GENERATING REFERENCE CURRENT AND VOLTAGE CONTROL OF STATIC COMPENSATOR DURING VOLTAGE SAGS
|
|
- Lilian Riley
- 5 years ago
- Views:
Transcription
1 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 nd tehnology, Trhy-60009,Ind. nsr863@yhoo.om Astrt Voltge sgs nd nterruptons re generlly used y the fults suh s short ruts, energzton of the hey lods, strtng of the lrge motors,sngle lne to ground fults nd et. These sgs produed y oe uses wll nterrupt the system nd t hs to e mtgted mmedtely. Ths pper presents omplete ontrol sheme ntended for stt ompenstors opertng under these norml ondtons.stt synhronous ompenstors he een rodly employed for the proson of eletrl networ seres, whh nlude oltge regulton, networ lne, nd stlty mproement. Here the ontrol sheme noel rete urrent referene genertor loop. The rete power support for the system s the mn rter for the system stlzton.ths n e heed y shunt onnetng stt ompenstor n to system. The urrent referene genertor hs s mn feture the pty to supply the reured rete urrent een when the oltge drops n mpltude durng the oltge sg. Thus, sfe system operton s esly gurnteed y fxng the lmt reured urrent to the mxmum rted urrent.. Keywords Rete ompenston,stt ompenstor, Rete referene urrent genertor, Voltge sg. I.INTRODUCTION Modern power system omprses of omplex networs, where mny genertng sttons nd lod entres re nteronneted through long power trnsmsson nd dstruton networs [6]. Utlty dstruton networs, rtl ommerl opertons nd senste ndustrl lods ll suffer from rous types of outges nd nterruptons whh n led to sgnfnt fnnl loss, loss of produton, dle wor fores et. Tody due to the hngng trends nd restruturng of power systems, the onsumers re loong forwrd to the ulty nd rellty of power supply t the lod entres. A power ulty prolem s n ourrene mnfested s nonstndrd oltge, urrent or freueny tht results n flure or ms-operton of end use eupments. The mn uses of poor power ulty re hrmon urrents, poor power ftor, supply-oltge rtons, et. Rpd growth of nonlner lods leds to lots of power ulty prolems suh s hrmons, unlne operton nd exesse soure-end neutrl urrent n three-phse supplyng networs. Power flow s funton of trnsmsson lne mpedne, the mgntude of Mohmed Bdh Y Assote professor Dept. of eletrl nd eletrons engneerng J.J ollege of engneerng nd tehnology, Trhy-60009,Ind. sheee@gml.om the sendng nd reeng end oltges, nd the phse ngle etween the oltges. By ontrollng one or omnton of the power flow rguments, t s possle to ontrol the te, s well s the rete power flow n the trnsmsson lne. In the pst, power systems were smple nd desgned to e selfsuffent. Ate power exhnge of nery power systems ws rre s trnsmsson systems nnot e ontrolled fst enough to hndle dynm hnges n the system nd, therefore, dynm prolems were usully soled y hng generous stlty mrgns so tht the system ould reoer from ntpted opertng ontngenes. The STATCOM hs the lty to nrese/derese the termnl oltge mgntude nd, onseuently, to nrese/derese power flows n the trnsmsson lne. The renewle energy s the new energy growng soures whh s loted ner the lod entres.for the generton of the power wth the renewle energy the nllry seres he to e proded. The mn seres re the rete power reurement, oltge stlty. To mproe the oltge stlty rete power support s needed. For ll renewle energy the rete power ontrol s low. As the nstllton of the dstruted energy soures,there s need of ontrol the rete power. A STATCOM s shunt-onneted rete power ompenston dee tht s ple of genertng nd/or sorng rete power nd n whh the output n e red to ontrol the spef prmeters of n eletr power system. A STATCOM n supply the reured rete power under rous