Elektrine Maine 2

Matija Sokola

Sinhrone MaineII deoFebruar 2011

Osnovni Delovi Magnetno kolo: Statora, rotora, meugvoe (zazor). Rotorsko magnetno kolo ini celinu sa vratilom maine i ima 2 p polova koji mogu biti ili od masivnog gvoa ili od limova. Statorsko magnetno kolo je uplji valjak od tankih limova, ravnomerno olebljen na svojoj unutarnjoj periferiji.Zazor treba da je to manji, ali ga diktiraju mehanike veliine.

NamotajiStatora, rotora/pobude, (amortizacioni). Pobudni namotaj (induktor) je smeten na rotoru i napajan je jednosmernom strujom.Dve izvedbe pobudnog namotaja :Za cilindrian rotor namotaj je distribuiran tj. sastavljen iz sekcija smetenih u lebovima.Za rotor sa istaknutim polovima namotaj je koncentrisan oko jezgra pola.Statorski trofazni, u ljebovima statora, obino spregnut u Y .

Sinhrona Maina - namot

Preseci rotora - cilindrini- zub- ljebpobudni namot rotora

Preseci rotora - cilindriniRotorski blok velikog turbo generatora. (Westinghouse)

Rotor generatora sa postavljenim provodnicima

Kompletan RotorRotor velikog generatora, kompletno sastavljen. (Westinghouse)

Preseci rotora istureni poloviIstureni polPobudni namot

Namotaji - amortizacioniNa rotoru moe da postoji i priguni (amortizacioni) namotaj, koji priguuje oscilovanje brzine obrtanja rotora oko sinhrone brzine u prelaznim procesima. Tada se ponaa kao kavezni rotor asinhronog motora. U ustaljenom stanju nema funkciju, jer nema indukcije. Ugrauje se u polne vrhove maina sa istaknutim polovima.Okrugli bakarni tapovi u ljebovima u polnom stopalu, kratko spojeni sa dva provodna prstena sa oba boka. U maine sa cilindrinim rotorom ugrauje se priguni namotaj kada se oekuju velika nesimetrina optereenja.

Princip RadaDC struja kroz pobudni namot stvara stalno magnetno polje.Magnetnopobudna sila (mps) pobude miruje u odnosu na rotor, pa se naziva stojeom. Obrtanjem rotora stvara se obrtno magnetsko polje. Ovo polje preseca statine provodnike statora i u njima indukuje elektromotornu silu (ems). Indukovane ems svake faze su jednake po vrednosti ali vremenski pomerene za treinu periode tj. za ugao 120 deg.Ako rotor ima jedan par polova, onda e se, pri jednom obrtaju, imati jedna potpuna promena ems, odnosno za p pari polova imaemo p promena ems.

Princip RadaPoto se u elektroenergetskim sistemima zahteva stabilnost uestanosti (Evropa 50Hz , a Severna Amerika 60Hz ), onda i brzina obrtanja sinhronih generator mora biti konstantna. n = 60 f / p = const.Dakle, u Evropi, imaemo sledee brzine obrtanja:

p123456n [o/min]300015001000750600500

Reakcija InduktaPri optereenju, trofazne struje statora daju ekvivalentnu obrtnu mps (Teslino obrtno polje), koje se obre istom brzinom kao rotor (a i rotorsko polje) tj. sinhronom brzinom - otuda potie i naziv sinhrone maine. Magnetno polje u meugvou nastaje zajednikim delovanjem magnetopobudnih sila rotore/pobude i statora. Povratno delovanje polja statora (indukta) na polje polova rotora (induktora), naziva se magnetna reakcija indukta i zavisi od karaktera optereenja. U zavisnosti od meusobnog poloaja magnetnih polja rotora i statora, razvijaju se odgovarajue sile i obrtni momenti.

Pobuda sinhronih mainaPobudni namotaj sinhrone maine napaja se iz posebnog izvora jednosmerne struje. Dve osnovne grupe:dinamiki (elektromainski) sistemi, gde se pobudni namotaj napaja pomou generatora jednosmerne struje,statiki sistemi, gde je izvor jednosmerne struje statiki pretvara energetske elektronike (ispravlja ili oper).Danas su dominantni statiki pobudni sistemi, uglavnom zbog lakoe i brzine upravljanja.

Oblik polja (mps) rotoraKod sinhronog generatora posebno je vano da oblik indukovane ems bude harmonian (sinusoidan). Kako je ems posledica promene fluksa, polje rotora treba da bude to priblinije harmonino u prostoru. Ako oblik polja nije potpuno harmonian, potrebno je vie harmonike komponente uiniti to manjim.Kod cilindrinog rotora polje ima oblik stepenastog trapeza. Navojni delovi u lebovima imaju pravougaoni oblik mps. Dizajnom statorskog namota optimiziramo ems.

Oblik polja (mps) rotoraKod rotora sa istaknutim polovima polje bi imalo oblik pravougaonika kada bi polovi bili takvi da je duina meugvoa pod polovima stalna. Meutim, da bi polje, a prema tome i ems bila to blia sinusoidnom obliku, meugvoe pod polnim nastavcima nije stalno, ve se zazor menja pod polnim nastavkom. Odnos duine polnog nastavka i polnog koraka namotaja iznosi oko 0,75.

Sprezanje namotaja 3~ generatoraTrofazni generatori se, u principu, spreu trougao ili zvezdu.Uglavnom se primenjuje sprega u zvezdu jer se: u linijskom naponu ponitava trei harmonik. ponitavaju sve harmonike komponente vieg reda deljive sa tri. izbegavaju lokalne struje koje su prisutne u namotaju generatrora u sprezi trougao,postoji neutralna taka - jednostavnija zatita pri istoj konstrukciji faznih namotaja dobija vii linijski napon.

Karakteristika praznog hodaKarakteristika praznog hoda je zavisnost AC napona indukta na prikljucima neoptereenog generatora E0 , od jednosmerne pobudne struje, Jp, pri konstantnoj nominalnoj brzini i uestanosti. Glavni deo pobudne struje, AB pripada mps meugvoa, a deo BC mps magnetskog kola.Znaajan podatak karakteristike praznog hoda je vrednost pobudne struje, J0 , pri kojoj se ima linijska ems po vrednosti jednaka nominalnom naponu.

Karakteristika ustaljenog kratkog spojaKarakteristika ustaljenog kratkog spoja prikazuje zavisnost AC struje na kratkospojenim prikljucima statora, Ik , od jednosmerne pobudne struje, Jp , kada je brzina obrtanja nominalna.Obino se ogled vri pri tropolnom kratkom spoju, do vrednosti struje kratkog spoja koja je neto vea od nominalne struje generatora.Na osnovu rezultata, nacrta se karakteristika kratkog spoja, koja je obino prava linija.Znaajan podatak je vrednost struje pobude, Jp, pri kojoj se ima linijska struja kratkog spoja jednaka nominalnoj.

