Vaxtang bancaZe,,arasimetriuli damyarebuli reJimebis analizi
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vaxtang bancaZe ,,arasimetriuli damyarebuli reJimebis analizi” წარმოდგენილია დოქტორის აკადემიური ხარისხის მოსაპოვებლად საქართველოს ტექნიკური უნივერსიტეტი თბილისი, 0175, საქართველო 2010 წელი საავტორო უფლება © 2010 ,,vaxtang bancaZe” 2010 weli 2 საქართველოს ტექნიკური უნივერსიტეტი ,,energetikisa da telekomunikaciis fakulteti” ჩვენ, ქვემორე ხელისმომწერნი ვადასტურებთ, რომ გავეცანით ,,vaxtang bancaZis” მიერ შესრულებულ სადისერტაციო ნაშრომს დასახელებით: ,,arasimetriuli damyarebuli reJimebis analizi” და ვაძლევთ რეკომენდაციას საქარველოს ტექნიკური უნივერსიტეტის ,,energetikisa da telekomunikaciis fakultetis” სადისერტაციო საბჭოში მის განხილვას დოქტორის აკადემიური ხარისხის მოსაპოვებლად. ხელმძღვანელი: /nina Turqia/ რეცენზენტი: რეცენზენტი: რეცენზენტი: 3 საქართველოს ტექნიკური უნივერსიტეტი 2010 წელი ავტორი: ,,vaxtang bancaZe” დასახელება: ,,arasimetriuli damyarebuli reJimebis analizi” ფაკულტეტი: ,,energetikisa da telekomunikaciis fakulteti” ხარისხი: დოქტორი სხდომა ჩატარდა: თარიღი : ინდივიდუალური პიროვნებების ან ინსტიტუტების მიერ ზემომოყვანილი დასახელების დისერტაციის გაცნობის მიზნით მოთხოვნის შემთხვევაში მისი არაკომერციული მიზნებით კოპირებისა და გავრცელების უფლება მინიჭებული აქვს საქართველოს ტექნიკურ უნივერსიტეტს. ავტორის ხელმოწერა ავტორი ინარჩუნებს დანარჩენ საგამომცემლო უფლებებს და არც მთლიანი ნაშრომის და არც მისი ცალკეული კომპონენტების გადაბეჭდვა ან სხვა რაიმე მეთოდით რეპროდუქცია დაუშვებელია ავტორის წერილობითი ნებართვის გარეშე. ავტორი ირწმუნება, რომ ნაშრომში გამოყენებული საავტორო უფლებებით დაცული მასალებზე მიღებულია შესაბამისი ნებართვა (გარდა ის მცირე ზომის ციტატებისა, რომლებიც მოითხოვენ მხოლოდ სპეციფიურ მიმართებას ლიტერატურის ციტირებაში, როგორც ეს მიღებულია სამეცნიერო ნაშრომების შესრულებისას) და ყველა მათგანზე იღებს პასუხისმგებლობას. 4 რეზიუმე vaxtang bancaZis disertacia ,,arasimetriuli damyarebuli reJimebis analizi” exeba aqtualur problemas. naSromi Sedgeba 141 gverdisagan da doqtoris akademiuri xarisxis mosapoveblad wardgenili disertaciis gaformebis instruqciis mixedviT moicavs: titulis gverds, xelmowerebis gverds, saavtoro uflebebis gverds, reziumes or enaze (qarTul-inglisuri), Sinaarss (sarCevs), naxazebis nusxas. ZiriTadi teqsti Sedgeba Sesavlis, literaturis mimoxilvis, eqvsi Tavis, daskvnis da gamoyenebuli literaturis siisagan. SesavalSi ganxilulia kvlevis aqtualoba, problemis Seswavlis mdgomareoba, kvlevis mizani da amocanebi, kvlevis sagani, Teoriuli da meTedologiuri safuZvlebi, kvlevis mecnieruli siaxle, naSromis praqtikuli mniSvneloba, naSromis aprobacia, misi moculoba da struqtura. pirvel TavSi ganxilulia aRniSnul problemasTan dakavSirebuli Teoriuli safuZvlebi. ganxilulia eleqtruli qselebis analizis topologiuri meTodebi. sistemis mdgomareobis amsaxveli gantolebebi (sxvadasxva safexuris mqone Zabvis qselebisaTvis), aRwerilia reJimis aqtiuri da pasiuri parametrebi, Canacvlebis sqemis saxeebi. ganxilulia aRniSnuli sakiTxTan dakavSirebuli literatura. meore TavSi mocemulia maTematikuri modelirebis sakiTxebi. damuSavebuli da aRwerilia ganzogadebuli parametrebis gaangariSebis meTodika, romelic iZleva garkveul upiratesobas arsebulTan SedarebiT da agreTve iZleva kompiuteruli resursebis dazogvis saSualebas. mesame TavSi mocemulia normaluri reJimis parametrebis gaangariSebis algoriTmi. Seicavs Zabvis regulirebis imitacias. iTvaliswinebs datvirTvis damokidebulebas Zabvaze, asaxuls statikuri maxasiaTebliT. programaSi gaTvaliswinebulia informaciis dagroveba monacemTa bazaSi cxrilebis saxiT, romelic warmoadgens SemdgomSi sawyis informacias sxvadasxva tipis (mokle SerTvebis reJimebis gaangariSebis SemTxvevaSi) gaangariSebebSi. meoTxe TavSi mocemulia kvlevebis ZiriTadi sakiTxebi dakavSirebuli simetriuli da arasimetriuli mokle SerTvebis angariSebTan. ganxilulia rTuli simetriuli mokle SerTvebis angariSi, simetriul mdgenelTa meTodis gamoyeneba arasimetriuli reJimebis gaangariSebisas. mexuTe TavSi damuSavebulia meTodika, romelic exeba erTdrouli simetriuli da arasimetriuli mokle SerTvebis gaangariSebas. arasimetriuli avariuli reJimebis parametrebis gaangariSebis erTiani meTodikis Camoyalibeba saSualebas iZleva Catardes Sesabamisi angariSebi nebismieri saxisa da kombinaciis avariis dros. rogorc cnobilia arasimetriuli dazianebebis analizi eyrdnoba simetriul mdgenelTa meTods, romlis arsi 5 mdgomareobs arasimetriuli reJimis daSlaSi sam simetriul reJimad, raTa Semdgom TiToeuli mimdevrobis sqemaSi gamoyenebuli iqnes yvela is meTodi, romelic samarTliania simetriuli sistemebisaTvis. amis uflebas iZleva is debuleba, rom calkeuli mimdevrobis sqemaSi cirkulirebs mxolod Sesabamisi mimdevrobis denebi da urTierTkavSiri Zabvebsa da denebs Soris aRiwereba cnobili kanonebiT, xolo kavSiri mimdevrobebs Soris myardeba avariis adgilas im sasazRvro pirobebis mixedviT, romelic axasiaTebs ama Tu im dazianebas. amgvarad winaswar unda dadgindes pirdapiri, uku da nulovani mimdevrobis sqemebis pasiuri parametrebi da gaiTvalos maTi Sesabamisi kvanZuri gamtareblobisa da kvanZuri winaRobebis matricebi ganivi asimetriis SemTxvevaSi. nebismieri saxis arasimetriuli reJimis warmodgena erTfaza dazianebebis Sesabamisi eleqtruli reJimebis superpoziciiT saSualebas iZleva sxvadasxva saxis arasimetriuli reJimi, da maT Soris mokle SerTvebic, aRiweros wrfivi gantolebebiT, rac Tavis mxriv SeuzRudavs gaxdis SesaZlo avariebis analizs. gantolebebis koeficientebi, anu kvanZebis sakuTari da urTierTwinaRobebi ganivi asimetriis dros gaTvlili unda iyos winaswar (sawyisi qselis Sesabamisad) pirdapiri, uku da nulovani mimdevrobis sqemebisaTvis. kvanZuri winaRobebis matricis elementebi ucvleli rCebian avariebis raodenobisa da kombinaciebis miuxedavad. dazianebis