Protection of ungrounded systems using an advanced relay element
|
|
- Letitia Powers
- 5 years ago
- Views:
Transcription
1 ENG 460 Prtectin f ungrunded systems using an advanced relay element A reprt submitted t the schl f Engineering and Energy, Murdch University in partial fulfilment f the requirements fr the degree f Bachelr f Engineering 2010 Student Name : Berty Siyambalapitiyage Dn Student Number : Year f submissin : 2010 Supervisr : Dr. Gregry Crebbin Prject crdinatr : Prfessr Parisa Bahri
2 ABSTRACT The aim f this thesis prject is t investigate single line t grund faults in an ungrunded system and determine an effective fault detectin methd. Ungrunded system analysis is cnducted using ICAP simulatin. The fault detectin methd is fcused n three different parts. The first part is used t identify the faulted feeder. Secnd part is fr identifying the faulted phase and the last part is fr estimating the fault distance. After simulating the mdel f an ungrunded system using ICAP, it can be bserved that when a grund fault is present, the vltage magnitude f the unfaulted phase increases. The secnd bservatin is that when the fault is present, a zer-sequence vltage and a zer-sequence current are created in the ungrunded system. Therefre zer-sequence cmpnents can be used t identify the faults in an ungrunded system. A directin element is used t identify the faulted feeder f an ungrunded system. The relay measures the zer-sequence vltage (3V) and zer-sequence current (3I) using a brken delta transfrmer and a current transfrmer. The relay calculates impedance (V/I), If this impedance value is abve the frward threshld then a directinal element identifies it as a frward fault. The simulatin result prves the abve methd and als shws the faulted feeder zersequence current lagging the vltage by 90 degrees and the unfaulted feeder zersequence current leads the vltage by 90 degrees. The phase difference between the psitive sequence vltage (V 1A ) f ne f the phases and zer-sequence current are used t detect a single line t grund fault n that phase. The simulatin results shw the abve methd is able t identify the faulted phase. In the final sectin, the simulatin results shw the magnitude f the zer-sequence current change accrding t the faulted distance therefre the single line t grund fault detectin algrithm can use this characteristic t measure the fault distance. 2
3 ACKNOWLEDGMENTS I wish t express my greatest thanks t Dr. Gregry Crebbin fr his excellent assistance, patience and prfessinal guidance thrughut this thesis prject. Gratitude is expressed t Dr. Gregry Crebbin fr his cmmitment in prviding gd learning pprtunity. Lastly, I thank my wife and sn fr their lve and invaluable supprt thrughut this thesis prject. 3
4 Table f Cntents ACKNOWLEDGMENTS General Intrductin Scpe f the prject Tpic utline Backgrund Ungrunded Pwer System Ungrunded system Vs Multigrunded system Relay cnnectins in an ungrunded system The vltage transfrmer Theretical backgrund Sequence cmpnents Sequence vltage The relay types used in ungrunded systems The 59N scheme The SEL-351 Relay Numerical Relay (fr ETESAL) Grund-fault lcatin algrithm fr ungrunded radial distributin systems Applicatin f Practical Criterin fr Single-phase-grund Fault in Ungrunded Pwer System Analysing an ungrunded system using the ICAP Intrductin t ICAP sftware Simulating the ungrunded system using ICAP Intrductin the simulatin diagram Assumptins fr simulatin Apprach Prcedure Results (the single line t grund fault effect) Result Analysis (the single line t grund fault effect) Apprach Prcedure Results (zer-sequence current and zer-sequence vltage wavefrm) Intrductin f the results Results Analysis The Functin f the Relay element Intrductin
5 4.2 The Functinal f the Blcks Directinal Element (faulted feeder detectin) Assumptins Phase Selectin Element Assumptins The Distance Measuring Element Simulatin fr detecting the faulted feeder Feeder 1 A-phase t grund fault Assumptins Results (detectin f the faulted feeder) Intrductin t the results General verview f the results Errrs appear in the results Analysis f Results General Analysis Analysis f the Directinal element functin Analysis f the errrs in the result Simulatin fr Identifying the Faulted Phase Simulatin Prcedure Simulatin Prcedure (A-phase t grund fault in feeder1) Simulatin Prcedure (B-phase t grund fault in feeder1) Simulatin Prcedure(C-phase t grund fault in feeder1) Assumptins Simulatin results(the faulted phase identificatin) Intrductin f the results General verview f the results Calculated results Analysis f Simulatin results (The Faulted Phase Identificatin) General analysis Analysis the results with the relay element functin Simulatin fr estimating the fault distance Prcedure Required Data The fault distance estimatin result
6 7.4 Analyse f the fault distance results Analysis f the Fault resistance Intrductin t the fault resistance Simulatin prcedure Results f the fault resistance analysis Analyse the results f the fault analysis Fault Detectin sensitivity discussin Imbalance f the system The current transfrmer sensitivity Grund sensitivity Cnclusin Limitatin f the relay element Future Recmmendatin References Appendices Appendix A Appendix B Appendix D Table f figures Figure 1: Delta cnnected ungrund pwer distributin system [11] Figure 2: Ungrunded System [2] Figure 3: Multigrunded system [2] Figure 4: Three-phase simplified representatin f an ungrunded distributin system Figure 5: Single-Line Diagram and New Brken-Delta VT Cnnectin Diagram [3] Figure 6: Current transfrmer arrangement [1] Figure 7: Icap simulatin diagram fr a ne kilmeter ungrunded pwer system( feeder 1) Figure 8: A-phase, B-phase and C-Phase wavefrms after A-phase t grund fault in an ungrunded system Figure 9: zer-sequence current and zer-sequence vltage wavefrm (A-phases t grund Fault) Figure 10: Functinal blck diagram f advanced relay element Figure 11: Impedance-plane directinal element characteristics [4] Figure 12: Zer-sequence netwrk fr the frward grund fault [3] Figure 13: Single line t grund faults in frnt f relay measuring pint [1] Figure 14: Simulatin diagram fr identify the faulted feeder Figure 15: Three feeders zer-sequence vltage and zer-sequence current wave frm after A-phase t grund fault in feeder ne Figure 16: Simulatin diagram fr identifying the faulted phase Figure 17: Resultant wavefrms f phase selectin analysis Figure 18: Simulatin diagram fr fault resistance analysis
7 Figure 19: 3I and 3V wavefrm at feeder 1(A-phase t grund fault in feeder 1) Figure 20: 3I and 3V wavefrm at feeder 2(A-phase t grund fault in feeder 1) Figure 21: 3I and 3V wavefrm at feeder 3(A-phase t grund fault in feeder 1) Figure 22: resulting wavefrm zer-sequence current and V 1a Figure 23: resulting wavefrm zer-sequence current and V 1a Figure 24: resulting wavefrm I and V 1a Figure 25: zer-sequence current wavefrm f fault distance measuring simulatin Figure 26: zer-sequence current wavefrm f fault distance measuring simulatin Figure 27: zer-sequence current wavefrm f fault distance measuring simulatin Figure 28: Resulting wavefrm zer-sequence current and V 1a (fr fault resistance simulatin) 63 Figure 29: Resulting wavefrm zer-sequence current and V 1a (fr fault resistance simulatin)63 Figure 30: Resulting wavefrm zer-sequence current and V 1a (fr fault resistance simulatin)64 Table f Tables Table 1: Distributin line parameters (refer t [13], pp 506) Table 3: Angle deferent zer-sequence current and zer-sequence vltage Table 4: impedance (V/I) Table 5: Angle different between V 1A and zer-sequence current Table 6: line parameters fr simulatin Table 7: zer sequence current variatin with the fault distance Table 8: fault resistance result Table 9: Distance measuring element results Table 10: Phase difference (between Va1 and zer-sequence current) vs fault resistance
8 Chapter 1 1 INTRODUCTION 1.1 General Intrductin Ungrunded pwer systems are attractive because they generate small fault currents when a grund fault ccurs. These systems prvide a lwer safety risk t humans and are able t maintain peratin under grund fault events. Hwever, the lw fault current makes it difficult t detect grund faults. As electrical system reliability and cntinuity f service in an electrical system are the tp pririties fr mst industries, an effective fault detectin methd is required fr these systems. The traditinal methd fr detecting grund faults in an ungrunded pwer netwrk is t use simple ver-vltage prtective relays. Fr advanced prtectin systems, simple ver vltage relays are nt effective elements fr detecting faults. This is because traditinal relays can nt identify the faulted feeder and faulted phase in an ungrunded pwer system. Instead, a switching methd is used t identify the fault. The system peratr de-energizes ne feeder at a time until the fault disappears. But this prcess discnnects a number f healthy feeders and disturbs the cntinuity f the pwer supply [1]. Accrding t histrical fault analysis data, ninety percent f all faults n ungrunded netwrks are single line t grund faults. This prject aims t develp an advanced element t detect and lcate single line t grund faults in radial ungrunded systems [1]. In particular, the element will be able t detect: a) the faulted feeder; b) the faulted phase, and: c) the distance t the fault pint. Due t the limitatins in traditinal fault detectin in ungrunded pwer systems, the Advanced Relay Element fault detectin methd culd play an imprtant rle in an industrial envirnment. 8