Indukcija u sinhronom generatoruNeoptereen sinhroni generator

IndukcijaGlavni fluks rotora svojom rotacijom indukuje napon u namotima statora:

Reakcija InduktaFluksevi rotora (f) i reakcije indukta (s).

Reakcija InduktaStruja statora izaziva rotirajui fluks koji se suprotstavlja fluksu rotora i smanjuje indukovani napon.

Reaktanse statoraReakcija indukta se manifestuje kao dodatna reaktansa namotaja statora. Pored nje, postoji i reaktansa rasipanja, X koja potie od rasipnih polja statora: eonih veza namotaja, zuba statora, feromagnetskog kola statora - polja koja ne dopiru do rotoraRelativna vrednost reaktanse rasipanja je x [%]=100 X /Xn i tipino iznosi od 10% do 15 %. Bazna reaktansa je definisana kao Xn = Un / (1.73 In ), koju izraunavamo iz podataka natpisne ploice.Za turbogeneratore, algebarski zbir reaktanse indukta i reaktanse rasipanja je sinhrona reaktansa : xs = x + xa.Za razne turbogeneratore xs iznosi od 60 do 120%.

Ekvivalentna emaPo fazi

Vektorski dijagram turbogeneratoraesto se crta u relativnim jedinicamauirs ij xs ie0 jdUslov proizvodnje reaktivne snage:

Aktivna SnagaProjekcija na gornju horizontalnu osu daje:Stoga se aktivna snaga dobija kao:

Reaktivna SnagaProjekcija na vertikalnu osu daje:Stoga se reaktivna snaga dobija kao:Q pozitivno nadpobudjen generatorQ negativno podpobudjen generator

Objanjenje Xd i XqXd - kad je rotor u takvom poloaju da fazni namot statora vidi najmanji zazor, pa je induktivnost najvea.Xq - kad je rotor u takvom poloaju da fazni namot statora vidi najvei zazor, pa je induktivnost najmanja.

Reaktanse indukta istureni poloviReaktansa zavisi od polozaja rotora (zazora), tj od vrste optereenja. Mps reakcije indukta - dve komponente:poduna reakcija indukta: Fad = Fa sinpoprena reakcija indukta: Faq = Fa cos.Blondelova dvo-osna teorija se moe primeniti za flukseve (ako nema zasienja) i elektrine sile.Na osnovu definicije induktivnosti L = / i dobija se da je induktivitet po d - osi (mali zazor) znaajno vei nego induktivitet u q - osi (vei zazor),Za hidrogeneratore mogu da iznose: xd = 120% , xq = 65%.

Vektorski dijagram hidrogeneratoraq-osauiid jdd-osaiq j (xd xq)iy

Vektorski dijagram hidrogeneratoraq-osauiid j xd ide0 jdd-osaiq j xq iqy

Aktivna snagaProjekcija na q osu daje:Dok projekcija na d osu daje:Izrazimo Isiny i Icosy pa zamenimo

Aktivna snagaDobijamo:Konano,Sinhrona i reluktantna komponenta.

Aktivna snaga

Chart8

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0.00007172460.01315571370.0262397027

000

Eo = 1

Eo = 1.25

Eo = 1.5

Eo = 0

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

P i Q od delta

pobudaXdEoEoEoEoEoEoEo

1111.251.5011.251.5

Xq

0.5

ugaougaoPPPPQQQ

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1803.1415926536000-0-2-2.25-2.5

P i Q od delta

Eo = 1

Eo = 1.25

Eo = 1.5

Eo = 0

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

Sheet2

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

Q (r.j.)

Reaktivna snaga hidrogeneratora

Sheet3

Reaktivna snagaKao i pre, projekcije na d i q ose:Izrazimo Isiny i Icosy pa zamenimo

Reaktivna snagaZamenama:Dobijamo

Reaktivna snaga

Chart5

00.250.5

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-0.19484716080.03854794590.2719430525

-0.2518892392-0.02350287480.2048834896

-0.3151008497-0.09234921860.1304024124

-0.3839745962-0.16746824530.0490381057

-0.4579611105-0.2482934685-0.0386258265

-0.5364745084-0.3342202598-0.1319660113

-0.6188981931-0.4246117028-0.2303252124

-0.7045909429-0.5188047365-0.3330185302

-0.7928932188-0.6161165235-0.4393398282

-0.8831336253-0.7158509737-0.5485683221

-0.9746354544-0.8173053566-0.6599752588

-1.0667232449-0.9197769318-0.7728306187

-1.1587292865-1.0225695278-0.886409769

-1.25-1.125-1

-1.3399021264-1.2264045015-1.1129068765

-1.4278286601-1.3261444993-1.2244603386

-1.5132044632-1.4236124758-1.3340204884

-1.5954915028-1.5182372542-1.4409830056

-1.6741936568-1.6094888955-1.5447841342

-1.748861038-1.6968831153-1.6449051926

-1.8190937931-1.7799851768-1.7408765606

-1.8845453371-1.8584132213-1.8322811055

-1.9449249914-1.9318410024-1.9187570133

-2-2-2

-2.0495969039-2.062680893-2.075764882

-2.0936022636-2.1197343795-2.1458664953

-2.1319627232-2.1710713394-2.2101799557

-2.1646844196-2.2166623423-2.268640265

-2.191831747-2.2565365083-2.3212412695

-2.2135254916-2.2907797402-2.3680339887

-2.2299403623-2.3195323497-2.4091243371

-2.2413019463-2.342986107-2.4446702678

-2.2478831259-2.3613807508-2.4748783758

-2.25-2.375-2.5

-2.2480073566-2.3841671153-2.5203268741

-2.2422937495-2.3892400626-2.5361863756

-2.2332762365-2.3906063342-2.547936432

-2.221394838-2.3886774896-2.5559601412

-2.2071067812-2.3838834765-2.5606601718

-2.1908805938-2.3766668002-2.5624530066

-2.173190116-2.3674766064-2.5617630968

-2.1545084972-2.3567627458-2.5590169944

-2.1353022464-2.3449698884-2.5546375304

-2.1160254038-2.3325317547-2.5490381057

-2.097113898-2.3198655291-2.5426171601

-2.0789801545-2.3073665189-2.5357528833

-2.0620080138-2.2954031204-2.528798227

-2.0465480191-2.2843121482-2.5220762773

-2.0329131244-2.274394581-2.5158760375

-2.0213748719-2.2659117721-2.5104486723

-2.0121600824-2.2590821676-2.5060042527

-2.005448095-2.2540785688-2.5027090427

-2.0013685871-2.2510259708-2.5006833544

-2-2.25-2.5

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

Q (r.j.)

