Power System Stability Enhancement Under Three Phase Fault with FACTS Devices TCSC, STATCOM and UPFC
|
|
|
- Milton Hudson
- 5 years ago
- Views:
Transcription
1 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, Power Syste Stlty Enhneent Under Three Phse Fult wth FTS Dees TS, STTOM nd UPF Dr. S. Ttus Deprtent of EEE MM ollege of Engneerng Trhrppll, Ind.J.Vnothu Deprtent of EEE MM ollege of Engneerng Trhrppll, Ind I. Mr nn Nshnth Deprtent of EEE MM ollege of Engneerng Trhrppll, Ind strt Wth the eer nresng oplextes n power systes ross the gloe nd the growng need prode stle, seure, ontrolled, eono nd hgh qulty power espelly n the deregulted power rket. It s ensged tht FTS ontrollers wll ply tl role n power systes. Ths pper nestgtes the proeent of trnsent stlty of test syste under three phse fult usng fts dese. TS Thyrsr ontrolled Seres pr nd STTOM Stt Synhronous opensr re utlzed s seres nd shunt opensn respetely. UPFUnfed Power Flow ontroller s onsdered s shuntseres opensr. Keywords TS; STTOM; UPF; Trnsent stlty. I. INTRODUTION Tody s power syste s oplex network oprsng of generr, trnssson lnes, rety of lods nd trnsforers. Wth the eer nrese n power dend soe trnssson lne s ore loded thn ws plnned when they were ult [1]. Wth nresed lodng of long trnssson lne the prole of trnsent stlty fter jor dsturne, wll use the entre syste susde. Power syste stlty s the lty of eletr power syste, for gen ntl opertng ondn regn stte of opertng equlru fter eng sujeted physl dsturne, wth ost syste rles ounded so tht prtlly the entre syste rens ntt [2]. nd the n hllenges of odern power syste s trnsent stlty s referred s the plty of the syste ntn synhronous opern n the eent of lrge dsturne nd ths knd of stlty depends on preters of syste nd ntensty of dsturne [3] [4]. The reent deelopent of power eletrons ntrodues the use of flexle trnssson syste (FTS) ontrollers n power syste [5]. FTS tehnology prodes the opportunty [6] [7] Inrese lodng pty of trnssson lnes. Preent lkouts. Iproe genern produtty. Redue rultng rete power. Iproes syste stlty lt. Redue oltge flker. Redue syste dpng nd osllns. ontrol power flow so tht t flows through the desgnted routes. ongesn ngeent The onennl ontrol dees lke synhronous ondenser, sturted rer, thyrsr ontrolled rer, fxed pr thyrsr ontrolled rer, thyrsr swthed pr hng less syste stlty lt, less enhneent of syste dpng, less oltge flker ontrol when opred eergng fts dees lke TS, STTOM nd UPF [8][9]. Ths pper nestgtes the proeent of syste stlty wth rous eergng FTS dees nd ther oprsons. [10] [13] II. DESRIPTION OF FTS DEVIES. TS The s oneptul TS odule oprses seres pr,, n prllel wth thyrsrontrolled rer, LS, s shown n Fg.1. TS s seresontrolled pte retne tht n prode ontnuous ontrol of power on the lne oer wde rnge. The prnple of rleseres opensn s sply nrese the fundentlfrequeny oltge ross n fxed pr n seres opensted lne through pproprte rn of the frng ngle. Ths enhned oltge hnges the effete lue of the serespte retne nd ontrol the rete power [9] [14].. STTOM STTOM s ontrolled retepower soure. It prodes the desred retepower genern nd sorpn entrely y ens of eletron proessng of the oltge nd urrent wefors n oltgesoure onerter (VS). snglelne STTOM power rut s shown n ll rghts Resered. Pge 66
2 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, rel nd rete power flows n trnssson lne. It s onfgured s shown n Fg.3 nd oprses two VSs oupled through oon d ternl. One VSonerter 1 s onneted n shunt wth the lne through ouplng trnsforer, the other VSonerter 2 s nserted n seres wth the trnssson lne through n nterfe trnsforer. The d oltge for oth onerters s proded y oon pr nk. The seres onerter s ontrolled njet oltge phsor, Vpq, n seres wth the lne, whh n e red fro 0 Fgure1onfgurn of TS Fgure3onfgurn of UPF Fgure 2onfgurn of STTOM where VS s onneted utlty us through gnet ouplng. The exhnge of rete power etween the onerter nd the syste n e ontrolled y