Design and Application of Fault Current Limiter in Iran Power System Utility

Size: px
Start display at page:

Download "Design and Application of Fault Current Limiter in Iran Power System Utility"

Transcription

1 Australian Journal of Basic an Applie Sciences, 7(): 76-8, 13 ISSN Design an Application of Fault Current Limiter in Iran Power System Utility M. Najafi, M. Hoseynpoor Department of Electrical Engineering, Bushehr Branch, Islamic Aza University, Bushehr, Iran. Abstract: Rectifier type fault current limiter is one of well known fault current limiters, because of using superconuctor in the structure of rectifier type FCL, using this type is limite to research projects an laboratory applications. In this paper we have been stuying on rectifier type fault current limiter using copper coil. Such reactor consists of copper coils an is applicable in Iran power system utility. The coil is connecte to the DC link of the brige circuit. The DC reactor effect of the current limiter has been stuie. This type of FCL is similar to the brige type SFCL but a copper DC ironcore reactor is use instea of superconucting reactor. The simplicity to be built an its low cost are the main avantageous of analyze system. The results show that the power loss is a very small percentage of protecte loa power. Key wors: Fault Current Limiter, Power Losses, Voltage isturbance, fault Current INTRODUCTION Electric power system esigners often face fault-current problems when expaning existing buses. Larger transformers result in higher fault-uty levels, forcing the replacement of existing buswork an switchgear not rate for the new fault uty. Alternatively, the existing bus can be broken an serve by two or more smaller transformers. Another alternative is use of a single, large, high-impeance transformer, resulting in egrae voltage regulation for all the customers on the bus. The classic traeoff between fault control, bus capacity, an system stiffness has persiste for ecaes (Bouslama-Bouaballah, S., et al., 1). Since a large fault current mechanically an thermally amages electric equipments in the system, it is esirable to incorporate a fault current limiter in the system. There are many types of fault current limiters: current limiting reactors, power fuses, current limiting wires an superconucting fault current limiters (SFCLs). Of the fault current limiters, SFCLs exhibit the best current limiting performance because (1) current limiting reactors, fuses an wires cause substantial power loss uring normal operation in the power system while SFCLs o not; () power fuses must be replace by han after their operation while SFCLs are recovere automatically; (3) current limiting wires have limite lifetime. SFCLs operate from the properties inherent to superconuctors (Hyo-Sang Choi, et al., 1; Boening, H.J., D.A. Paice, 1983). Superconucting fault current limiter (SFCL) using rectifier brige circuit is well known. As mentione before, using superconuctors is because of their no-loss uring normal an fault conitions. Unfortunately, ue to high technology an cost of these evices those are not commercially available. There are many attempts to realize using superconucting coils for example in high temperature but most of propose methos results in more complicate technology an cost. On the other han, it is interesting to analytical analysis an comparison of using near zero resistance copper coils with superconuctors in FCL structure (Ishigohka, T., A. Ninomiya et al., ; Uea, T., M. Morita et al., 1993). Obviously, using copper coils for making FCLs is very easy an initial cost woul be much lower than superconuctors. But, there will be power losses uring normal an fault conitions using copper coils so we shoul pay for power loss cost. This paper eals with analytical analysis of DC reactor type superconuctor an non-superconuctor type FCLs. Designing formulas an useful characteristics are use to compare the mentione FCLs. Ours stuies show that power losses of near zero resistance copper coils which have enough copper cross section area, have less than 1% power loss of their protecte loas power. On the han, it woul be interesting to present new methos for recovery of generate heat by copper coil FCLs for example to warming up of their cooling water. It seems, using copper coil FCLs coul be a suitable way for less-evelope countries especially those with low electrical energy cost such as mile-east area.. Circuit Topology: The power circuit of the propose fault current limiter (FCL) is shown in Fig. 1. In this case, a simple ioe Brige is use. This brige consists of four ioes D1-D4. L is the inuctance of coil. The positive half cycle of current flows through D1 an D3 an the negative half cycle through D an D4. The higher value of inuctance prouces almost a DC current through the inuctor coil. It keeps the ioes continuously conucting. Again, the higher inuctance effectively reuces the fault current. On the other han, the loa increasing effect is expecte to be worse at higher value of the inuctance. Corresponing Author: M. Najafi, M. Hoseynpoor, Department of Electrical Engineering, Bushehr Branch, Islamic Aza University, Bushehr, Iran. 75

2 Aust. J. Basic & Appl. Sci., 7(): 75-8, 13 v( t) V. Sin( wt) Fig. 1: Power circuit topology of analyze FCL 3. Ripple Current: Fig. shows the line an FCL current waveforms in normal operation case of the circuit. The line current is a sinusoial waveform while the reactor current i, is a rectifie current. The reactor current is perioic with time interval between t to t 3. The circuit has two moes of operation as follows: (a) Charging moe (b) Discharging moe Charging moe begins at t an it continues until t. At t the ioes D1 an D3 turns ON an DC reactor connects in series with utility. Eq. (1) shows the system current formula in charging moe. ( rl)( tt ) V VDF it () e i sin( t ) z r V VDF sin( t ) z r (1) Where: i ( t) i ( t) i( t) L S r r r r L L S L L L L v DF is the forwar voltage rop of the ioes that is assume to be constant i i( ) t z r ( L) tan L r. Line Current Reactor Current Fig. : The Line an FCL current waveforms in normal operation case of circuit 76

