CHAPTER-2. S.No Name of the Sub-Title No. 2.5 Use of Modified Heffron Phillip's model in Multi- Machine Systems 32

Transcription

1 9 HAPT- hapr : MODIFID HFFON PHILLIP MODL.No Nam of h ub-tl Pag No.. Inroucon..3 Mollng of Powr ym Hffron Phllp Mol.4 Mof Hffron Phllp Mol 7.5 U of Mof Hffron Phllp mol n Mul- Machn ym 3

2 HAPT-.. Inroucon Th chapr prn h mahmacal rvaon of boh Hffron Phllp Mol [],[] an h mof Hffron Phllp mol a propo n [47], [48]. Th maral rprouc from [] an [49] for h ak of compln. In h h, h mof Hffron Phllp mol wll b conr for h vlopmn of cnralz a fback powr ym ablzr... Mollng of Powr ym ably analy rur h mollng of om mporan powr ym componn uch a xcaon ym, ynchronou gnraor an A nwork. Th currn gn mak u of I Mol.[5] o corrpon o h ynchronou gnraor havng hgh gan an conan ac xcr of low m [5]. Th followng ar h ynamc uaon ha govrn h MIB ym: nraor mchancal uaon B m (.) m T mch Tlc D m H (.) -Ax flux lnkag uaon To f (.3)

3 nra lcrcal oru uaon T lc (.4) ac xcaon ym uaon A f f A rf p T (.5) Appnx A conan h fnon an h anar manng of h varabl. Th uaon of aor algbra ar no by a (.6) a Fgur -: ngl Machn Infn Bu ym.3. Hffron Phllp Mol Th MIB crron lnar mol, known a Hffron Phllp mol (alo call -conan mol) n [8] can b achv by lnarzng h ym uaon aroun oprang conon. onvron of h machn uaon prn n Park rfrnc fram o h ron rfrnc fram roang ynchronouly can ablh an nrfac of ynchronou machn wh h

4 xrnal nwork. Th followng ar h MIB ym uaon: + j = + j j j j b (.7) Th ju h law of rchhoff olag bwn h nfn bu an rmnal gnraor. In Park rfrnc fram ubcrp an rprn an ax an n ron rfrnc fram Q an D rprn Q an D-ax rpcvly. parang ral an magnary par of (.7) w g v = x + co δ (.8) v = + x n δ (.9) b co n b (.) whr Th xpron for an can b oban by olvng (.) a gvn blow: = [ n δ + x + x co δ ] (.) = [(x +x ) n δ co δ ] (.) whr A = (x + x )x + x + Lnarzng (.) an (.) gv = δ + (.3)

5 3 = δ + (.4) whr = A [ co δ x + x n δ] = A x + x = A [ (x + x ) co δ + n δ ] = A Lnarzng (.8) an (.9) an ubung from (.3) an (.4) Toru Angl Loop: Lnarzng (.4) w g v = x δ + ( + x ) (.5) v = x δ x (.6) T = x x + (x x ) (.7) ubung (.5) an (.6) n (.7), w can xpr T a whr T = δ + (.8) = (x x ) = + (x x ) = (x x ) Lnarzng (.) an (.) an applyng Laplac ranform, w g

6 4 B (.9) m m [ Tm - T - D m ] (.) H Th combn. (.8), (.9) an. (.) can b pc n h form of a block agram a play n Fgur.. Th an for h oru-angl loop of h ynchronou machn. Fgur -: Toru Angl Loop For clacal machn mol, an h characrc uaon gvn by H + D + ω = (.) For ably, boh D an houl b pov. If D nglgbl, h roo of h characrc uaon ar n (.) H B, j j Whr ωn h naural (raan) fruncy of ocllaon of h roor. Typcally, h rang of ocllaon fruncy bwn.5 an. Hz alhough

7 5 xrm valu of. Hz a h low n an 4 Hz a h hgh n ar alo pobl. prnaon of Flux Dcay: Th uaon for h fl wnng can b xpr a T o f x x (.3) Lnarzng. (.3) an ubung from. (.3) w hav T x o f x ( ) (.4) Takng laplac ranform of (.4) w g, ( + T ) = (.5) whr 3 [ ( x x ) ] (.6) = (x x ) (.7).(.5) can b xpr hrough h block agram a play n Fgur -3.

