A Control Strategy for Unified Power Quality Conditioner
|
|
- Roxanne Martin
- 5 years ago
- Views:
Transcription
1 A Control Strtegy for Unfed Power Qulty Condtoner Luís FC Montero, Student memer, IEEE, Murío Aredes, Memer, IEEE, nd João A Moor Neto COPPE/UFJ, Eletrl Engneerng Progrm POox 68504, o de Jnero, rzl E-ml: lfm@oeufrjr Astrt Ths pper presents ontrol strtegy for Unfed Power Qulty Condtoner Ths ontrol strtegy s used n three-phse three-wre systems The UPQC dee omnes shunt-te flter together wth seres-te flter n kto-k onfgurton, to smultneously ompenste the supply oltge nd the lod urrent Preous works presented ontrol strtegy for shunt-te flter tht gurntees snusodl, lned nd mnmzed soure urrents een f under unlned nd / or dstorted system oltges, lso known s Snusodl Fryze Currents Then, ths ontrol strtegy ws extended to deelop dul ontrol strtegy for seres-te flter Now, ths pper deelops the ntegrton prnples of shunt urrent ompenston nd seres oltges ompenston, oth sed on nstntneous te nd non-te powers, dretly lulted from -- phse oltges nd lne urrents Smulton results re presented to ldte the proposed UPQC ontrol strtegy Index Terms Ate Flters, Ate Power Lne Condtoners, Instntneous Ate nd ete Power, Snusodl Fryze Currents, Snusodl Fryze Voltges O I INTODUCTION NE of the serous prolems n eletrl systems s the nresng numer of eletron omponents of dees tht re used y ndustry s well s resdenes These dees, whh need hgh-qulty energy to work properly, t the sme tme, re the most responsle ones for njetons of hrmons n the dstruton system Therefore, dees tht soften ths drwk he een deeloped One of them s the unfed power qulty ondtoner UPQC, s shown n Fg It onssts of shunt-te flter together wth seres-te flter Ths omnton llows smultneous ompenston of the lod urrents nd the supply oltges, so tht ompensted urrent drwn from the network nd the ompensted supply oltge delered to the lod re snusodl, lned nd mnmzed The seresnd shunt-te flters re onneted n k-to-k onfgurton, n whh the shunt onerter s responsle for regultng the ommon DC-lnk oltge In the 0 s of the lst entury, Fryze [] proposed set of te nd non-te rete power defntons n the tme domn From these onepts, Tent et l [] deeloped ontrol strtegy for shunt-te flters tht gurntees ompensted urrents n the network tht re snusodl een f the system oltge t the pont of ommon ouplng PCC lredy ontns hrmons Howeer, ths ontrol strtegy does not gurntee lned ompensted urrents f the system oltge tself s unlned e t ontns fundmentl negte-sequene omponent In [], ths drwk ws oerome, y the ddton of postesequene oltge detetor n the shunt-te flter ontroller Ths ontrol rut determnes the phse ngle, frequeny nd mgntude of the fundmentl postesequene oltge omponent Ths new ontrol strtegy hs een denomnted s the Snusodl Fryze Currents on- S C S L C L C L V d f PWM oltge ontrol C * C * PWM urrent ontrol f S S UPQC ontroller L Fg enerl onfgurton of the Unfed Power Qulty Condtoner UPQC
2 trol strtegy Ths work explots the use of tht poste-sequene oltge detetor to deelop new ontrol strtegy for seres-te flter It s sed on dul mnmzton method for oltge ompenston, together wth synhronzng rut PLL rut The synhronzng rut s responsle to detet the fundmentl frequeny, s well s the phse ngle of the poste-sequene oltge omponent The dul mnmzton method s responsle to urtely determne the mgntude of ths oltge omponent Ths ontrol strtegy s denomnted here s the Snusodl Fryze Voltges ontrol strtegy Further, ths pper presents the ntegrton the Snusodl Fryze Currents nd the Snusodl Fryze Voltges ontrol strteges nto n UPQC ontroller Addtonlly, the proposed UPQC ontroller nludes n lgorthm tht prodes dmpng n hrmon oltge propgton nd hnders lod hrmon urrents to flow nto the network A omplete model of the UPQC pproh s mplemented n dgtl smultor nd results s presented to ldte the proposed ontrol strtegy II THE UPQC CONTOLLE Fg shows the omplete funtonl lok dgrm of the UPQC ontroller The prt shown n Fg s responsle to determne the ompenstng urrent referenes for PWM ontrol of the UPQC shunt onerter, wheres the other prt shown n Fg genertes the ompenstng oltge referenes for PWM seres onerter Next, eh funtonl lok of Fg wll e detled s s s DC V Voltge Detetor DC Voltge egultor 4 loss s s s 5 Dmpng h h Controller h l l l Current Mnmzton s s s Compenstng Voltges lulton Fg The funtonl lok dgrm of the UPQC ontroller for shunt UPQC onerter nd seres UPQC onerter A The Poste-Sequene Voltge Detetor V A poste-sequene oltge detetor [V oltgedetetor lok n Fg ] n terms of "mnmzed oltges" s deeloped A dul prnple for oltge mnmzton s employed, together wth phse-lokedloop rut PLL rut, s shown n Fg The used PLL rut s detled n the next seton In ft, ths dul prnple of oltge mnmzton s used here for extrtng "nstntneously" the fundmentl poste-sequene omponent V n phsor notton, or,, s nstntneous lues, s the outputs of Fg from gener three-phse oltge The dstorted nd unlned oltges s, s, s of the power supply re mesured nd gen s nputs to the PLL rut As shown n the next seton, t determnes the sgnls,,, whh re n phse wth the fundmentl poste-sequene omponent V ontned n s, s, s Thus, only the mgntude of V s mssng The fundmentl hrterst of the used PLL llows the use of dul expresson for determnng te oltges n the form p p p s s s s n rtfe to extrt the V omponent from s, s, s The reson s tht the sgnls,, re three symmetr snus funtons wth unty mpltude, whh orrespond to n uxlry fundmentl poste-sequene urrent I tht s n phse wth V Hene, the erge lue of the "three-phse nstntneous power", V I osφ, s mxmum would e zero f V nd I re orthogonl, nd the erge sgnl r n Fg omprses the totl mpltude of V Therefore, t s possle to gurntee tht the sgnls,, re snusodl nd he the sme mgntude nd phse ngle of the fundmentl poste-sequene omponent of the mesured system oltge s s s s PLL Synhronzng Crut s s r r r Low Pss Flter 5 th Order Cut freq 50 Hz r Fg The V oltge detetor dgrm lok