3 Aust. J. Basic & Appl. Sci., 7(): 75-8, 13 It is interesting to notice that the current waveform in charging moe is not sinusoial ue to transient of insertion of DC reactor. Obviously, the resistance of DC reactor is not so important in this subject because it is much more less than sum of line an loa resistors. So, using inuctive FCLs woul result in istortion of line current. Discharging moe begins at t an it continuous until t 3. At t=t 1, ue to changing the irection of current through L, the polarity of its voltage v L (t), changes an between t 1 to t its magnitue begins to increase. It is possible to write eq. () at t=t in which v L (t) equals v r (t) with opposite polarity an the ioes D an D4 turns ON because of their forwar biasing. [ vl ( t) vr ( t)] [ vdf1( t) vdf 4( t)] [ vdf ( t) vdf3( t)] () v L Where i ( t) ( t) L (3) t During ischarging moe, the inuctor current free-wheels through the ioes D3-D an D4-D1. The line current il flows both the upper an lower ioes of rectifier brige. Eq. (4) an Eq. (5) show the line current an DC reactor current formula uring ischarging moe, respectively. ( rl)( tt) V V il () t e i sin( t ) sin( t ) (4) z z ( r L )( t t) () VDF V i DF t e i (5) r r Where: r r S r L L L S L L i i( ). t Eq. (1) an eq. (5) show the charging an ischarging current formulas of DC reactor, respectively. Obviously, these currents consist of a DC value in aition to a ripple current. Existence of ripple current, results in voltage rop across L uring normal system operation case. So, it is appropriate to ecrease the ripple currents as much as possible. Eq. (6) is use for efinition of DC value of inuctor current, I DC : ir, p p I DC i Max (6) Where i Max stans for the maximum current of reactor an it is equal with i 1 an ir, p p stans for the peak to peak of ac ripple current of reactor an it is equal with ( i1 i3). Eq. (7) shows the formula of DC value of inuctor current. r T VDFT I DC imax (1 ) (7) 4L L i The ir p p, coul be obtaine using eq. (8) as follows: T r imax ( V ) (8) L r( p. p) DF Where T is ( t3 t ) an it equals 1 (ms) for power frequency of 5 Hz. By consiering the inuctor resistor r equal with zero it is possible getting eq. s (9) an (1) which show the DC value an the peak to peak of ac ripple current of a superconucting FCL, respectively. VDFT I DC imax L (9) i T r( p. p) VDF (1) L 77

4 Aust. J. Basic & Appl. Sci., 7(): 75-8, 13 Comparison of eq. (8) with eq. (1) shows that existence of resistance in copper coil FCL woul result in increasing of ir, p p through inuctor. On the other han, increasing of L coul ecrease the ir, p p in aition to increasing of DC value of current through inuctor. 4. Power Losses: The main objective for using superconuctors in FCLs is their zero resistance an no power loss in normal operation case as well as fault conition. Eq. (11) shows the magnitue of DC power losses in reactor consiering this fact that I as follows: ir, p p is very small compare with DC r T VDFT P c r I DC r imax (1 ) (11) 4L L 5. Simulation Results: During fault conition, the line current increases because the fault impeance z f = r f +jl f is substitute to loa impeance z L. The power circuit topology of Fig. 1 is use for analyzing the fault conition. The simulation parameters are as follows: z L = 9.4+j. () z s = +j.1 () z f = +j () v s (t) =3.81 Sin(314t) (kv) = 3 r = () L =.1 (v) (H) Fig. (3) an (4) show the variations of ir, p p versus DC reactor inuctance for ifferent values of line current an inuctor resistance. Consiering these figures, it seems choosing the DC reactor inuctance near to. (H) woul result in acceptable value of ir, p p. Peak to peak of ripple current in DC reactor (A) A 1A A 3A 5A 7A r =.5 (ohm) Fig. 3: The DC reactor inuctance (H) ir, p p vs. the variations of L for ifferent values of line current 78

5 Aust. J. Basic & Appl. Sci., 7(): 75-8, 13 Peak to peak of ripple current in DC reactor (A) r= r=.5 r=.75 r=.15 i L =7 (A) Fig. 4: DC reactor inuctance (H) ir, p p vs. the variations of L for ifferent values of inuctor resistance. Fig. (5) an (6) show DC power losses variations versus DC reactor inuctance where its resistor an line current is as the parameter of curves. This figures show that the power loss in resistance of reactor is less 1% of its protecte loa power. 7 6 r=.5 r=.15 r=.75 r= DC power losses in reactor (W) i L =7 (A) DC reactor inuctance (H) Fig. 5: DC power losses vs. DC reactor inuctance for ifferent values of reactors resistance DC power losses in reactor (W) A 1A A 3A 5A 7A DC reactor inuctance (H) r =.5 (ohm) Fig. 6: DC power losses vs. DC reactor inuctance for ifferent values of line current 79

6 Aust. J. Basic & Appl. Sci., 7(): 75-8, 13 The energy store in inuctor can be obtaine using eq. (1). Fig. (7) show the storage energy value versus ifferent values of L. This figure shows that the store energy is a function of L in almost linear form. 1 r T VDFT W DC L imax (1 ) (1) 4L L DC store energy in reactor A 1A A 3A 5A 7A r =.5 (ohm) DC reactor inuctance (H) Fig. 7: Storage energy in inuctor vs. ifferent values of L Conclusion: The analytical analysis an esigning characteristics for DC reactor "superconuctor" an "copper coil" type FCLs presente. The overall operation of mentione FCLs in normal an fault cases stuie, carefully. The results show the power loss of copper coil FCL is less than 1% of its protecte loa power. On the other han, the simulation results show that there is not significant ifference between superconuctor an copper coil FCLs operation in limiting the fault currents magnitue. It seems, the lower initial cost an simpler technology for builing an using the copper coil FCLs in aition to the possibility for recovering of its heat energy coul make this kin of FCLs a goo alternative for more researches in this fiel. ACKNOWLEDGMENT This research paper has been financially supporte by the office of vice chancellor for research of Islamic Aza University, Bushehr Branch. REFERENCES Boening, H.J., D.A. Paice, Fault current limiter using superconucting coil, IEEE Trans. Magn., 19(3): Bouslama-Bouaballah, S., M. Tagina, A. Fault Detection an Isolation Fuzzy System Optimize by Genetic Algorithms an Simulate Annealing, 1. International Review of Moelling an Simulations (IREMOS), 3(): Hyo-Sang Choi, Hye-Rim Kim, Ok-Bae Hyun, 1. Operating properties of superconucting fault current limiters base on YBCO thin films, Cryogenics, 41(3): Ishigohka, T., A. Ninomiya et al.,. Fabrication an test of cryogenic fault current limiter combining semiconuctors an DC reactor, Proc. IPEC, pp: Uea, T., M. Morita et al., Soli-state current limiter for power istribution system, IEEE Trans. Power Delivery, 8(4):

Non-Superconducting Fault Current Limiter

Non-Superconducting Fault Current Limiter Proceeings o the 5th WEA International Conerence on Applications o Electrical Engineering, Prague, Czech Republic, March -, 6 (pp-7) Non-uperconucting Fault Current Limiter A. CHARMIN*, M. TARAFDAR HAQUE,