Reaktivna snaga hidrogeneratora

Sheet1

pobudaXdEoEoEoEoEoEo

1111.251.511.251.5

Xq

0.5

ugaougaoPPPQQQ

0000000.250.5

30.05235987760.10460018790.11768417690.130768166-0.00410951760.24554786610.4952052498

60.10471975510.20848430870.23461642450.2607485403-0.01640430430.23222616960.4808566434

90.15707963270.31094296220.35005157850.3891601947-0.03678340130.21013868390.457060769

120.20943951020.41128001240.46325793510.5152358578-0.06507967040.17945722970.4239941299

150.26179938780.50881904510.57352380640.6382285677-0.10106147180.14041998480.3819014413

180.31415926540.60290962050.68016386910.7574181177-0.14443498650.09332914260.3310932716

210.36651914290.69293325270.78252524010.8721172275-0.19484716080.03854794590.2719430525

240.41887902050.77830905580.87999321660.9816773774-0.2518892392-0.02350287480.2048834896

270.4712388980.85849899690.97199662191.0854942468-0.3151008497-0.09234921860.1304024124

300.52359877560.93301270191.05801270191.1830127019-0.3839745962-0.16746824530.0490381057

330.57595865321.00141176381.13757152261.2737312813-0.4579611105-0.2482934685-0.0386258265

360.62831853071.06331351041.21025982351.3572061366-0.5364745084-0.3342202598-0.1319660113

390.68067840831.11839419141.27572428921.4330543869-0.6188981931-0.4246117028-0.2303252124

420.73303828581.1663915541.33367420561.5009568572-0.7045909429-0.5188047365-0.3330185302

450.78539816341.20710678121.38388347651.5606601718-0.7928932188-0.6161165235-0.4393398282

480.8377580411.24040577321.42619197951.6119781859-0.8831336253-0.7158509737-0.5485683221

510.89011791851.26621976181.46050625221.6547927426-0.9746354544-0.8173053566-0.6599752588

540.94247779611.28454525251.48679950111.6890537497-1.0667232449-0.9197769318-0.7728306187

570.99483767361.29544329681.50511093881.7147785807-1.1587292865-1.0225695278-0.886409769

601.04719755121.29903810571.51554445661.7320508076-1.25-1.125-1

631.09955742881.29551502141.51826665241.7410182835-1.3399021264-1.2264045015-1.1129068765

661.15191730631.28511787041.51350423481.7418905992-1.4278286601-1.3261444993-1.2244603386

691.20427718391.26814572971.50154083631.7349359429-1.5132044632-1.4236124758-1.3340204884

721.25663706141.24494914241.48271327151.7204774006-1.5954915028-1.5182372542-1.4409830056

751.3089969391.21592582631.45740728291.6988887394-1.6741936568-1.6094888955-1.5447841342

781.36135681661.18151592231.42605282251.6705897226-1.748861038-1.6968831153-1.6449051926

811.41371669411.14219683781.38911892291.6360410081-1.8190937931-1.7799851768-1.7408765606

841.46607657171.09847774081.34710821461.5957386885-1.8845453371-1.8584132213-1.8322811055

871.51843644921.05089376641.30055115011.5502085338-1.9449249914-1.9318410024-1.9187570133

901.570796326811.251.5-2-2-2

931.62315620440.94636530311.19602268681.4456800705-2.0495969039-2.062680893-2.075764882

961.67551608190.890566051.13919652381.3878269976-2.0936022636-2.1197343795-2.1458664953

991.72787595950.83317984341.08010192861.3270240137-2.1319627232-2.1710713394-2.2101799557

1021.7802358370.77477927921.01931617941.2638530796-2.1646844196-2.2166623423-2.268640265

1051.83259571460.71592582630.95740728291.1988887394-2.191831747-2.2565365083-2.3212412695

1081.88495559220.65716389010.89492801921.1326921483-2.2135254916-2.2907797402-2.3680339887

1111.93731546970.59901512330.83241022991.0658053366-2.2299403623-2.3195323497-2.4091243371

1141.98967534730.54197304490.77035940930.9987457737-2.2413019463-2.342986107-2.4446702678

1172.04203522480.4864980270.7092496580.9320012891-2.2478831259-2.3613807508-2.4748783758

1202.09439510240.43301270190.64951905280.8660254038-2.25-2.375-2.5

1232.146754980.38189783910.59156548110.8012331231-2.2480073566-2.3841671153-2.5203268741

1262.19911485750.33348873620.53574298480.7379972334-2.2422937495-2.3892400626-2.5361863756

1292.25147473510.28807216110.48235865150.6766451418-2.2332762365-2.3906063342-2.547936432

1322.30383461260.24588387780.43167008420.6174562905-2.221394838-2.3886774896-2.5559601412

1352.35619449020.20710678120.38388347650.5606601718-2.2071067812-2.3838834765-2.5606601718

1382.40855436780.17186965870.33915231030.5064349619-2.1908805938-2.3766668002-2.5624530066

1412.46091424530.14024659070.29757668840.4549067862-2.173190116-2.3674766064-2.5617630968

1442.51327412290.11225699410.25920330720.4061496203-2.1545084972-2.3567627458-2.5590169944

1472.56563400040.08786630620.22402606490.3601858237-2.1353022464-2.3449698884-2.5546375304

1502.6179938780.06698729810.19198729810.3169872981-2.1160254038-2.3325317547-2.5490381057

1532.67035375560.04948200260.16297962750.2764772524-2.097113898-2.3198655291-2.5426171601

1562.72271363310.03516423030.13684839110.2385325519-2.0789801545-2.3073665189-2.5357528833

1592.77507351070.02380264640.11339463380.2029866211-2.0620080138-2.2954031204-2.528798227

1622.82743338820.01512436820.09237861680.1696328654-2.0465480191-2.2843121482-2.5220762773

1652.87979326580.00881904510.07352380640.1382285677-2.0329131244-2.274394581-2.5158760375

1682.93215314340.00454336930.0565212920.1084992147-2.0213748719-2.2659117721-2.5104486723

1712.98451302090.00192596790.04103458410.0801432004-2.0121600824-2.2590821676-2.5060042527

1743.03687289850.00057261790.02670473370.0528368495-2.005448095-2.2540785688-2.5027090427

1773.0892327760.00007172460.01315571370.0262397027-2.0013685871-2.2510259708-2.5006833544

1803.1415926536000-2-2.25-2.5

Sheet1

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora

Sheet2

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

Q (r.j.)