9 1.2 Scpe f the prject The aim f this thesis prject is t investigate single line t grund faults in ungrunded systems and investigate an advanced element t detect these faults. The fault identificatin system will be develped using zer-sequence current and zer-sequence vltage that are frmed when single line t grund faults are present. This element will detect the faulted feeder, identify the faulted phase and estimate the distance t the fault lcatin. The simulatin is cnducted using ICAP simulatin sftware t verify the theretical results. The advantage and the limitatins f this system will als be discussed. 1.3 Tpic utline a) Chapter 1:Intrductin An utline f the bjectives and need fr this thesis prject b) Chapter 2:Backgrund Ungrunded pwer system Ungrunded system Vs Multigrunded system Relay cnnectins in an ungrunded system The vltage transfrmer Current Transfrmer Theretical backgrund The relay types used in ungrunded systems c) Chapter 3:The apprach Analysing an ungrunded system using the ICAP sftware Intrductin f ICAP sftware Simulate the ungrunded system using ICAP Assumptins fr simulatin Simulatin results Analysis f the result d) Chapter 4:The Functin f the Relay element Intrductin f the blck diagram Directinal element The Functin f the phase selectin element The Functin f the Distance measuring element e) Chapter 5:Simulatin fr detecting the faulted feeder Fault feeder detectin result Detectin f the faulted feeder result Analysis f the results f) Chapter 6:Simulatin fr identifying the faulted phase 9
10 Simulatin results fr the faulted phase identificatin Analysis f the simulatin results g) Chapter 7:Simulatin fr estimating the fault distance The fault distance estimatin result Analyse f the fault distance results Analyse f the fault distance results h) Chapter 8:Analysis f the fault Resistance Intrductin f the fault resistance Simulatin prcedure fr analysis the fault resistance Result f the fault resistance Analyse the fault resistance result i) Chapter 9: Fault detectin sensitivity discussin j) Chapter 10: Cnclusin and future recmmendatins 10
11 Chapter2 2 Backgrund 2.1 Ungrunded Pwer System The mst ppular ungrunded pwer distributin system in current industries is the three phase three-wire delta cnnected ungrunded pwer system. In this ungrunded system, there is n intentinal grund cnnectin in any part f the electrical system. Hwever, each line f the system is cupled t grund thrugh a per-phase capacitance as shw in figure 1. The figure has been remved Figure 1: Delta cnnected ungrund pwer distributin system [11]. The advantage f this system is that the lads are cnnected phase t phase and therefre a single line-t-grund fault des nt effect the lad peratin. Thus the system can perate with a grund fault in ne phase. This avids the need fr an immediate shutdwn f the system [1]. In an ungrunded system, when the first line t grund fault ccurs a very lw fault current flws and the healthy phases rise t the line-t-line vltage 3 times the phase vltage. Therefre a secnd grund fault wuld be very dangerus because the system has high ptential phases [1]. Hwever, the ungrunded systems have attractive characteristics such as, safety fr humans and ability t perate with single line grund faults. Therefre mine sites and Navy ships cmmnly use ungrunded systems fr their pwer system applicatins [9]. 11
12 2.2 Ungrunded system Vs Multigrunded system The figure has been remved The figure has been remved Figure 2: Ungrunded System [2] Figure 3: Multigrunded system [2] Figure 2 shws an ungrunded distributin feeder, it has n neutral cnductr running thugh the system. The phase-t-grund distributin capacitance determines the magnitude f the fault current. The lads are cnnected phase t phase. Figure 3 shws a fur wire multigrunded distributin feeder. The neutral wire is typically grunded at each distributin transfrmer pint. In this system service lads can be cnnected phase t phase r phase t neutral. The zer-sequence current can create an imbalance f the lads. When a fault is present the relay measures the zersequence current created by the lad imbalance and fault current. The multigrunded systems ften becme unbalanced because the lads are mstly cnnected phase t neutral. In the ungrunded system, fault current (If) depends n the line-t-grund capacitance f the unfaulted pwer system phases. This is the mst imprtant difference between a single line t grund fault n an ungrunded system cmpared t a multigrunded pwer system [2]. 12
13 2.3 Relay cnnectins in an ungrunded system Figure 4 shws the wiring cnnectin f the new relay. This is a radial ungrunded pwer distributin netwrk system. Therefre nly ne nde is feeding pwer t the system and pwer will flw tp t bttm. In this system all lads are cnnected phase t phase. The lengths f the cnductrs are less than 80km. It has three feeders; each feeder is mnitred with a relay. The brken delta transfrmer (BDVT) and current transfrmers are cnnected t the relays as shwn in figure 4. The cnnectin f the brken delta transfrmer and current transfrmers t the relays are shwn in figure 5 and figure 6 respectively [2]. Figure 4: Three-phase simplified representatin f an ungrunded distributin system. 13
14 2.3.1 The vltage transfrmer Intrductin f vltage transfrmer Three different types f vltage transfrmer are used in relays. They are three-phase fur-wire, pen-delta and brken delta. The figure 5 shws the brken delta vltage transfrmer (VT) cnnectin f the vltage transfrmer. This methd is very suitable fr ungrunded and resnant-grunded system directinal element applicatins. Using this methd the relay can measure each phase vltage and calculate the zer-sequence vltage (3V) fr the directinal element and phase selectin element [3] Advantages f the Brken Delta Transfrmer Cnnectin. The relay can measure directly each individual phase vltage and calculate the necessary sequence cmpnents. The wire cnnectin is als simpler than the traditinal system. This advanced brken Delta Cnnectin is used t measure zer-sequence vltage f the relay element in the prject. The figure has been remved Figure 5: Single-Line Diagram and New Brken-Delta VT Cnnectin Diagram [3] 14
15 Current Transfrmer The figure has been remved Figure 6: Current transfrmer arrangement [1] The current transfrmer arrangement fr zer-sequence current is shwn in Figure 6. The relay can measure Ia, Ib and Ic that will be used fr the directinal element, phase selectin element and distance measuring element [1]. 2.4 Theretical backgrund Sequence cmpnents In 1918 C.L. Frtescue develped the methd f symmetrical cmpnents. This is a very pwerful methd fr analysing unbalanced three-phase systems. He identified a linear transfrmatin frm phase cmpnents t a new set f cmpnents called symmetrical cmpnents. The symmetrical cmpnents methd facilitates the analysis f the cmplicated unbalance phenmena in a relatively simple manner [6] Sequence vltage Accrding t Frtescue, phase vltages can be cnverted int three sets f sequence cmpnents, zer sequence, psitive sequence and negative sequence. 15
16 1. Zer-sequence cmpnents V a V b V c The set f zer-sequence cmpnents cnsist f the three phasrs (V a,v b,v c ) with equal magnitudes and zer phase displacements such that V a =V b = V c =V 2. Psitive-sequence cmpnents. V c1 V a1 =V 2 V b1 Psitive-sequence cmpnents cnsist f three phasrs with equal magnitudes and 120 phase displacement in a psitive sequence [12]. V a1= V 1 0 V b2= av 2 = V V c2= a 2 0 V 2 =V Negative-sequence cmpnents. V b2 V a1 =V 2 V c2 Negative-sequence cmpnents cnsist f three phases with (V a2, V b2,v c2 ) equal magnitudes,120 phase displacement and negative sequence[12]. V a2 =V 2 V b1 =a 2 0 V 1 =V V c1 =av 1 =V
17 The phase vltages can be written as fllws V a =V +V 1 +V 2 (1) V b =V +a 2 V 1 +av 2 (2) V c =V +av 1 +a 2 V 2 (3) The sequence vltage can be btained frm the phase vltage using the transfrmatin. V = 3 1 ( Va+ V b+ V c ) (4) V 1 = 3 1 ( Va+ av b+ a 2 V c ) (5) V 2 = 3 1 ( Va+ a 2 V b+ av c ) (6) Sequence Currents 1. Zer-sequence current cmpnents The set f zer-sequence current cmpnents cnsist f the three phasrs (I a,i b,i c ) with equal magnitudes and zer phase displacements such that I a =I b = I c =I 2. Psitive-sequence current cmpnents Psitive-sequence cmpnents cnsist f three phasrs with equal magnitudes and 120 phase displacement in a psitive sequence[12]. I a1= I 1 I b= a 2 0 I 1 = I I c1= ai 1 =I