unificirebis mizniT sxvadasxva saxis mokle SerTvebi warmodginda, rogorc erTfaza mokle SerTvebis kombinacia. raTa eleqtruli reJimis aRmweri gantolebebi Sedges erTiani wesiT garkveuli (mokle SerTvis saxeobidan gamomdinare) SemzRudavi (sasazRvro) pirobebis gaTvaliswinebiT. mag. orfaza mokle SerTva miwaze - rogorc ori erTfaza mokle SerTva, samfaza mokle SerTva rogorc sami erTfaza mokle SerTva. am dros aucileblad gaTvaliswinebuli unda iyos kvanZebis Serwymis piroba (im kvanZebis sadac ganixileba erTfaza mokle SerTvebi), rac gulisxmobs am kvanZebis sakuTari da urTierTwinaRobebis tolobas. erTiani midgomis Camosayalibeblad fazaTaSoriso mokle SerTvac warmodginda erTfaza mokle SerTvebis kombinaciiT. daeyrdno orfaza mokle SerTvis (miwaze) SemTxvevisaTvis miRebul gantolebas da gaiTvaliswina fazaTaSorisi mokle SerTvis pirobebi, romlebic daedo am gantolebaTa sistemas. bolos mocemulia daskvnebi da gamoyenebuli literaturis CamonaTvali. 6 Abstract Vakhtang Bantsadze’s dissertation “Analysis of asymmetric established regimen” concerns actual problems. The work consists of 141 pages and according the guidance for thesis drawing up, presented for receiving academic degree of Doctor, contains: pages of a title, a signature, author’s rights, abstract in two languages (Georgian- English), content, the list of drawings. Main text consists of introduction, discussion of the literature, six chapters, conclusion and the list of used literature. Actuality of the research, conditions of problem learning, objects and goals, subject of the research, theoretical and methodological basis, scientific news of the research, approbation of the work, its size and structure are reviewed in the introduction. Theoretical principles associated with mentioned problem are discussed in the first chapter. Topological methods of electrical network analysis are discussed. Equations expressing the condition of the system (for networks of various level voltage), active and passive parameters of regimen, replacement schemes are discussed. Literature associated to this issue is reviewed. The issues of mathematical modeling are given in the second chapter. Plural methods of calculation of generalized parameters are worked out and discussed, which give certain preference in comparison with existed ones and it lets to preserve computer resources. The algorithm of calculation of normal regimen parameters is given in the third chapter. It contains imitation of voltage regulation. It considers relation of loading and voltage, expressed with statistical characters. Accumulation of information in database as tables is considered in the program, which consequently represents an initial information in various (in the case of calculation of short circuits) calculations. Main issues associated with symmetric and asymmetric short circuits are given in the fourth chapter. Calculation of complex symmetric short circuits, using symmetric part during the calculation of asymmetric regimens are discussed. In the fifth chapter the plural methods, which concern calculation of simultaneous symmetric and asymmetric short circuits, are discussed. Formation of the united plural methods for calculation of parameters of asymmetric faulty regimen lets conduct corresponding calculations at any type and combination faults. As it is known the analysis of asymmetric faults is based on the method of symmetric parts, the main point of which is division of existing asymmetric regimen into three symmetric ones to use consequently in the scheme of each sequence all those methods, which are valid for symmetric systems. This is allowed by the regulation, which says that in the scheme of separate sequence only currents of corresponding sequence circulate and interface between voltages and currents are described by known laws, and a connection between sequences is established at the area of faults according those boundary conditions which is characteristic for various faults. Thus passive parameters of direct, back or zero sequences schemes must be determined and in the case of asymmetry lateral matrixes of corresponding nodular conductivity and resistance must be calculated preliminarily. Presenting any type asymmetric regimen with super-position of electrical regimens corresponding to single-phase faults lets describe various type asymmetric regimens, including short circuits, with linear equations, which makes the analysis of probable faults unlimited. 7 Coefficients of equations i.e. own and inter-resistance of nodes at lateral asymmetry must be calculated preliminarily (corresponding initial network) for the schemes of direct, back and zero sequences. In the purpose of faults unification we have represented different types of short circuits as combination of single-phase short-circuits. To make equations describing electrical regimens according united rule (coming out of circuit type) considering restrictive (boundary) conditions. For example: double-phase short-circuit on the ground – as two single-phase short circuit, three-phase short circuit as three single- phase short circuit. In this case circumstances of nodes (those nodes which are reviewed as single-phase short circuits) confluence must be considered, which means equality of theses nodes own and inter-resistance. For establishing united attitude we have represented inter-phase short circuits too with combination of single-phase short circuits. We came out of the equation received for double-phase short circuits (on the ground) and considered conditions of inter-phase short circuits which were added to these system of equations. At the end conclusions and the list of used literature is given. 