3 The PLL Crut The used PLL rut Fg 4 n operte stsftorly under hgh dstorted nd unlned system oltges The nputs re s s nd s s The outputs of the PLL rut re,, The lgorthm s sed on the nstntneous te three-phse power expresson p φ The urrent feedk sgnls wt snwt nd wt snwt π/ re ult up y the PLL rut, just usng the tme ntegrl of output ω of the PI-Controller Note tht they he unty mpltude nd wt leds 0 o wt Thus, they represent feedk from postesequene omponent t frequenyω The PLL rut n reh stle pont of operton only f the nput p φ of the PI-Controller hs zero erge lue p 0 nd hs φ mnmzed low-frequeny oslltng portons n ~ p φ p φ p ~ φ p φ One the rut s stlzed, the erge lue of p φ s zero nd, wth ths, the phse ngle of the poste-sequene system oltge t fundmentl frequeny s rehed At ths ondton, the uxlry urrents ωt nd ωt snωt π/, eomes orthogonl to the fundmentl poste-sequene omponent of the mesured oltges s, s respetely Therefore, ωt snωt π/ s n phse wth the fundmentl poste-sequene omponent ontned n s The DC oltge regultor The d oltge regultor s used to generte ontrol sgnl loss, s shown n Fg Ths sgnl fores the shunt te flter to drw ddtonl te urrent from the network, to ompenste for losses n the power rut of the UPQC Addtonlly, t orrets d oltge rtons used y norml operton nd trnsent ompenston errors Ths pont s lrfed lter, where smulton results re dsussed Fg 5 shows the d oltge regultor rut It onssts only of PI-Controller [s K p K I /s], where, for normlzed nputs, K p 050 nd K I 80 ω t snω t X p φ ω Σ PI-Controller X V DC_ref ω t snω t π/ ω t s snω t π/ snω t π/ π/ snω t π/ π/ Fg 4: The Synhronzng Crut PLL Crut Σ low-pss flter PI ontroller loss C Current Mnmzton Fg 6 shows n detls tht funtonl lok nmed "Current Mnmzton" n Fg It determnes the nstntneous ompenstng urrent referenes, whh should e syntheszed y the shunt PWM onerter of the UPQC It hs the sme kernel s the enerlzed Fryze Currents methods wdely used, lke n [4], [5] nd [6] The nputs of the ontroller re the lod urrents,,, the ontrol oltges,, determned y the V detetor, nd the DC oltge regultor sgnl loss The ondutne s determned n Fg 6 orresponds to the te urrent of the lod In other words, t omprses ll urrent omponents tht n produe te power wth the oltges,, A low-pss ffth order flter s used to extrt the erge lue of, whh s denomnted s r Now, sne,, omprses only the VD omponent, r must orrespond to the te porton of the fundmentl poste-sequene omponent I of the lod urrent The ontrol sgnl ontrol s the sum of r nd loss, whh, together wth the ontrol oltges,,, re used to determne the urrents w, w, w These ontrol sgnls re pure snusodl wes n phse wth,, nd nlude the mgntude of the poste-sequene lod urrent proportonl to r nd the te urrent proportonl to loss tht s neessry to ompenste for losses n the UPQC Sne the shunt te flter of the UPQC ompenstes the dfferene etween the lulted te urrent nd the mesured lod urrent, t s possle to gurntee tht the l l l l l l w w w ontrol ontrol ontrol r ontrol Low Pss Flter 5 th Order Cut freq 50 Hz Σ w w w l loss l w w w l l l l DC Fg 5: The DC oltge regultor Fg 6 The Current Mnmzton ontrol lgorthm
4 ompensted urrents s, s, s drwn from the network re lwys snusodl, lned nd n phse wth the postesequene system oltges Ths hrterst represents gret mproement done t the enerlzed Fryze Currents ontrol strtegy D The Dmpng Control Algorthm In UPQC onfgurton, nstlty prolems due to resonne phenomen my our In order to enhne the oerll system stlty, n uxlry rut n e dded to the ontroller of the seres te flter The s de onssts n nresng hrmon dmpng, s seres resstne, ut effete only n hrmon frequenes, others thn the fundmentl one Ths dmpng prnple ws frst proposed y Peng [7], n terms of omponents defned n the pq Theory nd used y Aredes [8] nd Fujt [9] The dmpng ontrol lgorthm, now deeloped n terms of rles n the phse mode, n e seen n Fg 7 The nputs to the dmpng rut re the soure urrents s, s, s ompensted urrents, whh re flowng through the seres trnsformers of the UPQC, nd the oltges determned y the V oltge detetor,, The te nd non-te nstntneous powers re determned y usng the equtons nd ; P s s s Q omp 7 omp 8 q s q / q / q / q q q p p p q q q 6 q q q s s s s q s q q s q q s s 4 omp omp omp omp q omp q omp q q s 6 q s q s h h h p p p q q q Hgh Pss Flter 5 th order Cut off freq 50 Hz Hgh Pss Flter 5 th order Cut off freq 50 Hz 5 h h h h ; h h h omp 7 omp h 8 K K K h h n K Fg 7 Dmpng ontrol lgorthm n terms of rles h h where, q q q / / / ; Note tht the oltges q, q, q re heed from the fundmentl poste-sequene oltges,, Therefore, t s possle to gurntee tht the oltges q, q, q re stll snusodl nd lg 90º the oltges,,, respetely A ondutne nd suseptne re determned from the lulted te nd non-te nstntneous powers, s shown n Fg 7 Then, hgh-pss, ffth order flters re used to extrt the oslltng prts of tht ondutne nd suseptne The uxlry urrents p, p, p nd q, q, q, re determned s follows: p os p os ; 4 p os q os q q os q 5 q os q Dmpng sgnls hrmon omponents stll present n the soure urrents re determned s desred n 6 h q p h q p 6 h q p Fnlly, the multplton etween the dmpng sgnls h, h, h nd gn K determnes the dmpng oltges h, h, h tht wll e dded to the ompenstng oltge referenes of the seres te flter of the UPQC, s wll e explned n the next seton Thus, the gn K ts s hrmon resstne to dmp resonne phenomen E Compenstng Voltges Clulton The lok dgrm tht determnes the ompenstng oltges,, [Fg ], whh s syntheszed y the seres PWM onerter, s shown n Fg 8 The nputs re the ontrol oltges determned y the V oltge detetor:,,, the soure oltges: s, s, s, nd the dmpng oltges: h, h, h The ompenstng oltge re: s s s h h h 7 Idelly, the ompensted oltges delered to the rtl lod wll omprse only the fundmentl poste-sequene omponent,, of the supply oltge S The dmpng oltges wll mproe stlty nd prode hrmon solton