ryng the pltude of the 3phse output oltge, Es, of the onerter. Tht s, f the pltude of the output oltge s nresed oe tht of the utlty us oltge, Et, then urrent flows through the retne fro the onerter the syste nd the onerter genertes pterete power for the syste. If the pltude of the output oltge s deresed elow the utlty us oltge, then the urrent flows fro the syste the onerter nd the onerter sors nduterete power fro the syste. If the output oltge equls the syste oltge, the retepower exhnge eoes zero, n whh se the STTOM s sd e n flotng stte [9] [15] [16].. UPF The UPF s the ost erstle FTS ontroller deeloped so fr, wth ll enopssng pltes of oltge reguln, seres opensn, nd phse shftng. It n ndependently nd ery rpdly ontrol oth Vpq x. Moreoer, the phse ngle of Vpq n e ndependently red fro degree. In ths proess, the seres onerter exhnges oth rel nd rete power wth the trnssson lne. lthough the rete power s nternlly generted/ sored y the seres onerter, the relpower genern/ sorpn s de fesle y the denergy srge dee tht s, the pr. The shunnneted onerter 1 s used nly supply the relpower dend of onerter 2, whh deres fro the trnssson lne tself. The shunt onerter ntns onstnt oltge of the d us. Thus the net rel power drwn fro the syste s equl the losses of the two onerters nd ther ouplng trnsforers. In ddn, the shunt onerter ehes lke STTOM nd ndependently regultes the ternl oltge of the nteronneted us y genertng/ sorng requste ount of rete power [9] [17] []. III. MODEL OF TEST SYSTEM The elow test network s tested wth TS, STTOM, nd UPF seprtely nestgte the ehor wth fe preters suh s generr oltge (Vg), generr urrent (Ig), generted lod ngle (δ), oltge ner nfnte us (V) nd urrent ner nfnte us (I). These re done through MTL/SIMULINK wth followng ll rghts Resered. Pge 67
3 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, Infnte us Seres Fts Dees G2 2 1 Sendng end Fgure 4. Test syste wth seres FTS dee Rel power G1 Infnte us G2 Sendng end 1 Shunt Fts Dees 2 Fgure 5. Test syste wth shunt FTS dee Stge 1 To desgn test syste shown n fg 6. Stge 2 To esure fe preters under norl opertng ondn. Stge 3 To rete three phse fult ner nfnte us n test syste. Fult durn 0.6 seonds. Shown n fg 7. Stge 4 To esure fe preters under three phse fult ondns Stge 5 To desgn FTS dees (TS, STTOM nd UPF) Shown n fg 8, fg 9 nd fg 10 respetely. Stge 6 To onnet FTS dees ( seonds) n test syste under three phse fult ondn nd esure ehorl hnge of syste. The test syste spefn s Generr 1, 2 10KV, 110MW, 300 rp, TS 10MVR, 10KV, STTOM 10MVR, 10KV nd UPF 10MVR, 10KV. IV. RESULT ND DISUSSION In ordne wth the oe SIMULINK work the fe dfferent preters generr oltge (Vg), generr urrent (Ig), generted lod ngle (δ), oltge Generr Voltge (Vg) n olts G1 ner nfnte us (V) nd urrent ner nfnte us (I) of test syste s esured nd the settlng te of eh preter s lulted for syste stlty nd lso xze the power flow n trnssson lne. The suln result for generr oltge (Vg) of phse s shown n fg 11. It s ler tht under three phse fult, wthout FTS dee the oltge flutun of generr s ore, wheres, t s less when the FTS dees re noled. tle for generr oltge (Vg) under dfferent te nterl s onstruted fro the osered result. Durng the te nterl of 0.8 seonds nd seonds the oltge rses fro olts nd fro 8000 olts respetely whh s greter thn the generr oltge (Vg) wthout the noleent of FTS dee. So, when FTS dees re onneted the syste, t tkes 2.4 seonds for TS, 2.0 seonds for STTOM nd 1.4 seonds for UPF reh the stlty leel. TLE 1. GENERTOR VOLTGE (Vg) IN VOLTS Te n seonds Wthout FTS dee TS 0 STTOM 0 UPF The fg 12 shows the generr urrent (Ig) of phse. The generr urrent (Ig) s rehed stle t 4.4 seonds when the FTS dees re not onneted. fter norportng the FTS dees TS, STTOM nd UPF, the settlng te of generr urrent (Ig) s redued s 2.4, 3.4 nd 2.3 seonds respetely for rehng the stle ondn, Whh s undersod through tle 2. Generr urrent (Ig) n peres Rel power TLE 2. GENERTOR URRENT (Ig) IN MPS Te n seonds Wthout FTS dee TS STTOM UPF ll rghts Resered Pge 68