8 Sinaarsi Sesavali............................................................................................................................................................. 11 Tavi I literaturis mimoxilva................................................................................................................... 14 1.1 eleqtruli sistemebis Canacvlebis sqemebi da maTi elementebi.......................................................................................................................................... 16 1.2 sistemis mdgomareobis amsaxveli ZiriTadi gantolebebi............... 21 1.3 kvanZuri Zabvebis gantolebebi..................................................................................... 21 1.4 incidenciis I da II matrica............................................................................................ 27 1.5 kirxhofis I da II kanonebiT asaxuli sistemis mdgomareobis gantolebebi...................................................................................................................................... 32 1.6 kvanZuri Zabvebis gantolebis Sedgena transformatoruli kavSirebis gaTvaliswinebiT............................................................................................ 35 1.7 konturuli gantolebebi.................................................................................................... 42 Tavi 2 maTematikuri modelirebis zogierTi sakiTxebi..................................................... 44 2.1 kvanZebis sakuTari da urTierTwinaRoba........................................................... 44 Sedegebi da maTi gansja 2.2 kvanZebis sakuTari da urTierTwinaRobebisa da Stoebis sakuTari da urTierTgamtarobebis matricebis gaangariSebis meTodebi............................................................................................................................................... 48 2.3 matricis Sebrunebis operaciis fizikuri arsi......................................... 57 2.4 gausis meTodis Sesabamisoba sqemis gardasaxvebTan............................. 62 Tavi 3 normaluri reJimis parametrebis gaangariSebis algoriTmi...................... 64 Tavi 4 damyarebuli reJimebis angariSi simetriuli da arasimetriuli mokle SerTvebis dros............................................................................ 69 4.1 rTuli simetriuli avariuli reJimebis analizi.................................... 69 4.2 simetriul mdgenelTa gamoyeneba arasimetriuli reJimebis angariSisas........................................................................................................................................ 82 4.3 orfaza mokle SerTva........................................................................................................... 86 4.4 erTfaza mokle SerTva......................................................................................................... 88 4.5 orfaza mokle SerTva miwaze........................................................................................ 90 Tavi 5 5.1 droSi Tanxvedrili erTfaza mokle SerTvebi........................................... 93 5.2 sxvadasxva saxis mokle SerTvis warmodgena erTfaza mokle SerTvebiT............................................................................................................................................ 100 5.3 samfaza mokle SerTva........................................................................................................... 101 5.4 orfaza mokle SerTva miwaze........................................................................................ 103 5.5 110kv-iani qselisaTvis Catarebuli angariSebis Sedegebis analizi.................................................................................................................................................. 107 Tavi 6 fazaTaSorisi mokle SerTvebi.................................................................................................. 120 daskvna................................................................................................................................................................. 133 danarTebi......................................................................................................................................................... 138 literatura................................................................................................................................................... 141 9 ნახაზების ნუსხა ნახაზი 1 martivi Sekruli qselis Canacvlebis sqema...................................... 21 ნახაზი 2 martivi qselis Canacvlebis sqema incidenciis I matricis misaRebad.............................................................................. 29 ნახაზი 3 martivi qselis Canacvlebis sqema incidenciis II matricis misaRebad.............................................................................. 31 ნახაზი 4 martivi qselis Canacvlebis sqema transformatoruli kavSirebis gaTvaliswinebiT............................................................. 34 ნახაზი 5 rTuli qselis Canacvlebis sqema konturuli gantolebebis misaRebad..................................................................... 43 ნახაზი 6 zogadi sqema kvanZebis n raodenobiT......................................... 44 ნახაზი 7 ,,T”_sebri sqema.................................................................................................. 45 ნახაზი 8 martivi qselis Canacvlebis sqema kvanZuri winaRobebis misaღebad................................................................................................... 46 ნახაზი 9 martivi qselis Canacvlebis sqemebi kvanZebis sakuTari da urTierTwinaRobebis matricis misaRebad........................... 