5 h 5 h h l s s s h h h s s s s Fg 9: Lod urrent, urrent of the shunt te flter nd soure urrent Fg 8 Compenstng oltges lulton As onluson, the proposed UPQC ontrol strtegy prodes ompensted oltges nd urrents tht re snusodl, lned nd mnmzed n phse Therefore, the power ftor s del, the oltges delered to the lod re snusodl nd lned, nd t s possle to gurntee tht the soure urrents wll e snusodl, lned nd mnmzed een f under unlned nd / or dstorted system oltges III SIMULATION ESULTS A test se ws mounted to nestgte the performne of the UPQC flter through dgtl smultons, n the Ser Desgner TM Per unt pu qunttes nnot e used dretly n ths smultor Thus, V phse to ground nd A lne urrent were used s the ss of the system A lned, V, three-phse, oltge soure s used A three-phse sxpulse thyrstor retfer, wth 0 A DC-urrent 0%, s used s non-lner lod The shunt-te flter nd the seres-te flter strt ts operton n 0s The totl smulton tme s 08s The thyrstor retfer s onneted t t 0s An ndutor nd resstor, whose lues orrespond to 0 % of the system se mpedne, ompose the soure mpedne In ths se, the short-rut power t the lod termnl s equl to 0 pu The smll hgh-pss flters to mtgte swthng frequeny hrmons t the seres nd shunt PWM onerters re 06 Ω nd C 70 µf Although t sems hgh ptor, t orresponds to 5% of the system sempedne A ptor of 400µF s used t the DC lnk of the UPQC The referene oltge s equl to 45 V To ge n de of the ptor s dmenson, the unt ptor onstnt UCC s lulted, y the followng equton: C V 400µ 45 UCC 8 8 ms P Fg 9 shows the lod, shunt nd soure urrents l,, s, efore, nd fter the strt of the shunt-te flter After the strt of the shunt te flter, the soure urrent eomes lmost snusodl It my e noted, tht the tme tht the soure urrents tke to reh the stedy stte s pretty smll Ths demonstrtes tht the proportonl nd ntegrl gns of the DC oltge regultor re well dmensoned Fg 0 shows the supply oltge s unompensted, left sde of the UPQC, the ompenstng oltge of the UPQC, nd ompensted oltge w, delered to the rtl lod, efore nd fter the strt of the seres te flter The soure oltge hs 0% of negte-sequene omponent t the fundmentl frequeny, plus 5% of 5 th hrmon nd 5% of 7 th hrmon The w oltge, fter the strt of the seres te flter, eomes lmost snusodl Fg shows the DC Lnk Voltge DC nd the losses n the UPQC, represented y the loss sgnl The referene lue t the termnls of the DC-lnk s equl to 45 olts It my e noted, tht the rpple t the DC-lnk oltge s ery smll, n the order of 04% of the referene lue durng short trnsent perod, fter the strt of the UPQC, nd less thn 0 %, n stedy-stte operton The swthng losses of the nerters my not represent the relty, sne del models of swthes n the dgtl smultor re used Ths ondton s needed n the proposed system, euse ss of V nd A ws hosen Fg shows the soure urrents s, s, s, the ompensted oltges w, w, w, nd the urrent s together wth oltge w repeted n seprted grph, efore nd fter s w Fg 0 Supply oltge, ompenstng oltge, nd the ompensted oltge delered to the rtl lod
6 the UPQC energzton It my e seen tht, when the UPQC strt ts operton the soure urrents, s well the ompensted oltges eome lmost snusodl nd lned The soure urrent s nd the ompensted oltge w re lmost n phse fter the strt of the UPQC It onfrms tht the ontrol strtegy proposed s useful n threephse three-wre system, where the system oltges re unlned nd dstorted nd the lod urrents wth hgh ontents of hrmons IV CONCLUSIONS DC loss A ontrol strtegy for Unfed Power Qulty Condtoner the UPQC s proposed Smulton results he ldted the proposed ontrol strtegy, for the use n three-phse three-wre systems In se of usng n threephse four-wre systems, there s the neessty of ompenstng the neutrl urrent In ths se, three-phse fourwre PWM onerter s neessry The omputtonl efforts to deelop the proposed ontrol strtegy s redued, f ompred wth pq-theory-sed ontrollers, sne the α-β-0 trnsformton s oded For three-phse three-wre systems, the performne of the proposed pproh s omprle wth those sed on the pq Theory, wthout loss of roustness een f opertng under dstorted nd unlned system oltge ondtons Presently, the uthors re workng on the posslty of extendng the proposed ontrol strtegy for the use n threephse four-wre systems Fg DC lnk oltge sgnl DC nd DC oltge regultor sgnl loss s w w s w s s w Fg Soure urrents, ompensted oltges nd the ompensted oltge w together wth the soure urrent s V EFEENCES [] S Fryze, Wrk-, lnd- und Shenlestung n elektrshen Stromknsen mt nht-snusfömgen Verluf on Strom und Spnnung, ETZ-Arh Elektroteh, ol 5, 9, pp , 65-67, [] L Mlesn, L osseto, P Tent, Ate Flter for ete Power nd Hrmons Compenston, IEEE PESC 986, pp -0 [] Luís FC Montero, M Aredes, A Comprte Anlyss Among Dfferent Control Strteges for Shunt Ate Flters, Pro CDOM of the V INDUSCON - Conferên de Aplções Industrs, Sldor, rzl, July 00, pp45-50 [4] T Furuhsh, S Okum, Y Uhkw, "A Study on the Theory of Instntneous ete Power," IEEE Trns on Industrl Eletrons, ol 7, no, pp 86-90, Fe 990 [5] L ossetto, P Tent, "Eluton of Instntneous Power Terms n Mult-Phse Systems: Tehnques nd Applton to Power- Condtonng Equpments," ETEP Eur Trns Elet Power Eng, ol 4, no 6, pp , No/De 994 [6] M Depenrok, D A