4 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, <Lod ngle K delt (deg)> <Output t e power Gn Dsply1 <Output ret e power Qeo (W)> Dsply2 Sope Inf nte us lod2 Synhronous Mhne1 lod3 fd1 Dsply3 es1 step1 Dsply es2 Dsrete, Ts = 5e005 s. pow ergu <Lod ngle Sope2 K delt (deg)> <Output t e power Gn1 <Output ret e power Qeo (W)> Sope3 Synhronous Mhne2 Sope1 Dsply4 fd2 step2 Fgure 6. Sulnk Model of Test Syste <Lod ngle K delt (deg)> <Output t e power G n D spl y1 <Output ret e power Qeo (W)> D spl y2 Sope Inf nte us ThreePhse Fult D sply es1 l od3 l od2 Synhronous M hne1 D spl y3 fd1 step1 es2 Dsrete, Ts = 5e005 s. pow ergu <Lod ngle Sope2 delt (deg)> <Output t e power KG n1 <Output ret e power Qeo (W)> Sope3 Synhronous Mh ne2 step2 Sope1 D spl y4 fd2 Fgure 7. Test Syste wth Three Phse ll rghts Resered. Pge 69
5 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, <Lod ngle delt (deg)> Sope13 K<Output t e power Sope7 Gn es1 lod3 Infnte us2 Gn2 Sope12 es4 Sope ThreePhse Fult1 ThreePhse reker1 10 kw3 lod4 fd2 step2 es3 Sope5 lod1 Synhronous Mhne3 fd3 Synhronous Mhne2 Infnte us1 step3 <Output ret e power Qeo (W)> <Output ret e power Qeo (W)> <Output t e power delt (deg)> Sope10 Sope2 <Output t e power Dsrete, Ts = 5e005 s. pow ergu <Lod ngle Sope9 <Lod ngle delt (deg)> Gn1 Sope4 K es2 Sope8 K Sope3 ThreePhse Fult lod2 Synhronous Mhne1 fd1 Sope1 step1 <Output ret e power Qeo (W)> 10 kw4 Sope11 n2 T S2 n2 n1 fd4 step4 n1 T S1 Synhronous Mhne4 n2 T S <Output ret e power Qeo (W)> n1 <Output t e power Sope14 delt (deg)> <Lod ngle K Gn3 Sope6 sour2 Fgure 8. Test Syste wth TS <Lod ngle delt (deg)> Sope14 K Sope13 <Output t e power G n Sope4 ThreePhse Fult K es2 Sope8 Sope3 Infnte us2 es1 lod3 lod2 Synhronous Mhne1 fd1 Sope1 step1 <Output ret e power Qeo (W)> G n2 Sope9 <Lod ngle delt (deg)> Sope12 onn3 STTOM1 Sope11 <Output t e power <Lod ngle delt (deg)> onn2 onn1 Sope7 10 kw4 K es4 Sope6 Gn3 ThreePhse Fult1 ThreePhse reker1 10 kw3 Sope lod4 fd2 step2 es3 lod1 Synhronous Mhne3 Sope5 fd3 Synhronous Mhne2 <Output ret e power Qeo (W)> Infnte us1 step3 <Output t e power Sope10 <Output ret e power Qeo (W)> step4 Synhronous Mh ne4 Sope2 <Output ret e power Qeo (W)> <Lod ngle delt (deg)> K Dsrete, Ts = 5e005 s. pow ergu Gn1 <Output t e power fd4 Fgure 9. Test Syste wth ll rghts Resered. Pge 70
6 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, <Lod ngle delt (deg)> Sope13 K<Output t e power Sope7 Gn <Output ret e power Qeo (W)> es1 lod3 Infnte us1 Sope4 K es2 Sope8 Sope3 ThreePhse Fult Sope12 lod2 Synhronous M hne1 Sope9 Infnte us2 fd1 Gn2 <Lod ngle l od1 ThreePhse Fult1 es4 Sope ThreePhse Trnsforer (Two Wndngs). lod4 ThreePhse Trnsforer (Two Wndngs)1 10 kw3 fd2 step2 Sope5 es3 Synhronous Mhne3 fd3 Synhronous M hne2 T <Output ret e power Qeo (W)> step3 <Output t e power <Output ret e power Qeo (W)> Sope10 Susyste onn4 onn3 onn2 onn5 onn4 onn2 onn1 Seres RL rnh1 Sope15 Susyste1 onn5 onn3 Sope11 <Out put t e power delt (deg)> <Lod ngle K 10 kw4 Gn3 Sope6 onn1 <Output ret e power Qeo (W)> Synhronous M h ne4 Sope2 <Output t e power delt (deg)> delt (deg)> <Lod ngle K Dsrete, Ts = 5e005 s. pow ergu Gn1 Sope1 step1 Sope14 step4 fd4 Fgure 10. Test Syste wth UPF Fgure 11. Suln Result for Generr Voltge (Vg) Fgure 12. Suln Result for Generr urrent ll rghts Resered. Pge 71