49 ნახაზი 10 martivi qselis Canacvlebis sqemebi Stoebis sakuTari da urTierTgamtarobebis matricis misaRebad........................ 55 ნახაზი 11 StoebSi CarTuli Zabvis wyaroebis Secvla denis wyaroebiT.................................................................................................. 58 ნახაზი 12 Zabvisa da denis wyaros moqmedebiT miRebuli Sekruli da gaxsnili oTxpolusebi................................................................ 59 ნახაზი 13 rTuli Sekruli qseli....................................................................... 62 ნახაზი 14 mokle SerTvis dros aqtiur da pasiur qselSi Zabvis wyaroebis CarTva................................................................................... 70 ნახაზი15 fizikur modelSi Zabvis wyaroebis Secvla denis wyaroebiT.................................................................................................. 72 ნახაზი 16 normaluri da avariuli reJimebis zeddeba............................ 74 ნახაზი 17 arasimetriul veqtorTa sistema.................................................... 82 ნახაზი 18 arasimetriuli veqtorebis daSla simetriul mdgenelebad............................................................................................. 83 ნახაზი 19 orfaza mokle SerTva......................................................................... 86 ნახაზი 20 Zabvebisa da denebis veqtoruli diagrama orfaza mokle SerTvis dros........................................................................... 88 ნახაზი 21 erTfaza mokle SerTva....................................................................... 88 ნახაზი 22 Zabvebisa da denebis veqtorul diagrama erTfaza mokle SerTvis dros........................................................................... 90 ნახაზი 23 orfaza mokle SerTva miwaze.......................................................... 90 ნახაზი 24 Zabvebisa da denebis veqtoruli diagrama orfaza miwaze mokle SerTvis dros............................................................ 92 ნახაზი 25 pirdapiri mimdevrobis sqema simetriuli samfaza mokle SerTvis dros................................................................................................................... 96 10 ნახაზი 26 uku mimdevrobis sqema simetriuli samfaza mokle SerTvis dros................................................................................................................... 96 ნახაზი 27 nulovani mimdevrobis sqema simetriuli samfaza mokle SerTvis dros................................................................................................. 96 ნახაზი 28 pirdapiri mimdevrobis sqemaSi mokle SerTvis modelireba denis wyaroebiT........................................................................... 97 ნახაზი 29 uku mimdevrobis sqemaSi mokle SerTvis modelireba denis wyaroebiT............................................................................................................. 97 ნახაზი 30 nulovani mimdevrobis sqemaSi mokle SerTvis modelireba denis wyaroebiT........................................................................... 97 ნახაზი 31 110kv Zabvis eleqtruli qseli........................................................................ 109 ნახაზი 32 pirdapiri mimdevrobis Canacvlebis sqema denebisa da Zabvebis angariSiT....................................................................................................... 110 ნახაზი 33 uku mimdevrobis Canacvlebis sqema............................................................ 110 ნახაზი 34 nulovani mimdevrobis Canacvlebis sqema............................................. 110 ნახაზი 35 110kv Zabvis eleqtruli qseli me-2 kvanZSi samfaza mokle SerTvis Semdeg............................................................................................. 113 ნახაზი 36 pirdapiri mimdevrobis Canacvlebis sqema Secvlili sqemisTvis.............................................................................................................................. 113 ნახაზი 37 uku mimdevrobis Canacvlebis sqema Secvlili sqemisTvis. 113 ნახაზი 38 nulovani mimdevrobis Canacvlebis sqema Secvlili sqemisTvis.............................................................................................................................. 113 ნახაზი 39 Secvlili sqemisTvis pirdapiri mimdevrobis Canacvle- bis sqemaSi denebisa da Zabvebis ganawileba.................................... 114 ნახაზი 40 denebis diagramebi a) erTfaza mokle SerTvis dros BfazaSi (i kvanZSi); b) erTfaza mokle SerTvis dros C fazaSi (j kvanZSi)..................................................................................................... 121 ნახაზი 41 denebis diagramebi: a) i kvanZis pirdapiri da uku mimdevrobis denebis diagrama. b) j kvanZis pirdapiri da uku mimdevrobis denebis diagrama 0 120 -iT Semobrune- bis Semdeg............................................................................................................................. 122 ნახაზი 42 pirdapiri mimdevrobis sqemaSi i(A faza) da j (B,C faza) kvanZebSi mokle SerTvis denebis modelireba denis wyaroebiT.............................................................................................................................. 124 ნახაზი 43 uku mimdevrobis sqemaSi i (A faza) da j(B,C faza)kvanZebSi m. S-is denebis modelireba denis wyaroebiT................................... 124 ნახაზი 44 pirdapiri mimdevrobis sqemaSi i(B faza) da j (B,C faza) kvanZebSi m.S-is denis modelireba denis wyaroebiT................ 126 ნახაზი 45 uku mimdevrobis sqemaSi i(B f) da j (B,C f) kvanZebSi m.S-is denebis modelireba denis wyaroebiT..................................... 126 ნახაზი 46 pirdapiri mimdevrobis sqemaSi i(C faza) da j (B,C faza) kvanZebSi m.S-is denis modelireba denis wyaroebiT................ 