opertng ondtons, to ontrol the networ oltge tely nd thus, mproe the stedy stte stlty of the networ. It n e operted oer ts full output urrent rnge een t ery low oltge leels nd the mxmum r generton or sorpton hnges lnerly wth the utlty or system oltge. The norml opertng ondton of the STATCOM ws studed n [] [5].The operton nd ntegrton of the STATCOM n we networ ws nlyzed n [1].The oltge flututon wll led to the system nterrupton lso the deton n the oltge wll redue performne of the power eletron dees onneted to the networ. The ojete of the pper s to mtgte the ourrng of the oltge sg y gng the rete power
2 support to the system wth the help of STATCOM. The rete urrent referene genertor n generte the rete urrent when the system oltge redued.. II. STATIC COMPENSATOR Ths pper fouses the rete power support under the oltge sgs. The Stt ompenstor hs to fulfl rete power ontrol,rete referene urrent reurement durng oltge sgs. When there s fult, t hs to mtgte the fult y genertng the rete urrent. Fg. 1. STATCOM onneted to the nduton mhne nd the grd through trnsformer. The system under onsderton s sethed n Fg. 1 nd onssts of n Induton genertor dretly onneted to the grd through trnsformer, nd STATCOM onneted t the termnls of the nduton mhne. A.Grd Code Reurements The generton of power should remn onneted een n fulty grd ondtons nd lso to support the grd oltge. It should e onneted een n the short durton when the oltge sg re deep. It hs to supply the rete power durng oltge sg. Fgure shows the ehor of the Stt ompenstor.when there s oltge dp t the grd the rete power njeton wll nrese the root men sure lue of the system oltge durng the oltge sg. The nputs for the ontroller re the mesured phse oltges t the PCC, the urrents flowng nd the d-ln oltge d. Voltge nd urrent re trnsformed nto SRF lues. Seuene extrtor extrts the Voltges nto the symmetr omponents α nd β. The symmetr seuene extrtor s ey spet to hrterze the grd oltge. Mny seuene extrtors n e found n the lterture to extrt oltge sg nformton..the DC ln oltge s gng the te power support. The oltge sg ws deteted y the oltge support lo. Ths n e done y omputng the oltge rms n eh phse. When rms lues drop elow predefned threshold, the oltge support ontrol s tted. The oltge support lo dedes whh strtegy should e mplemented ordng to grd odes nd system lmttons. Then the oe nformton re gen to the referene urrent genertor. Ths referene urrent genertor genertes the referene urrent α -, β. Fnlly the referene urrents re ompred wth the urrents n the urrent loop nd then the duty yle re generted y the pulse wdth modultor to trgger the Stt ompenstor. The mn ojete of ths wor s to present method to rde through oltge sgs nd support the grd oltge. In three phse lned oltge sgs. the ontrol strtegy should e to rse the oltge n ll phses B. Chrtersts of Voltge sg A oltge sg s n norml ondton n the grd oltges,hrterzed y short-tme reduton n one or rous phses[8]. The uses of oltge sgs re Fg..Control dgrm of Stt Compenstor under fult ondton
3 mnly phse-to-ground short rut, phse-to-phse (to ground) short rut, nd the strt-up of lrge motor.the most wdely epted lssfton of oltge sgs s presented n [9].Poste seuene,negte seuene nd zero seuene oltges re three seuenes.of those zero seuenes re not onsdered Usng the lres trnsformton the seuenes omponents re extrted.the euton re follows The oe phse oltges re trnsferred to poste nd negte seuenes of β nd α.. (5) (6) The referene urrent loop s responsle for genertng referene urrent, expressed n (7) nd (8), ordng to the set ponts V d nd I s follows α = αp + α (7) β = βp + β (8) where αp, βp, α, β re the te nd rete urrent