More information

Chapter 6. Electromagnetic Oscillations and Alternating Current

Chapter 6. Electromagnetic Oscillations and Alternating Current hapter 6 Electromagnetic Oscillations an Alternating urrent hapter 6: Electromagnetic Oscillations an Alternating urrent (hapter 31, 3 in textbook) 6.1. Oscillations 6.. The Electrical Mechanical Analogy

More information

A New Approach in Analytical Analysis of Eddy Currents in Laminated Core

A New Approach in Analytical Analysis of Eddy Currents in Laminated Core J. Basic. Appl. Sci. Res., (7)741-745, 1 1, TextRoa Publication ISSN 9-434 Journal of Basic an Applie Scientific Research www.textroa.com A New Approach in Analtical Analsis of E Currents in Laminate Core

More information

Homework 7 Due 18 November at 6:00 pm

Homework 7 Due 18 November at 6:00 pm Homework 7 Due 18 November at 6:00 pm 1. Maxwell s Equations Quasi-statics o a An air core, N turn, cylinrical solenoi of length an raius a, carries a current I Io cos t. a. Using Ampere s Law, etermine

More information

CAPACITANCE: CHAPTER 24. ELECTROSTATIC ENERGY and CAPACITANCE. Capacitance and capacitors Storage of electrical energy. + Example: A charged spherical

CAPACITANCE: CHAPTER 24. ELECTROSTATIC ENERGY and CAPACITANCE. Capacitance and capacitors Storage of electrical energy. + Example: A charged spherical CAPACITANCE: CHAPTER 24 ELECTROSTATIC ENERGY an CAPACITANCE Capacitance an capacitors Storage of electrical energy Energy ensity of an electric fiel Combinations of capacitors In parallel In series Dielectrics

More information

Electronic Devices and Circuit Theory

Electronic Devices and Circuit Theory Instructor s Resource Manual to accompany Electronic Devices an Circuit Theory Tenth Eition Robert L. Boylesta Louis Nashelsky Upper Sale River, New Jersey Columbus, Ohio Copyright 2009 by Pearson Eucation,

More information

PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR

PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR. THE PARALLEL-PLATE CAPACITOR. The Parallel plate capacitor is a evice mae up by two conuctor parallel plates with total influence between them (the surface

More information

CURRENT ELECTRICITY Q.1

CURRENT ELECTRICITY Q.1 CUENT EECTCTY Q. Define Electric current an its unit.. Electric Current t can be efine as the time rate of flow of charge in a conuctor is calle Electric Current. The amount of flow of charge Q per unit

More information

Harmonic Modelling of Thyristor Bridges using a Simplified Time Domain Method

Harmonic Modelling of Thyristor Bridges using a Simplified Time Domain Method 1 Harmonic Moelling of Thyristor Briges using a Simplifie Time Domain Metho P. W. Lehn, Senior Member IEEE, an G. Ebner Abstract The paper presents time omain methos for harmonic analysis of a 6-pulse

More information

Chapter 31: RLC Circuits. PHY2049: Chapter 31 1

Chapter 31: RLC Circuits. PHY2049: Chapter 31 1 Chapter 31: RLC Circuits PHY049: Chapter 31 1 LC Oscillations Conservation of energy Topics Dampe oscillations in RLC circuits Energy loss AC current RMS quantities Force oscillations Resistance, reactance,

More information

Designing Information Devices and Systems II Spring 2019 A. Sahai, J. Roychowdhury, K. Pister Midterm 1: Practice

Designing Information Devices and Systems II Spring 2019 A. Sahai, J. Roychowdhury, K. Pister Midterm 1: Practice EES 16B Designing Information Devices an Systems II Spring 019 A. Sahai, J. Roychowhury, K. Pister Miterm 1: Practice 1. Speaker System Your job is to construct a speaker system that operates in the range

More information

Modelling of Three Phase Short Circuit and Measuring Parameters of a Turbo Generator for Improved Performance

Modelling of Three Phase Short Circuit and Measuring Parameters of a Turbo Generator for Improved Performance Moelling of Three Phase Short Circuit an Measuring Parameters of a Turbo Generator for Improve Performance M. Olubiwe, S. O. E. Ogbogu, D. O. Dike, L. Uzoechi Dept of Electrical an Electronic Engineering,

More information

4. CONTROL OF ZERO-SEQUENCE CURRENT IN PARALLEL THREE-PHASE CURRENT-BIDIRECTIONAL CONVERTERS

4. CONTROL OF ZERO-SEQUENCE CURRENT IN PARALLEL THREE-PHASE CURRENT-BIDIRECTIONAL CONVERTERS 4. CONRO OF ZERO-SEQUENCE CURREN IN PARAE HREE-PHASE CURREN-BIDIRECIONA CONVERERS 4. A NOVE ZERO-SEQUENCE CURREN CONRO 4.. Zero-Sequence Dynamics he parallel boost rectifier moel in Figure.4 an the parallel

More information

AN3400 Application note

AN3400 Application note Application note Analysis an simulation of a BJT complementary pair in a self-oscillating CFL solution ntrouction The steay-state oscillation of a novel zero-voltages switching (ZS) clampe-voltage (C)

More information

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur Moule 2 DC Circuit Lesson 9 Analysis of c resistive network in presence of one non-linear element Objectives To unerstan the volt (V ) ampere ( A ) characteristics of linear an nonlinear elements. Concept

More information

Goal of this chapter is to learn what is Capacitance, its role in electronic circuit, and the role of dielectrics.

Goal of this chapter is to learn what is Capacitance, its role in electronic circuit, and the role of dielectrics. PHYS 220, Engineering Physics, Chapter 24 Capacitance an Dielectrics Instructor: TeYu Chien Department of Physics an stronomy University of Wyoming Goal of this chapter is to learn what is Capacitance,

More information

SiC-based Power Converters for High Temperature Applications

SiC-based Power Converters for High Temperature Applications Materials Science orum Vols. 556-557 (7) pp 965-97 online at http://www.scientific.net (7) Trans Tech Publications Switzerlan Online available since 7/Sep/5 -base Power Converters for High Temperature

More information

PES 1120 Spring 2014, Spendier Lecture 36/Page 1

PES 1120 Spring 2014, Spendier Lecture 36/Page 1 PES 0 Spring 04, Spenier ecture 36/Page Toay: chapter 3 - R circuits: Dampe Oscillation - Driven series R circuit - HW 9 ue Wenesay - FQs Wenesay ast time you stuie the circuit (no resistance) The total