128 ნახაზი 47 uku mimdevrobis sqemaSi i (C faza) da j (B,C faza) kvanZebSi m.S-is denebis modelireba denis wyaroebiT 128 11 შესავალი eleqtruli energiis gadacema da ganawileba unda xdebodes qselis muSaobis normalur reJimSi, anu uzrunveyofili unda iyos muSaobis saimedooba da energiis xarisxi. xSirad normaluri reJimis darRveva xdeba sxvadasxva avariuli situaciebisas. magaliTad mokle SerTvebiT, xazis an fazis gawyvetebiT, an maTi kombinaciiT (sxvadasxva saxis grZivi da ganivi dazianebebiT). qselis elementebi daculi unda iyos avariuli denebis mier dazianebisagan. energetikuli sistemis mdgradi, uavario da ekonomiuri muSaoba SeuZlebelia sareleo dacvisa da avtomatikis mowyobilobebis gareSe. dazianebuli ubnis swrafi da seleqtiuri gamorTva xdeba Tanamedrove sareleo dacvis mowyobilobebiT. maTi saimedo muSaobisaTvis gaTvlili unda iyos SesaZlo avariuli parametrebi. am parametrebis gaTvla gaangariSebas eZRveneba mravali naSromi da jer kidev mimdinareobs am mimarTulebiT kvleva Zieba. Cven SevecadeT Cveni wvlili Segvetana am saqmeSi da davamuSaveT meTodika rTuli avariuli reJimebis gasaangariSeblad. arsebuli meTodebi saSualebas iZlevian gaviangariSoT erTjeradi avariis dros reJimis parametrebi. dazianebebi SeiZleba iyos simetriuli da arasimetriuli mokle SerTvebi, xazisa da fazis gawyvetebi. es meTodebi aseve iZlevian saSualebas gaangariSebuli iqnas denebi da Zabvebi erTroulad ori dazianebis SemTxvevaSi, rogoricaa magaliTad erT ubanSi fazis gawyveta da meore ubanSi simetriuli an arasimetriuli mokle SerTva. Cvens mier damuSavda meTodika, romelic avariuli parametrebis gaangariSebis saSualebas iZleva nebismieri saxisa da raodenobis ganivi dazianebis (anu mokle SerTvis nebismieri kombinaciis) dros. amis SesaZleblobas arsebuli meTodebi ar iZleodnen. 12 warmodgenili meTodikis safuZvelze SevqmeniT maTematikuri modeli. am meTodis gamoyenebiT konkretuli qselisaTvis CavatareT angariSebi erTdrouli arasimetriuli dazianebebis SemTxvevaSi. angariSebs vawarmoebdiT programa MATLAB-is saSualebiT. am modelis safuZvelze unda damuSavdes programa monacemTa bazis marTvis sistemaSi Tanamedrove dizainiTa da grafikiT. naSromSi warmodgenilia arasimetriuli avariuli reJimebis parametrebis gaangariSebis algoriTmebi, dafuZvnebuli sistemis mdgomareobis amsaxvel kvanZur gantolebebze. arasimetriuli mokle SerTvis SemTxvevaSi, simetriuli sistemebisaTvis Camoyalibebuli Teoria gadaitaneba avariuli reJimebis simetriul mdgenelebSi. raki avariuli denebis mdgenelebi cirkulireben mxolod Sesabamisi mimdevrobis sqemaSi, yvela is kanoni da debuleba, rac samarTliania simetriuli sistemebisaTvis, samarTliania TiToeuli mimdevrobis sqemaSia rsebuli eleqtruli reJimebisaTvis. e.i TiToeuli mimdevrobis sqemaSi damokidebuleba denebsa da Zabvebs Soris aRiwereba kvanZuri gantolebebiT, winaswar, TiToeuli mimdevrobis sqemisaTvis gaTvlili kvanZuri winaRobebis matricis saSualebiT. am gantolebaTa gaangariSeba xdeba erTfaza mokle SerTvisaTvis dadgenili sasazRvro pirobebis gaTvaliswinebiT, rasac ucnobebis ricxvi dahyavs dazianebaTa ricxvamde. amgvarad erTfaza mokle SerTvis sasazRvro pirobebi mosaxerxebelia unificirebuli gantolebebis misaRebad. amitom yvela saxis mokle SerTvas ganvixilavT rogorc erTfaza mokle SerTvis reJimebis zeddebas. ase magaliTad, Tu sami erTfaza mokle SerTvis (A, B da C fazebSi) aRmwer gantolebebs davadebT kvanZebis Serwymis pirobas, rac iTvaliswinebs kvanZebis sakuTari da urTierTwinaRobebis tolobas samive mimdevrobis sqemebisaTvis, miviRebT dazianebis adgilas denebis fazur 13 mniSvnelobebs. igive iTqmis miwaze orfaza mokle SerTvis SemTxvevaSi. aRniSnuli gantolebebi nebismieri saxis da raodenobis erTdrouli arasimetriuli mokle SerTvis (miwaze) gaangariSebis saSualebas iZlevian. ganxiluli meTodikis Tavisebureba mdgomareobs imaSi, rom nebismieri saxis dazianeba warmoidgineba rogorc erTfaza mokle SerTvebis reJimebis zeddeba. am meTodiT movaxdineT aseve fazaTaSoriso mokle SerTvebis gaangariSebac. fazaTaSorisi mokle SerTvebic warmovadgineT aRniSnuli gantolebebiT, romelTac daedoT damatebiTi piroba, ganpirobebuli erTi fazis meore fazasTan uSualo SeerTebiT. am damatebiT pirobas Seesabameba erT-erTi dazianebuli fazis denebis (pirdapiri da uku mimdevrobis sqemebSi) Semobruneba 120 0 -iT. amgvarad Cven saSualeba mogveca, raki yvela dazianeba warmoadgens erTfaza mokle SerTvebis kombinacias, gaviangariSoT nebismieri simetriuli da arasimetriuli avariuli reJimebi. 14 Tavi I naSromSi warmodgenil problemasTan dakavSirebiT arsebuli literaturis mimoxilva energosistemis proeqtireba da eqspluatacia moiTxovs didi raodenobiT kvlevebs da gaangariSebis Catarebas normaluri da avariuli reJimebis parametrebis gansazRvrasTan dakavSirebiT. am kvlevebs miekuTvnebian damyarebuli normaluri reJimebis gaangariSebebi, statikuri da dinamikuri mdgradobis analizi, aqtiuri da reaqtiuli simZlavreebis ganawilebis optimizacia, mokle SerTvis denebis gansazRvra, maregulirebeli mowyobilobebisa da avariis sawinaaRmdego avtomatikis danayenTa parametrTa ganszRvra da sxva. energosistemis ganviTareba iwvevs am tipis samuSaoebis garTulebas, rac Tavis mxriv moiTxovs Tanamedrove kompiuteruli teqnologiebis maRal dones. damyarebuli reJimis gaangariSebas gansakuTrebuli mniSvneloba eniWeba im garemoebebis gamo, rom am angariSis Sedegebi (nakadganawileba, kvanZuri Zabvebi, Zabvisa da simZlavris danakargebi) aucilebelia ara marto eqspluataciis procesisaTvis, aramed aucilebelia sxvadasxva amocanebis amoxsnisas. rogorebicaa reJimebis optimizacia, gardamavali procesebis angariSi mokle SerTvebis angariSi da sxva. eleqtroenergetikuli sistemis reJimebis gaangariSebasTan dakavSirebiT gamoqveynebulia didi raodenobiT literatura. [1] am SromebSi ganxilulia am problemis, kerZod reJimis parametrebis gaangariSebis