18 3. Negative-sequence current cmpnents Negative-sequence cmpnents cnsist f three phases with (I a2, I b2,i c2 ) with equal magnitudes,120 phase displacement and negative sequence. I a2 =I 2 0 I b2 =ai 2 =I I c2 =ai =I The symmetrical cmpnent transfrmatin can als be applied t currents, as fllws: I a =I +I 1 +I 2 (7) I b =I +a 2 I 1 +ai 2 (8) I c =I 0 +ai 1 +a 2 I 2 (9) The sequence current can be btained frm the phase currents using the transfrmatin: I= 3 1 ( Ia + I b + I c ) (10) I 1 = 3 1 ( Ia + ai b + a 2 I c ) (11) I 2 = 3 1 ( Ia + a 2 I b + ai c ) (12) The psitive-sequence quantities are present during balanced three-phase cnditins Negative-sequence quantities can be measured nly when the pwer system is unbalanced. Zer-sequence quantities can be bserved nly in grund fault cnditins. Therefre negative and zer-sequence cmpnents are nly present in unbalanced systems with grund faults. Therefre the zer-sequence current and zer-sequence vltage can be used t detect faults in ungrunded pwer system relays. Thus zersequence current and vltage are used t develp the single line t grund fault detectin element in this thesis prject [6]. 18
19 2.5 The relay types used in ungrunded systems The 59N scheme The 59N is the mst ppular ver vltage prtective relay fr ungrunded pwer distributin netwrks. It uses the zer-sequence vltage cmpnent t detect single line t grund faults. The disadvantage f the 59N relay is that it can nt detect the faulted feeder r faulted phase. This is because when a grund fault is present any ne f the feeders faulted prduces the same magnitude f zer-sequence vltage. The 59N systems are still in use in several industrial applicatins [1] The SEL-351 Relay The Schweitzer Engineering Labratries develped the SEL-351 Relay fr ungrunded systems and ther pwer system applicatins. The SEL-351 has a very high sensitivity. It includes an advanced directinal element fr ungrunded systems. This relay respnds t the quadrature cmpnent f the dt prduct f the zer-sequence vltage and current. Hwever this relay has n fault lcatin identificatin system [5] Numerical Relay (fr ETESAL) This relay has desirable elements t detect faults in ungrunded systems. It uses an advanced current transfrmer t identify the grund faults[1] Grund-fault lcatin algrithm fr ungrunded radial distributin systems The Department f Electrical Engineering f the Myngji University has prpsed a single phase-t-grund fault lcatin algrithm fr an ungrunded radial distributin system. This algrithm uses the vltage equatin frm the relay lcatin t the fault lcatin. Zer-sequence current, fault resistance and fault distance are the unknwns. The fault resistance is remved by extracting the cmpnents rthgnal t the zersequence current frm the equatin. Finally the fault distance can be calculated [13] Applicatin f Practical Criterin fr Single-phasegrund Fault in Ungrunded Pwer System The Schl f Autmatin and Electrical Engineering at Lanzhu Jia Tng University, in China built an intelligent prtectin device. This element can identify the faulted phase in an ungrunded system rapidly and accurately accrding t the system structure and perating characteristics. 19
20 In this intelligent device, phase-t-grund vltage changes during pre-and-pst fault cnditin in the ungrunded pwer system are used as criteria f searching fr the faulted phase. The intelligent prtectin device detects the circular changes in the three phase-tgrund vltages and zer-sequence vltage. If the zer-sequence vltage ges beynd the limits f the set value the device will determine the faulted phase [14]. 20
21 Chapter 3 3 Analysing an ungrunded system using the ICAP 3.1 Intrductin t ICAP sftware The Intusft Cmpany prvides IsSpice4 simulatin sftware. This sftware is based n Berkeley SPICE 3F.2. SPICE 3F.2 was develped by the Department f Electrical Engineering and Cmputer Science at University f Califrnia, USA [15]. IsSpice4 simulatin sftware is a simulatin package designed t be user friendly and highly interactive. It can be used t explain pwer system peratin t a nn-technical audience. Therefre it is a better simulatin tls fr analysis f sinusidal the sine wavefrms f an ac pwer electrical distributin system than ther simulatin packages. This particular sftware tl will be used t analyses the single line t grund faults in the ungrunded pwer system netwrks used in this thesis prject. 3.2 Simulating the ungrunded system using ICAP Intrductin the simulatin diagram The ICAP simulatin diagram mdel fr a ne feeder ungrunded system is shwn in Figure 7. There are three phases with a feeder each. V1, V2 and V3 are the vltage surces, generating 50Hz sine wave with phase angle shift f 0,120 and 240 respectively.the line resistances are represented by R1, R2 andr3. The line inductance are represented by L1, L2 and L3. The line capacitances are represented by C1, C2 and C3. The values fr the transmissin line parameters were taken frm reference [13]. The Trigger switch is used t create a single line t grund fault. In this analysis line three is selected as phase A. The resister R4 (1MΩ) is used t vercme a simulatin prblem f using ungrunded vltage surce. R4 is a very large resistance s that the system functins effectively as an ungrunded system. 21
22 The vltage surce pints V4, V5 and V6 are used as test pints t measure zersequence current. The tw cmpnents in the bttm f the diagram are used t calculate zer-sequence current and zer-sequence vltage frm the system when the single line t grund fault is present in A-phase Required mdel Data The line impedance use values given in Table1 R L C Ω/km mh/km µf/km Table 1: Distributin line parameters (refer t [13], pp 506) Figure 7: Icap simulatin diagram fr a ne kilmeter ungrunded pwer system( feeder 1) 22
23 3.3 Assumptins fr simulatin The single line t grund faults is nt affected by the lads in an ungrunded pwer system. This is because the system lads are cnnected phase t phase. Therefre the lads are nt included in this ICAP simulatin. Fr this analysis the grund resistance is equal t zer. All transmissin lines are the same type. 3.4 Apprach Prcedure Investigate the single line t grund fault effect The system in Figure 7 was used t investigate the single line t grund fault behaviur in the system. The simulatin is cnducted and the wave frm f the A-phase, B-phase and C-phase are recrded. Distributin line parameters shwn in Table 1 are used in the simulatin mdel. Figure 8 shws the utputs f the three phases. 23
24 3.5 Results (the single line t grund fault effect) Vlts Time in secnds Figure 8: A-phase, B-phase and C-Phase wavefrms after A-phase t grund fault in an ungrunded system 3.6 Result Analysis (the single line t grund fault effect) The number (1-black), (2-blue) and (3-green) are A-phase, B-phase and C-phase simulatin utput wavefrms respectively. The vertical line [1] represents the start f the grund fault event. It is clear that after the grund fault ccurred, the A-phase vltage drps t zer. Als the B-phase and C-phase vltages are increased by the A- phase grund fault. The increase in the values is apprximately equal t the pre-fault vltages. 3 times the The simulatin prves the case that the unfaulted phases can reach 3 times their nrmal magnitude. This characteristic f an ungrunded system can be used t identify the faulted phase. 24
25 3.7 Apprach Prcedure Investigate zer-sequence current and zer-sequence vltage The ungrunded system mdel in Figure 7 is used t analyse the zer-sequence current and zer-sequence vltage f an ungrunded system. The simulatin is cnducted and the wavefrms f the zer-sequence current and zer-sequence vltage are recrded. The Table 1 distributin line parameters are used fr the simulatin line mdels. Figure 9 shws the results f the simulatin. 3.8 Results (zer-sequence current and zer-sequence vltage wavefrm) Vlts Time in Secnds Figure 9: zer-sequence current and zer-sequence vltage wavefrm (A-phases t grund Fault) Intrductin f the results Black Wavefrm- Zer-sequence current (3I) Blue Wavefrm- Zer-sequence vltage (3V) Results Analysis Accrding t the results in Figure 9, after the fault, zer-sequence current and zersequence vltage are created in the ungrunded system. Therefre, these zer-sequence cmpnents can be used t detect the single line t grund fault in an ungrunded system. 25