Reaktivna snaga hidrogeneratora

Sheet3

Mordejeve V-kriveZavisnost struje statora od struje pobude.Za poetak sa nultom aktivnom snagom.E0 = Uui=0e0 uij xs ie0 juij xs ie0 j Ako se povea pobuda, E0 > UAko se smanji pobuda, E0 < U

Mordejeve V-kriveDobija seIJ0JpP=0 Prava bez zasienja, Kriva sa zasienjem i sa p > 0

kapind

Mordejeve V-kriveZa razne aktivne snage, sa zasienjem.

Chart1

0.951.01980390271.07703296141.1661903791.2806248475

0.90.80173961140.80622577480.8768635840.9926625181

0.80.6835054330.68232895950.76269225480.894427191

0.70.57748148110.58402694350.68436774730.8366798151

0.60.47815180650.50434051390.6324555320.8069359442

0.50.38517426380.44446422840.60505463270.8003810635

0.40.30134143680.40861928740.6012811580.8137413234

0.30.23453597280.40076158350.61926366040.8439694852

0.20.2010179240.42102054610.65587946440.8880983661

0.10.21603063380.4649049630.70742814690.9433981132

00.27123437610.52604032830.7704028851.0075201738

0.10.34778367450.59886020160.84190572861.0785464348

0.20.43441766530.67942131480.91972139821.1549629622

0.30.52610479050.76515205781.0022218939

0.40.62056299170.85440871081.088229385

0.50.7166668660.946131532

0.60.8138127771.0396232065

0.70.911653045

0.81.0099753718

0.9

1

p=0

p=0,2

p=0,4

p=0,6

p=0,8

Struja pobude (r.j.)

Struja statora (r.j.)

Mordejeve Krive Turbogeneratora

Sheet1

E0IpE0E0 trend

0000.05

0.10.10.10.1585

0.20.20.20.264

0.30.30.30.3665

0.40.40.40.466

0.50.50.50.5625

0.60.60.60.656

0.70.70.70.7465

0.80.80.80.834

0.90.90.90.9185

1111

1.11.21.11.154

1.21.41.21.296

1.31.61.31.426

1.41.81.41.544

1.521.51.65

1.62.31.61.7865

1.72.61.71.896

1.82.91.81.9785

1.93.21.92.034

23.522.0625

Sheet1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

E0

Sheet2

00.05

0.10.1585

0.20.264

0.30.3665

0.40.466

0.50.5625

0.60.656

0.70.7465

0.80.834

0.90.9185

11

1.11.154

1.21.296

1.31.426

1.41.544

1.51.65

1.61.7865

1.71.896

1.81.9785

1.92.034

22.0625

E0

E0 trend

Sheet3

p0xs1

u1

p0

e0dqs,iipabcdiscrip1ip2

0.050-0.950.950-0.151.101.217.33333333330

0.10-0.90.90.0457398363-0.151.1-0.051.187.28759349710.0457398363

0.20-0.80.80.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30-0.70.70.234789953-0.151.1-0.251.067.09854338030.234789953

0.40-0.60.60.3333333333-0.151.1-0.35170.3333333333

0.50-0.50.50.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60-0.40.40.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70-0.30.30.648204954-0.151.1-0.650.826.68512837940.648204954

0.80-0.20.20.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90-0.10.10.8777999116-0.151.1-0.850.76.45553342180.8777999116

10001-0.151.1-0.950.646.33333333331

1.100.10.11.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.200.20.21.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.300.30.31.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.400.40.41.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.500.50.51.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.600.60.61.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.700.70.72.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.800.80.82.3333333333-0.151.1-1.750.1652.3333333333

1.900.90.92.6125741133-0.151.1-1.850.14.72075922012.6125741133

20113-0.151.1-1.950.044.33333333333

p0.2

e0dqs,iipabcdiscrip1ip2

0.21.5707963268-11.01980390270.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30.7297276562-0.77639320230.80173961140.234789953-0.151.1-0.251.067.09854338030.234789953

0.40.5235987756-0.65358983850.6835054330.3333333333-0.151.1-0.35170.3333333333

0.50.4115168461-0.54174243050.57748148110.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.3398369095-0.43431457510.47815180650.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.2897517014-0.32917960680.38517426380.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.2526802551-0.22540333080.30134143680.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.2240930923-0.12250356130.23453597280.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.2013579208-0.02020410290.2010179241-0.151.1-0.950.646.33333333331

1.10.1828351370.08166538260.21603063381.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.16744807920.18321595660.27123437611.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.15445959850.28452325790.34778367451.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.14334756890.38564064610.43441766531.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.13373158940.48660687470.52610479051.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.12532783120.58745078660.62056299171.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.1179201520.68819430160.7166668662.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.11134101430.7888543820.8138127772.3333333333-0.151.1-1.750.1652.3333333333

1.90.10545852540.88944436280.9116530452.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.10016742120.98997487421.00997537183-0.151.1-1.950.044.33333333333

p0.4

e0dqs,iipabcdiscrip1ip2

0.41.5707963268-11.07703296140.3333333333-0.151.1-0.35170.3333333333

0.50.927295218-0.70.80622577480.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.7297276562-0.55278640450.68232895950.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.6082455789-0.42554373530.58402694350.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.5235987756-0.3071796770.50434051390.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.4605539917-0.19377422520.44446422840.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.4115168461-0.0834848610.40861928741-0.151.1-0.950.646.33333333331

1.10.3721685340.02469507660.40076158351.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.33983690950.13137084990.42102054611.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.31276672190.23693168770.4649049631.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.28975170140.34164078650.52604032831.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.26993279580.44568322950.59886020161.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.25268025510.54919333850.67942131481.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.23752117080.65227116420.76515205782.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.22409309230.75499287750.85440871082.3333333333-0.151.1-1.750.1652.3333333333

1.90.21211331050.85741756210.9461315322.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.20135792080.95959179421.03962320653-0.151.1-1.950.044.33333333333

p0.6

e0dqs,iipabcdiscrip1ip2

0.50000.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.61.5707963268-11.1661903790.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.71.0296968008-0.63944487250.8768635840.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.848062079-0.47084973780.76269225480.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.7297276562-0.32917960680.68436774730.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.6435011088-0.20.6324555321-0.151.1-0.950.646.33333333331

1.10.5769313452-0.07804555430.60505463271.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.52359877560.03923048450.6012811581.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.47972863770.15325625950.61926366041.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.44291104410.26491106410.65587946441.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.41151684610.37477270850.70742814691.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.38439677450.48323969740.7704028851.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.36071272040.59059737210.84190572862.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.33983690950.69705627480.91972139822.3333333333-0.151.1-1.750.1652.3333333333

