calculus
Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More informationSoftware Cost Estimation Model Based on Integration of Multi-agent and Case-Based Reasoning
Journl of Computer Science 2 (3): 276-282, 2006 ISSN 1549-3636 2006 Science Publictions Softwre Cost Estimtion Model Bsed on Integrtion of Multi-gent nd Cse-Bsed Resoning Hsn Al-Skrn Informtion Technology
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only
More information** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand
Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl
More informationConcept Formation Using Graph Grammars
Concept Formtion Using Grph Grmmrs Istvn Jonyer, Lwrence B. Holder nd Dine J. Cook Deprtment of Computer Science nd Engineering University of Texs t Arlington Box 19015 (416 Ytes St.), Arlington, TX 76019-0015
More information, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.
Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge
More informationRTL Power Optimization with Gate-level Accuracy
RTL Power Optimiztion with Gte-level Accurcy Qi Wng Cdence Design Systems, Inc Sumit Roy Clypto Design Systems, Inc 555 River Oks Prkwy, Sn Jose 95125 2903 Bunker Hill Lne, Suite 208, SntClr 95054 qwng@cdence.com
More informationBayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
More informationCS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001
CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic
More informationThe Acoustic Design of Soundproofing Doors and Windows
3 The Open Acoustics Journl, 1, 3, 3-37 The Acoustic Design of Soundproofing Doors nd Windows Open Access Nishimur Yuy,1, Nguyen Huy Qung, Nishimur Sohei 1, Nishimur Tsuyoshi 3 nd Yno Tkshi 1 Kummoto Ntionl
More informationFactoring 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 informationUnit 6: Exponents and Radicals
Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -
More informationAnswer, 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 information1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
More informationUnderstanding Basic Analog Ideal Op Amps
Appliction Report SLAA068A - April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).
More informationMorgan Stanley Ad Hoc Reporting Guide
spphire user guide Ferury 2015 Morgn Stnley Ad Hoc Reporting Guide An Overview For Spphire Users 1 Introduction The Ad Hoc Reporting tool is ville for your reporting needs outside of the Spphire stndrd
More informationThe 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 informationModule 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 informationNetwork Configuration Independence Mechanism
3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting
More informationFAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University
SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility
More information9.3. 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 informationBabylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity
Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University
More informationaddition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix.
APPENDIX A: The ellipse August 15, 1997 Becuse of its importnce in both pproximting the erth s shpe nd describing stellite orbits, n informl discussion of the ellipse is presented in this ppendix. The
More informationBinary 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 informationand 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 informationA Network Management System for Power-Line Communications and its Verification by Simulation
A Network Mngement System for Power-Line Communictions nd its Verifiction y Simultion Mrkus Seeck, Gerd Bumiller GmH Unterschluerscher-Huptstr. 10, D-90613 Großhersdorf, Germny Phone: +49 9105 9960-51,
More informationTITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING
TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING Sung Joon Kim*, Dong-Chul Che Kore Aerospce Reserch Institute, 45 Eoeun-Dong, Youseong-Gu, Dejeon, 35-333, Kore Phone : 82-42-86-231 FAX
More informationLectures 8 and 9 1 Rectangular waveguides
1 Lectures 8 nd 9 1 Rectngulr wveguides y b x z Consider rectngulr wveguide with 0 < x b. There re two types of wves in hollow wveguide with only one conductor; Trnsverse electric wves
More informationMeasuring Similarity between Graphs Based on the Levenshtein Distance
Appl. Mth. Inf. Sci. 7, No. 1L, 169-175 (01) 169 Applied Mthemtics & Informtion Sciences An Interntionl Journl Mesuring Similrity etween Grphs Bsed on the Levenshtein Distnce Bin Co, ing Li nd Jinwei in
More information4. DC MOTORS. Understand the basic principles of operation of a DC motor. Understand the operation and basic characteristics of simple DC motors.
4. DC MOTORS Almost every mechnicl movement tht we see round us is ccomplished by n electric motor. Electric mchines re mens o converting energy. Motors tke electricl energy nd produce mechnicl energy.
More informationRotating DC Motors Part I
Rotting DC Motors Prt I he previous lesson introduced the simple liner motor. Liner motors hve some prcticl pplictions, ut rotting DC motors re much more prolific. he principles which eplin the opertion
More informationCHAPTER 11 Numerical Differentiation and Integration
CHAPTER 11 Numericl Differentition nd Integrtion Differentition nd integrtion re bsic mthemticl opertions with wide rnge of pplictions in mny res of science. It is therefore importnt to hve good methods
More informationBypassing Space Explosion in Regular Expression Matching for Network Intrusion Detection and Prevention Systems
Bypssing Spce Explosion in Regulr Expression Mtching for Network Intrusion Detection n Prevention Systems Jignesh Ptel, Alex Liu n Eric Torng Dept. of Computer Science n Engineering Michign Stte University
More information4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
More informationT H E S E C U R E T R A N S M I S S I O N P R O T O C O L O F S E N S O R A D H O C N E T W O R K
Z E S Z Y T Y N A U K O W E A K A D E M I I M A R Y N A R K I W O J E N N E J S C I E N T I F I C J O U R N A L O F P O L I S H N A V A L A C A D E M Y 2015 (LVI) 4 (203) A n d r z e j M r c z k DOI: 10.5604/0860889X.1187607
More informationSection 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 informationHow To Write A Recipe Card
Interntionl Journl of Forecsting 18 (2002) 625 646 www.elsevier.com/ locte/ ijforecst A genetic lgorithms pproch to growth phse forecsting of wireless suscriers 1,2 Rjkumr Venktesn, V. Kumr* ING Center
More informationQuick Reference Guide: One-time Account Update
Quick Reference Guide: One-time Account Updte How to complete The Quick Reference Guide shows wht existing SingPss users need to do when logging in to the enhnced SingPss service for the first time. 1)
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationMath 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.
Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose
More informationMA 15800 Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!
MA 5800 Lesson 6 otes Summer 06 Rememer: A logrithm is n eponent! It ehves like n eponent! In the lst lesson, we discussed four properties of logrithms. ) log 0 ) log ) log log 4) This lesson covers more
More informationNew Internet Radio Feature
XXXXX XXXXX XXXXX /XW-SMA3/XW-SMA4 New Internet Rdio Feture EN This wireless speker hs een designed to llow you to enjoy Pndor*/Internet Rdio. In order to ply Pndor/Internet Rdio, however, it my e necessry
More informationOne Minute To Learn Programming: Finite Automata
Gret Theoreticl Ides In Computer Science Steven Rudich CS 15-251 Spring 2005 Lecture 9 Fe 8 2005 Crnegie Mellon University One Minute To Lern Progrmming: Finite Automt Let me tech you progrmming lnguge
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationNovel Methods of Generating Self-Invertible Matrix for Hill Cipher Algorithm
Bibhudendr chry, Girij Snkr Rth, Srt Kumr Ptr, nd Sroj Kumr Pnigrhy Novel Methods of Generting Self-Invertible Mtrix for Hill Cipher lgorithm Bibhudendr chry Deprtment of Electronics & Communiction Engineering
More informationSmall Businesses Decisions to Offer Health Insurance to Employees
Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults
More informationDynamic TDMA Slot Assignment in Ad Hoc Networks
Dynmic TDMA Slot Assignment in Ad Hoc Networks Akimitsu KANZAKI, Toshiki UEMUKAI, Tkhiro HARA, Shojiro NISHIO Dept. of Multimedi Eng., Grd. Sch. of Informtion Science nd Technology, Osk Univ. Dept. of
More informationLecture 9 Microwave Network Analysis A. Nassiri - ANL June 19, 2003. Microwave Physics and Techniques UCSB June 2003 1
Lecture 9 Microwve Network nlysis. Nssiri - NL June 9, 003 Microwve Physics nd Techniques UC June 003 -Prmeter Mesurement Technique VVM: The vector voltmeter mesures the mgnitude of reference nd test voltge
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationAPPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS
APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS TABLE OF FIGURES Figure 1: Spectrl Response of CMOS Imge Sensor...3 Figure 2: Byer CFA Ptterns...4
More informationAntibody Screening. Antibody Screening in Pre-transfusion Testing and Antenatal Screening
Antiody Screening in Pre-trnsfusion Testing nd Antentl Screening Antiody Screening in Pre-trnsfusion Testing nd Antentl Screening Q. Wht re nturlly occurring or expected ntiodies? Q. Wht re typicl or unexpected
More informationModule 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 information1.2 The Integers and Rational Numbers
.2. THE INTEGERS AND RATIONAL NUMBERS.2 The Integers n Rtionl Numers The elements of the set of integers: consist of three types of numers: Z {..., 5, 4, 3, 2,, 0,, 2, 3, 4, 5,...} I. The (positive) nturl
More informationHow To Make A Network More Efficient
Rethinking Virtul Network Emedding: Sustrte Support for Pth Splitting nd Migrtion Minln Yu, Yung Yi, Jennifer Rexford, Mung Ching Princeton University Princeton, NJ {minlnyu,yyi,jrex,chingm}@princeton.edu
More informationTwo 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 informationLINEAR 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 informationWeek 11 - Inductance
Week - Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationPHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
More informationVector differentiation. Chapters 6, 7
Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts
More informationScalable Mining of Large Disk-based Graph Databases
Sclle Mining of Lrge Disk-sed Grph Dtses Chen Wng Wei Wng Jin Pei Yongti Zhu Bile Shi Fudn University, Chin, {chenwng, weiwng1, 2465, shi}@fudn.edu.cn Stte University of New York t Bufflo, USA & Simon
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationWEB 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 informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationBasic Research in Computer Science BRICS RS-02-13 Brodal et al.: Solving the String Statistics Problem in Time O(n log n)
BRICS Bsic Reserch in Computer Science BRICS RS-02-13 Brodl et l.: Solving the String Sttistics Prolem in Time O(n log n) Solving the String Sttistics Prolem in Time O(n log n) Gerth Stølting Brodl Rune
More informationAn Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
More informationPower consumption In operation At rest For wire sizing. Rated impulse voltage Control pollution degree 3. Non-operating temperature
echnicl dt sheet SRF2A-5(-O) Rotry ctutor with emergency function for utterfly vlves orque orue 2 2 2 m m m ominl voltge AC/DC 2 V Control Control Open-close Oen-close SRF2A-5 SRF2A-5 Deenergised C C SRF2A-5-O
More informationNeighborhood Based Fast Graph Search in Large Networks
Neighborhood Bsed Fst Grph Serch in Lrge Networks Arijit Khn Dept. of Computer Science University of Cliforni Snt Brbr, CA 9306 rijitkhn@cs.ucsb.edu Ziyu Gun Dept. of Computer Science University of Cliforni
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationA Conditional Model of Deduplication for Multi-Type Relational Data
A Conditionl Model of Dedupliction for Multi-Type Reltionl Dt Aron Culott, Andrew McCllum Deprtment of Computer Science University of Msschusetts Amherst, MA 01003 {culott, mccllum}@cs.umss.edu Astrct
More informationLecture 5. Inner Product
Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More informationPhysics 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