More information

State Space Analysis of Power System Stability Enhancement with Used the STATCOM

State Space Analysis of Power System Stability Enhancement with Used the STATCOM tate pace Analysis of Power ystem tability Enhancement with Use the ACOM M. Mahavian () - G. hahgholian () () Department of Electrical Engineering, Islamic Aza University, Naein Branch, Esfahan, Iran ()

More information

Electronic Power Conversion

Electronic Power Conversion Electronic Power Conersion Switch Moe DC-DC Conerters with Isolation Challenge the future Switch moe c-c conerters Frequent requirements: regulate output isolation (safety) multiple outputs Solutions:

More information

Dynamics of the synchronous machine

Dynamics of the synchronous machine ELEC0047 - Power system ynamics, control an stability Dynamics of the synchronous machine Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct These slies follow those presente in course

More information

UNIT 4:Capacitors and Dielectric

UNIT 4:Capacitors and Dielectric UNIT 4:apacitors an Dielectric SF7 4. apacitor A capacitor is a evice that is capable of storing electric charges or electric potential energy. It is consist of two conucting plates separate by a small

More information

A Simple Model for the Calculation of Plasma Impedance in Atmospheric Radio Frequency Discharges

A Simple Model for the Calculation of Plasma Impedance in Atmospheric Radio Frequency Discharges Plasma Science an Technology, Vol.16, No.1, Oct. 214 A Simple Moel for the Calculation of Plasma Impeance in Atmospheric Raio Frequency Discharges GE Lei ( ) an ZHANG Yuantao ( ) Shanong Provincial Key

More information

Quasi optimal feedforward control of a very low frequency high-voltage test system

Quasi optimal feedforward control of a very low frequency high-voltage test system Preprints of the 9th Worl Congress The International Feeration of Automatic Control Quasi optimal feeforwar control of a very low frequency high-voltage test system W. Kemmetmüller S. Eberharter A. Kugi

More information

Situation awareness of power system based on static voltage security region

Situation awareness of power system based on static voltage security region The 6th International Conference on Renewable Power Generation (RPG) 19 20 October 2017 Situation awareness of power system base on static voltage security region Fei Xiao, Zi-Qing Jiang, Qian Ai, Ran

More information

Transmission Line Matrix (TLM) network analogues of reversible trapping processes Part B: scaling and consistency

Transmission Line Matrix (TLM) network analogues of reversible trapping processes Part B: scaling and consistency Transmission Line Matrix (TLM network analogues of reversible trapping processes Part B: scaling an consistency Donar e Cogan * ANC Eucation, 308-310.A. De Mel Mawatha, Colombo 3, Sri Lanka * onarecogan@gmail.com

More information

EVALUATION OF LIQUEFACTION RESISTANCE AND LIQUEFACTION INDUCED SETTLEMENT FOR RECLAIMED SOIL

EVALUATION OF LIQUEFACTION RESISTANCE AND LIQUEFACTION INDUCED SETTLEMENT FOR RECLAIMED SOIL 386 EVALUATION OF LIQUEFACTION RESISTANCE AND LIQUEFACTION INDUCED SETTLEMENT FOR RECLAIMED SOIL Lien-Kwei CHIEN 1, Yan-Nam OH 2 An Chih-Hsin CHANG 3 SUMMARY In this stuy, the fille material in Yun-Lin

More information

Impact of DFIG based Wind Energy Conversion System on Fault Studies and Power Swings

Impact of DFIG based Wind Energy Conversion System on Fault Studies and Power Swings Impact of DFIG base Win Energy Conversion System on Fault Stuies an Power Swings Likin Simon Electrical Engineering Department Inian Institute of Technology, Maras Email: ee133@ee.iitm.ac.in K Shanti Swarup

More information

Lecture 6: Control of Three-Phase Inverters

Lecture 6: Control of Three-Phase Inverters Yoash Levron The Anrew an Erna Viterbi Faculty of Electrical Engineering, Technion Israel Institute of Technology, Haifa 323, Israel yoashl@ee.technion.ac.il Juri Belikov Department of Computer Systems,

More information

Modelling of Permanent Magnet Synchronous Motor Incorporating Core-loss

Modelling of Permanent Magnet Synchronous Motor Incorporating Core-loss Research Journal of Applie Sciences, Engineering an Technology 4(7): 846-85, ISSN: 4-7467 Maxwell Scientific Organization, Submitte: November, Accepte: December 9, Publishe: September, Moelling of Permanent

More information

PREPARATION OF THE NATIONAL MAGNETIC FIELD STANDARD IN CROATIA

PREPARATION OF THE NATIONAL MAGNETIC FIELD STANDARD IN CROATIA n IMEKO TC 11 International Symposium METROLOGICAL INFRASTRUCTURE June 15-17, 11, Cavtat, Dubrovni Riviera, Croatia PREPARATION OF THE NATIONAL MAGNETIC FIELD STANDARD IN CROATIA A. Pavić 1, L.Ferović,

More information

Vectors in two dimensions

Vectors in two dimensions Vectors in two imensions Until now, we have been working in one imension only The main reason for this is to become familiar with the main physical ieas like Newton s secon law, without the aitional complication

More information

An inductance lookup table application for analysis of reluctance stepper motor model

An inductance lookup table application for analysis of reluctance stepper motor model ARCHIVES OF ELECTRICAL ENGINEERING VOL. 60(), pp. 5- (0) DOI 0.478/ v07-0-000-y An inuctance lookup table application for analysis of reluctance stepper motor moel JAKUB BERNAT, JAKUB KOŁOTA, SŁAWOMIR

More information

State-Space Model for a Multi-Machine System

State-Space Model for a Multi-Machine System State-Space Moel for a Multi-Machine System These notes parallel section.4 in the text. We are ealing with classically moele machines (IEEE Type.), constant impeance loas, an a network reuce to its internal

More information

Basic RL and RC Circuits R-L TRANSIENTS: STORAGE CYCLE. Engineering Collage Electrical Engineering Dep. Dr. Ibrahim Aljubouri

Basic RL and RC Circuits R-L TRANSIENTS: STORAGE CYCLE. Engineering Collage Electrical Engineering Dep. Dr. Ibrahim Aljubouri st Class Basic RL and RC Circuits The RL circuit with D.C (steady state) The inductor is short time at Calculate the inductor current for circuits shown below. I L E R A I L E R R 3 R R 3 I L I L R 3 R