sxvadasxva meTodebi. mocemulia topologiuri analizis safuZvlebi da am problemis gadawyvetis Tanamedrove midgoma kompiuteruli teqnologiebis gamoyenebiT [2] detalurad aris ganxiluli sistemis mdgomareobis ZiriTadi gantolebebi da am gantolebebis klasifikacia [3] naSromi eZRvneba eleqtruli sistemis damyarebuli reJimebis gaangariSebis sxvadasxva meTodebs (kvanZurs, konturuls). garda 15 amisa ganxilulia am amocanis amoxsnis sxvadasxva meTodebi rogorc pirdapiri aseve iteraciuli. gamokveTilia am meTodebis gansxvaveba da upiratesoba konkretuli amocanebis gadawyvetis dros. gansakuTrebuli adgili ukavia Tanamedrove algoriTmebs, romlebic didi ganzomilebis amocanebis gadawyvetis saSualebas iZleva da uzrunvelyofs kompiuteruli resursebis efeqturad gamoyenebas. rogorc ukve aRvniSneT normaluri reJimis parametrebi gamoiyenebian avariuli reJimebis gasaangariSebladac. TviTon avariuli reJimis parametrebis gansazRvra aseve aucilebel amocanas warmoadgens, vinaidan am avariuli parametrebis winaswari gansazRvris gareSe warmoudgenelia sistemis usafrTxo muSaobis uzrunvelyofa. eleqtruli reJimebis angariSis Casatareblad aucilebelia eleqtruli sistemis principialuri sqemis warmodgena misi Canacvlebis sqemiT nebismieri eleqtruli reJimi rogorc normaluri aseve avariuli aRiwereba erTi da igive gantolebebiT. amitom gansakuTrebuli yuradReba eqceva sistemis mdgomareobis aRmwer gantolebebs. warmodgenil literaturaSi [4] ganxilulia sistemis mdgomareobis amsaxveli kvanZuri da konturuli gantolebebi. gaanalizebulia am meTodebis Taviseburebani da gamokveTilia kvanZuri gantolebebis upiratesoba konturulTan SedarebiT. ganxilulia agreTve miRebuli gantolebebis amoxsnis pirdapiri da iteraciuli meTodebi. mocemulia topolologuri analizis safuZvlebi, sistemis mdgomareobis amsaxveli gantolebebis warmodgena incidenciis matricebis saSualebiT, gantolebaTa amoxsnis rogorc pirdapiri (matricis Sebruneba, gausis meTodi da sxva), aseve iteraciuli meTodebi (martivi iteracia, zeidelisa da niutonis meTodi). gansakuTrebuli yuradReba aqvs daTmobili ganzogadoebuli parametrebiani matriculi gantolebebiT sistemis mdgomareobis aRweras. am gantolebebis gamoyenebas rogorc normaluri aseve avariuli reJimebis parametrebis gaangariSebis dros. 16 avariuli reJimebis gaangariSebis Sedegad miRebuli aqtiuri parametrebi warmoadgenen erT-erT safuZvels sareleo dacvis samsaxuris gamarTuli muSaobisaTvis. amJamad arsebuli meTodebiT [2,9] warmoebs erTjeradi grZivi da ganivi dazianebebis gaangariSeba. samfaza mokle SerTva, erTfaza mokle SerTva, fazaTaSorisi mokle SerTva, orfaza mokle SerTva miwaze, aseve xazisa da fazis gawyvetebi. am monacemebis safuZvelze xdeba sareleo dacvis danayenis SerCeva - Semowmeba. bolo dros warmodgenili kompiuteruli programebiT gaangariSebas axdenen erTdroulad ori dazianebis, simetriuli da arasimetriuli, SemTxvevebisTvis. Cven CavatareT samuSaoebi da kvleva-Zieba raTa mogvexerxebina yvela tipis ganivi dazianebis gaangariSeba. arasimetriuli reJimis angariSi ganxilulia simetriul mdgenelTa meTodis bazaze [2]. am meTodis Tanaxmad arasimetriuli reJimi warmoadgens sam simetriuli reJimis zeddebas, romlebic Seesabamebian pirdapiri, uku da nulovani mimdevrobis sqemebs. TiToeuli am mimdevrobis reJimis angariSisas samarTliania yvela is meTodika, rac samarTliania simetriuli sistemebisaTvis. $1.1 eleqtruli sistemebis Canacvlebis sqemebi da maTi elementebi imisaTvis rom viangariSoT eleqtruli sistemis muSaobis reJimi saWiroa, rom Tavdapirvelad SevadginoT misi Canacvlebis sqema. Canacvlebis sqemas (an ubralod sqemas) uwodeben eleqtruli wredis grafikul gamosaxulebas romelic gviCvenebs misi monakveTebis Tanmimdevrul SeerTebas da amasTanave asaxavs gansaxilveli eleqtruli wredis Tvisebebs. Eeleqtruli wredi da Sesabamisad misi sqema Seicaven Stoebs, kvanZebs da konturebs. 17 Sto_es aris eleqtruli wredis nawili romelic Sedgeba mimdevrobiT SeerTebuli elementebisagan (maTSi unda gaedinebodes erTi da igive sididis deni). kvanZi_es aris ori an meti Stos SeerTebis adgili. konturi_es aris nebismieri Caketili gza romelic gadis ramodenime Stoze. Tu eleqtruli wredis sqemas ar gaaCnia konturebi, maSin mas ewodeba gaxsnili. Ggaxsnil sqemebSi TiToeuli kvanZis kveba xorcieldeba mxolod erTi mxridan. TiToeuli kvanZi iRebs kvebas araumetes erTi Stodan. romelime Stos gamorTva gamoiwvevs yvela im kvanZis kvebis Sewyvetas romlebic kvebas iRebdnen am Stos gavliT. sqema, romelic Seicavs Tundac erT konturs ewodeba Caketili sqema. Caketil sqemaSi arsebobs erTi kvanZi mainc, romelic kvebas iRebs ori an meti Stodan. romelime Stos gamorTva ar gamoiwvevs kvebis Sewyvetas. eleqtruli sqemis elementebi iyofian aqtiur da pasiur elementebad. pasiuri elementebi qmnian eleqtruli denebis gavlis gzebs. eleqtruli sistemis pasiuri elementebi iyofian grZiv da ganiv elementebad. ganivi pasiuri elementebi – es aris Stoebi, romlebic CarTulni arian el. sqemis kvanZebsa da neitrals Soris, anu Zabvis mqone kvanZsa daNnulovani potencialis mqone kvanZs Soris. grZivi pasiuri elementebi es aris Stoebi, romlebic aerTeben yvela kvanZs garda kvanZisa romelsacAaqvs nulis toli Zabva anu grZivi Stoebi ar arian SeerTebulni neitralTan. grZivi elementebi Seicaven eleqtrogadamcemi xazebis aqtiur da induqtiur winaRobebs, transformatorebis gragnilebis aqtiur da induqtiur winaRobebs, grZivi sakompensacio mowyobilobebis tevadur winaRobebs. ganivi pasiuri elementebi Seesabamebian xazebis gamtareblobebs miwis mimarT, reaqtorebs da kondensatorebs, romlebic CarTulni arian miwasTan (kondensatorTa batareebi, maSuntebeli reaqtorebi). Aaseve transformatoris foladSi simZlavris 18 danakargebi, Canacvlebis sqemaze warmodgeba rogorc ganivi gamtareblobebi. Canacvlebis sqemebis aqtiuri elementebi arian Zabvisa da denis wyaroebi, romlebic ZiriTadad