referenes, respetely. (1) () (3) (4) C. Voltge unlne ftor The rto of the poste seuene oltge to the negte seuene oltge t the pont of ouplng s nown s the unlned ftor. n (9) When the n lue s zero then the system oltge s lned otherwse the system s unlned.aordng to the lue of the Stt ompenstor ontrol rut re depended. D. Ate nd Rete referene urrent genertors The urrent suppled to the networ durng unlned oltge sgs n e hghly dstorted y hrmons. Seuene detetor, together wth the followng te urrent referenes [7], the hrmons of the urrent re strongly redued: p 3 p (10) p 3 p (11) Also the Rete referene urrent re (1 ) 1 (1 ) 1 Q Q (1) (13) Where s the rete element. re the onstnts for tht element Fg3.Smuln of Rete referene urrent genertor usng MATLAB
4 III.GENERATING REACTIVE REFERENCE CURRENT From the lres trnsformton the referene urrent s otned whh n e wrtten s I 3 n 1 os n mn 1 Q n 1 V (14) When the lue of re ether zero or 1.The oe euton (14) wll redued to I (15) V Q 3 Q s rete power, njeton of the rete urrent n ether poste or negte seuenes. When the lue of s 1,t n e njeted through poste seuene nd when s 0 t n e delered through negte seuene. Clerly the lue of should regulted etween 0 nd 1 By nsertng the euton (1) nd (13) n oe euton numer (14).The rete referene urrent euton s otned s n n ( 1 ) (1 )os mn (1 )os n (1 ) ( 1 ) mn n (1 ) I V I V (16) (17) Poste- nd negte seuene omponents of the PCC oltge re dretly otned t the output of the oltge seuene detetor, s shown n Fg..The two set pont I nd the ontrol gn should e hosen n order to fulfll spef ontrol ojete. The urrent set pont ontrol the rete power delered to the system,so the referene of the urrent set pont s to regulte the poste seuene oltge. When the oltge leel t the pont of ommon ouplng dereses, wll njet the desred oltge to the system. The negte seuene lue dereses y deresng the lue. Therefore the oordnted ontrol of poste nd negte seuene s employed. TABLE I PARAMETERS OF THE SYSTEM AND STATIC COMPENSATOR Symol Vlues V g Grd oltge 110 K f g Freueny 50 Hz R s Lne resstne 10 Ω L s Indutne 8 10 H V p, d Proportonl 0.3V V, d V p, + Controller Of V d Integrl ontroller Of V d Proportonl gn Of V + loop V, + Integrl gn Of V + V p, - loop Proportonl gn Of V - loop V,, - Integrl gn Of V - loop 15Vs 0.1V 15A/Vs 0.1V 0.A/Vs Phse oltges t the PCC for the seleted oltge sgs re shown n Fgs. 4 nd 5. Before the fult, the oltge n eh phse s round 415 V. The oltge leel s then onerted nto the per unt lue. At tme t = 0.4 s, the oltge sg ours n the Fg 4. Instntly, the oltge support strtegy s tted. Then t hnges from For ths tme perod the prmeter s set n order to mtgte the oltge sg.the flexle propertes of the proposed oltge support ontrol sheme. The proposed STATCOM ws tested wth oltge sg presented n [10].Also the oltge sg for the dfferent tme durton ws smulted Fg. 5 hs lrge stedy-stte mlne (see the tme nterl from 0.3 to 0.6 s) nd rle oltge profle durng the trnsent stte. For ths reson, the hosen oltge sg s good nddte to elute the performne of the proposed ontrol soluton n derse strngent networ ondtons. IV. EXPERIMENTAL RESULTS The expermentl ldton whh shows the theoretl explnton of ths pper. The smulton of ontrol rut of the rete referene frme s shown n Fg 3. Tle I lsts the ontrol prmeters of the system nd the Stt ompenstor tht fulfll ths reurement. The freueny of the system s ssumed to e 50Hz.The oltge t the PCC hs fst enough trnsent response nd error n stedy stte s redued sne the oltge seuene detetor hs enough tme to e updted. Tme(se) ()