1.90.32128858930.80277563771.00222189392.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.3046926540.90787840281.0882293853-0.151.1-1.950.044.33333333333

p0.8

e0dqs,iipabcdiscrip1ip2

0.50000.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60000.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70000.648204954-0.151.1-0.650.826.68512837940.648204954

0.81.5707963268-11.28062484750.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.91.0949140771-0.58768943740.99266251810.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.927295218-0.40.8944271911-0.151.1-0.950.646.33333333331

1.10.8143399421-0.24501655650.83667981511.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.7297276562-0.1055728090.80693594421.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.66287382370.02469507660.80038106351.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.60824557890.14891252930.81374132341.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.56253624450.2688577540.84396948521.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.52359877560.38564064610.88809836611.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.48995732630.50.94339811322.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.46055399170.61245154971.00752017382.3333333333-0.151.1-1.750.1652.3333333333

1.90.43460552560.7233687941.07854643482.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.41151684610.8330302781.15496296223-0.151.1-1.950.044.33333333333

Sheet3

p=0

p=0,2

p=0,4

p=0,6

p=0,8

Struja pobude (r.j.)

Struja statora (r.j.)

Mordejeve Krive Turbogeneratora

Mordejeve V-kriveZa razne aktivne snage, sa zasienjem.

Chart3

0.80.85503841861.01862463521.34163971541.5710215377

0.70.75473559060.91119982421.17803113711.2801835582

0.60.65610607950.81048149841.05238880341.1431136438

0.50.55948252130.71608629790.94534035281.038909972

0.40.4656718320.62868732910.85203094180.956110914

0.30.37639056850.55009999020.77130746230.8912557143

0.20.29541741060.48339351480.70396789390.8436951351

0.10.23129350040.43309876190.65176840560.8134398593

00.20056832530.40469693180.61679400390.8005507431

0.10.21765434230.40225703130.60090751440.8045533442

0.20.27361057310.42584442970.60475447090.8243120515

0.30.35020112750.4713072960.62738247730.8581131077

0.40.4366486120.53287671170.66644704040.9038862156

0.50.52810002270.60554393060.71892029770.9596392545

0.60.62232987480.68566775220.78197111811.0234770538

0.70.71822939840.77086451060.85300313751.0937953798

0.80.81519741030.85957185280.93016864041.1693119571

0.90.91288272570.95081709861.0118815484

11.01107152121.04384939881.0971076837

p=0

p=0,2

p=0,4

p=0,6

p=0,8

Struja pobude (%)

Struja statora (%)

Mordejeve Krive Hidrogeneratora (Xd=1,Xq=0,5)

Sheet1

E0IpE0E0 trend

0000.05

0.10.10.10.1585

0.20.20.20.264

0.30.30.30.3665

0.40.40.40.466

0.50.50.50.5625

0.60.60.60.656

0.70.70.70.7465

0.80.80.80.834

0.90.90.90.9185

1111

1.11.21.11.154

1.21.41.21.296

1.31.61.31.426

1.41.81.41.544

1.521.51.65

1.62.31.61.7865

1.72.61.71.896

1.82.91.81.9785

1.93.21.92.034

23.522.0625

Sheet1

E0

Sheet2

E0

E0 trend

Sheet3

p0xd1xd+xq3

xq0.5xd-xq1

u1

e0dqs,iipabcdiscrip1ip2

0.20-0.80.80.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30-0.70.70.234789953-0.151.1-0.251.067.09854338030.234789953

0.40-0.60.60.3333333333-0.151.1-0.35170.3333333333

0.50-0.50.50.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60-0.40.40.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70-0.30.30.648204954-0.151.1-0.650.826.68512837940.648204954

0.80-0.20.20.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90-0.10.10.8777999116-0.151.1-0.850.76.45553342180.8777999116

10001-0.151.1-0.950.646.33333333331

1.100.10.11.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.200.20.21.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.300.30.31.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.400.40.41.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.500.50.51.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.600.60.61.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.700.70.72.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.800.80.82.3333333333-0.151.1-1.750.1652.3333333333

1.900.90.92.6125741133-0.151.1-1.850.14.72075922012.6125741133

20113-0.151.1-1.950.044.33333333333

p0.2

e0dqs,iipabcdiscrip1ip2

0.20.16949-0.83131864970.85503841860.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30.15592-0.727753950.75473559060.234789953-0.151.1-0.251.067.09854338030.234789953

0.40.14443-0.62488013850.65610607950.3333333333-0.151.1-0.35170.3333333333

0.50.13455-0.52251381960.55948252130.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.12596-0.42053567640.4656718320.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.11841-0.31885711540.37639056850.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.11173-0.21741997720.29541741060.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.10577-0.11617522680.23129350040.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.10042-0.01508817760.20056832531-0.151.1-0.950.646.33333333331

1.10.095590.08586857810.21765434231.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.091210.18671568150.27361057311.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.087210.28747318080.35020112751.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.083550.38815204540.4366486121.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.0801890.48876337220.52810002271.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.077090.58931695470.62232987481.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.074220.6898213310.71822939842.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.0715540.79028274550.81519741032.3333333333-0.151.1-1.750.1652.3333333333

1.90.0690770.89070470460.91288272572.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.0667650.99109314451.01107152123-0.151.1-1.950.044.33333333333

prva iter

drez1izvod

0.16949-0.00000140973.02641718

0.15592-0.00000809233.1516726755

0.144430.00000117593.2715429573

0.134550.00000416343.3875125912

0.125960.00000821833.5005533749

0.11841-0.00000026893.6113652762

0.111730.00000060143.7204213598

0.10577-0.00000148293.8280965903

0.10042-0.00000243223.9346601971

0.09559-0.0000022954.0403203231

0.091210.00000527744.1452345833

0.08721-0.00000217324.2495415708

0.08355-0.00000431644.3533301721

0.0801890.00000031574.4566808486

0.077090.00000680584.5596614304

0.074220.00000592564.6623288265

0.071554-0.00000266484.7647265313

0.069077-0.0000005824.8668844683

0.066765-0.00000241044.9688384152

p0.4

e0dqs,iipabcdiscrip1ip2

0.20.35984-0.9368010181.01862463520.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30.32649-0.81870942320.91119982420.234789953-0.151.1-0.251.067.09854338030.234789953

0.40.29956-0.70489733950.81048149840.3333333333-0.151.1-0.35170.3333333333

0.50.27716-0.59395251160.71608629790.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.2581-0.48502346110.62868732910.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.2417-0.37763739120.55009999020.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.2274-0.27142087270.48339351480.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.2147-0.16605582670.43309876190.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.2035-0.06147850530.40469693181-0.151.1-0.950.646.33333333331