26 Chapter 4 Methd 4 The Functin f the Relay element 4.1 Intrductin The blck diagram in Figure 10 shws the internal functins f the new relay. Phase vltages (Va,Vb,Vc) and line currents in each phases (Ia,Ib,Ic) feed in t the relay thugh an pen delta transfrmer cnnectin and current transfrmer. Then the functin f the directin element begins. It measures the impedance (V/I) value. If the measured impedance is abve the frward threshld the fault is declared frward. If the fault is in frnt f the relay then the directin element sends a signal t the phase selectin element. The phase selectin element detects the zer-sequence current and zer-sequence vltage extracted frm the feeder. Then the phase selectin element starts analysing the phase angle between zer-sequence current and psitive sequence vltage(v 1a ) f the phase-a(surce vltage f A-phase in used as reference).accrding t the phase different between the zer-sequence current vltage(v 1a )f phase-a, the faulted phase can be determined. and psitive sequence After selecting the faulted phase the selectin element and the directinal element send signals t the AND gates. After receiving these tw high inputs the AND gate gives a high utput t the distance measuring element. Then the distance measuring element starts the peratin that calculates the distance (km) frm feeder t the fault pint. If the fault presents in frnt f the relay it detects the fault and gives an utput f the faulted cnditin. The display unit represented in Figure 10 shws the utput f the relay. Frm this display unit, the relay peratr r any ther authrity is able t identify the faulted feeder, faulted phase and distance t the fault. They can discnnect nly the faulted phase withut disturbing ther pwer supplies f the ungrunded system. It is desirable t discuss the functin f the each blck f the system separately. The fllwing sectins discuss the functins f each functin blck. 26
27 Figure 10: Functinal blck diagram f advanced relay element 4.2 The Functinal f the Blcks Directinal Element (faulted feeder detectin) The functin f the directinal element is t determine frward and reverse cnditins f the fault. It functins accrding t the impedance-plane directinal element characteristics as shwn in Figure
28 The figure has been remved Figure 11: Impedance-plane directinal element characteristics [4] The phase vltages V a, V b and V c are input t the relay frm a brken delta vltage transfrmer. Phasr currents I a, I b and I c are input t the relay frm current transfrmer. Then the relay is able t measure the zer-sequence vltage and zer-sequence current accrding t the equatins V = 3 1 ( Va+ V b+ V c ) (13) I = 3 1 ( Ia + I b + I c ) (14) The relay then calculates the impedance (V/I). If this impedance value is abve the frward threshld then the directinal element identifies it as a frward fault. If the measured impedance value is abve the reverse fault threshld then the directinal element identifies it as a reverse fault [4]. The figure has been remved Figure 12: Zer-sequence netwrk fr the frward grund fault [3] 28
29 XC OS - zer-sequence capacitive reactance f the remaining system. XC OL -zer-sequence capacitive reactance f the prtected line Z OL -zer-sequence line impedance The Figure 11 shws the impedance-plane directinal element characteristics. The Figure 12 shws the zer-sequence netwrk fr the frward grund fault. Accrding thse tw figures If the zer-sequence current lags zer-sequence vltage by 90 degrees and Z O = V = +XCOS then the relay interprets this as a frward fault I If the zer-sequence current leads the zer-sequence vltage by 90 degrees and Z O = V = -XCOL then the relay interprets this as a reverse fault I If the directinal element identifies the fault in frnt f the relay measuring pint then these element sends a signal t the phase selectin element t identify the faulted phase. If a reverse fault is fund the fault detectin des is nt cntinue within this relay, as the fault culd be in any ther place within the ungrunded system [3] Assumptins The zer-sequence impedance f an ungrunded system has a very high magnitude. Therefre the psitive and negative sequence impedances can be neglected. There is n significant lss f accuracy in this calculatin. It is assumed that XC OL >>Z OL and then V=-jXC OL I Phase Selectin Element After detecting the faulted feeder, the next step is t select the faulted phase. When selecting the faulted phase, the value f phase difference between psitive sequence 29
30 vltage (V 1A ) f A-phase (surce vltage f A-phase is used as reference) and zersequence current need t be cnsidered. If the single line t grund fault is in frnt f the relay measuring pint, the algrithm illustratin in Figure 13 is used t select the faulted phase, (The A-phase is cnsidered as the reference in calculating the value f the psitive sequence vltage V 1 [2]) Assumptins Fr this calculatin, psitive sequence and negative sequence impedances are negligible. The figure has been remved Figure 13: Single line t grund faults in frnt f relay measuring pint [1] In figure 13,V1a is the psitive sequence vltage f the A-phase (A-phase surce vltage as reference),and I is the zer-sequence current. The angle (θ) is the phase difference between psitive sequence vltage (V 1A ) and zersequence current. When the angle (θ) is between -5 and 95 the relay identifies the A- phase as faulted. And als if the angle (θ) is between -25 and-125 the relay identifies the B-Phase faulted. If the angle (θ) is between 125 and-145 the relay identifies the C- Phase faulted. After detecting the faulted feeder the phase selectin element and feeder selectin element send a signal t the distance measuring element The Distance Measuring Element After receiving a signal frm the phase selectin element and the directinal element, the fault distance measuring element starts its peratin. When presenting the single line t grund fault the magnitude f the zer-sequence current is used t measure the fault distance. 30
31 Relevant equatin Applying Kirchff s Current Law t the single line t grund fault sequence diagram, the grund fault algrithm can be written [13]. 2 k = 2 V d Z I 3R I = 0 (15) k k = lk V k -relay vltage d- fault distance Z lk -line impedance I k -relay current R f -fault resistance I f -zer-sequence fault current Assumptins k f f The fllwing assumptins are made fr calculating the fault distance. The zer-sequence impedance f an ungrunded system has a very high magnitude. Therefre the psitive and negative sequence impedances can be neglected. There is n significant lss f accuracy in this calculatin. It is assumed that the fault resistance is equal t zer. Therefre the equatin can be written; V +V 1 +V 2 -dz L0 I 0 =0 (16) d ( V + V + 1 V2 ) = (17) Z LO I where d- fault distance V- zer-sequence vltage V 1 - psitive sequence vltage V 2 -Negative sequence vltage Z L0 -Line impedance in zer sequence(per unit length) I 0 -Zer-sequence current 31
32 Sequence vltage calculatin The brken delta vltage cnnects t the relay V a,v b and V c. thus using these vltages,the relay can calculate the zer-sequence vltage, the negative sequence vltage and the psitive sequence vltage as [6]: V = 1 ( Va+ V b+ V c ) (18) 3 V 1 = 3 1 ( Va+ av b+ a 2 V c ) (19) V 2 = 3 1 ( Va+ a 2 V b+ av c ) (20) The zer-sequence line impedance per unit length can be written as [16]: Z LO = (R+jωL) (21) Estimatin f the fault distance Substituting the zer-sequence current magnitude value, V, V 1, V 2 and Z LO t the equatin (10), the fault distance can be estimated. d ( V + V + V2 ) 1 = (22) ( R + jωl) I Verify the methd using simulatin Accrding t equatin (21), nly the zer-sequence current will vary with distance t the fault. Therefre the equatin can be written as fllws K d = (23) I d- fault distance K-cnstant I -zer-sequence current 32
33 Chapter 5 5 Simulatin fr detecting the faulted feeder 5.1 Feeder 1 A-phase t grund fault The ICAP simulatin diagram mdel is shwn in Figure 14. There are three phases fr each feeder.v1,v2 and V3 are the vltage surces. The line resistance is represented as by ntatin R; L signifies the line inductance. The ntatin C represents the line grund capacitance. The values fr these transmissin line elements were given in Table 1 f chapter 3. The Trigger switch is used t create the single line t grund fault. In this analysis, line three is selected as the A-phase. The vltage pints V4, V5 and V6 are used t measure the zer-sequence current frm feeder ne. The V8, V9 and V10 vltage pints are used t measure the zer-sequence current frm feeder tw. V11, V12 and V13 are used t measure the zer-sequence current frm feeder three. The 1MEG resistr is used t ver cme simulatin prblem. The 1MEG is a very large resistance, therefre the system functin runs effectively as an ungrunded system. 33
34 Figure 14: Simulatin diagram fr identify the faulted feeder 5.2 Assumptins The single lines t grund faults are nt effected by the lads in an ungrunded pwer system. This is because the system lads are cnnected phase t phase. Therefre the lads are nt included in this ICAP simulatin. Fault resistance equal t zer. 34