More information

EE 330 Lecture 12. Devices in Semiconductor Processes. Diodes

EE 330 Lecture 12. Devices in Semiconductor Processes. Diodes EE 330 Lecture 12 evices in Semiconuctor Processes ioes Review from Last Lecture http://www.ayah.com/perioic/mages/perioic%20table.png Review from Last Lecture Review from Last Lecture Silicon opants in

More information

Suppression Method of Rising DC Voltage for the Halt Sequence of an Inverter in the Motor Regeneration

Suppression Method of Rising DC Voltage for the Halt Sequence of an Inverter in the Motor Regeneration Suppression Metho of Rising DC Voltage for the Halt Sequence of an Inverter in the Motor Regeneration Jun-ichi Itoh Wataru Aoki Goh Teck Chiang Akio Toba Nagaoka University of Technology Fuji Electric

More information

Modeling and analysis of parallel connected permanent magnet synchronous generators in a small hydropower plant

Modeling and analysis of parallel connected permanent magnet synchronous generators in a small hydropower plant Proceeings of the 2006 IASME/WSEAS International Conference on Energy & Environmental Systems, Chalkia, Greece, May 8-10, 2006 (pp83-88) Moeling an analysis of parallel connecte permanent magnet synchronous

More information

Simulink model for examining dynamic interactions involving electro-mechanical oscillations in distribution systems

Simulink model for examining dynamic interactions involving electro-mechanical oscillations in distribution systems University of Wollongong Research Online Faculty of Engineering an Information Sciences - Papers: Part A Faculty of Engineering an Information Sciences 205 Simulink moel for examining ynamic interactions

More information

Keywords: Superconducting Fault Current Limiter (SFCL), Resistive Type SFCL, MATLAB/SIMULINK. Introductions A rapid growth in the power generation

Keywords: Superconducting Fault Current Limiter (SFCL), Resistive Type SFCL, MATLAB/SIMULINK. Introductions A rapid growth in the power generation IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Performance of a 3.3kV Resistive type Superconducting Fault Current Limiter S.Vasudevamurthy 1, Ashwini.V 2 1 Department of Electrical

More information

A Parametric Device Study for SiC Power Electronics

A Parametric Device Study for SiC Power Electronics A Parametric evice Stuy for SiC Power Electronics Burak Ozpineci urak@ieee.org epartment of Electrical an Computer Engineering The University of Tennessee Knoxville TN 7996- Leon M. Tolert tolert@utk.eu

More information

Railway Research. Study of Superconducting Fault Current Limiter Device in a AC Railway System. 1. Introduction. International Journal of

Railway Research. Study of Superconducting Fault Current Limiter Device in a AC Railway System. 1. Introduction. International Journal of International Journal of Railway Research, (2015), Vol.2, No1, pp 10-14 ISSN: 236153768187 International Journal of Railway Research Study of Superconducting Fault Current Limiter Device in a AC Railway

More information

A Comparison between a Conventional Power System Stabilizer (PSS) and Novel PSS Based on Feedback Linearization Technique

A Comparison between a Conventional Power System Stabilizer (PSS) and Novel PSS Based on Feedback Linearization Technique J. Basic. Appl. Sci. Res., ()9-99,, TextRoa Publication ISSN 9-434 Journal of Basic an Applie Scientific Research www.textroa.com A Comparison between a Conventional Power System Stabilizer (PSS) an Novel

More information

Maxwell s Equations 5/9/2016. EELE 3332 Electromagnetic II Chapter 9. Maxwell s Equations for static fields. Review Electrostatics and Magnetostatics

Maxwell s Equations 5/9/2016. EELE 3332 Electromagnetic II Chapter 9. Maxwell s Equations for static fields. Review Electrostatics and Magnetostatics Generate by Foxit PDF Creator Foxit oftware 5/9/216 3332 lectromagnetic II Chapter 9 Maxwell s quations Islamic University of Gaza lectrical ngineering Department Prof. Dr. Hala J l-khozonar 216 1 2 Review

More information

Journal of Chemical and Pharmaceutical Research, 2014, 6(2): Research Article

Journal of Chemical and Pharmaceutical Research, 2014, 6(2): Research Article Available online www.jocpr.com Journal of Chemical an Pharmaceutical Research, 4, 6():78-86 Research Article ISSN : 975-7384 CODEN(USA) : JCPRC5 Comparison of impeance analysis an fiel analysis in ey current

More information

Superconducting Fault Current Limiter in DC Systems with MLI Fed to IM

Superconducting Fault Current Limiter in DC Systems with MLI Fed to IM Superconducting Fault Current Limiter in DC Systems with MLI Fed to IM 1 Rama Rao P.V.V., 2 M.Swathi 1,2 Shri Vishnu Engineering for Women, Bhimavaram, India Abstract: In this paper, an application of

More information

d dx But have you ever seen a derivation of these results? We ll prove the first result below. cos h 1

d dx But have you ever seen a derivation of these results? We ll prove the first result below. cos h 1 Lecture 5 Some ifferentiation rules Trigonometric functions (Relevant section from Stewart, Seventh Eition: Section 3.3) You all know that sin = cos cos = sin. () But have you ever seen a erivation of

More information

Thermal conductivity of graded composites: Numerical simulations and an effective medium approximation

Thermal conductivity of graded composites: Numerical simulations and an effective medium approximation JOURNAL OF MATERIALS SCIENCE 34 (999)5497 5503 Thermal conuctivity of grae composites: Numerical simulations an an effective meium approximation P. M. HUI Department of Physics, The Chinese University

More information

The Energy Flow Approach for Oscillation Source Location and Damping Evaluation

The Energy Flow Approach for Oscillation Source Location and Damping Evaluation 1 The Energy Flow Approach for Oscillation Source Location an Damping Evaluation Lei CHEN PhD, Associate Professor Department of Electrical Engineering Tsinghua University chenlei08@tsinghua.eu.cn Backgroun

More information

Moving Charges And Magnetism

Moving Charges And Magnetism AIND SINGH ACADEMY Moving Charges An Magnetism Solution of NCET Exercise Q -.: A circular coil of wire consisting of turns, each of raius 8. cm carries a current of. A. What is the magnitue of the magnetic