1.10.19340.04255254670.40225703131.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.18430.14609407350.42584442971.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.1760.24926003940.4713072961.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.168450.35207611370.53287671171.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.16150.45462451740.60554393061.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.155150.5569023850.68566775221.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.14930.65896289260.77086451062.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.14390.76083097340.85957185282.3333333333-0.151.1-1.750.1652.3333333333

1.90.13880.86258515810.95081709862.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.13410.9641688481.04384939883-0.151.1-1.950.044.33333333333

prva iter

drez1izvod

0.35984-0.00000307282.44324071630.33898

0.32649-0.00000584852.66698260420.31184

0.29956-0.00000208822.85968311220.28886

0.27716-0.00000480683.03169390130.2691

0.2581-0.00006420853.1892291740.25192

0.2417-0.00005636863.33591198320.23682

0.2274-0.0000024953.4744513840.22346

0.2147-0.00008843283.60698344460.21154

0.20350.00002642793.73430279960.20084

0.19340.00002965483.85785485970.19118

0.18430.00006502963.97817580690.18242

0.1760.00000854294.09597263680.17442

0.16845-0.00000223644.21153597350.1671

0.1615-0.00009527484.32534313810.160378

0.15515-0.00008255984.43750740860.15418

0.1493-0.00004065134.54833609520.14844

0.14390.0000486944.65800760080.143108

0.1388-0.00010180414.76687496660.138154

0.1341-0.00010500024.87479247650.13353

p0.6

e0dqs,iipabcdiscrip1ip2

0.20.6435-1.19999880251.34163971540.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30.5465-1.0137836851.17803113710.234789953-0.151.1-0.251.067.09854338030.234789953

0.40.4861-0.86459365811.05238880340.3333333333-0.151.1-0.35170.3333333333

0.50.4415-0.73052609990.94534035280.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.4062-0.60494357240.85203094180.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.377-0.48468051480.77130746230.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.3523-0.36819939670.70396789390.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.3311-0.25456247660.65176840560.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.3125-0.14295049220.61679400391-0.151.1-0.950.646.33333333331

1.10.2961-0.03301273790.60090751441.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.28140.07568335360.60475447091.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.268170.18332695620.62738247731.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.25620.29008905130.66644704041.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.24540.3960383750.71892029771.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.23540.50147664910.78197111811.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.22630.60631209170.85300313752.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.21780.71078386280.93016864042.3333333333-0.151.1-1.750.1652.3333333333

1.90.210.81480320811.01188154842.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.202730.91850164381.09710768373-0.151.1-1.950.044.33333333333

prva iter

drez1izvod

0.6435-0.00000048791.00000651970.50847

0.5465-0.00008475141.63577483740.46776

0.4861-0.00006382462.0441148820.43329

0.4415-0.0000285132.35656405980.40365

0.40620.00004278112.61445182680.37788

0.377-0.00002700532.83771065420.35523

0.3523-0.00008946883.03647736420.33519

0.33110.00000180573.21704118270.31731

0.3125-0.00001284893.38445730660.30126

0.29610.00006524433.54127394950.28677

0.28140.00001923933.69009452950.27363

0.26817-0.00004585193.83228863150.26163

0.2562-0.00009579543.9690149760.25065

0.24540.00008234234.1009285640.240567

0.2354-0.00002914634.22949088390.23127

0.22630.00008740144.3545949660.22266

0.2178-0.00007495614.47732644490.214662

0.21-0.00004596384.59752555890.207231

0.20273-0.00009090934.71580427210.200295

p0.8

e0dqs,iipabcdiscrip1ip2

0.2err000.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.3err000.234789953-0.151.1-0.251.067.09854338030.234789953

0.40.89-1.35207569021.57102153770.3333333333-0.151.1-0.35170.3333333333

0.50.67445-0.99943481171.28018355820.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.5944-0.81652238341.14311364380.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.5391-0.66282269871.0389099720.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.49657-0.52359152010.9561109140.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.46185-0.39285716020.89125571430.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.4327-0.26799530050.84369513511-0.151.1-0.950.646.33333333331

1.10.4076-0.14725625540.81343985931.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.3857-0.02968993440.80055074311.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.36630.08547563150.80455334421.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.348950.19872181120.82431205151.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.33330.31041602030.85811310771.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.319180.42072590930.90388621561.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.306250.53000707440.95963925452.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.29440.63836140211.02347705382.3333333333-0.151.1-1.750.1652.3333333333

1.90.28350.74591442741.09379537982.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.27340.8528132581.16931195713-0.151.1-1.950.044.33333333333

prva iter

drez1izvod

err001.07952

err000.97947

0.89-0.0000729976-0.37127819420.89868

0.67445-0.00002515321.05076481350.83148

0.5944-0.00003178771.61541173450.7743

0.5391-0.00009131422.01946511090.7251

0.496570.00000246312.34156357590.6822

0.46185-0.00003660912.61432356620.6441

0.43270.00000081692.85284376380.6105

0.4076-0.00002081983.06705083110.5802

0.38570.00001917983.26264850820.5529

0.36630.00001477553.44407069290.528

0.34895-0.00001916223.61420520360.50535

0.3333-0.00009649833.77523722950.4845

0.319180.00000053193.92841110750.46545

0.30625-0.00001768284.07554029760.4479

0.2944-0.00001996344.21738068690.4317

0.28350.00001548244.35470462820.4164

0.2734-0.00000834114.48829514150.4023

Sheet3

p=0

p=0,2

p=0,4

p=0,6

p=0,8

Struja pobude (%)

Struja statora (%)

Mordejeve Krive Hidrogeneratora (Xd=1,Xq=0,5)

Rad na sopstvenu mreuObino je to relativno mali generator koji napaja malu mreu, koja nema mogunost prikljuka na veu mreu. Generator predstavlja jedini izvor i P i Q u mrei.Napon mree zavisi od pobude, a uestanost od brzine obrtanja generatora tj. pogonske maine. Frekvencija i napon mogu da fluktuiraju tokom rada, ponekad u znaajnoj meri.Pobuda, magnetski fluks u meugvou i napon na prikljucima maine su meusobno zavisne veliine.

Rad na optu mreuMnogo ei sluaj je rad sinhronog generatora na optu (vrstu) mreu.Paralelnim povezivanjem generatora, elektrana i celih elektroenergetskih sistema dobijaju se mree veih snaga, na koje pojedini generatori/elektrane malo mogu da utiu. to je snaga mree vea, njen napon moemo smatrati stalnijim (vrim) u pogledu veliine, faznog pomeraja i uestanosti.Kod prikljuivanja generatora na optu mreu, mora se provesti poseban postupak, sinhronizacija.