35 5.3 Results (detectin f the faulted feeder) Vlts Time in secnd Figure 15: Three feeders zer-sequence vltage and zer-sequence current wave frm after A-phase t grund fault in feeder ne Intrductin t the results Feeder 1: (1) Black line-zer-sequence current (3I) (2) Blue line-zer-sequence vltage (3V) The zer-sequence current [3I] lags the zer-sequence vltage [3V] Feeder 2: (3) Green line-zer-sequence current(3i) (4) Red line zer-sequence vltage(3v) The zer-sequence current [3I] leads the zer-sequence vltage [3v] 35
36 Feeder 3: (5) Black line-zer-sequence current (3I) (6) Blue line zer-sequence vltage(3v) The zer-sequence current [3I] leads the zer-sequence vltage [3v] General verview f the results The zer-sequence vltage (3V) and zer-sequence current (3I) wavefrms are represented in Figure 15 when the A-phase t grund fault is present in feeder ne. The vertical line [1] represents the start time f the single-line t grund fault event. After that time, the zer-sequence [3V0] current and zer-sequence vltage [3I] are created in each feeder. These tw wavefrms are sinusidal Errrs appear in the results It can be bserved the errr in the zer-sequence current and zer-sequence vltage wavefrm. Prir t the fault the zer-sequence currents and vltages have a sinusidal cmpnent where they shuld be zer. Right after the fault ccurs, the zer-sequence current (3I) sinusidal wave frm has scillatins n each feeder current. The scillatins can create in fault situatin f the system Calculated data f the results Table 2 shws, the angle difference between the zer-sequence current and zersequence vltage in the three feeders. Feeder Angle deference 3V and 3I 1 Zer-sequence current lags zer-sequence vltage by 86.4 degrees 2 Zer-sequence current leads zer-sequence vltage by 89.2 degrees 3 Zer-sequence current leads zer-sequence vltage by 86.2 degrees Table 2: Angle deferent zer-sequence current and zer-sequence vltage Nte: - Refer t Appendix A fr calculatins f the angle difference between zersequence current and zer-sequence vltage 36
37 Feeder (V/I) 1 + Z m1 j 2 Z m2 j 3 Z m3 j Table 3: impedance (V/I) Z m1 -zer-sequence impedance at feeder 1 Z m2 - zer-sequence impedance at feeder 2 Z m3 - zer-sequence impedance at feeder 3 Nte: - Please refer t the Appendix A fr calculatin 5.4 Analysis f Results 5.4.1General Analysis The zer-sequence current and zer-sequence vltage are generated in all three feeders after the A-phase t grund fault. In the faulted feeder, zer-sequence current lags the zer-sequence vltage by 90 degrees. In the ther tw feeders, the zer-sequence current leads the vltage by 90 degrees. Therefre using the abve methd a faulted feeder can be identified in an ungrunded pwer system Analysis f the Directinal element functin The Table 3 shws the rati between V and I (impedance). It can be bserved that the faulted feeder (feeder 1) value is Z m1 j. Accrding Figure 11, if the measured impedance is abve the frward fault threshld then the fault is declared frward.(accrding t the directinal element thery Z m1 are equal t XC OS ). Fr feeder 2 and feeder 3, the rati between V and I (impedance) are -Z m2 j and -Z m3 j respectively. Accrding t Figure 4, the measured impedance is abve the reverse fault threshld therefre the fault is declared reverse (Accrding t the directinal element thery Z m2 and Z m3 are equal t XC OL ). It is clear that using the impedance-plane directinal element, the faulted feeder can be identified. 37
38 5.4.3 Analysis f the errrs in the result Accrding t results in Figure 15, zer-sequence current and zer-sequence vltage sinusidal wave frms can be bserved in the pre-faulted situatin. In pre-faulted situatin the system shuld perate as a balanced system. Zer-sequence current and zer-sequence vltage shuld nt be generated in a balanced system, therefre it is clear that sme errrs in the simulatin befre A-phase t grund fault in feeder 1. Right after the fault at feeder 1 the zer-sequence current(3i) wavefrm has sme scillatins due t the fault. The smth zer-sequence current sinusidal wavefrm can be bserved after 120 milisecnd. In the figure 9, right after the fault at feeder 1 the zer-sequence current (3I) and the zer-sequence vltage(3v) have sme scillatins due t the fault. Hwever these errrs are nt large enugh t affect the final results f identifying the faulted feeder. Therefre the abve faulted feeder identifying methd can be used in an ungrunded system. 38
39 Chapter 6 6 Simulatin fr Identifying the Faulted Phase 6.1 Simulatin Prcedure The simulatin diagram in Figure 16 (fr line parameters, please refer t Table 1) is used fr identifying the faulted phase in the system. First, the A-phase (line 3 in feeder1) psitive sequence vltage (V 1A ) (A-phase surce vltage) is btained. Then the Trigger switch is activated t create a grund fault with three phases, ne at a time. The zer-sequence current wavefrm is recrded each time. The zer-sequence current wave frm is btained using elements V4, V5 and V6 in the simulatin diagram. The angle between zer-sequence current and psitive sequence vltage is checked with diagram in Figure 13 t find the faulted phase. Figure 16: Simulatin diagram fr identifying the faulted phase 39
40 6.1.1 Simulatin Prcedure (A-phase t grund fault in feeder1) The grund fault activatr is cnnected t the A-phase (line 3 in feeder1) t create a grund fault. Then ICAP simulatin is cnducted and btained the zer-sequence current wavefrm is btained. Then the phase difference between psitive sequence vltage (V 1A ) and zer-sequence current is calculated. After the simulatin, the result is mapped nt Figure 13 t find the faulted phase. Fr A-phase fault the angle difference shuld lie - between -5 degrees and 95 degrees Simulatin Prcedure (B-phase t grund fault in feeder1) The grund fault activatr (Trigger switch) is cnnected t the B-phase (line 2 in the circuit diagram) t create a grund fault. Then ICAP simulatin is cnducted and btained the zer-sequence current wavefrm. Then calculate the phase different between psitive sequence vltage (V 1A ) and zer-sequence current. After that the result is tested with Figure 13 t detect the faulted phase. Fr B-phase fault the angle difference shuld lie-between -25 degrees and -125 degrees Simulatin Prcedure(C-phase t grund fault in feeder1) The grund fault activatr (Trigger switch) is cnnected t the B-phase (line 3 in the circuit diagram) t create a grund fault. Then ICAP simulatin is cnducted and btained the zer-sequence current wavefrm. Then calculate the phase different between psitive sequence vltage (V 1A ) and zer-sequence current. After that the result is checked with Figure 13 t detect the faulted phase. C-phase fault sectr: - between 125 degree and -145 degree 6.2 Assumptins The single lines t grund faults are nt effected by the lads in an ungrunded pwer system. This is because the system lads are cnnected phase t phase. Therefre the lads are nt included in this ICAP simulatin. Fault resistance is equal t zer. 40
41 6.3 Simulatin results(the faulted phase identificatin) Vlts Figure 17: Resultant wavefrms f phase selectin analysis Time in secnds Intrductin f the results The wavefrms in the result can be represented as fllws [1] The Black wavefrm: - Psitive sequence vltage (V 1A ) [3] The Green wavefrm: - zer-sequence current wavefrm (the A-phase t grund fault) [4] The Red wavefrm: - zer-sequence current wavefrm (the B- phase t grund fault) [2] The Blue wavefrm: - zer-sequence current wavefrm (the C-phase t grund fault) General verview f the results The verview f the simulatin results are represented in Figure 17. The vertical line [1] represents the fault psitin (The trigger switch activatin pint).the zer-sequence current generated after each and every phase fault. 41
42 6.4 Calculated results Table 4 shws the calculated data f the angle between psitive sequence vltage (V 1A ) and zer-sequence current in each phase when the grund fault is present. Faulted Phase V1a and I angle difference A-phase degrees( zer-sequence current lead V 1A By 69.1 degrees) B-phase degrees(zer-sequence current lag V 1A By 59.1 degrees) C-phase -171 degrees( zer-sequence current lag V 1A By171.1 degrees) Table 4: Angle different between V 1A and zer-sequence current In the table, V 1A is the psitive sequence vltage (A-phase surce vltage) which is used as reference 1. I is the zer-sequence current when there is the A-phase t grund fault in feeder Nte:- Fr the Calculatin f the angle difference please refer t Appendix B 6.5 Analysis f Simulatin results (The Faulted Phase Identificatin) General analysis Accrding t abve results, all zer-sequence sinusidal wavefrms are created after the fault. The scillatin in the A-phase and C-phase zer-sequence current sinusidal wavefrms can be bserved. The A-phase zer-sequence current wavefrm has a pure sine shape as expected Analysis the results with the relay element functin Accrding t the results in Table 5, it is clear that when the single phase t grund fault is present, the angle differences between the zer-sequence current and psitive sequence vltage (A-phase surce vltage, V 1A ) are in the expected detectin range. This result has prved that the faulted phase can be identified by the phase selectin methd discussed in the sectin