More information

Capacitance and Dielectrics

Capacitance and Dielectrics 6 Capacitance an Dielectrics CHAPTER OUTLINE 6. Definition of Capacitance 6. Calculating Capacitance 6.3 Combinations of Capacitors 6.4 Energy Store in a Charge Capacitor 6.5 Capacitors with Dielectrics

More information

Research Article Development of Digital Control for High Power Permanent-Magnet Synchronous Motor Drives

Research Article Development of Digital Control for High Power Permanent-Magnet Synchronous Motor Drives Mathematical Problems in Engineering Volume 214, Article ID 926727, 1 pages http://x.oi.org/1.1155/214/926727 Research Article Development of Digital Control for High Power Permanent-Magnet Synchronous

More information

Linear First-Order Equations

Linear First-Order Equations 5 Linear First-Orer Equations Linear first-orer ifferential equations make up another important class of ifferential equations that commonly arise in applications an are relatively easy to solve (in theory)

More information

Modeling time-varying storage components in PSpice

Modeling time-varying storage components in PSpice Moeling time-varying storage components in PSpice Dalibor Biolek, Zenek Kolka, Viera Biolkova Dept. of EE, FMT, University of Defence Brno, Czech Republic Dept. of Microelectronics/Raioelectronics, FEEC,

More information

Motion-Copying System Using FPGA-based Friction-Free Disturbance Observer

Motion-Copying System Using FPGA-based Friction-Free Disturbance Observer IEEJ Journal of Inustry Applications Vol.3 No.3 pp.248 259 DOI: 10.1541/ieejjia.3.248 Paper Motion-Copying System Using FPGA-base Friction-Free Disturbance Observer Thao Tran Phuong a) Member, Kiyoshi

More information

Superconducting Fault Current Limiters

Superconducting Fault Current Limiters Superconducting Fault Current Limiters Prof. Dr.-Ing. Mathias Noe, Karlsruhe Institute of Technology Institute for Technical Physics EASITrain Summer School,, September 3rd-7th 2018, Vienna KIT-ENERGY

More information

Physics 2212 GJ Quiz #4 Solutions Fall 2015

Physics 2212 GJ Quiz #4 Solutions Fall 2015 Physics 2212 GJ Quiz #4 Solutions Fall 215 I. (17 points) The magnetic fiel at point P ue to a current through the wire is 5. µt into the page. The curve portion of the wire is a semicircle of raius 2.

More information

Systematic Design of Virtual Component Method for Inverter-Based Microgrids

Systematic Design of Virtual Component Method for Inverter-Based Microgrids Systematic Design of Virtual Component Metho for Inverter-Base Microgris Po-Hsu Huang 1, Petr Vorobev 1, Mohame Al Hosani, James L. Kirtley 1, an Konstantin Turitsyn 1 1 Massachusetts Institute of Technology

More information

Dynamics of a Microgrid Supplied by Solid Oxide Fuel Cells 1

Dynamics of a Microgrid Supplied by Solid Oxide Fuel Cells 1 Bulk Power System Dynamics an Control - VII, August 19-4, 007, Charleston, South Carolina, USA 1 Dynamics of a Microgri Supplie by Soli Oxie Fuel Cells 1 Eric M. Fleming Ian A. Hiskens Department of Electrical

More information

1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity

1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity AP Physics Multiple Choice Practice Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity. A soli conucting sphere is given a positive charge Q.

More information

Lecture 12. Energy, Force, and Work in Electro- and Magneto-Quasistatics

Lecture 12. Energy, Force, and Work in Electro- and Magneto-Quasistatics Lecture 1 Energy, Force, an ork in Electro an MagnetoQuasistatics n this lecture you will learn: Relationship between energy, force, an work in electroquasistatic an magnetoquasistatic systems ECE 303

More information

Conductor Requirements for Superconducting Fault Current Limiters

Conductor Requirements for Superconducting Fault Current Limiters superior performance. powerful technology. Conductor Requirements for Superconducting Current Limiters Chuck Weber, Director HTS Applications Coated Conductors in Applications 2008 Houston, Texas - December

More information

Vector Control Strategies to Enable Equal Frequency Operation of the Modular Multilevel Matrix Converter

Vector Control Strategies to Enable Equal Frequency Operation of the Modular Multilevel Matrix Converter Vector Control Strategies to Enable Equal Frequency Operation of the Moular Multilevel Matrix Converter M. Diaz 1, M. Espinosa, F. Rojas 1, P. Wheeler, R. Carenas 4 1 University of Santiago of Chile, Chile,

More information

ECE 422 Power System Operations & Planning 7 Transient Stability

ECE 422 Power System Operations & Planning 7 Transient Stability ECE 4 Power System Operations & Planning 7 Transient Stability Spring 5 Instructor: Kai Sun References Saaat s Chapter.5 ~. EPRI Tutorial s Chapter 7 Kunur s Chapter 3 Transient Stability The ability of

More information

KIT-ENERGY CENTRE. KIT The research University in the Helmholtz Association

KIT-ENERGY CENTRE.  KIT The research University in the Helmholtz Association Superconducting Fault Current Limiters Prof. Dr.-Ing. Mathias Noe, Karlsruhe Institute of Technology Institute for Technical Physics EUCAS Short Course Power Applications,, September 17th 2017, Geneva

More information

WITH high operating frequencies and scaled geometries,

WITH high operating frequencies and scaled geometries, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 56, NO. 7, JULY 2009 585 Inuctance Moel of Interigitate Power an Groun Distribution Networks Renatas Jakushokas, Stuent Member, IEEE,

More information

COMPACT BANDPASS FILTERS UTILIZING DIELECTRIC FILLED WAVEGUIDES

COMPACT BANDPASS FILTERS UTILIZING DIELECTRIC FILLED WAVEGUIDES Progress In Electromagnetics Research B, Vol. 7, 105 115, 008 COMPACT BADPASS FILTERS UTILIZIG DIELECTRIC FILLED WAVEGUIDES H. Ghorbanineja an M. Khalaj-Amirhosseini College of Electrical Engineering Iran

More information

Static Equilibrium. Theory: The conditions for the mechanical equilibrium of a rigid body are (a) (b)

Static Equilibrium. Theory: The conditions for the mechanical equilibrium of a rigid body are (a) (b) LPC Physics A 00 Las Positas College, Physics Department Staff Purpose: To etermine that, for a boy in equilibrium, the following are true: The sum of the torques about any point is zero The sum of forces