Mrshll, J D n Wyk, "Formultng equrements for Unerslly Applle Power Theory s Control Algorthm n Power Compenstors," ETEP Eur Trns Elet Power Eng, ol 4, no 6, pp , No/De 994 [7] FZ Peng, H Akg, A Ne, A New Approh to Hrmon Compenston n Power Systems A Comned System of Shunt Psse nd Seres Ate Flters, IEEE Trns Ind Appl, ol6, no6, No/De 990, pp [8] M Aredes, J Häfner, K Heumnn, A Comned Seres nd Shunt Ate Power Flter, IEEE/KTH Stokholm Power Teh Conf, ol Power Eletrons, pp 7-4, Stokholm, Sweden, June 995 [9] H Fujt, H Akg, The Unfed Power Qulty Condtoner: The Integrton of Seres nd Shunt Ate Flters, IEEE Trns on Power Eletrons, ol, No, Mrh 998 VI IOAPHIES Luís Fernndo Corrê Montero ws orn n o de Jnero Stte on Mrh 975 He reeed the S Degree from Federl Unersty of o de Jnero n 00 He s enrolled n MS t COPPE/UFJ n Power Eletrons where s deelopng ontrol strteges for te flters nd dees to mproe the power qulty n the eletrl system Hs Mn reserh res of nterest re Custom Power nd FACTS The engneer Luís F C Montero s student memer of the rzln Power Eletrons Soety SOAEP, Interntonl Eletrl nd Eletrons Engneerng IEEE, nd Counl on Lrge Eletr Systems CIE Murío Aredes S 94, M 97 ws orn n São Pulo Stte, rzl, on August 4, 96 He reeed the S degree from Flumnense Federl Unersty, o de Jnero Stte n 984, the MS degree n Eletrl Engneerng from Federl Unersty of o de Jnero n 99, nd the Dr-Ing Degree mgn um lude from Tehnshe Unerstät erln n 996 From 985 to 988 he worked t the Itpu HVDC Trnsmsson System nd from 988 to 99 n the SCADA Projet of Itpu Power Plnt From 996 to 997 he worked wthn CEPEL Centro de Pesquss de Energ Elétr, o de Jnero, s &D Engneer In 997, he eme n Assote Professor t the Federl Unersty of o de Jnero, where he tehes Power Eletrons Hs mn reserh re nludes HVDC nd FACTS systems, te flters, Custom Power nd Power Qulty Issues Dr Aredes s memer of the rzln Soety for Automt Control nd the rzln Power Eletrons Soety João A Moor Neto ws orn n o de Jnero Stte on 965 He reeed the S Degree from UCP-J n 99, nd MS from Federl Unersty of Itjuá n 995 He s enrolled n DS t COPPE/UFJ n Power Eletrons sne 00 In 995 he eme Professor t UNIJUI-S, where he tehes Power System Hs mn reserh res of nterest re FACTS nd Custom Power
" = #N d$ B. Electromagnetic Induction. v ) $ d v % l. Electromagnetic Induction and Faraday s Law. Faraday s Law of Induction
Eletromgnet Induton nd Frdy s w Eletromgnet Induton Mhel Frdy (1791-1867) dsoered tht hngng mgnet feld ould produe n eletr urrent n ondutor pled n the mgnet feld. uh urrent s lled n ndued urrent. The phenomenon
More informationPerformance Comparison of Three-Phase Shunt Active Power Filter Algorithms
Amern Journ of Apped Senes 5 (11): 144-148, 008 ISSN 1546-939 008 Sene Pubtons Performne Comprson of Three-Phse Shunt Ate Power Fter Agorthms 1 Moeykutty George nd Krtk Prd Bsu 1 Futy of Engneerng nd Tehnoogy,
More informationGENERATING REFERENCE CURRENT AND VOLTAGE CONTROL OF STATIC COMPENSATOR DURING VOLTAGE SAGS
GENERATING REFERENCE CURRENT AND VOLTAGE CONTROL OF STATIC COMPENSATOR DURING VOLTAGE SAGS Thmeem Ansr R PG sholr, power systems engneerng, Dept. of eletrl nd eletrons engneerng J.J ollege of engneerng
More informationLecture 7 Circuits Ch. 27
Leture 7 Cruts Ch. 7 Crtoon -Krhhoff's Lws Tops Dret Current Cruts Krhhoff's Two ules Anlyss of Cruts Exmples Ammeter nd voltmeter C ruts Demos Three uls n rut Power loss n trnsmsson lnes esstvty of penl
More informationAC/DC/AC Converters: Two-Level and Multilevel VSI
Sortes Ersmus Visit A/D/A onerters: Two-Leel nd Multileel VSI Josep Pou Antoni Aris Pge 1 Sortes Ersmus Visit Outline 1. Two-Leel Inerter 2. Multileel Inerters - sde H-Bridge Inerter - Flying-pitor Inerter
More informationGrid Connected Renewable Energy Sources with Four Leg Inverter for Power Quality Improvement
Proeedngs of tonl onferene on omputng, Eletrl, Eletrons nd Sustnle Energy Systems Grd onneted Renewle Energy Soures wth Four Leg verter for Power Qulty Improvement Y.nthonmm 1.Tejsr 2 1PG Sholr, Deprtment
More informationVECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors
1. Defnton A vetor s n entt tht m represent phsl quntt tht hs mgntude nd dreton s opposed to slr tht ls dreton.. Vetor Representton A vetor n e represented grphll n rrow. The length of the rrow s the mgntude
More informationCONTINUE ON LEADS PLACEMENT
Hert Letrure ECG leds, ECE4610, Z. Moussv CONTINUE ON LEADS PLACEMENT A I L LA I II III 0 II F III Three ddtonl leds re unpolr eletrodes euse they onsst of the potentl pperng on one eletrode tken th respet
More information8 THREE PHASE A.C. CIRCUITS
8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),
More informationAbhilasha Classes Class- XII Date: SOLUTION (Chap - 9,10,12) MM 50 Mob no
hlsh Clsses Clss- XII Dte: 0- - SOLUTION Chp - 9,0, MM 50 Mo no-996 If nd re poston vets of nd B respetvel, fnd the poston vet of pont C n B produed suh tht C B vet r C B = where = hs length nd dreton
More informationObject Oriented Backward/Forward Algorithm for Unbalanced and Harmonic Polluted Distribution Systems
Oet Orented Bkwrd/Forwrd Algorthm for Unlned nd Hrmon Polluted Dstruton ystems Bogdn omogă, Mre Chndrş Power ystems Deprtment ehnl Unversty of Clu-po Clu-po, omân ogdn.tomog@eps.utlu.ro mre.hndrs@eps.utlu.ro
More informationElectrical Circuits II (ECE233b)
Eletril Ciruits (ECE2) Polyhse Ciruits Anestis Dounis The Uniersity of Western Ontrio Fulty of Engineering Siene ThreePhse Ciruits Blned three hse iruit: ontins three oltge soures tht re equl in mgnitude
More informationTrigonometry. Trigonometry. Solutions. Curriculum Ready ACMMG: 223, 224, 245.