7 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, Fgure 13. Suln Result for Generr Lod ngle (δ) Fgure 15. Suln Result for urrent ner Infnte us (I) Generr Lod ngle (δ) n degree efore onnetng the FTS dees n test syste the lod ngle (δ) of generr s red up degree nd tkes round 7.4 seonds settle down stle regon fter the fult reoery. ut due the nterfng of FTS dee the settlng te s redued 4.2, 4.4 nd 4.2 seonds for TS, STTOM nd UPF respetely s shown n fg 13 nd tle 3. Fgure 14. Suln Result for Voltge ner Infnte us (V) TLE 3. GENERTOR LOD NGLE (δ) IN DEGREE Te n seonds Wthout FTS dee TS STTOM UPF Fro Fg 14 t s osered tht the settlng te for the oltge ner nfnte us (V) s 5.4 seonds when the FTS dees re not onneted. fter onnetng the FTS dees settlng te s redued s 0.4, nd 0.2 seonds for stle ondn. Slrly the urrent ner nfnte us (I) oes stle wthn 0.4, nd 0.2 seonds for TS, STTOM nd UPF respetely fter the fult reoery. ut wthout those dees t tkes 3.4 seonds reh stlty s shown n fg 15. The settlng te of Vg, Ig, δ, V, I for TS, STOM nd UPF re studed nd shown n tle 4. It ll rghts Resered. Pge 72
8 S.Ttus* et l. / (IJITR) INTERNTIONL JOURNL OF INNOVTIVE TEHNOLOGY ND RESERH Volue No. 1, Issue No. 1, DeeerJnury 2013, found tht the syste stlty s heed n short nterl whle nterfng UPF. [8] Enrque h, ludo R. Fuerte Esquel, Hugo rz Perez, esr ngeles ho, FTS Modellng nd Suln n Power Networks, John Wley & sons LTD, TLE 5. OMPRISON OF SETTLING TIME [9] R. Mohn Mthur, Rj K. Vr, Thyrsr sed FTS ontrollers for Eletrl Trnssson Systes, IEEE press seres on Power Engneerng, John Wley & Sons LTD, [10] S. Shnkr, S. lj, S. rul, Suln nd oprson of Vrous FTS dees n power syste, Internnl Journl of Engneerng Sene nd Tehnology, olue 2 (4), 2010, [11] lrez Sef, Ssn Ghol, n Shnpour, Power Flow Studt nd oprson of FTS: Seres (SSS), Shunt (STTOM) nd shunt seres (UPF), The Pf Journl of Sene nd Tehnology olue 11. No. 1. My 2010 (sprng). [12] rthtsode Yoe, N. Mthulnnthn, oprson of Shunt pr, SV nd STTOM n Stt Voltge Stlty Mrgn Enhneent, Internnl Journl of Eletrl Engneerng Edun, 41/2. [13] J. rt,. Seedn, S. S. Mortz, Dpng Power Syste Oslln Iproeent y FTS Dees: oprson etween SSS nd STTOM, Worl dy of Sene, Engneerng nd Tehnology [14]. Kze,. drzdeh, Modellng nd Suln of SV nd TS Study ther Lts on Mxu Lodlty Pont, Eletrl Power nd Energy Syste 26 (2004) , Elseer LTD. [15] P. Venkt Kshore, Dr. S. R Reddy, Voltge Sg Mtgn n Eght us Syste usng D STTOM for Power Qulty Iproeent, Internnl Journl of Engneerng Sene nd Tehnology, olue 2 (4), 2010, [16] Syed Mojt Shrn oroujen, Rez Het, Hdeh Delfkr, Elhe ehzdpour, Voltge Support nd Stlty Enhneent usng STTOM, ern Journl of Sentf Reserh, Euro Journl Pulshng, [17] N. Dzdre, G. nderson, Power Flow Reguln y use of UPF s Injen Model, IEEE Power Teh 99 onferene, [] S. Muthu Krshnn, Dr.. Nrl Kur oprson of Suln nd Experentl Results of UPF used for Power Qulty Iproeent, Internnl Journl of oputer nd Eletrl Engneerng, olue 2, No. 3, June Settlng te n seonds Preters Generr oltge (Vg) Generr urrent(ig) Generr lod ngle(δ) Voltge ner nfnte us(v) urrent ner nfnte us(i) Wthout FTS dees TS STTOM UPF V. ONLUSION In ths pper the power syste stlty enhneent of test network wth FTS dees TS, STTOM nd UPF s presented nd dsussed under three phse short rut fult. It s ler tht the syste regns ts stlty under ny one of the FTS dee s noled. lso the settlng te reh the stlty of the syste wth UPF for dfferent preters (Generr Voltge 1.4 ses, Generr urrent 2.3 ses, Generr Lod ngle 4.2 ses, Voltge ner Infnte us 0.2 ses nd urrent ner Infnte us 0.1 ses) s oprtely uh etter thn STTOM s well s TS. REFERENES [1] Dr. M. Rjr, N. Rek, D. Murl, oprson of FTS dees for power syste stlty enhneent, Internnl Journl of oputer pplns ( ), olue 8 No. 4, Oer [2] P. Kundur, J. Pser, V. jjrpu, G. nderson,. ose,. nzres, N. Htzrgyrou, D. Hll,. Stnko,. Tylor, T. V. uste, V. Vttl, Defenn nd lssfn of Power Syste Stlty, IEEE Trnsn on Power Syste, 2004, 19(2) [3] Hd Sdt, Power syste nlyss, TT MGrw Hll edn, [4] K. R. Pdyr, Power Syste Dyn Stlty nd ontrol, seond edn 2002,. S. puln, Hyderd [5] S. K. Srst, dned Power Eletrons sed Fts ontrollers nd Oerew, sn Power Eletrons Journl, olue 4, No. 3 Deeer [6] hntu Rz Mkkr, Llle Dewn, Trnsent stlty enhneent usng roust FTS ontrollers ref ur, ndn Journl on Eletrl & Eletrons Engneerng olue 1, No. 7, Deeer [7] t Grg, Snjy Kur grwl, Voltge ontrol nd Dyn Perforne of Power Trnssson Syste usng STTOM nd ts oprson wth SV, Internnl Journl of dnes n Engneerng nd Tehnology, Jnury ll rghts Resered. Pge 73
a) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points.
Prole 3: Crnot Cyle of n Idel Gs In this prole, the strting pressure P nd volue of n idel gs in stte, re given he rtio R = / > of the volues of the sttes nd is given Finlly onstnt γ = 5/3 is given You
" = #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
AC/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
8 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),
Electrical 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
Lecture 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
Abhilasha 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
Trigonometry. 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
FLICKER CONTRIBUTION OF INDUCTION GENERATORS IN WIND ENERGY CONVERSION SYSTEMS
Journl of Eletril Engineering FLIKER ONTRIUTION OF INDUTION GENERTORS IN WIND ENERGY ONVERSION SYSTEMS k. s. Sndhu sudhir Shr 2 Professor, Deprtent of Eletril Engineering, Ntionl Institute of Tehnology,
GENERATING 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
VECTORS 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
This conversion box can help you convert units of length. b 3 cm = e 11 cm = b 20 mm = cm. e 156 mm = b 500 cm = e cm = b mm = d 500 mm =
Units of length,, To onvert fro to, ultiply y 10. This onversion ox n help you onvert units of length. To onvert fro to, divide y 10. 100 100 1 000 10 10 1 000 Convert these lengths to illietres: 0 1 2
Intermediate 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
Industrial 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
Magnetically 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
ECEN 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
Dorf, 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
CS 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
Polyphase 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
1 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
NON-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
NEW 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)
Lecture 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
Lecture 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
Polyphase 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
POLYPHASE CIRCUITS. Introduction:
POLYPHASE CIRCUITS Introduction: Three-phse systems re commonly used in genertion, trnsmission nd distribution of electric power. Power in three-phse system is constnt rther thn pulsting nd three-phse
About 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
Performance 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,
Exercise 3 Logic Control
Exerise 3 Logi Control OBJECTIVE The ojetive of this exerise is giving n introdution to pplition of Logi Control System (LCS). Tody, LCS is implemented through Progrmmle Logi Controller (PLC) whih is lled
Analele Universităţii din Oradea, Fascicula: Protecţia Mediului, Vol. XIII, 2008
Alele Uverstăţ d Orde Fsul: Proteţ Medulu Vol. XIII 00 THEORETICAL AND COMPARATIVE STUDY REGARDING THE MECHANICS DISPLASCEMENTS UNDER THE STATIC LOADINGS FOR THE SQUARE PLATE MADE BY WOOD REFUSE AND MASSIF
I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
CONTINUE 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
1 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
Modeling 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
Solution 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
Solubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,
Learning 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
LESSON 11: TRIANGLE FORMULAE
. THE SEMIPERIMETER OF TRINGLE LESSON : TRINGLE FORMULE In wht follows, will hve sides, nd, nd these will e opposite ngles, nd respetively. y the tringle inequlity, nd..() So ll of, & re positive rel numers.