5 Tme n seonds () () () Fg.5. Voltge t the grd when the sg ours durng tme perod ( )seonds. () Grd oltge when Sttom ws nte ()Compensted Grd oltge () Injeton of rete urrent. (d) Fg.4. Voltge t the grd when the sg ours durng tme perod ( )seonds. () Grd oltge when Sttom ws nte () Swthng perod of ontrol ruts ()Compensted Grd oltge (d) Injeton of rete urrent. () The swthng tme of the Stt ompenstor ws shown n fg 4().When the oltge sg ours t ny tme,oltge support detetor n Fg dedues the sg leel nd lso the durton of the sg. Durng tht tme nterl the njeton of the rete referene ws shown n Fgs 4(d) nd 5(). The sg our n the system s 0% (the oltge leel redues to 0.8pu) ws shown n Fg 4() nd Fg 5() shows tht the 30% of the system oltge dp lso ompenston of the oe mentoned oltge sg durton ws shown n Fg 4() nd Fg 5().The dfferent type of oltge sg wth the rous tme durton of the sg ws smulted n the MATLAB. Ths spefton defnes the onentonl sheme of rete power njeton y prodng the mnmum rete urrent tht must e njeted durng oltge sg s funton of the oltge t the PCC. The results shows tht mtgton of oltge sg y the njeton of the urrent through the Stt ompenstor ws effete. () V. CONCLUSION Results from rtl Sg nd gener shorter fult ndte the generl ppllty of the tehnue to dpt the STATCOM ontrol to the needs of the system durng reoery fter ny nd of ontngenes. Ths oltge ontrol sheme whh hs the hs the dntges of 1) oltge support durng sgs ) oltge regulton. Two dfferent senros he een expermentlly tested to llustrte the results of the proposed oltge support ontrol wth dfferent sg leel n the
6 rous tme durton. Seleted expermentl tests onfrm the theoretl fetures of ths ontrol lgorthm. To erfy nd proe the lty nd effeteness of the proposed oltge ontrol loop n stedy-stte nd dynm operton modes, smulton model ws reted.. The rete power support wth the help of the STATCOM ws smulted under dfferent oltge nd tme durton. Smulton results show the effeteness of STATCOM n te flterng nd flututons of oltge under rndomly ryng sg n e effetely redued.thus the sg ourred n the system ws mtgted lso AC oltge regulton nd power ftor of the trnsmsson lne lso mproed. REFERENCES [1] C. Hn, A. Hung, M. Brn, S. Bhtthry, W. Ltzenerger, L. Anderson, A. Johnson, nd A. A. Edrs, STATCOM mpt study on the ntegrton of lrge wnd frm nto we loop power system, IEEETrns. Energy Coners., ol. 3, no. 1, pp. 6 33, Mr [] M. Molns, J. A. Suul, nd T. Undelnd, Low oltge rde through of wnd frms wth ge genertors: STATCOM ersus SVC, IEEE Trns. Power Eletron., ol. 3, no. 3, pp , My 008. [3] K. L, J. Lu, Z. Wng, nd B. We, Strteges nd opertng pont optmzton of STATCOM ontrol for oltge unlne mtgton n three-phse three-wre systems, IEEE Trns. Power Del., ol., no. 1, pp , Jn [4] T. Lee, S. Hu, nd Y. Chn, D-STATCOM wth posteseuene dmttne nd negte-seuene ondutne to mtgte oltge flututons n hgh-leel penetrton of dstruted generton systems, IEEE Trns. Ind. Eletron., ol. 60, no. 4, pp , Apr. 013 [5] A. Yzdn, H. Sephnd, M. L. Crow, nd M. Ferdows, Fult deteton nd mtgton n multleel onerter STATCOMs, IEEE Trns. Ind. Eletron., ol. 58, no. 4, pp , Apr [6] J. M. Crrso, L. G. Frnuelo, J. T. Blsewz, E. Glán, R. C. Gusdo, M. A. Prts, J. I. León, nd N. Moreno- Alfonso, Power eletron systems for the grd ntegrton of renewle energy soures: A surey, IEEE Trns. Ind. Eletron., ol. 53, no. 4, pp , Jun. 006 [7] P. Rodrıute;guez, A. Tmus, R. Teodoresu, M. Lserre, nd F. Bljerg, Independent PQ ontrol for dstruted power generton systems under grd fults, n Pro. IEEE IECON, 006, pp [8] IEEE Reommended Prte for Montorng Eletr Power Qulty, IEEE Std , 1995 [9] M. Bollen, Chrterston of oltge sgs experened y three phse djustle-speed dres, IEEE Trns. Power Del., ol. 1, no. 4,pp , Ot [10] S. Cunde, R. Neumnn, M. Bollen, Z. Koolns, J. Vulet, A. Krole, S. Djo, K. n Reusel, nd K. Stomn, Immunty gnst oltge dps Mn reommendtons to steholders of the CIGRE/CIRED/UIE jont worng group C4.110, Int. J. Emerg. S., ol. 1, no. 4, pp , De. 011