Trgonometry Trgonometry Solutons Currulum Redy CMMG:, 4, 4 www.mthlets.om Trgonometry Solutons Bss Pge questons. Identfy f the followng trngles re rght ngled or not. Trngles,, d, e re rght ngled ndted
More informationECEN 5807 Lecture 26
ECEN 5807 eture 6 HW 8 due v D Frdy, rh, 0 S eture 8 on Wed rh 0 wll be leture reorded n 0 he week of rh 5-9 Sprng brek, no le ody: Conlude pled-dt odelng of hghfrequeny ndutor dyn n pek urrentode ontrolled
More informationRank One Update And the Google Matrix by Al Bernstein Signal Science, LLC
Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses
More informationSolution of Tutorial 5 Drive dynamics & control
ELEC463 Unversty of New South Wles School of Electrcl Engneerng & elecommunctons ELEC463 Electrc Drve Systems Queston Motor Soluton of utorl 5 Drve dynmcs & control 500 rev/mn = 5.3 rd/s 750 rted 4.3 Nm
More informationPolyphase Systems. Objectives 23.1 INTRODUCTION
Polyphse Systems 23 Ojetives eome fmilir with the opertion of threephse genertor nd the mgnitude nd phse reltionship etween the three phse voltges. e le to lulte the voltges nd urrents for three-phse Y-onneted
More informationSIMULATION OF ELECTROMAGNETIC PHENOMENA DUE TO INDIRECT LIGHTNING STRIKES ON WIND TURBINES
SEF 2 - XV nterntonl Symposum on Eletromgnet Felds n Mehtrons, Eletrl nd Eletron Engneerng Funhl, Mder, Septemer -3, 2 SMULATON OF ELECTROMAGNETC PHENOMENA DUE TO NDRECT LGHTNNG STRKES ON WND TURBNES R.B.
More informationDistributed Generation Placement in Unbalanced Distribution System with Seasonal Load Variation
Distriuted Genertion Plement in Unlned Distriution System with Sesonl Lod Vrition Rvi Tej Bhimrsetti Dept. of Eletril Engg., NT Kurukshetr Kurukshetr, ndi svrtej@gmil.om Ashwni Kumr, Memer, EEE Dept. of
More informationPolyphase Systems 22.1 INTRODUCTION
22 Polyphse Systems 22.1 INTRODUTION n genertor designed to develop single sinusoidl voltge for eh rottion of the shft (rotor) is referred to s single-phse genertor. If the numer of oils on the rotor is
More informationEE 330/330L Energy Systems (Spring 2012) Laboratory 1 Three-Phase Loads
ee330_spring2012_l_01_3phse_lods.do 1/5 EE 330/330L Energy Systems (Spring 2012) Lortory 1 ThreePhse Lods Introdution/Bkground In this lortory, you will mesure nd study the voltges, urrents, impednes,
More informationLearning Enhancement Team
Lernng Enhnement Tem Worsheet: The Cross Produt These re the model nswers for the worsheet tht hs questons on the ross produt etween vetors. The Cross Produt study gude. z x y. Loong t mge, you n see tht
More informationModeling and Simulation of Permanent Magnet Brushless Motor Drives using Simulink
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 72102, DECEMBER 27-29, 2002 25 Modeling nd Simultion of Permnent Mgnet Brushless Motor Dries using Simulink Mukesh Kumr, Bhim Singh nd B.P.Singh Astrt: Permnent
More informationThree-phase Unity-Power-Factor VIENNA Rectifier with Unified Constantfrequency
0- Three-phse Unity-Power-Ftor VIENNA Retifier with Unified Constntfrequeny Integrtion Control Chongming Qio nd Keyue M. Smedley Deprtment of Eletril nd Computer Engineering Uniersity of Cliforni, Irine,
More informationINTRODUCTION TO COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS The numers -4, -3, -, -1, 0, 1,, 3, 4 represent the negtve nd postve rel numers termed ntegers. As one frst lerns n mddle school they cn e thought of s unt dstnce spced
More informationSymmetrical Components 1
Symmetril Components. Introdution These notes should e red together with Setion. of your text. When performing stedy-stte nlysis of high voltge trnsmission systems, we mke use of the per-phse equivlent
More information1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the
More informationOverview of Generic HVDC-MMC Control under Unbalanced Grid Conditions
Overvew of Gener HVDMM ontrol uner Unlne Gr ontons Anton Stepnov, Hn S, Jen Mhserejn, Aurélen Wtré AstrtThs pper presents summry of gener Moulr Multlevel onverter (MM) ontrol tehnues tht re pplle uner
More informationConcept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]
Conept of Atvty Equlbrum onstnt s thermodynm property of n equlbrum system. For heml reton t equlbrum; Conept of Atvty Thermodynm Equlbrum Constnts A + bb = C + dd d [C] [D] [A] [B] b Conentrton equlbrum
More informationIndustrial Electrical Engineering and Automation
CODEN:LUTEDX/(TEIE-719)/1-7/(7) Industril Electricl Engineering nd Automtion Estimtion of the Zero Sequence oltge on the D- side of Dy Trnsformer y Using One oltge Trnsformer on the D-side Frncesco Sull
More informationCS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014
S 224 DIGITAL LOGI & STATE MAHINE DESIGN SPRING 214 DUE : Mrh 27, 214 HOMEWORK III READ : Relte portions of hpters VII n VIII ASSIGNMENT : There re three questions. Solve ll homework n exm prolems s shown
More informationGeneralized Lorentz Transformation Allowing the Relative Velocity of Inertial Reference Systems Greater Than the Light Velocity
Generlzed Lorentz Trnsformton Allowng the Relte Veloty of Inertl Referene Systems Greter Thn the Lght Veloty Yu-Kun Zheng Memer of the Chnese Soety of Grtton nd Reltst Astrophyss Eml:yzheng@puorgn Astrt:
More informationDorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
orf, R.C., Wn,. T- Equivlent Networks The Eletril Engineering Hndook Ed. Rihrd C. orf Bo Rton: CRC Press LLC, 000 9 T P Equivlent Networks hen Wn University of Cliforni, vis Rihrd C. orf University of
More informationProject 6: Minigoals Towards Simplifying and Rewriting Expressions
MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy
More information1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.