Sinhronizacija na optu mreuRedosled aktivnosti:kod prvog putanja u pogon proverava se redosled faza;priblino izjednaiti uestanost generatora i mree;generator pobuditi tako da napon generatora bude priblino jednak naponu mree;finom kontrolom brzine postii istofaznost istoimenih faza, tj. istofaznost napona na kontaktima sklopke;ukljuiti na mreu u trenutku kada je fazni pomeraj izmeu istoimenih napona maine i mree najmanji.

Sinhronizacija na optu mreuZa manje snage sinhronizacija se moe vriti runo, pomou npr. voltmetra i sinhronizacionih sijalica. U toku postupka istovremeno se deluje na brzinu turbine i na struju pobude generatora.

Kod generatora veih snaga sinhronizacija se vri poluautomatski ili automatski.

Karakteristike regulacijeZavisnost pobudne struje od struje indukta, pri raznim faktorima snage, tj.J p= f (I, cos) , uz U = const i n = const .Ova karakteristika je znaajna za automatsku regulaciju konstantnosti napona sinhronog generatora. Iz vektorskih dijagrama se vidi da induktivno optereenje jako smanjuje napon sinhronog generatora, jer reakcija indukta deluje u osi polova a suprotno od fluksa pobude.Dakle, da bi se zadrao zadani nominalni napon, mora se znaajno poveati pobudna struja.

Karakteristike regulacije

Chart2

111

1.05494571011.00306051390.9500126962

1.11467914241.01221854860.9052118483

1.17909383451.02740597360.8658731283

1.24815311921.0485168520.8323057187

1.32189598591.0754177250.8048328304

1.40044479931.10796006940.7837668919

1.48401662081.14599361680.7693810665

1.57294037071.1893794890.7618806265

1.66768312791.23800252750.7613791143

1.76889092581.29178266240.767884288

1.87745345281.35068560110.7812971381

1.99461035961.41473349820.8014242151

2.1221351141.48401662080.828000356

2.26267653831.55870743740.8607169479

2.42046019751.63907915660.8992506889

0,8 ind

cos fi = 1

0,8 kap

Struja statora (r.j.)

Struja pobude (r.j.)

Karakteristika regulacije Turbogeneratora

kriva magnecenja

E0IpE0E0 trend

0000.05

0.10.10.10.1585

0.20.20.20.264

0.30.30.30.3665

0.40.40.40.466

0.50.50.50.5625

0.60.60.60.656

0.70.70.70.7465

0.80.80.80.834

0.90.90.90.9185

1111

1.11.21.11.154

1.21.41.21.296

1.31.61.31.426

1.41.81.41.544

1.521.51.65

1.62.31.61.7865

1.72.61.71.896

1.82.91.81.9785

1.93.21.92.034

23.522.0625

kriva magnecenja

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

E0

Mordej

00.05

0.10.1585

0.20.264

0.30.3665

0.40.466

0.50.5625

0.60.656

0.70.7465

0.80.834

0.90.9185

11

1.11.154

1.21.296

1.31.426

1.41.544

1.51.65

1.61.7865

1.71.896

1.81.9785

1.92.034

22.0625

E0

E0 trend

Regulacija

p0xs1

u1

p0

e0dqs,iipabcdiscrip1ip2

0.050-0.950.950-0.151.101.217.33333333330

0.10-0.90.90.0457398363-0.151.1-0.051.187.28759349710.0457398363

0.20-0.80.80.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30-0.70.70.234789953-0.151.1-0.251.067.09854338030.234789953

0.40-0.60.60.3333333333-0.151.1-0.35170.3333333333

0.50-0.50.50.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60-0.40.40.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70-0.30.30.648204954-0.151.1-0.650.826.68512837940.648204954

0.80-0.20.20.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90-0.10.10.8777999116-0.151.1-0.850.76.45553342180.8777999116

10001-0.151.1-0.950.646.33333333331

1.100.10.11.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.200.20.21.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.300.30.31.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.400.40.41.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.500.50.51.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.600.60.61.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.700.70.72.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.800.80.82.3333333333-0.151.1-1.750.1652.3333333333

1.900.90.92.6125741133-0.151.1-1.850.14.72075922012.6125741133

20113-0.151.1-1.950.044.33333333333

p0.2

e0dqs,iipabcdiscrip1ip2

0.21.5707963268-11.01980390270.1389982519-0.151.1-0.151.127.19433508140.1389982519

0.30.7297276562-0.77639320230.80173961140.234789953-0.151.1-0.251.067.09854338030.234789953

0.40.5235987756-0.65358983850.6835054330.3333333333-0.151.1-0.35170.3333333333

0.50.4115168461-0.54174243050.57748148110.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.3398369095-0.43431457510.47815180650.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.2897517014-0.32917960680.38517426380.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.2526802551-0.22540333080.30134143680.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.2240930923-0.12250356130.23453597280.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.2013579208-0.02020410290.2010179241-0.151.1-0.950.646.33333333331

1.10.1828351370.08166538260.21603063381.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.16744807920.18321595660.27123437611.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.15445959850.28452325790.34778367451.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.14334756890.38564064610.43441766531.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.13373158940.48660687470.52610479051.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.12532783120.58745078660.62056299171.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.1179201520.68819430160.7166668662.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.11134101430.7888543820.8138127772.3333333333-0.151.1-1.750.1652.3333333333

1.90.10545852540.88944436280.9116530452.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.10016742120.98997487421.00997537183-0.151.1-1.950.044.33333333333

p0.4

e0dqs,iipabcdiscrip1ip2

0.41.5707963268-11.07703296140.3333333333-0.151.1-0.35170.3333333333

0.50.927295218-0.70.80622577480.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60.7297276562-0.55278640450.68232895950.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70.6082455789-0.42554373530.58402694350.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.5235987756-0.3071796770.50434051390.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.4605539917-0.19377422520.44446422840.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.4115168461-0.0834848610.40861928741-0.151.1-0.950.646.33333333331

1.10.3721685340.02469507660.40076158351.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.33983690950.13137084990.42102054611.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.31276672190.23693168770.4649049631.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.28975170140.34164078650.52604032831.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.26993279580.44568322950.59886020161.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.25268025510.54919333850.67942131481.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.23752117080.65227116420.76515205782.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.22409309230.75499287750.85440871082.3333333333-0.151.1-1.750.1652.3333333333