Distributed 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
Spacetime 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
4. 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
A Battery Energy Storage Based Virtual Synchronous Generator
3 IREP Syposiu-ulk Syste Dynis nd ontrol -IX (IREP), ugust 5-3, 3, Rethynon, Greee ttery Energy Storge sed Virtul Synhronous Genertor. Vssilkis, V. Krpnos P. Kotspopoulos, N. Htzirgyriou IEEE ener Ntionl
Instructions to students: Use your Text Book and attempt these questions.
Instrutions to students: Use your Text Book nd ttempt these questions. Due Dte: 16-09-2018 Unit 2 Chpter 8 Test Slrs nd vetors Totl mrks 50 Nme: Clss: Dte: Setion A Selet the est nswer for eh question.
Trigonometry Revision Sheet Q5 of Paper 2
Trigonometry Revision Sheet Q of Pper The Bsis - The Trigonometry setion is ll out tringles. We will normlly e given some of the sides or ngles of tringle nd we use formule nd rules to find the others.
Chapter 10: Symmetrical Components and Unbalanced Faults, Part II
Chpter : Symmetricl Components nd Unblnced Fults, Prt.4 Sequence Networks o Loded Genertor n the igure to the right is genertor supplying threephse lod with neutrl connected through impednce n to ground.
Effects 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
Controller 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
CONTROL 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
Chapter 14. Gas-Vapor Mixtures and Air-Conditioning. Study Guide in PowerPoint
Chpter 14 Gs-Vpor Mixtures nd Air-Conditioning Study Guide in PowerPoint to ccopny Therodynics: An Engineering Approch, 5th edition by Yunus A. Çengel nd Michel A. Boles We will be concerned with the ixture
Synchronous 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
A Study on the Properties of Rational Triangles
Interntionl Journl of Mthemtis Reserh. ISSN 0976-5840 Volume 6, Numer (04), pp. 8-9 Interntionl Reserh Pulition House http://www.irphouse.om Study on the Properties of Rtionl Tringles M. Q. lm, M.R. Hssn
Proving 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
CS311 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
Problem 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
Section 1.3 Triangles
Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior
THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL
THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL P3.1 Kot Iwmur*, Hiroto Kitgw Jpn Meteorologil Ageny 1. INTRODUCTION Jpn Meteorologil Ageny
I 3 2 = I I 4 = 2A
ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents
EE 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,
The University of New South Wales FINAL EXAMINATION. Session ELEC4613 ELECTRIC DRIVE SYSTEMS. 1. Time allowed 3 hours
The University of New South Wles FINAL EXAMINATION Session 010 ELEC4613 ELECTRIC DRIVE SYSTEMS 1. Tie llowed 3 hours. Reding tie: 10 inutes 3. Totl nuber of questions in this pper = SIX 4. Answer ny FOUR
GM1 Consolidation Worksheet
Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet GM1 Consolidtion Worksheet 1 Clulte the size of eh ngle mrked y letter. Give resons for your nswers. or exmple, ngles on stright line dd up
Effectiveness 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
ME306 Dynamics, Spring HW1 Solution Key. AB, where θ is the angle between the vectors A and B, the proof
ME6 Dnms, Spng HW Slutn Ke - Pve, gemetll.e. usng wngs sethes n nltll.e. usng equtns n nequltes, tht V then V. Nte: qunttes n l tpee e vets n n egul tpee e sls. Slutn: Let, Then V V V We wnt t pve tht:
The linear system. The problem: solve
The ler syste The prole: solve Suppose A s vertle, the there ests uue soluto How to effetly opute the soluto uerlly??? A A A evew of dret ethods Guss elto wth pvotg Meory ost: O^ Coputtol ost: O^ C oly
Algorithm Design and Analysis
Algorithm Design nd Anlysis LECTURE 8 Mx. lteness ont d Optiml Ching Adm Smith 9/12/2008 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov, K. Wyne Sheduling to Minimizing Lteness Minimizing
Algorithm Design and Analysis
Algorithm Design nd Anlysis LECTURE 5 Supplement Greedy Algorithms Cont d Minimizing lteness Ching (NOT overed in leture) Adm Smith 9/8/10 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov,
Behavior Composition in the Presence of Failure
Behior Composition in the Presene of Filure Sestin Srdin RMIT Uniersity, Melourne, Austrli Fio Ptrizi & Giuseppe De Giomo Spienz Uni. Rom, Itly KR 08, Sept. 2008, Sydney Austrli Introdution There re t
Educational 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
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES. Two liner equtions in the sme two vriles re lled pir of liner equtions in two vriles. The most generl form of pir of liner equtions is x + y + 0 x + y + 0 where,,,,,,
Vibration with more (than one) degrees of freedom (DOF) a) longitudinal vibration with 3 DOF. b) rotational (torsional) vibration with 3 DOF
irtion with ore (thn one) degrees of freedo (DOF) ) longitudinl irtion with DOF ) rottionl (torsionl) irtion with DOF ) ending irtion with DOF d) the D (plnr) irtion of the fleil supported rigid od with
Technote 6. Op Amp Definitions. April 1990 Revised 11/22/02. Tim J. Sobering SDE Consulting
Technte 6 prl 990 Resed /22/02 Op mp Dentns Tm J. Sberng SDE Cnsultng sdecnsultng@pbx.cm 990 Tm J. Sberng. ll rghts resered. Op mp Dentns Pge 2 Op mp Dentns Ths Technte summrzes the bsc pertnl mpler dentns
THE 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
xl yl m n m n r m r m r r! The inner sum in the last term simplifies because it is a binomial expansion of ( x + y) r : e +.
Ler Trsfortos d Group Represettos Hoework #3 (06-07, Aswers Q-Q re further exerses oer dots, self-dot trsfortos, d utry trsfortos Q3-6 volve roup represettos Of these, Q3 d Q4 should e quk Q5 s espelly
Damping 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
3-Way Mixing and Sequencing Globe Valves, Flared (5/8 in. O.D.) with Electric, Hydraulic, and Pneumatic Actuators
lectric, Hydrulic, nd Pneumtic ctutors TL 1. Select Vlve ody including P ode (Vlve Size, v Rting, Port ode) or select Vlve ssemly correct (refer to Tle 3 nd Tle 3 lso) less ctutor ode (XXX) including the
April 8, 2017 Math 9. Geometry. Solving vector problems. Problem. Prove that if vectors and satisfy, then.
pril 8, 2017 Mth 9 Geometry Solving vetor prolems Prolem Prove tht if vetors nd stisfy, then Solution 1 onsider the vetor ddition prllelogrm shown in the Figure Sine its digonls hve equl length,, the prllelogrm
Module 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
System Validation (IN4387) November 2, 2012, 14:00-17:00
System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise
Pythagorean Theorem and Trigonometry
Ptgoren Teorem nd Trigonometr Te Ptgoren Teorem is nient, well-known, nd importnt. It s lrge numer of different proofs, inluding one disovered merin President Jmes. Grfield. Te we site ttp://www.ut-te-knot.org/ptgors/inde.stml
Individual Group. Individual Events I1 If 4 a = 25 b 1 1. = 10, find the value of.