1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the
More informationx=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions
Knemtc Quntte Lner Moton Phyc 101 Eyre Tme Intnt t Fundmentl Tme Interl Defned Poton x Fundmentl Dplcement Defned Aerge Velocty g Defned Aerge Accelerton g Defned Knemtc Quntte Scler: Mgntude Tme Intnt,
More informationSpacetime and the Quantum World Questions Fall 2010
Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1
More information4. UNBALANCED 3 FAULTS
4. UNBALANCED AULTS So fr: we hve tudied lned fult ut unlned fult re more ommon. Need: to nlye unlned ytem. Could: nlye three-wire ytem V n V n V n Mot ommon fult type = ingle-phe to ground i.e. write
More informationAbout phases dependence in a switched reluctance generator
Aout phses dependene n swthed relutne genertor Ds,. J., Coelho, A. nd Fleury, A. Deprtmento de Engenhr d Unversdde Ctól de Goás (UCG) Av. Unverstár, 144, Áre III, Bloo G, Sl 18, CEP 7465-1, Goân-GO, Brsl
More informationAn Adaptive Control Algorithm for Multiple-Input Multiple-Output Systems Using Neural Networks
An Adptve Control Algorthm for Multple-Input Multple-Output Systems Usng Neurl Networks JOSE NORIEGA Deprtmento de Investgón en Fís Unversdd de Sonor Rosles y Blvd. Lus Enns, Col. Centro, CP, Hllo, Son.
More information6 Random Errors in Chemical Analysis
6 Rndom Error n Cheml Anl 6A The ture of Rndom Error 6A- Rndom Error Soure? Fg. 6- Three-dmenonl plot howng olute error n Kjeldhl ntrogen determnton for four dfferent nlt. Anlt Pree Aurte 4 Tle 6- Pole
More informationCHENG Chun Chor Litwin The Hong Kong Institute of Education
PE-hing Mi terntionl onferene IV: novtion of Mthemtis Tehing nd Lerning through Lesson Study- onnetion etween ssessment nd Sujet Mtter HENG hun hor Litwin The Hong Kong stitute of Edution Report on using
More information4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
More informationDirect Current Circuits
Eler urren (hrges n Moon) Eler urren () The ne moun of hrge h psses hrough onduor per un me ny pon. urren s defned s: Dre urren rus = dq d Eler urren s mesured n oulom s per seond or mperes. ( = /s) n
More informationSynchronous Generator Modeling Using SimuLink
ynhronou Genertor Moelng Ung mun Outlne ner Moel Ung Eulent Crut ner Moel Ung Emee Mt Nonlner Moel Eulent Crut on Ax From we get m m l m t t m l r ) ( t t m l ) ( t t m l ) ( Eulent Crut on Ax From we
More informationSECTION A STUDENT MATERIAL. Part 1. What and Why.?
SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are
More informationEffects of polarization on the reflected wave
Lecture Notes. L Ros PPLIED OPTICS Effects of polrzton on the reflected wve Ref: The Feynmn Lectures on Physcs, Vol-I, Secton 33-6 Plne of ncdence Z Plne of nterfce Fg. 1 Y Y r 1 Glss r 1 Glss Fg. Reflecton
More informationCENTROID (AĞIRLIK MERKEZİ )
CENTOD (ĞLK MEKEZİ ) centrod s geometrcl concept rsng from prllel forces. Tus, onl prllel forces possess centrod. Centrod s tougt of s te pont were te wole wegt of pscl od or sstem of prtcles s lumped.
More informationProbability. b a b. a b 32.
Proility If n event n hppen in '' wys nd fil in '' wys, nd eh of these wys is eqully likely, then proility or the hne, or its hppening is, nd tht of its filing is eg, If in lottery there re prizes nd lnks,
More informationTELCOM 2130 Time Varying Queues. David Tipper Associate Professor Graduate Telecommunications and Networking Program University of Pittsburgh Slides 7
TELOM 3 Tme Vryng Queues Dvd Tpper Assote Professor Grdute Teleommuntons nd Networkng Progrm Unversty of Pttsburgh ldes 7 Tme Vryng Behvor Teletrff typlly hs lrge tme of dy vrtons Men number of lls per
More informationA SVC Based Control Algorithm for Load Balancing
Proeedings of the 7th WSEAS nterntionl onferene on Power Systems, eijing, hin, September 5-7, 7 A S sed ontrol Algorithm for od lning AHAD KAZEM kzemi@iust..ir A. MORAD KOOH Arshmordi@ee.iust..ir Ele.
More informationCS 491G Combinatorial Optimization Lecture Notes
CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,
More informationAppendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities
Appendi Prtil dishrges. Reltionship Between Mesured nd Atul Dishrge Quntities A dishrging smple my e simply represented y the euilent iruit in Figure. The pplied lternting oltge V is inresed until the
More informationa = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114
Lner Accelerton nd Freell Phyc 4 Eyre Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Mgntude Mgntude Unt Unt Drecton Drecton 4/3/07 Module 3-Phy4-Eyre 4/3/07 Module
More informationPrefix-Free Regular-Expression Matching
Prefix-Free Regulr-Expression Mthing Yo-Su Hn, Yjun Wng nd Derik Wood Deprtment of Computer Siene HKUST Prefix-Free Regulr-Expression Mthing p.1/15 Pttern Mthing Given pttern P nd text T, find ll sustrings
More informationDennis Bricker, 2001 Dept of Industrial Engineering The University of Iowa. MDP: Taxi page 1
Denns Brcker, 2001 Dept of Industrl Engneerng The Unversty of Iow MDP: Tx pge 1 A tx serves three djcent towns: A, B, nd C. Ech tme the tx dschrges pssenger, the drver must choose from three possble ctons:
More information22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:
22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)
More informationEstimation of Sequence Components using Magnitude Information
6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 47 Estimtion of Sequene Components using Mgnitude Informtion P.S. Ngendr ro nd Ssikirn Veknuru Deprtment of Eletril Engineering Indin Institute
More informationGEOMETRY OF THE CIRCLE TANGENTS & SECANTS
Geometry Of The ircle Tngents & Secnts GEOMETRY OF THE IRLE TNGENTS & SENTS www.mthletics.com.u Tngents TNGENTS nd N Secnts SENTS Tngents nd secnts re lines tht strt outside circle. Tngent touches the
More informationragsdale (zdr82) HW6 ditmire (58335) 1 the direction of the current in the figure. Using the lower circuit in the figure, we get
rgsdle (zdr8) HW6 dtmre (58335) Ths prnt-out should hve 5 questons Multple-choce questons my contnue on the next column or pge fnd ll choces efore nswerng 00 (prt of ) 00 ponts The currents re flowng n
More informationLecture 36. Finite Element Methods
CE 60: Numercl Methods Lecture 36 Fnte Element Methods Course Coordntor: Dr. Suresh A. Krth, Assocte Professor, Deprtment of Cvl Engneerng, IIT Guwht. In the lst clss, we dscussed on the ppromte methods
More informationKinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!