More information

Design A Robust Power System Stabilizer on SMIB Using Lyapunov Theory

Design A Robust Power System Stabilizer on SMIB Using Lyapunov Theory Design A Robust Power System Stabilizer on SMIB Using Lyapunov Theory Yin Li, Stuent Member, IEEE, Lingling Fan, Senior Member, IEEE Abstract This paper proposes a robust power system stabilizer (PSS)

More information

CHARACTERISTICS OF A DYNAMIC PRESSURE GENERATOR BASED ON LOUDSPEAKERS. Jože Kutin *, Ivan Bajsić

CHARACTERISTICS OF A DYNAMIC PRESSURE GENERATOR BASED ON LOUDSPEAKERS. Jože Kutin *, Ivan Bajsić Sensors an Actuators A: Physical 168 (211) 149-154 oi: 1.116/j.sna.211..7 211 Elsevier B.V. CHARACTERISTICS OF A DYNAMIC PRESSURE GENERATOR BASED ON LOUDSPEAKERS Jože Kutin *, Ivan Bajsić Laboratory of

More information

Revisiting the Charge Concept in HBT/BJT Models

Revisiting the Charge Concept in HBT/BJT Models evisiting the Charge Concept in HBT/BJT Moels Zoltan Huska an Ehrenfrie Seebacher austriamicrosystems AG 23r Bipolar Arbeitkeis BipAK Meeting at STM Crolles, France, 5 October 2 Outline recalling the junction

More information

From last time. Attention. Capacitance. Spherical capacitor. Energy stored in capacitors. How do we charge a capacitor? Today:

From last time. Attention. Capacitance. Spherical capacitor. Energy stored in capacitors. How do we charge a capacitor? Today: Attention From last time More on electric potential an connection to Efiel How to calculate Efiel from V Capacitors an Capacitance switch off computers in the room an be prepare to a very lou noise Toay:

More information

Electric Motor Performance Improvement Using Auxiliary Windings and Capacitance Injection

Electric Motor Performance Improvement Using Auxiliary Windings and Capacitance Injection Electric Motor Performance Improvement Using Auxiliary Winings an Capacitance Injection 2 Nicolae DV Tshwane University of Technology South Africa 1 Introuction Generally, some electric machines such as

More information

Vehicle Stability Improvement Based on Electronic Differential Using Sliding Mode Control

Vehicle Stability Improvement Based on Electronic Differential Using Sliding Mode Control 7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 1-3, 007 331 Vehicle Stability Improvement Base on Electronic Differential Using

More information

Study on aero-acoustic structural interactions in fan-ducted system

Study on aero-acoustic structural interactions in fan-ducted system Stuy on aero-acoustic structural interactions in fan-ucte system Yan-kei CHIANG 1 ; Yat-sze CHOY ; Li CHENG 3 ; Shiu-keung TANG 4 1,, 3 Department of Mechanical Engineering, The Hong Kong Polytechnic University,

More information

Systematic Design of Virtual Component Method for Inverter-Based Microgrids

Systematic Design of Virtual Component Method for Inverter-Based Microgrids Systematic Design of Virtual Component Metho for Inverter-Base Microgris Po-Hsu Huang 1, Petr Vorobev 1, Mohame Al Hosani 3, James L. Kirtley 1, an Konstantin Turitsyn 1 1 Massachusetts Institute of Technology

More information

Assessment of the Buckling Behavior of Square Composite Plates with Circular Cutout Subjected to In-Plane Shear

Assessment of the Buckling Behavior of Square Composite Plates with Circular Cutout Subjected to In-Plane Shear Assessment of the Buckling Behavior of Square Composite Plates with Circular Cutout Sujecte to In-Plane Shear Husam Al Qalan 1)*, Hasan Katkhua 1) an Hazim Dwairi 1) 1) Assistant Professor, Civil Engineering

More information

A Model of Electron-Positron Pair Formation

A Model of Electron-Positron Pair Formation Volume PROGRESS IN PHYSICS January, 8 A Moel of Electron-Positron Pair Formation Bo Lehnert Alfvén Laboratory, Royal Institute of Technology, S-44 Stockholm, Sween E-mail: Bo.Lehnert@ee.kth.se The elementary

More information

6.003 Homework #7 Solutions

6.003 Homework #7 Solutions 6.003 Homework #7 Solutions Problems. Secon-orer systems The impulse response of a secon-orer CT system has the form h(t) = e σt cos(ω t + φ)u(t) where the parameters σ, ω, an φ are relate to the parameters

More information

MEASUREMENT OF LOSSES IN DIRECT TORQUE CONTROLLED PERMANENT MAGNET SYNCHRONOUS MOTOR BY ANALYSIS AND EXPERIMENTAL SETUP

MEASUREMENT OF LOSSES IN DIRECT TORQUE CONTROLLED PERMANENT MAGNET SYNCHRONOUS MOTOR BY ANALYSIS AND EXPERIMENTAL SETUP IJRET: International Journal of Research in Engineering an Technology eissn: 2319-1163 pissn: 2321-738 MEASUREMENT OF LOSSES IN DIRECT TORQUE CONTROLLED PERMANENT MAGNET SYNCHRONOUS MOTOR BY ANALYSIS AND

More information

Investigation of local load effect on damping characteristics of synchronous generator using transfer-function block-diagram model

Investigation of local load effect on damping characteristics of synchronous generator using transfer-function block-diagram model ORIGINAL ARTICLE Investigation of local loa effect on amping characteristics of synchronous generator using transfer-function block-iagram moel Pichai Aree Abstract of synchronous generator using transfer-function

More information

Lithium-ion Battery Electro-thermal Model and Its Application in the Numerical Simulation of Short Circuit Experiment

Lithium-ion Battery Electro-thermal Model and Its Application in the Numerical Simulation of Short Circuit Experiment EVS27 Barcelona, Spain, November 17-20, 2013 Lithium-ion Battery Electro-thermal Moel an Its Application in the Numerical Simulation of Short Circuit Experiment Chengtao Lin 1, Can Cui 2, Xiaotian Xu 3

More information

AIEEE Physics Model Question Paper

AIEEE Physics Model Question Paper IEEE Physics Moel Question Paper ote: Question o. 11 to 1 an 1 to consist of Eight (8) marks each for each correct response an remaining questions consist of Four (4) marks. ¼ marks will be eucte for inicating