Answers: (000-0 HKMO Het Events) Creted y: Mr. Frnis Hung Lst udted: July 0 00-0 33 3 7 7 5 Individul 6 7 7 3.5 75 9 9 0 36 00-0 Grou 60 36 3 0 5 6 7 7 0 9 3 0 Individul Events I If = 5 = 0, find the vlue
Something found at a salad bar
Nme PP Something found t sld r 4.7 Notes RIGHT TRINGLE hs extly one right ngle. To solve right tringle, you n use things like SOH-H-TO nd the Pythgoren Theorem. n OLIQUE TRINGLE hs no right ngles. To solve
A 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:
ON AN INEQUALITY FOR THE MEDIANS OF A TRIANGLE
Journl of Siene nd Arts Yer, No. (9), pp. 7-6, OIGINAL PAPE ON AN INEQUALITY FO THE MEDIANS OF A TIANGLE JIAN LIU Mnusript reeived:.5.; Aepted pper:.5.; Pulished online: 5.6.. Astrt. In this pper, we give
PHYS 2421 Fields and Waves
PHYS 242 Felds nd Wves Instucto: Joge A. López Offce: PSCI 29 A, Phone: 747-7528 Textook: Unvesty Physcs e, Young nd Feedmn 23. Electc potentl enegy 23.2 Electc potentl 23.3 Clcultng electc potentl 23.4
Appendix 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
AVL 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
A Detailed Comparative Study of ABC and Symmetrical Component Classification for Fault Analysis
The 2 nd Interntionl Power Engineering nd Optimiztion onferene (PEOO28), Shh lm, Selngor, MLYSI. 4-5 June 28. Detiled omprtive Study of nd Symmetril omponent lssifition for Fult nlysis Muhmmd Sufi Kmrudin,
CHENG 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
Chapter 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
1/16/2013. Overview. 05-Three Phase Analysis Text: Three Phase. Three-Phase Voltages. Benefits of Three-Phase Systems.
oltge () 1/16/21 Overview 5Three Phse Alysis Text: 2.4 2.7 ECEGR 451 Power Systems ThreePhse Soures Delt d Y Coetios ThreePhse Lods ThreePhse Power ThreePhse Alysis PerPhse Alysis Dr. Louie 2 ThreePhse
CPM-12A. Multifunction Power meter Manual d d-454e-53-41, Rev 1.2
CPM-12 Multifuntion Power meter Mnul 43504d313241-4d-454e-53-41, ev 1.2 2018-06-01 CPM-12 Mnul CPM-12 multifuntion power meter provide high ury single phse nd three-phse mesuring nd displying, energy umulting,
A, Electromagnetic Fields Final Exam December 14, 2001 Solution
304-351, Electrognetic Fiels Finl Ex Deceer 14, 2001 Solution 1. e9.8. In chpter9.proles.extr.two loops, e of thin wire crry equl n opposite currents s shown in the figure elow. The rius of ech loop is
Power 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
Green s Theorem. (2x e y ) da. (2x e y ) dx dy. x 2 xe y. (1 e y ) dy. y=1. = y e y. y=0. = 2 e
Green s Theorem. Let be the boundry of the unit squre, y, oriented ounterlokwise, nd let F be the vetor field F, y e y +, 2 y. Find F d r. Solution. Let s write P, y e y + nd Q, y 2 y, so tht F P, Q. Let
For a, b, c, d positive if a b and. ac bd. Reciprocal relations for a and b positive. If a > b then a ab > b. then
Slrs-7.2-ADV-.7 Improper Definite Integrls 27.. D.dox Pge of Improper Definite Integrls Before we strt the min topi we present relevnt lger nd it review. See Appendix J for more lger review. Inequlities:
m 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:
332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006
2:221 Principles of Electricl Engineering I Fll 2006 Nme of the student nd ID numer: Hourly Exm 2 Novemer 6, 2006 This is closed-ook closed-notes exm. Do ll your work on these sheets. If more spce is required,
Revision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax
.9.1: AC power analyss Reson: Deceber 13, 010 15 E Man Sute D Pullan, WA 99163 (509 334 6306 Voce and Fax Oerew n chapter.9.0, we ntroduced soe basc quanttes relate to delery of power usng snusodal sgnals.
Chapter 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
GEOMETRY 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
RIEMANN INTEGRATION. Throughout our discussion of Riemann integration. B = B [a; b] = B ([a; b] ; R)
![RIEMANN INTEGRATION. Throughout our discussion of Riemann integration. B = B [a; b] = B ([a; b] ; R)](/thumbs/92/109668177.jpg "RIEMANN INTEGRATION. Throughout our discussion of Riemann integration. B = B [a; b] = B ([a; b] ; R)")
RIEMANN INTEGRATION Throughout our disussion of Riemnn integrtion B = B [; b] = B ([; b] ; R) is the set of ll bounded rel-vlued funtons on lose, bounded, nondegenerte intervl [; b] : 1. DEF. A nite set