" = #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 informationA Control Strategy for Unified Power Quality Conditioner
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:
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationCONTROL AND PROTECTION OF DISTRIBUTION NETWORKS WITH DISTRIBUTED GENERATORS
ASTRACT ELMARKA, SMAL MOHAMED. Control nd Proteton of Dstruton Networs wth Dstruted Genertors, under the dreton of Dr. Mesut rn. The onneton of dstruted genertors to dstruton networs gretly nfluenes 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 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 informationReducing the Computational Effort of Stochastic Multi-Period DC Optimal Power Flow with Storage
Redung the Computtonl Effort of Stohst Mult-Perod DC Optml Power Flow wth Storge Olver Mégel Görn Andersson Power Systems Lbortory ETH Zürh Zürh, Swtzerlnd {megel, ndersson}@eeh.ee.ethz.h Johnn L. Mtheu
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 informationPartially Observable Systems. 1 Partially Observable Markov Decision Process (POMDP) Formalism
CS294-40 Lernng for Rootcs nd Control Lecture 10-9/30/2008 Lecturer: Peter Aeel Prtlly Oservle Systems Scre: Dvd Nchum Lecture outlne POMDP formlsm Pont-sed vlue terton Glol methods: polytree, enumerton,
More information1/4/13. Outline. Markov Models. Frequency & profile model. A DNA profile (matrix) Markov chain model. Markov chains
/4/3 I529: Mhne Lernng n onformts (Sprng 23 Mrkov Models Yuzhen Ye Shool of Informts nd omputng Indn Unversty, loomngton Sprng 23 Outlne Smple model (frequeny & profle revew Mrkov hn pg slnd queston Model
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 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 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 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 informationController Design for Networked Control Systems in Multiple-packet Transmission with Random Delays
Appled Mehans and Materals Onlne: 03-0- ISSN: 66-748, Vols. 78-80, pp 60-604 do:0.408/www.sentf.net/amm.78-80.60 03 rans eh Publatons, Swtzerland H Controller Desgn for Networed Control Systems n Multple-paet
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 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 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 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 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 informationGEOM/GEOM[A]/1/ QUEUE WITH LATE ARRIVAL SYSTEM WITH DELAYED ACCESS AND DELAYED MULTIPLE WORKING VACATIONS
Yugosl Journl of Opertons Reserch 24 (24) Numer 27-43 DOI:.2298/YJOR26274C GEOM/GEOM[A]// QUEUE WITH LATE ARRIVAL SYSTEM WITH DELAYED ACCESS AND DELAYED MULTIPLE WORKING VACATIONS Jng CHENG School of Mthemtcs
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 informationProblem Set 4 Solutions
4 Eoom Altos of Gme Theory TA: Youg wg /08/0 - Ato se: A A { B, } S Prolem Set 4 Solutos - Tye Se: T { α }, T { β, β} Se Plyer hs o rte formto, we model ths so tht her tye tke oly oe lue Plyer kows tht
More informationNEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE
NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE V.S. Gordeev, G.A. Myskov Russin Federl Nuler Center All-Russi Sientifi Reserh Institute of Experimentl Physis (RFNC-VNIIEF)
More informationBrander and Lewis (1986) Link the relationship between financial and product sides of a firm.