gamoiyenebian mokledSerTvis denebis angariSis dros. denis wyaroebs Seesabamebian eleqtro sadgurebis generatorebi da momxmarebelTa datvirTvebi. denis wyaroebi arian eqtroenergiis wyaroebi romelTac datvirTvis winaRobis cvlilebisas denis mniSvneloba ar ecvlebaT. aseTi reJimi SesaZlebelia maSin roca Sida winaRoba gacilebiT aRemateba datvirTvis winaRobas. marTlac generatoris winaRoba damyarebul reJimSi, 3-4-jer metia gare datvirTvis winaRobaze. amitom nominaluri parametrebiT muSaobis dros, gare winaRobis mcire cvlilebisas, generatoris denis mniSvneloba SegviZlia ucvlelad CavTvaloT. rac Seexeba Zabvis wyaroebs_isini aseve warmoadge- nenLelqtroenergiis wyaroebs, romelTa gamomyvanebze Zabva ar icvlis mniSvnelobas datvirTvis cvlilebisas sakmaod did zRvrebSi. Ees niSnavs imas, rom Zabvis wyaros Sida winaRoba imdenad mcirea, rom Zabvis vardna masze Zalzed pataraa. Aamis gamo Zabvis wyaros SeuZlia SeinarCunos ucvleli sididis Zabva momWerebze gare denis cvlilebisas sakmaod didfarglebSi. zemoT CamoTvlili pasiuri elementebis ZiriTadi parametrebi arian aqtiuri winaRoba r, iduqtivoba L , da tevadoba C . wredis parametrebi ama Tu im xarisxiT damokidebulni arian denze da Zabvaze. magaliTad winaRoba r damokidebulia denze, radganac denis gazrdisas izrdeba gamtaris temperatura. kondensatoris tevadoba damokidebulia Zabvaze, xolo koWas induqtivoba ki denze. Ees damokidebuleba umravles SemTxvevaSi Zalzed sustia da amitom SegviZlia misi ugulebelyofa. Ee. i. Cven SegviZlia wredis pasiuri elementebis maxasiaTeblebi warmovidginoT swori xazebiT. wredis aseT elementebs ewodebaT wrfivi. wrfiv elementebSi winaRoba _ r, tevadoba _ C, induqtivoba _ L mudmivi 19 sidideebia anuAar arian elementSi gamaval denze da modebul Zabvaze damokidebulni. eleqtruli wredis damyarebuli reJimi, mudmivi denisa da Zabvis wyaroebis arsebobisas, aris wredis iseTi mdgomareoba, romlis drosac deni nebismier StoSi da Zabva nebismier kvanZSi aris ucvleli xangrZlivi drois ganmavlobaSi. damyarebul reJimSi gvaqvs wrfivi pasiuri elementebi da moduliTa da faziT ucvleli denis wyaroebi. aseT SemTxvevaSi damyarebuli reJimi aRiwereba wrfivi algebruli gantolebebiT. aseT wredebs ewodebaT wrfivi eleqtruli wredebi. es SemTxveva Seesabameba eleqtruli sistemis damyarebuli reJimis angariSs, rodesac datvirTvebisa da generatorebis denebs, eleqtrosistemis nebismier kvanZSi gaaCniaT ucvleli sididis modulida faza. Tu eleqtruli wredis pasiuri elementebis parametrebi damokidebulni arian gamaval denze da modebul Zabvaze, maSin aseTi elementebis maxasiaTeblebic arawrfivia, da aseT elementebs ewodebaT arawrfivi. viciT, rom iseT eleqtrul wreds romelic Seicavs Tundac erT arawrfiv elements ewodeba arawrfivi. E eleqtruli sistemebis damyarebuli reJimebis angariSisas, pasiuri elementebis arawrfivoba, rogorc wesi ar aris gaTvaliswinebuli. am mxriv Canacvlebis sqemis grZivi nawili, yovelTvis wrfivia. amave dros, rogorc wesi, damyarebuli reJimebis angariSisas iTvaliswineben denis wyaroebis arawrfiv maxasiaTeblebs. denis wyaroebis arawrfivoba Seesabameba kvanZebSi generatorebisa da momxmareblebis tvirTebis mocemas mudmivi simZlavriT,Aaseve datvirTvebis mocemas maTi statikuri maxasiaTeblebiT, romlebic warmoadgenen momxmareblis tvirTis damokidebulebas Zabvaze. aseTi arawrfivi denis wyaroebis arsebobisas eleqtruli sistemis damyarebuli reJimebi aRiwereba arawrfivi algebruli gantolebebiT anu damyarebuli reJimis arawrfivi gantolebebiT. 20 sabolood Cven SegviZlia davaskvnaT: Tu energosistemis Canacvlebis sqema, romelic warmodgenilia wrfivi pasiuri elementebiTr, L, Cda denis wyaroebi mocemulia mocemulia mudmivi sididis deniTa daFfaziT, maSin aseTi reJimi aRiwereba wrfivi algebruli gantolebebiT. xolo Tu energosistemis Canacvlebis sqema (romelic warmodgenilia arawrfivi pasiuri elementebiT r, L, C) da denis wyaroebi mocemulia simZlavriT: I kv =S kv * /√3U k * (1.1.1), maSin es reJimi aRiwereba arawrfivi algebruli gantolebebiT. aseTi saxiT warmodgenil denis wyaroze amboben, rom igi arawrfivia, radganac is damyarebuli reJimis amsaxvel gantolebaSi jdeba ara rogorc mudmivi sidide (rogorc R,X L), Aaramed rogorc Zabvis funqcia. es Cans (1.1.1) gantolebidanac, sadac S kv * =const – K - uri kvanZis, simZlavris SeuRlebuli mniSvnelobaa. U kv * - K - uri kvanZis Zabvis SeuRlebuli komleqsuri mniSvnelobaa. I kv (U) – arawrfivi denia, romelic damokidebulia Zabvaze. 21 $ 1.2 sistemis mdgomareobis amsaxveli ZiriTadi gantolebebi avariuli reJimebis maTematikuri modelebi aRiwerebian sistemis mdgomareobis amsaxveli igive gantolebebiT rogoric miRebulia normaluri reJimebis analizis dros. sistemis mdgomareobis amsaxveli yvela gantoleba emyareba kirxhofis kanonebs. am gantolebebis pirdapiri amoxsna iZleva kvanZur Zabvebsa da denebs StoebSi da maTi ricxvi udris damoukidebeli konturebisa da kvanZebis jams. amitom ufro xSiri gamoyeneba aqvs kirxhofis gantolebebis gardasaxviT miRebul kvanZur da konturul gantolebebs, romelTa ganzomilebac mniSvnelovnad naklebia uSualod kirxhofis kanonebis mixedviT Sedgenil gantolebebTan SedarebiT [1] [3] [11]. $1.3 kvanZuri Zabvebis gantolebebi ganvixiloT kvanZuri Zabvebis gantolebis miRebis konkretuli magaliTi: 1 I I 2 y 1 y 2 II I 3 y 4 y 3 5 y 4 2 I 3 2 I 4 3 I 1 4 I nax 1. martivi Sekruli qselis Canacvlebis sqema me_4 kvanZi aviRoT mabalansirebel kvanZad. amave kvanZis Zabva iyos bazisuri Zabva 4 U . movaxdinoT Cveni mosazrebiT denebis miaxloebiTi ganawileba StoebSi (StoebSi denebis mimarTulebebis dadgena). Tu amoxsnis Semdeg denis sidides miviRebT uaryofiTi niSniT, maSin am denis realuri mimarTuleba 22 ar emTxveva Cvens mier aRebul nakadganawilebas, maSin dens naxazze Seecvleba mimarTuleba da misi sidide aiReba “+” niSniT. nax 1_ze mocemuli wredisaTvis 1, 2, 3 kvanZebisaTvis davweroT