43 Chapter 7 7 Simulatin fr estimating the fault distance 7.1 Prcedure The circuit diagram in Figure 16 is used t validate the grund fault distance algrithm. The A-phase in the first feeder is cnsidered fr this analysis. The trigger switch is used t create single line t grund fault. Step 1: The simulatin is cnducted and zer-sequence current wavefrm is btained then the magnitude f the zer-sequence current is calculated. Step 2: T check the different fault distances f the line, the resistr value, line inductr and line capacitance values are increased by the same amunt and the zer-sequence current magnitude is captured fr each value. Step3: Magnitude f the zer-sequence current is substituted in t the equatin 23 and the fault distance is calculated as the zer-sequence current varies with the fault distance d ( V + V + V2 ) 1 = (23) ( R + jwl) I K ( V + V1 + V2 ) = (24) ( R + jwl) K d = (25) I d- Fault distance K-cnstant I -zer-sequence current 43
44 7.2 Required Data R L C Ω/km mh/km µf/km Table 5: line parameters fr simulatin 7.3 The fault distance estimatin result Distance in KM Zer-sequence current I 1km km km Table 6: zer sequence current variatin with the fault distance Nte: Please refer Appendix C fr calculatin 7.4 Analyse f the fault distance results Accrding t Table 6, the zer-sequence current decreases when the fault distance increases. Therefre the denminatr f the equatin 24 decreases when the fault distance increases. In this analysis the fllwing recmmendatin can be made. Equatin 23 can be used t calculate the fault distance In an ungrunded system, the fault value f the zer-sequence current depends n the fault distance. 44
45 Chapter 8 8 Analysis f the Fault resistance 8.1 Intrductin t the fault resistance The fault resistance analysis is imprtant in an ungrunded pwer system. This is because the fault current depends upn the fault resistance and that requires the relay element t be set accrdingly. Fr this analysis the fault resistance is increased fr an A-phase single-line-t-grund fault in frnt f the relay measuring pint and the resulting characteristic is investigated. The fault resistance is increased and checked the angle between the zersequence current and the psitive-sequence vltage (V1a) is measured. 45
46 8.2 Simulatin prcedure The circuit diagram in Figure 18 is used fr this analysis. The trigger switch is cnnected t a variable resistance (R13). The line parameters and vltage surces are the same as used in Figure 16. The angle difference between zer-sequence current and psitive sequence vltage (A-phase surces vltage) is measured by changing the resistr values. Figure 18: Simulatin diagram fr fault resistance analysis 46
47 8.3 Results f the fault resistance analysis Fault resistance value(ω) Phase difference(betweenv a1 and zer-sequence current) Table 7: fault resistance result 8.4 Analyse the results f the fault analysis Accrding t the abve results it can be bserved when the fault resistance increases, phase difference between psitive sequence vltage (A-phase surce vltage Va1) and zer-sequence current decrease. Therefre this analysis is imprtant fr the faulted phasr selectin element. It can be seem that the grund fault resistance is effect t the relay sensitivity f an ungrunded pwer system. 47
48 Chapter 9 9 Fault Detectin sensitivity discussin 9.1 Imbalance f the system The imbalance f the system is ne f the main factrs in setting fault detectin sensitivity. The imbalance f the system is present because line-t-grund capacitance per phase is nt always equal. This imbalance is applied t the system and all ther equipment cnnected t the grid. The lad dynamics can als affect the balance f the system. Therefre due t the imbalance f the pwer line and lad the maximum sensitivity f the detectin element is required [2]. 9.2 The current transfrmer sensitivity The current transfrmer used in the system fr measuring zer-sequence current als impacts n the sensitivity f the fault detectin relay. The higher the current rati the lwer the fault sensitivity and lwer current rati gives higher fault sensitivity. Therefre the current transfrmer shuld have the lwest errr when perating in the linear regin [2]. 9.3 Grund sensitivity The grund sensitivity depends n the type f sil n the grund. Experiments prved that different sils can have different fault resistance. The fault sensitivity is different in areas with vegetatin. Different weather cnditins leads t different fault resistances. Rain and thunderstrms cause varying single line t grund sensitivities [2]. 48
Synchronous Motor V-Curves
Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel
More information1. Transformer A transformer is used to obtain the approximate output voltage of the power supply. The output of the transformer is still AC.
PHYSIS 536 Experiment 4: D Pwer Supply I. Intrductin The prcess f changing A t D is investigated in this experiment. An integrated circuit regulatr makes it easy t cnstruct a high-perfrmance vltage surce
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More information1.1 The main transmission network of Eskom The classical two generator model 11
LIST OF FIGURS Figure Page 1.1 The main transmissin netwrk f skm 4 2.1 The classical tw generatr mdel 11 2.2 Obtaining the lcatin f the electrical centre. The line cnnecting A with B represents the netwrk
More informationRevision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax
.7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical
More informationRelationships Between Frequency, Capacitance, Inductance and Reactance.
P Physics Relatinships between f,, and. Relatinships Between Frequency, apacitance, nductance and Reactance. Purpse: T experimentally verify the relatinships between f, and. The data cllected will lead
More informationA Novel Isolated Buck-Boost Converter
vel slated uck-st Cnverter S-Sek Kim *,WOO-J JG,JOOG-HO SOG, Ok-K Kang, and Hee-Jn Kim ept. f Electrical Eng., Seul atinal University f Technlgy, Krea Schl f Electrical and Cmputer Eng., Hanyang University,
More informationTechnical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology
Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)
More informationLab 11 LRC Circuits, Damped Forced Harmonic Motion
Physics 6 ab ab 11 ircuits, Damped Frced Harmnic Mtin What Yu Need T Knw: The Physics OK this is basically a recap f what yu ve dne s far with circuits and circuits. Nw we get t put everything tgether
More informationECE 2100 Circuit Analysis
ECE 00 Circuit Analysis Lessn 6 Chapter 4 Sec 4., 4.5, 4.7 Series LC Circuit C Lw Pass Filter Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 00 Circuit Analysis Lessn 5 Chapter 9 &
More informationEdexcel GCSE Physics
Edexcel GCSE Physics Tpic 10: Electricity and circuits Ntes (Cntent in bld is fr Higher Tier nly) www.pmt.educatin The Structure f the Atm Psitively charged nucleus surrunded by negatively charged electrns
More informationLecture 02 CSE 40547/60547 Computing at the Nanoscale
PN Junctin Ntes: Lecture 02 CSE 40547/60547 Cmputing at the Nanscale Letʼs start with a (very) shrt review f semi-cnducting materials: - N-type material: Obtained by adding impurity with 5 valence elements
More informationI. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is
Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,
More informationCopyright Paul Tobin 63
DT, Kevin t. lectric Circuit Thery DT87/ Tw-Prt netwrk parameters ummary We have seen previusly that a tw-prt netwrk has a pair f input terminals and a pair f utput terminals figure. These circuits were
More informationApplying Kirchoff s law on the primary circuit. V = - e1 V+ e1 = 0 V.D. e.m.f. From the secondary circuit e2 = v2. K e. Equivalent circuit :
TRANSFORMERS Definitin : Transfrmers can be defined as a static electric machine which cnverts electric energy frm ne ptential t anther at the same frequency. It can als be defined as cnsists f tw electric
More informationABSORPTION OF GAMMA RAYS
6 Sep 11 Gamma.1 ABSORPTIO OF GAMMA RAYS Gamma rays is the name given t high energy electrmagnetic radiatin riginating frm nuclear energy level transitins. (Typical wavelength, frequency, and energy ranges
More informationAn Introduction to Symmetrical Components, System Modeling and Fault Calculation
An ntrductin t Symmetrical Cmpnents, System Mdeling and Fault Calculatin Presented at the 3 th Annual HANDS-ON Relay Schl March 6 -, 5 Washingtn State University Pullman, Washingtn By Stephen Marx, and
More informationElectric Current and Resistance