Brander and Lews (1986) Lnk the relatonshp between fnanal and produt sdes of a frm. The way a frm fnanes ts nvestment: (1) Debt: Borrowng from banks, n bond market, et. Debt holders have prorty over a
More informationMagnetically Coupled Coil
Mgnetilly Coupled Ciruits Overview Mutul Indutne Energy in Coupled Coils Liner Trnsformers Idel Trnsformers Portlnd Stte University ECE 22 Mgnetilly Coupled Ciruits Ver..3 Mgnetilly Coupled Coil i v L
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 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 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 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 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 informationRenewable Energy 50 (2013) 378e386. Contents lists available at SciVerse ScienceDirect. Renewable Energy
Renewle Energy 5 (13) 378e386 Contents lists ville t SiVerse SieneDiret Renewle Energy journl homepge: www.elsevier.om/lote/renene Control of wind energy onversion system equipped y DFIG for tive power
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 informationFEEDBACK AMPLIFIERS. v i or v s v 0
FEEDBCK MPLIFIERS Feedback n mplers FEEDBCK IS THE PROCESS OF FEEDING FRCTION OF OUTPUT ENERGY (VOLTGE OR CURRENT) BCK TO THE INPUT CIRCUIT. THE CIRCUIT EMPLOYED FOR THIS PURPOSE IS CLLED FEEDBCK NETWORK.
More informationME 501A Seminar in Engineering Analysis Page 1
More oundr-vlue Prolems nd genvlue Prolems n Os ovemer 9, 7 More oundr-vlue Prolems nd genvlue Prolems n Os Lrr retto Menl ngneerng 5 Semnr n ngneerng nlss ovemer 9, 7 Outlne Revew oundr-vlue prolems Soot
More informationAdaptive Remedial Action Scheme based on Transient Energy Analysis
Adptve Remedl Aton Sheme sed on Trnsent Energy Anlyss Y Zhng nd Kevn Tomsov, Senor emer, IEEE Astrt-- Remedl ton shemes re desgned to vod wde spred outges ter severe ontngeny. In prte, these shemes re
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 informationAl-Zangana Iraqi Journal of Science, 2016, Vol. 57, No.2A, pp:
Results n Projetve Geometry PG( r,), r, Emd Bkr Al-Zngn* Deprtment of Mthemts, College of Sene, Al-Mustnsryh Unversty, Bghdd, Ir Abstrt In projetve plne over fnte feld F, on s the unue omplete ( ) r nd
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 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 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 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 informationPower System Representation and Equations. A one-line diagram of a simple power system
Power ystem epresenttion nd Equtions Lod B Lod A Bus Bus A oneline digrm of simple power system Oil or liquid iruit reker otting mhine Twowinding power trnsformer Wye onnetion, neutrl ground PerPhse, Per
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 informationLec 3: Power System Components
Lec 3: Power System Components Dr. Mlbik Bsu 8/0/2009 Lesson pln 3 nd L.O. Sequence nlysis exmple ( detil fult nlysis next sem) Trnsformer model recp, tp chnge nd phse chnge, 3-phse Modeling of Synchronous
More informationLecture Notes No. 10
2.6 System Identifition, Estimtion, nd Lerning Leture otes o. Mrh 3, 26 6 Model Struture of Liner ime Invrint Systems 6. Model Struture In representing dynmil system, the first step is to find n pproprite
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 informationEffectiveness and Efficiency Analysis of Parallel Flow and Counter Flow Heat Exchangers
Interntonl Journl of Applton or Innovton n Engneerng & Mngement (IJAIEM) Web Ste: www.jem.org Eml: edtor@jem.org Effetveness nd Effeny Anlyss of Prllel Flow nd Counter Flow Het Exngers oopes wr 1, Dr.Govnd
More informationResearch Article Comparative Studies of Different Switching Patterns for Direct and Indirect Space Vector Modulated Matrix Converter
dvnes in Power Eletronis Volume, rtile ID 854, 8 pges doi:.55//854 Reserh rtile omprtive Studies of Different Swithing Ptterns for Diret nd Indiret Spe Vetor Modulted Mtrix onverter min Shnpour, Ssn Gholmi,
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 informationIntroduction to Numerical Integration Part II
Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w
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 informationSeries-Hybrid Components
-Hyrid Components roportionl Electro-Hydrulic Controls ypes rphic Symols x. perting ressure (SI) ximum Flow U.S..5 3 5 0 30 0 00 3 5 0 30 0 00 300 0 00 L/min ge ilot Relief s (35) EHD 0 658 ressure Control
More informationThe DOACROSS statement
The DOACROSS sttement Is prllel loop similr to DOALL, ut it llows prouer-onsumer type of synhroniztion. Synhroniztion is llowe from lower to higher itertions sine it is ssume tht lower itertions re selete
More informationRepresenting Curves. Representing Curves. 3D Objects Representation. Objects Representation. General Techniques. Curves Representation
Reresentng Crves Fole & n Dm, Chter Reresentng Crves otvtons ehnqes for Ojet Reresentton Crves Reresentton Free Form Reresentton Aromton n Interolton Prmetr Polnomls Prmetr n eometr Contnt Polnoml Slnes
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 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 informationELE B7 Power Systems Engineering. Power System Components Modeling
Power Systems Engineering Power System Components Modeling Section III : Trnsformer Model Power Trnsformers- CONSTRUCTION Primry windings, connected to the lternting voltge source; Secondry windings, connected
More informationNumbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point
GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply
More informationJens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers
Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for
More informationANALOG CIRCUIT SIMULATION BY STATE VARIABLE METHOD
U.P.B. Sc. Bull., Seres C, Vol. 77, Iss., 25 ISSN 226-5 ANAOG CIRCUIT SIMUATION BY STATE VARIABE METHOD Rodc VOICUESCU, Mh IORDACHE 22 An nlog crcut smulton method, bsed on the stte euton pproch, s presented.
More informationNew Algorithms: Linear, Nonlinear, and Integer Programming
New Algorthms: ner, Nonlner, nd Integer Progrmmng Dhnnjy P. ehendle Sr Prshurmhu College, Tl Rod, Pune-400, Ind dhnnjy.p.mehendle@gml.om Astrt In ths pper we propose new lgorthm for lner progrmmng. Ths
More informationm A 1 1 A ! and AC 6
REVIEW SET A Using sle of m represents units, sketh vetor to represent: NON-CALCULATOR n eroplne tking off t n ngle of 8 ± to runw with speed of 6 ms displement of m in north-esterl diretion. Simplif:
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 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 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 informationREGULARIZATION IN QUANTUM GAUGE THEORY OF GRAVITATION WITH DE SITTER INNER SYMMETRY
THEORETICAL PHYSICS REGULARIZATION IN QUANTUM GAUGE THEORY OF GRAVITATION WITH DE SITTER INNER SYMMETRY V. CHIRIÞOIU 1, G. ZET 1 Poltehn Unversty Tmºor, Tehnl Physs Deprtment, Romn E-ml: vorel.hrtou@et.upt.ro
More informationPrinciple Component Analysis
Prncple Component Anlyss Jng Go SUNY Bufflo Why Dmensonlty Reducton? We hve too mny dmensons o reson bout or obtn nsghts from o vsulze oo much nose n the dt Need to reduce them to smller set of fctors
More informationSOLUTIONS TO ASSIGNMENT NO The given nonrecursive signal processing structure is shown as
SOLUTIONS TO ASSIGNMENT NO.1 3. The given nonreursive signl proessing struture is shown s X 1 1 2 3 4 5 Y 1 2 3 4 5 X 2 There re two ritil pths, one from X 1 to Y nd the other from X 2 to Y. The itertion
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 informationVariable time amplitude amplification and quantum algorithms for linear algebra. Andris Ambainis University of Latvia
Vrble tme mpltude mplfcton nd quntum lgorthms for lner lgebr Andrs Ambns Unversty of Ltv Tlk outlne. ew verson of mpltude mplfcton;. Quntum lgorthm for testng f A s sngulr; 3. Quntum lgorthm for solvng
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 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 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 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 information