kirxofis I kanonis gantolebebi: 0 34 23 2 12 23 24 1 12 41 I I I I I I I I I #3_ kvanZi #2_ kvanZi #1_ kvanZi (1.3.1) (4) kvanZisTvis gantolebis daweras, rogorc aRvniSneT azri ar aqvs. StoSi gamavali denebi gamovsaxoT am StoSi Zabvis vardnebiT, gveqneba: 0 5 5 4 4 2 3 3 4 4 2 2 1 2 2 1 1 U Y U Y I U Y U Y U Y I U Y U Y (1.3.2) StoebSi Zabvis vardnebi gamovsaxoT kvanZuri Zabvebis meSveobiT: 4 3 5 3 2 4 4 2 3 2 1 2 1 4 1 U U U U U U U U U U U U U U U (1.3.3) Tu (1.3.3) _s SevitanT (1.3.2) _Si gveqneba: 0 ) ( ) ( ) ( ) ( ) ( ) ( ) ( 4 3 5 3 2 4 2 4 2 3 3 2 4 2 1 2 1 2 1 2 1 4 1 U U Y U U Y I U U Y U U Y U U Y I U U Y U U Y aqedan 4 5 3 5 4 2 4 4 3 2 3 4 2 4 3 2 1 2 4 1 1 1 2 1 2 1 0 ) ( ) ( ) ( U Y U Y Y U Y U Y I U Y U Y Y Y U Y U Y I U Y U Y Y (1.3.4) Y 1 +Y 2 ; Y 2 +Y 3 +Y 4 ; Y 4 +Y 5 =Y 33 _warmoadgenen kvanZebis sakuTar gamtareblobebs. isini sididiT tolia kvanZSi SerTuli Stoebis gamtareblobebis jamis. igulisxmeba is Stoc romelic aerTebs mabalansirebel kvanZsa da mocemul kvanZs. danarCeni sidideebi 23 Y 2 ; Y 4 warmoadgenen kvanZebis urTierT gamtareblobebs konkretuli sqemisaTvis (nax.1). Tu davuSvebT, rom Y 1 +Y 2 =Y 11 ; Y 2 +Y 3 +Y 4 =Y 22 ; Y 4 +Y 5 =Y 33 ; da Y 12 =Y 21 =Y 2 ; Y 32 =Y 23 =Y 4 ; (1.5.4) gantolebaTa sistema miiRebs Semdeg saxes: 4 5 3 33 2 32 4 3 2 3 23 2 22 1 21 4 1 1 2 12 1 11 0 U Y U Y U Y U Y I U Y U Y U Y U Y I U Y U Y (1.3.5) Tu eleqtruli wredi Sedgeban+1raodenobis kvanZisagan, maSinnraodenobis damoukidebeli kvanZisaTvis daweril kvanZuri Zabvebis gantolebebs zogadad eqnebaT Semdegi saxe: n n nn n n n n n n n I U Y U Y U Y U Y I U Y U Y U Y U Y I U Y U Y U Y U Y 3 3 2 2 1 1 2 2 3 23 2 22 1 21 1 1 3 13 2 12 1 11 (1.3.6) (1.3. 6) gantolebaTa sistemaSi kvanZebSi denis wyaroebis niSani ar aris miTiTebuli. Mmisi niSani damokidebulia imaze Tu ra saxis kvanZs warmoadgens mocemuli kvanZi_datvirTvis Tu generaciis. Tu or kvanZs Soris, eleqtrul wredSi ar aris SemaerTebeli Sto, maSin (1.3.5) gantolebaTa sistemaSi Sesabamisi gamtarebloba aiReba 0-is toli. Tu wredis StoebSi CarTulia e.m.Z-ebi, maSin K-uri kvanZis deni I K tolia jamisa, am kvanZTan SerTuli Stoebis e.m.Z-ebis namravli Sesabamis gamtareblobebze_ I k = ∑E ki Y ki. Tu e.m.Z. mimarTulia kvanZisaken jamSi aiReba “+” niSniT, xolo Tu ar aris mimarTuli kvanZisaken aiReba “-“ niSniT. (1.3.6) gantolebaSi Stoebis sakuTari da urTierTgamtareb- lobebi ganvalagoT matriculad: 33 32 23 22 21 12 11 0 0 Y Y Y Y Y Y Y aseve kvanZuri denebi da kvanZuri Zabvebi davalagoT veqtor- svetebis saxiT: 24 0 2 1 I I I ; 3 2 1 U U U U zemoTTqmulis safuZvelze kvanZuri Zabvebis gantoleba miiRebs saxes: 5 4 3 4 1 4 2 1 3 2 1 33 32 23 22 21 12 11 0 0 0 Y U Y U Y U I I U U U Y Y Y Y Y Y Y anu kvanZuri Zabvebis gantoleba Caiwereba Semdegnairad: b b kv kv kv U I U (1.3.7) (1.3.5) gantoleba SegviZlia gadavweroT Semdegi saxiTac: 0 ) ( ) ( ) ( ) ( ) ( ) ( ) ( 4 3 33 4 2 32 2 4 3 23 4 2 22 4 1 21 1 4 2 12 4 1 11 U U Y U U Y I U U Y U U Y U U Y I U U Y U U Y rogorc ukve aRvniSneT bolo gantolebaTa sistema analogiuria (1.3.5) gantolebaTa sistemis. gantolebaTa sistema warmovadginoT matriculi saxiT: 0 0 0 2 1 4 3 4 2 4 1 33 32 23 22 21 12 11 I I U U U U U U Y Y Y Y Y Y Y Tu U b =0, anu Cvens SemTxvevaSi U 4 =0, maSin Y kv U kv =I kv ; yuradReba unda mivaqcioT imas, rom TuU Cven vatarebT wrfivi eleqtruli wredis angariSs, maSin kvanZebSi Zabvebi da StoebSi denebi ar arian damokidebuli imaze TuU romel kvanZs aviRebT Cven mabalansireblad denis mixedviT, Tu yvela (n+1) kvanZis denebis jami aris 0-is toli. amitom wrfiv eleqtrul sistemebSi, mabalansirebeli kvanZis arCeva, aseve misi Zabvis arCeva (U b =0, U b ≠0) ar axdens zegavlenas angariSis rezultatze. Y kv (U-U b )=I kv gantolebis amoxsna gvaZlevs (U-U b )=∆U veqtorsvets. igi warmoadgens ZabvaTa vardnis sidiedebs mabalansirebel kvanZsa da mocemul kvanZs Soris _ ∆U 1 ; ∆U 2 ; ∆U 3 ; ……. ∆U n . amis Semdeg Cven SegviZlia ganvsazRvroT ZabvaTa 25 realuri sidideebi kvanZebSi U-U b =∆U;U=∆U+U b . da Sesabamisad U 1 =∆U 1 +U b ; U 2 =∆U 2 +U b ; U 3 =∆U 3 +U b .............. U n =∆U n +U b ; umetes SemTxvevaSi angariSis mizans warmoadgens denebis gnsazRvra StoebSi I ij = (U i -U j )Y ij ; U i =U b +∆U i ; U j =U b +∆U j . amis gaTvaliswinebiT: I ij =(U b +∆U i -U b -∆U j )Y ij =(∆U i -∆U i )Y ij . arawrfivi denis wyaroebis SemTxvevaSi kvanZuri Zabvebis gantolebebs aqvT Semdegi saxe: Y kv (U-U b )=S * /U * anuY kv ∆U= S * /U * 3 faza cvladi denis wredisaTvis, sadac denebi kvanZebSi, kvanZuri Zabvebi da kvanZuri gamtareblobebi kompleqsuri sidideebia. am SemTxvevaSiMmatricul gantolebas eqneba Semdegi saxe: Y kv U kv =S/U kv + U b Y b kvanZuri Zabvebis gantolebis amoxsna SesaZlebelia im SemTxvevaSic, rodesac saqme gvaqvs kompleqsur ricxvebTan. amisaTvis mimarTavenn-uri rigis kompleqr wevrebiani gantolebaTa sistemis gardaqmnas 2nrigis eqvivalentur, namdvilwevrebian gantolebaTa sistemad. am saxiT Cawerili gantolebaTa sistema advilad ixsneba e.g.m-is saSualebiT. am gardaqmnis arsi mdebareobs SemdegSi: Cvenn-ucnobian kompleqsurwevrebian gantolebaTa sistemas, warmovadgenT 2nucnobian, namdvilwevrebian gantolebaTa sistemad, sadac pirvelin raodenobis ucnobi aris saZiebeli sidideebis (Zabvebis) namdvili wevrebi, meoren raodenobis ucnobi aris saZiebeli sidideebis warmosaxviTi nawilebi. sabolood gveqneba 2nraodenobis gantoleba 2nucnobiT. vnaxoT, Tu rogor xdeba, zogadad kvanZuri Zabvebis gantolebaTa sistemis gardaqmna kompleqsuridan namdvil saxeSi. kompleqsur formaSi kvanZuri gamtareb-lobebis matrica, Caiwereba Semdegi saxiT: Y kv =G kv –jB kv (1.3.8). kvanZuri Zabvebisa da kvanZuri denebis veqtor-svetebi Caiwereba Semdegi saxiT: U=U’+jU" daI=I’+jI" (1.3.9) Yüklə 1,86 Mb. 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