Knemtc Quntte Lner Phyc 11 Eyre Tme Intnt t Fundmentl Tme Interl t Dened Poton Fundmentl Dplcement Dened Aerge g Dened Aerge Accelerton g Dened Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed
More informationComparing the Pre-image and Image of a Dilation
hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity
More informationIntermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths
Intermedite Mth Cirles Wednesdy 17 Otoer 01 Geometry II: Side Lengths Lst week we disussed vrious ngle properties. As we progressed through the evening, we proved mny results. This week, we will look t
More informationHumidity Profiling with a VHF Wind Profiler and GPS Measurements
Humdty Proflng wth VHF Wnd Profler nd GPS esurements Vldslv Klus, Joël Vn Belen*, nd Yves Pontn* ( ) entre Ntonl de Reherhes étéorologues (NR), étéo Frne, Toulouse, Frne (*) Lortore de étéorologe Physue
More informationOn Adaptive Control of Simulated Moving Bed Plants. Plants Using Comsol s Simulink Interface. Speaker: Marco Fütterer
daptve Smulated Movng ed Plants Usng Comsol s Smulnk Interfae Speaker: Maro Fütterer Insttut für utomatserungstehnk Otto-von-Guerke Unverstät Unverstätsplatz, D-39106 Magdeburg Germany e-mal: maro.fuetterer@ovgu.de
More informationNovel Modulation Schemes Minimizing the Switching Losses of Sparse Matrix Converters
Novel Modlton Shemes Mnmzng the Swthng Losses of Sprse Mtrx Converters Johnn W. Kolr nd Frnk Shfmester ETH Zrh, Power Eletron Systems Lortory ETH Zentrm / ETL H, Physkstr. 3, CH-9 Zrh/SWTZERLAND Tel.:
More informationLecture 6. CMOS Static & Dynamic Logic Gates. Static CMOS Circuit. PMOS Transistors in Series/Parallel Connection
NMOS Trnsistors in Series/Prllel onnetion Leture 6 MOS Stti & ynmi Logi Gtes Trnsistors n e thought s swith ontrolled y its gte signl NMOS swith loses when swith ontrol input is high Peter heung eprtment
More informationKalman-Filter Based Recursive Regression for Three- Phase Line Parameter Estimation using Synchrophasor Measurements
Klmn-Filter Bsed Reursive Regression for Three- Phse Line Prmeter Estimtion using Synhrophsor Mesurements Chetn Mishr, StMIEEE Virgilio A. Centeno, SMIEEE Brdley Deprtment of Eletril nd Computer Engineering,
More informationProving the Pythagorean Theorem
Proving the Pythgoren Theorem W. Bline Dowler June 30, 2010 Astrt Most people re fmilir with the formul 2 + 2 = 2. However, in most ses, this ws presented in lssroom s n solute with no ttempt t proof or
More informationHysteresis Band Controller Based Vector Control Of PMSG For Wind Power
ISSN (Onlne) : 2319-8753 ISSN (Prnt) : 2347-671 Interntonl Journl of Innovtve Reserh n Sene, Engneerng nd Tehnology Volume 3, Spel Issue 3, Mrh 214 214 Interntonl Conferene on Innovtons n Engneerng nd
More informationChapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
More informationName: SID: Discussion Session:
Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether
More informationModule 3: Element Properties Lecture 5: Solid Elements
Modue : Eement Propertes eture 5: Sod Eements There re two s fmes of three-dmenson eements smr to two-dmenson se. Etenson of trngur eements w produe tetrhedrons n three dmensons. Smr retngur preeppeds
More informationDesigning Information Devices and Systems I Anant Sahai, Ali Niknejad. This homework is due October 19, 2015, at Noon.
EECS 16A Designing Informtion Devices nd Systems I Fll 2015 Annt Shi, Ali Niknejd Homework 7 This homework is due Octoer 19, 2015, t Noon. 1. Circuits with cpcitors nd resistors () Find the voltges cross
More informationPYTHAGORAS THEOREM WHAT S IN CHAPTER 1? IN THIS CHAPTER YOU WILL:
PYTHAGORAS THEOREM 1 WHAT S IN CHAPTER 1? 1 01 Squres, squre roots nd surds 1 02 Pythgors theorem 1 03 Finding the hypotenuse 1 04 Finding shorter side 1 05 Mixed prolems 1 06 Testing for right-ngled tringles
More informationCS311 Computational Structures Regular Languages and Regular Grammars. Lecture 6
CS311 Computtionl Strutures Regulr Lnguges nd Regulr Grmmrs Leture 6 1 Wht we know so fr: RLs re losed under produt, union nd * Every RL n e written s RE, nd every RE represents RL Every RL n e reognized
More informationGeometry of the Circle - Chords and Angles. Geometry of the Circle. Chord and Angles. Curriculum Ready ACMMG: 272.