More information

Thermal runaway during blocking

Thermal runaway during blocking Thermal runaway uring blocking CES_stable CES ICES_stable ICES k 6.5 ma 13 6. 12 5.5 11 5. 1 4.5 9 4. 8 3.5 7 3. 6 2.5 5 2. 4 1.5 3 1. 2.5 1. 6 12 18 24 3 36 s Thermal runaway uring blocking Application

More information

qq 1 1 q (a) -q (b) -2q (c)

qq 1 1 q (a) -q (b) -2q (c) 1... Multiple Choice uestions with One Correct Choice A hollow metal sphere of raius 5 cm is charge such that the potential on its surface to 1 V. The potential at the centre of the sphere is (a) zero

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Capacitors Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 12 Capacitors are evices that can store electrical energy Capacitors are use in many every-ay applications Heart efibrillators

More information

Published in: Proceedings of The 34th Annual Conference of IEEE Industrial Electronics, IECON 2008

Published in: Proceedings of The 34th Annual Conference of IEEE Industrial Electronics, IECON 2008 Aalborg Universitet Fault etection of a Five-Phase Permanent-Magnet Machine Bianchini, Clauio; Matzen, Torben.; Bianchi, icola; Fornasiero, Emanuele; Bellini, Alberto Publishe in: Proceeings of The 34th

More information

Negative-Index Refraction in a Lamellar Composite with Alternating. Single Negative Layers

Negative-Index Refraction in a Lamellar Composite with Alternating. Single Negative Layers Negative-Inex Refraction in a Lamellar Composite with Alternating Single Negative Layers Z. G. Dong, S. N. Zhu, an H. Liu National Laboratory of Soli State Microstructures, Nanjing University, Nanjing

More information

Finite element analysis of electromagnetic bulging of sheet metals

Finite element analysis of electromagnetic bulging of sheet metals International Journal of Scientific & Engineering Research Volume 3, Issue 2, Febraury-212 1 Finite element analysis of electromagnetic bulging of sheet metals Ali M. Abelhafeez, M. M. Nemat-Alla, M. G.

More information

The total derivative. Chapter Lagrangian and Eulerian approaches

The total derivative. Chapter Lagrangian and Eulerian approaches Chapter 5 The total erivative 51 Lagrangian an Eulerian approaches The representation of a flui through scalar or vector fiels means that each physical quantity uner consieration is escribe as a function

More information

Australian Journal of Basic and Applied Sciences

Australian Journal of Basic and Applied Sciences Australian Journal of Basic an Applie Sciences, 9(1) January 015, Pages: 38-45 AENSI Journals Australian Journal of Basic an Applie Sciences ISSN:1991-8178 Journal home page: www.ajbasweb.com Velocity

More information

Neural Network Training By Gradient Descent Algorithms: Application on the Solar Cell

Neural Network Training By Gradient Descent Algorithms: Application on the Solar Cell ISSN: 319-8753 Neural Networ Training By Graient Descent Algorithms: Application on the Solar Cell Fayrouz Dhichi*, Benyounes Ouarfi Department of Electrical Engineering, EEA&TI laboratory, Faculty of

More information

Vibration Analysis of Railway Tracks Forced by Distributed Moving Loads

Vibration Analysis of Railway Tracks Forced by Distributed Moving Loads IJR International Journal of Railway Vol. 6, No. 4 / December 13, pp. 155-159 The Korean Society for Railway Vibration Analysis of Railway Tracks Force by Distribute Moving Loas Sinyeob Lee*, Dongkyu Kim*,

More information

INTEGRATED CIRCUITS. For a complete data sheet, please also download:

INTEGRATED CIRCUITS. For a complete data sheet, please also download: INTEGRATED CIRCUITS DATA SEET For a complete ata sheet, please also ownloa: The IC6 74C/CT/CU/CMOS ogic Family Specifications The IC6 74C/CT/CU/CMOS ogic Package Information The IC6 74C/CT/CU/CMOS ogic

More information

FET Inrush Protection

FET Inrush Protection FET Inrush Protection Chris Pavlina https://semianalog.com 2015-11-23 CC0 1.0 Universal Abstract It is possible to use a simple one-transistor FET circuit to provie inrush protection for low voltage DC

More information

inflow outflow Part I. Regular tasks for MAE598/494 Task 1

inflow outflow Part I. Regular tasks for MAE598/494 Task 1 MAE 494/598, Fall 2016 Project #1 (Regular tasks = 20 points) Har copy of report is ue at the start of class on the ue ate. The rules on collaboration will be release separately. Please always follow the

More information

PCCP PAPER. 1 Introduction. A. Nenning,* A. K. Opitz, T. M. Huber and J. Fleig. View Article Online View Journal View Issue

PCCP PAPER. 1 Introduction. A. Nenning,* A. K. Opitz, T. M. Huber and J. Fleig. View Article Online View Journal View Issue PAPER View Article Online View Journal View Issue Cite this: Phys. Chem. Chem. Phys., 2014, 16, 22321 Receive 4th June 2014, Accepte 3r September 2014 DOI: 10.1039/c4cp02467b www.rsc.org/pccp 1 Introuction

More information

ECE341 Test 2 Your Name: Tue 11/20/2018

ECE341 Test 2 Your Name: Tue 11/20/2018 ECE341 Test Your Name: Tue 11/0/018 Problem 1 (1 The center of a soli ielectric sphere with raius R is at the origin of the coorinate. The ielectric constant of the sphere is. The sphere is homogeneously

More information

Closed and Open Loop Optimal Control of Buffer and Energy of a Wireless Device

Closed and Open Loop Optimal Control of Buffer and Energy of a Wireless Device Close an Open Loop Optimal Control of Buffer an Energy of a Wireless Device V. S. Borkar School of Technology an Computer Science TIFR, umbai, Inia. borkar@tifr.res.in A. A. Kherani B. J. Prabhu INRIA

More information

THE VAN KAMPEN EXPANSION FOR LINKED DUFFING LINEAR OSCILLATORS EXCITED BY COLORED NOISE

THE VAN KAMPEN EXPANSION FOR LINKED DUFFING LINEAR OSCILLATORS EXCITED BY COLORED NOISE Journal of Soun an Vibration (1996) 191(3), 397 414 THE VAN KAMPEN EXPANSION FOR LINKED DUFFING LINEAR OSCILLATORS EXCITED BY COLORED NOISE E. M. WEINSTEIN Galaxy Scientific Corporation, 2500 English Creek

More information