Electric Current and Resistance Electric Current Electric current is the rate f flw f charge thrugh sme regin f space The SI unit f current is the ampere (A) 1 A = 1 C / s The symbl fr electric current
More informationSupplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
More informationELECTRON CYCLOTRON HEATING OF AN ANISOTROPIC PLASMA. December 4, PLP No. 322
ELECTRON CYCLOTRON HEATING OF AN ANISOTROPIC PLASMA by J. C. SPROTT December 4, 1969 PLP N. 3 These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated. They are fr private
More informationLECTURES 4 AND 5 THREE-PHASE CONNECTIONS (1)
ECE 330 POWER CIRCUITS AND ELECTROMECHANICS LECTURES 4 AND 5 THREEPHASE CONNECTIONS (1) AcknwledgmentThese handuts and lecture ntes given in class are based n material frm Prf. Peter Sauer s ECE 330 lecture
More information^YawataR&D Laboratory, Nippon Steel Corporation, Tobata, Kitakyushu, Japan
Detectin f fatigue crack initiatin frm a ntch under a randm lad C. Makabe," S. Nishida^C. Urashima,' H. Kaneshir* "Department f Mechanical Systems Engineering, University f the Ryukyus, Nishihara, kinawa,
More informationBootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >
Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);
More informationBicycle Generator Dump Load Control Circuit: An Op Amp Comparator with Hysteresis
Bicycle Generatr Dump Lad Cntrl Circuit: An Op Amp Cmparatr with Hysteresis Sustainable Technlgy Educatin Prject University f Waterl http://www.step.uwaterl.ca December 1, 2009 1 Summary This dcument describes
More informationOscillator. Introduction of Oscillator Linear Oscillator. Stability. Wien Bridge Oscillator RC Phase-Shift Oscillator LC Oscillator
Oscillatr Intrductin f Oscillatr Linear Oscillatr Wien Bridge Oscillatr Phase-Shift Oscillatr L Oscillatr Stability Oscillatrs Oscillatin: an effect that repeatedly and regularly fluctuates abut the mean
More informationAnalysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network
Research Jurnal f Applied Sciences, Engineering and Technlgy 5(2): 465-469, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organizatin, 2013 Submitted: May 08, 2012 Accepted: May 29, 2012 Published:
More informationElectric power distribution feeders are frequently subjected
21 nternatinal Cnference n Pwer System > REPLACE THS LNE WTH YOUR PAPER DENTFCATON NUMBER (DOUBLE-CLCK HERE TO EDT) < Lcating Fault Using Vltage Sags Prfile fr Undergrund Distributin System H. Mkhlis,
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationA Comparison of AC/DC Piezoelectric Transformer Converters with Current Doubler and Voltage Doubler Rectifiers
A Cmparisn f AC/DC Piezelectric Transfrmer Cnverters with Current Dubler and ltage Dubler Rectifiers Gregry vensky, Svetlana Brnstein and Sam Ben-Yaakv* Pwer Electrnics abratry Department f Electrical
More informationo o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions.
BASD High Schl Frmal Lab Reprt GENERAL INFORMATION 12 pt Times New Rman fnt Duble-spaced, if required by yur teacher 1 inch margins n all sides (tp, bttm, left, and right) Always write in third persn (avid
More informationSimulation of Line Outage Distribution Factors (L.O.D.F) Calculation for N-Buses System
Simulatin f Line Outage Distributin Factrs (L.O.D.F) Calculatin fr N-Buses System Rashid H. AL-Rubayi Department f Electrical Engineering, University f Technlgy Afaneen A. Abd Department f Electrical Engineering,
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationCurrent/voltage-mode third order quadrature oscillator employing two multiple outputs CCIIs and grounded capacitors
Indian Jurnal f Pure & Applied Physics Vl. 49 July 20 pp. 494-498 Current/vltage-mde third rder quadrature scillatr emplying tw multiple utputs CCIIs and grunded capacitrs Jiun-Wei Hrng Department f Electrnic
More informationGENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin
GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS J.e. Sprtt PLP 924 September 1984 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.
More informationBASIC DIRECT-CURRENT MEASUREMENTS
Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard
More informationSupplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
More informationChapter 4. Unsteady State Conduction
Chapter 4 Unsteady State Cnductin Chapter 5 Steady State Cnductin Chee 318 1 4-1 Intrductin ransient Cnductin Many heat transfer prblems are time dependent Changes in perating cnditins in a system cause
More informationCHAPTER 5. Solutions for Exercises
HAPTE 5 Slutins fr Exercises E5. (a We are given v ( t 50 cs(00π t 30. The angular frequency is the cefficient f t s we have ω 00π radian/s. Then f ω / π 00 Hz T / f 0 ms m / 50 / 06. Furthermre, v(t attains
More informationEREC G5 Stage 2 Sub-group. Meeting No. 1
EREC G5 Stage 2 Sub-grup Meeting N. 1 Held at William Gilbert Meeting Rm, REEC Building, Sir William Siemens Huse, Princess Rad, Manchester, M20 2UR On Mnday 13th June 2016 10:30-14:30 Meeting Ntes Attendee
More informationBASD HIGH SCHOOL FORMAL LAB REPORT
BASD HIGH SCHOOL FORMAL LAB REPORT *WARNING: After an explanatin f what t include in each sectin, there is an example f hw the sectin might lk using a sample experiment Keep in mind, the sample lab used
More informationLeast Squares Optimal Filtering with Multirate Observations
Prc. 36th Asilmar Cnf. n Signals, Systems, and Cmputers, Pacific Grve, CA, Nvember 2002 Least Squares Optimal Filtering with Multirate Observatins Charles W. herrien and Anthny H. Hawes Department f Electrical
More informationQ1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.
Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther
More informationApplication Note - Energy Metering at a Medium Voltage Connection Point using a Voltage Transformer
Applicatin Nte - Energy Metering at a Medium Vltage Cnnectin Pint using a Vltage Transfrmer This dcument describes the cnnectin and cnfiguratin f a Janitza meter at a medium vltage (MV) cnnectin pint t
More information3D FE Modeling Simulation of Cold Rotary Forging with Double Symmetry Rolls X. H. Han 1, a, L. Hua 1, b, Y. M. Zhao 1, c
Materials Science Frum Online: 2009-08-31 ISSN: 1662-9752, Vls. 628-629, pp 623-628 di:10.4028/www.scientific.net/msf.628-629.623 2009 Trans Tech Publicatins, Switzerland 3D FE Mdeling Simulatin f Cld
More informationA Novel Electro-thermal Simulation Approach to Power IGBT Modules for Automotive Traction Applications
Special Issue Recent R&D Activities f Pwer Devices fr Hybrid Electric Vehicles 27 Research Reprt A Nvel Electr-thermal Simulatin Apprach t Pwer IGBT Mdules fr Autmtive Tractin Applicatins Takashi Kjima,
More informationMath Foundations 20 Work Plan
Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant
More informationDead-beat controller design
J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable
More informationMetering Principles & Configurations
Metering Principles & Cnfiguratins CT PT Startc Western Energy Cmpany DCS Presenters Western Energy Cmpany Mnte Wilke Electrical Superintendent Curt Brckel Electrical Supervisr Brady Clbert Electrical
More informationMODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:
MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use
More informationLecture 13: Electrochemical Equilibria
3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: 10.21.05 Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins
More informationQ1. A) 48 m/s B) 17 m/s C) 22 m/s D) 66 m/s E) 53 m/s. Ans: = 84.0 Q2.
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 1 Q1. A string, f length 0.75 m and fixed at bth ends, is vibrating in its fundamental mde. The maximum transverse speed
More informationWRITING THE REPORT. Organizing the report. Title Page. Table of Contents
WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive
More informationStudy Group Report: Plate-fin Heat Exchangers: AEA Technology
Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery
More informationAPPLICATION GUIDE (v4.1)
2.2.3 VitalSensrs VS-300 Sensr Management Statin Remte/Relay Guide Implementing Remte-IN/Relay-OUT Digital I/O Fieldbus Objective: Equipment: Becme familiar with the instrument wiring requirements fr the
More informationPeripheral Zone Card.
Peripheral Zne Card Cmpatible with Standard r Dide Bases Up t * devices per circuit (*device range dependant) Individually Cnfigured Zne circuits Shrt = Alarm Optin Intrinsic Safety Optin Nn-latching Optin
More informationHigh penetration of renewable resources and the impact on power system stability. Dharshana Muthumuni
High penetratin f renewable resurces and the impact n pwer system stability Dharshana Muthumuni Outline Intrductin Discussin f case studies Suth Australia system event f September 2016 System Study integratin
More informationPhysics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
More informationFigure 1a. A planar mechanism.
ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,
More informationJ. C. Sprott OHMIC HEATING RATE IN A TOROIDAL OCTUPOLE. August 1975 PLP 643. Plasma Studies. University of Wisconsin
OHMC HEATNG RATE N A TORODAL OCTUPOLE J. C. Sprtt August 1975 PLP 643 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated. Tbey
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationT(s) 1+ T(s) 2. Phase Margin Test for T(s) a. Unconditionally Stable φ m = 90 o for 1 pole T(s) b. Conditionally Stable Case 1.
Lecture 49 Danger f Instability/Oscillatin When Emplying Feedback In PWM Cnverters A. Guessing Clsed Lp Stability Frm Open Lp Frequency Respnse Data. T(s) versus T(s) + T(s) 2. Phase Margin Test fr T(s)
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationDisplacement and Deflection Sensitivity of Gas-coupled Laser Acoustic. Detector
1st Internatinal Sympsium n Laser Ultrasnics: Science, echnlgy and Applicatins July 16-18 008, Mntreal, Canada Displacement and Deflectin Sensitivity f Gas-cupled Laser Acustic Detectin James N. CARON
More information1996 Engineering Systems Design and Analysis Conference, Montpellier, France, July 1-4, 1996, Vol. 7, pp
THE POWER AND LIMIT OF NEURAL NETWORKS T. Y. Lin Department f Mathematics and Cmputer Science San Jse State University San Jse, Califrnia 959-003 tylin@cs.ssu.edu and Bereley Initiative in Sft Cmputing*
More informationDepartment of Electrical Engineering, University of Waterloo. Introduction
Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flip-flps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd
More informationPOLARISATION VISUAL PHYSICS ONLINE. View video on polarisation of light
VISUAL PHYSICS ONLINE MODULE 7 NATURE OF LIGHT POLARISATION View vide n plarisatin f light While all the experimental evidence s far that supprts the wave nature f light, nne f it tells us whether light
More informationCHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review
Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system
More informationLab 1 The Scientific Method
INTRODUCTION The fllwing labratry exercise is designed t give yu, the student, an pprtunity t explre unknwn systems, r universes, and hypthesize pssible rules which may gvern the behavir within them. Scientific
More informationmaking triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=
Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents
More information5.4 Measurement Sampling Rates for Daily Maximum and Minimum Temperatures
5.4 Measurement Sampling Rates fr Daily Maximum and Minimum Temperatures 1 1 2 X. Lin, K. G. Hubbard, and C. B. Baker University f Nebraska, Lincln, Nebraska 2 Natinal Climatic Data Center 1 1. INTRODUCTION
More informationECE 2100 Circuit Analysis
ECE 2100 Circuit Analysis Lessn 25 Chapter 9 & App B: Passive circuit elements in the phasr representatin Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 2100 Circuit Analysis Lessn
More informationThree charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).
Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)
More informationECEN 4872/5827 Lecture Notes
ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals
More informationNGSS High School Physics Domain Model
NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship
More informationCBSE Board Class XII Physics Set 1 Board Paper 2008 (Solution)
CBSE Bard Class XII Physics Set 1 Bard Paper 2008 (Slutin) 1. The frce is given by F qv B This frce is at right angles t &. 2. Micrwaves. It is used in radar & cmmunicatin purpses. 3. Or As m e e m S,
More informationChapter 16. Capacitance. Capacitance, cont. Parallel-Plate Capacitor, Example 1/20/2011. Electric Energy and Capacitance
summary C = ε A / d = πε L / ln( b / a ) ab C = 4πε 4πε a b a b >> a Chapter 16 Electric Energy and Capacitance Capacitance Q=CV Parallel plates, caxial cables, Earth Series and parallel 1 1 1 = + +..
More informationKing Fahd University of Petroleum and Minerals. Electrical Engineering Department EE 420. Fiber Optics Communication.
King Fahd University f Petrleum and Minerals Electrical Engineering Department EE 420 Fiber Optics Cmmunicatin Labratry Manual July 2005 2 PREFACE This manual cntains ten labratry experiments t be perfrmed
More informationCS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007
CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is
More informationinitially lcated away frm the data set never win the cmpetitin, resulting in a nnptimal nal cdebk, [2] [3] [4] and [5]. Khnen's Self Organizing Featur
Cdewrd Distributin fr Frequency Sensitive Cmpetitive Learning with One Dimensinal Input Data Aristides S. Galanpuls and Stanley C. Ahalt Department f Electrical Engineering The Ohi State University Abstract
More informationOTHER USES OF THE ICRH COUPL ING CO IL. November 1975
OTHER USES OF THE ICRH COUPL ING CO IL J. C. Sprtt Nvember 1975 -I,," PLP 663 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.
More informationHow do scientists measure trees? What is DBH?
Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between
More informationVerification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance
Verificatin f Quality Parameters f a Slar Panel and Mdificatin in Frmulae f its Series Resistance Sanika Gawhane Pune-411037-India Onkar Hule Pune-411037- India Chinmy Kulkarni Pune-411037-India Ojas Pandav
More informationDYNAMIC MODELLING OF N-CARDAN TRANSMISSIONS WITH SHAFTS IN SPATIAL CONFIGURATION. Part II. THE ALGORITHM OF DYNAMIC MODELLING
Fascicle f Management and Technlgical Engineering, Vlume VI (XVI), 7 DYNAMIC MODELLING OF N-CARDAN TRANSMISSIONS WITH SHAFTS IN SPATIAL CONFIGURATION. Part II. THE ALGORITHM OF DYNAMIC MODELLING Cdrua
More informationOn Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION
Malaysian Jurnal f Mathematical Sciences 4(): 7-4 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate
More informationPhysical Layer: Outline
18-: Intrductin t Telecmmunicatin Netwrks Lectures : Physical Layer Peter Steenkiste Spring 01 www.cs.cmu.edu/~prs/nets-ece Physical Layer: Outline Digital Representatin f Infrmatin Characterizatin f Cmmunicatin
More informationMedium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]
EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just
More informationNEW Pecan Scab Model Description
Edited: June 28, 2005 NEW Pecan Scab Mdel Descriptin Mdel active frm March 1 t August 31 The Oklahma Mesnet, in cperatin with scientists and prfessinals frm Oklahma State University and the University
More informationA Matrix Representation of Panel Data
web Extensin 6 Appendix 6.A A Matrix Representatin f Panel Data Panel data mdels cme in tw brad varieties, distinct intercept DGPs and errr cmpnent DGPs. his appendix presents matrix algebra representatins
More information11. DUAL NATURE OF RADIATION AND MATTER
11. DUAL NATURE OF RADIATION AND MATTER Very shrt answer and shrt answer questins 1. Define wrk functin f a metal? The minimum energy required fr an electrn t escape frm the metal surface is called the
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion
.54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References -- J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (Addisn-Wesley, Reading, 966) T study neutrn diffusin
More informationDocument for ENES5 meeting
HARMONISATION OF EXPOSURE SCENARIO SHORT TITLES Dcument fr ENES5 meeting Paper jintly prepared by ECHA Cefic DUCC ESCOM ES Shrt Titles Grup 13 Nvember 2013 OBJECTIVES FOR ENES5 The bjective f this dcument
More informationSection I5: Feedback in Operational Amplifiers
Sectin I5: eedback in Operatinal mplifiers s discussed earlier, practical p-amps hae a high gain under dc (zer frequency) cnditins and the gain decreases as frequency increases. This frequency dependence
More informationAn Efficient Load Shedding Scheme from Customer s Perspective
Internatinal Jurnal f Advanced Research in Electrical, Electrnics and Instrumentatin Engineering (An ISO 3297: 2007 Certified Organizatin) Vl. 2, Issue 10, Octber 2013 An Efficient Lad Shedding Scheme
More informationAttempts at Ion Cyclotron Heating. In a Toroidal Octupole. Presented at the Los Angeles Meeting of the American Physical Society. November 12-15, 1969
Attempts at n Cycltrn Heating n a Tridal Octuple by J. C. Sprtt Presented at the Ls Angeles Meeting f the American Physical Sciety Nvember 1215, 1969 PLP 321 These PLP Reprts are infnnal and preliminary
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationAP Statistics Notes Unit Two: The Normal Distributions
AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).
More informationCHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
More informationDesign and Simulation of Dc-Dc Voltage Converters Using Matlab/Simulink
American Jurnal f Engineering Research (AJER) 016 American Jurnal f Engineering Research (AJER) e-issn: 30-0847 p-issn : 30-0936 Vlume-5, Issue-, pp-9-36 www.ajer.rg Research Paper Open Access Design and
More informationEXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE
EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2
More information