Geometry of the irle - hords nd ngles Geometry of the irle hord nd ngles urriulum Redy MMG: 272 www.mthletis.om hords nd ngles HRS N NGLES The irle is si shpe nd so it n e found lmost nywhere. This setion
More informationAVL Trees. D Oisín Kidney. August 2, 2018
AVL Trees D Oisín Kidne August 2, 2018 Astrt This is verified implementtion of AVL trees in Agd, tking ides primril from Conor MBride s pper How to Keep Your Neighours in Order [2] nd the Agd stndrd lirr
More informationLecture 6: Coding theory
Leture 6: Coing theory Biology 429 Crl Bergstrom Ferury 4, 2008 Soures: This leture loosely follows Cover n Thoms Chpter 5 n Yeung Chpter 3. As usul, some of the text n equtions re tken iretly from those
More informationNovel Voltage Control of 18 Level Multilevel Inverter
Noel Voltge Control of 18 Leel Multileel Inerter Sd Mekhilef Dept. of Eletril Engineering Uniersity of Mly Kul Lumpur 50603, Mlysi sd@um.ed.my Mohmd N. Adul Kdir Dept. of Eletril Engineering Uniersity
More informationPhysics for Scientists and Engineers I
Phscs for Scentsts nd Engneers I PHY 48, Secton 4 Dr. Betr Roldán Cuen Unverst of Centrl Flord, Phscs Deprtment, Orlndo, FL Chpter - Introducton I. Generl II. Interntonl Sstem of Unts III. Converson of
More informationCHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation:
HPT 3 xercses 3. The emtter current s gen by the Shockley equaton: S exp VT For operaton wth, we hae exp >> S >>, and we can wrte VT S exp VT Solng for, we hae 3. 0 6ln 78.4 mv 0 0.784 5 4.86 V VT ln 4
More informationThe Schur-Cohn Algorithm
Modelng, Estmton nd Otml Flterng n Sgnl Processng Mohmed Njm Coyrght 8, ISTE Ltd. Aendx F The Schur-Cohn Algorthm In ths endx, our m s to resent the Schur-Cohn lgorthm [] whch s often used s crteron for
More informationElectrical Engineering Department Network Lab.
Electrcal Engneerng Department Network Lab. Objecte: - Experment on -port Network: Negate Impedance Conerter To fnd the frequency response of a smple Negate Impedance Conerter Theory: Negate Impedance
More informationPhysics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions:
Physcs 121 Smple Common Exm 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7 Nme (Prnt): 4 Dgt ID: Secton: Instructons: Answer ll 27 multple choce questons. You my need to do some clculton. Answer ech queston on the
More informationSECONDAR Y - MRIEĦEL HALF-YEARLY EXAMINATIONS 2017/2018
Yer 9 PHYSICAL EDUCATION (OPTION) TIME: 1h 30mn SECONDAR Y - MRIEĦEL HALF-YEARLY EXAMINATIONS 2017/2018 Nme: Clss: Seton A Seton B Seton C Seton D TOTAL MARK 16 20 32 12 THEORY PAPER (80) 40% THEORY PAPER
More informationDamping of Power System Oscillations using Unified Power Flow Controller (UPFC)
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 73, DECEMBER 7-9, 47 of Power System Osilltions using Unified Power Flow Controller (UPFC) Neelim Tmey M. L. Kothri Astrt--This pper presents systemti pproh for
More informationCAMBRIDGE UNIVERSITY ENGINEERING DEPARTMENT. PART IA (First Year) Paper 4 : Mathematical Methods
Engneerng Prt I 009-0, Pper 4, Mthemtl Methods, Fst Course, J.B.Young CMBRIDGE UNIVERSITY ENGINEERING DEPRTMENT PRT I (Frst Yer) 009-00 Pper 4 : Mthemtl Methods Leture ourse : Fst Mths Course, Letures
More informationAdaptive Control of Shunt Active Power Filter Using Interval Type-2 Fuzzy Logic Controller
Proeengs of the 4 th Interntonl Mle Est Power Systems onferene (MEPO ), ro Unersty, Egypt, Deemer 9-2, 2, Pper ID 59. Apte ontrol of Shnt Ate Power Flter Usng Interl Type-2 Fzzy og ontroller G. M. Srhn
More informationNON-DETERMINISTIC FSA
Tw o types of non-determinism: NON-DETERMINISTIC FS () Multiple strt-sttes; strt-sttes S Q. The lnguge L(M) ={x:x tkes M from some strt-stte to some finl-stte nd ll of x is proessed}. The string x = is
More informationPower System Stability Enhancement Under Three Phase Fault with FACTS Devices TCSC, STATCOM and UPFC
S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, 066073 Power Syste Stlty Enhneent Under Three Phse Fult wth FTS Dees TS, STTOM nd
More informationThe Trapezoidal Rule
_.qd // : PM Pge 9 SECTION. Numericl Integrtion 9 f Section. The re of the region cn e pproimted using four trpezoids. Figure. = f( ) f( ) n The re of the first trpezoid is f f n. Figure. = Numericl Integrtion
More informationDigital Electronics Part I Combinational and Sequential Logic
9//24 Dgtl Eletrons Prt I Comntonl nd Sequentl Log Dr I J Wssell Introduton 9//24 Ams To fmlrse students wth Comntonl log ruts Sequentl log ruts How dgtl log gtes re ult usng trnsstors Desgn nd uld of
More information4. Introduction and Chapter Objectives
Rel Anlog Crcuts 1 Chpter 4: Systems nd Network Theorems 4. Introducton nd Chpter Ojectes In preous chpters, numer of pproches he een presented for nlyzng electrcl crcuts. In these nlyss pproches, we he
More informationChapter 4 State-Space Planning
Leture slides for Automted Plnning: Theory nd Prtie Chpter 4 Stte-Spe Plnning Dn S. Nu CMSC 722, AI Plnning University of Mrylnd, Spring 2008 1 Motivtion Nerly ll plnning proedures re serh proedures Different
More informationEducational Modeling for Fault Analysis of Power Systems with STATCOM Controllers using Simulink
University of New Orlens SholrWorks@UNO University of New Orlens Theses nd Disserttions Disserttions nd Theses Fll 12-18-2014 Edutionl Modeling for Fult nlysis of Power Systems with STTOM ontrollers using
More informationTHE ANALYSIS AND CALCULATION OF ELECTROMAGNETIC FIELD AROUND OVERHEAD POWER LINE HongWang Yang
5th Interntionl Conferene on Advned Mterils nd Computer Siene (ICAMCS 6) THE ANALYSIS AN CALCULATION OF ELECTROMAGNETIC FIEL AROUN OVERHEA POWER LINE HongWng Yng eprtment of eletril engineering, North
More information(a) A partition P of [a, b] is a finite subset of [a, b] containing a and b. If Q is another partition and P Q, then Q is a refinement of P.
Chpter 7: The Riemnn Integrl When the derivtive is introdued, it is not hrd to see tht the it of the differene quotient should be equl to the slope of the tngent line, or when the horizontl xis is time
More informationMATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER
MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER I One M Queston Fnd the unt veto n the deton of Let ˆ ˆ 9 Let & If Ae the vetos & equl? But vetos e not equl sne the oespondng omponents e dstnt e detons
More information