8 6 Fgur -3: prnaon of flux cay prnaon of xcaon ym: Th Block agram of h xcaon ym conr pc n Fgur -4 Fgur -4: xcaon ym Th prurbaon n h rmnal volag can b xpr a v v (.8) o o v v v v o o ubung from.(.5) an (.6) n (.8), w g (.9) 5 6 whr v x v x o o 5 3+ v v o o (.3)

9 7 v v o o 6 x4+ ( x ) (.3) v o o For =, h xpron for h conan o 6 ar mplf a gvn blow: o ( x x ) n b o o b o ( x x ) ( x x ) ( x x ) b n I ( x x ) ( x x ) 3 ( x x ) ( x x ) ( x x ) n 4 b ( x x) 5 x o x n ( x x ) ( x x ) o b o b o o 6 x o ( x x ) o I no ffcul o prcv ha for x grar han, h conan,, 3, 4 an 6 ar pov. Th bcau δ gnrally l han 9 an o pov. 3 npnn of h oprang pon an l han uny (a xl hanx). No ha x gnrally pov unl h gnraor fng a larg capacv loa (whch no ralc)..4. Mof Hffron Phllp Mol Fgur.5 conr a ngl gnraor havng a powr ranformr nrconnc o h xrnal ym [48]. Th roor angl pranng o h volag

10 8 of h hgh volag bu llura a. Th followng ar h xpron for an,, : an a a Q P Q P (.3) whr p a p a I an Q I P n co From aor algbrac uaon (.6) h followng uaon can b oban: for n co (.33) Fgur -5: A ngl machn connc o xrnal nwork Th mof aor algbrac uaon rfrr o h ranformr bu ar gvn by n co (.34)

11 9 rchhoff olag law bwn ranformr bu an h rmnal volag of h gnraor ar gvn hr a: j j j j (.35) Th h mofcaon ugg n [48] o mak h P gn npnn of h xrnal ym paramr. placng by n h abov uaon gv j j j (.36) ualzng h ral an hypohcal componn n h abov uaon prov h algbrac uaon of h mof aor rfrr o h ranformr bu. Th mof aor uaon of algbra whch ar rfrr o h ranformr bu ar oban by uang h ral an hypohcal con of h abov uaon. Th valy of h uaon hol goo for any machn vn n h ambnc of mulpl machn. n co (.37) uang (.6), (.3) an rarrangng on can g co (.38) n (.39) Th abov uaon n marx form n co (.4)

12 3 Th rmnal volag of h machn gvn by (.4) Lnarzng (.6) aroun an oprang conon mployng fr orr Taylor r approxmaon an upon mplfcaon on can oban 4 3 (.4) whr o co n o co n 3 4 o co n o co n,,, f m an no h valu a h nal oprang conon. Th lnarz vron of h uaon (.) o (.5) an (.7) ar a follow: T (.43) m B (.44) m m m D T T H (.45)

13 3 f o T (.46) (.47) rf A A f T (.48) Th conan o 6 an o 3 ar gvn blow: n co 3 4 n 5 n co 6 v I co n v co 3 co n v

14 3 whr Th fn conan o 6 ar mlar o ho of h mol conan o 6 of h orgnal Hffron Phllp (HP).Howvr, hr no furhr rfrncng o an b an hy o no pn on h uvaln racanc. In h mo, u o h nably of urng lnarzaon hr mor conan v o v3 ar a a h oru, volag of h fl an rmnal volag juncon pon rpcvly, whch nguh h mol from h orgnal HP mol a prn n Fgur.6. In nanc of gnorng volag vaon n h ranformr, h mol accuraly rflc a frm ym havng xrnal racanc ncal o h racanc of h ranformr. In ca h nomnal ym alo gnf h conon of full loang, hn h mol P furnh h umo pha lag. Informaon of loa flow boh a h ranformr an h rmnal of h gnraor can nabl h acuon of h -conan n ral m. Hnc, h paramr of h gn of any P pnng on h mol can aly b alr a rgular m nrval hrough local maurmn, n orr o accommoa conrabl chang n h ym rucur.

15 33 Fgur -6: Lnarz mol of a ngl machn n a connc nwork.5. U of Mof Hffron Phllp mol n Mul-Machn ym Th mol rv abov vry gnral n naur bcau vry gnrang aon n h powr ym uually nr-connc o h ranmon nwork of hgh volag hrough h man of a p-up ranformr. o h mol can b u npnnly for ach gnraor n a mul-machn nvronmn. For h gnraor n mul-machn powr ym o 6 ar conanan o 3 ar gvn blow: co n

16 n co n 5 6 n v I co v n co v3 whr co Th lnar a pac mol for ach machn can b oban a A B P B (.49) whr

17 35 B D H H H H A ; ; 4 B B (.5) To 3 To T o T A o A5 A6 TA A 3 TA TA TA TA a varabl ar ; m; ; f,,, m m f f In h h h a pac mol aop for vlopng h a fback conrollr n h conx of powr ym of mulpl machn. I can b obrv ha h parcular a pac marx ju 4 x 4 z marx an pn only on h paramr local o h gnrang aon. Th ranform h larg powr ym a fback conrollr gn o mall cnralz a fback conrollr gn. In h followng chapr hown ha h LQ an pol placmn gn ba on h mol rul n coorna conrollr.