1.90.21211331050.85741756210.9461315322.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.20135792080.95959179421.03962320653-0.151.1-1.950.044.33333333333

p0.6

e0dqs,iipabcdiscrip1ip2

0.50000.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.61.5707963268-11.1661903790.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.71.0296968008-0.63944487250.8768635840.648204954-0.151.1-0.650.826.68512837940.648204954

0.80.848062079-0.47084973780.76269225480.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.90.7297276562-0.32917960680.68436774730.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.6435011088-0.20.6324555321-0.151.1-0.950.646.33333333331

1.10.5769313452-0.07804555430.60505463271.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.52359877560.03923048450.6012811581.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.47972863770.15325625950.61926366041.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.44291104410.26491106410.65587946441.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.41151684610.37477270850.70742814691.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.38439677450.48323969740.7704028851.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.36071272040.59059737210.84190572862.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.33983690950.69705627480.91972139822.3333333333-0.151.1-1.750.1652.3333333333

1.90.32128858930.80277563771.00222189392.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.3046926540.90787840281.0882293853-0.151.1-1.950.044.33333333333

p0.8

e0dqs,iipabcdiscrip1ip2

0.50000.4348800951-0.151.1-0.450.946.89845323830.4348800951

0.60000.5397228268-0.151.1-0.550.886.79361050650.5397228268

0.70000.648204954-0.151.1-0.650.826.68512837940.648204954

0.81.5707963268-11.28062484750.7607340376-0.151.1-0.750.766.57259929570.7607340376

0.91.0949140771-0.58768943740.99266251810.8777999116-0.151.1-0.850.76.45553342180.8777999116

10.927295218-0.40.8944271911-0.151.1-0.950.646.33333333331

1.10.8143399421-0.24501655650.83667981511.1280756314-0.151.1-1.050.586.2052577021.1280756314

1.20.7297276562-0.1055728090.80693594421.2629658164-0.151.1-1.150.526.0703675171.2629658164

1.30.66287382370.02469507660.80038106351.4058900056-0.151.1-1.250.465.92744332771.4058900056

1.40.60824557890.14891252930.81374132341.5584815599-0.151.1-1.350.45.77485177341.5584815599

1.50.56253624450.2688577540.84396948521.7230160351-0.151.1-1.450.345.61031729831.7230160351

1.60.52359877560.38564064610.88809836611.9028324593-0.151.1-1.550.285.4305008741.9028324593

1.70.48995732630.50.94339811322.1031947467-0.151.1-1.650.225.23013858662.1031947467

1.80.46055399170.61245154971.00752017382.3333333333-0.151.1-1.750.1652.3333333333

1.90.43460552560.7233687941.07854643482.6125741133-0.151.1-1.850.14.72075922012.6125741133

20.41151684610.8330302781.15496296223-0.151.1-1.950.044.33333333333

Regulacija

p=0

p=0,2

p=0,4

p=0,6

p=0,8

Struja pobude (r.j.)

Struja statora (r.j.)

Mordejeve Krive Turbogeneratora

Regulacijaxs0.7

cosfi 0.8cosfi 1cosfi 1

iRe{E0}Im{E0}E0abcdiscrip2cdiscrip2cdiscrip2

r.j.cosfi 0.8cosfi 1cosfi 0.8cosfi 0.8cosfi 1cosfi 0.8cosfi 0.8cosfi 1cosfi 0.8

0111000111-0.151.1-0.950.641-0.950.641-0.950.641

0.11.04210.9580.0560.070.0561.04350371351.00244700610.9596353474-0.151.1-0.99350371350.61389777191.0549457101-0.95244700610.63853179641.0030605139-0.90963534740.66421879160.9500126962

0.21.08410.9160.1120.140.1121.08977061811.00975244490.9228217596-0.151.1-1.03977061810.58613762921.1146791424-0.95975244490.63414853311.0122185486-0.87282175960.68630694420.9052118483

0.31.12610.8740.1680.210.1681.13846387731.02181211580.89-0.151.1-1.08846387730.55692167361.1790938345-0.97181211580.62691273051.0274059736-0.840.7060.8658731283

0.41.16810.8320.2240.280.2241.18928549981.03846039890.8616263691-0.151.1-1.13928549980.52642870011.2481531192-0.98846039890.61692376071.048516852-0.81162636910.72302417850.8323057187

0.51.2110.790.280.350.281.24197423481.0594810050.8381527307-0.151.1-1.19197423480.49481545911.3218959859-1.0094810050.6043113971.075417725-0.78815273070.73710836160.8048328304

0.61.25210.7480.3360.420.3361.29630243381.0846197490.82-0.151.1-1.24630243380.46221853971.4004447993-1.0346197490.58922815061.1079600694-0.770.7480.7837668919

0.71.29410.7060.3920.490.3921.35207248331.1135977730.8075270893-0.151.1-1.30207248330.428756511.4840166208-1.0635977730.57184133621.1459936168-0.75752708930.75548374640.7693810665

0.81.33610.6640.4480.560.4481.40911319631.14612390260.8009993758-0.151.1-1.35911319630.39453208221.5729403707-1.09612390260.55232565851.189379489-0.75099937580.75940037450.7618806265

0.91.37810.6220.5040.630.5041.46727638841.18190524150.8005623024-0.151.1-1.41727638840.3596341671.6676831279-1.13190524150.53085685511.2380025275-0.75056230240.75966261860.7613791143

11.4210.580.560.70.561.52643375221.22065556160.8062257748-0.151.1-1.47643375220.32413974871.7688909258-1.17065556160.50760666311.2917826624-0.75622577480.75626453510.767884288

1.11.46210.5380.6160.770.6161.58647407791.26210142220.8178630692-0.151.1-1.53647407790.28811555321.8774534528-1.21210142220.48273914671.3506856011-0.76786306920.74928215850.7812971381

1.21.50410.4960.6720.840.6721.64730082261.30598621740.8352245207-0.151.1-1.59730082260.25161950651.9946103596-1.25598621740.45640826961.4147334982-0.78522452070.73886528760.8014242151

1.31.54610.4540.7280.910.7281.70883000911.35207248330.8579627032-0.151.1-1.65883000910.21470199452.122135114-1.30207248330.428756511.4840166208-0.80796270320.72522237810.828000356

1.41.58810.4120.7840.980.7841.77098842461.40014284990.885663593-0.151.1-1.72098842460.17740694532.2626765383-1.35014284990.39991429011.5587074374-0.8356635930.70860184420.8607169479

1.51.6310.370.841.050.841.83371208211.450.9178779875-0.151.1-1.78371208210.13977275072.4204601975-1.40.371.6390791566-0.86787798750.68927320750.8992506889

0,8 ind

cos fi = 1

0,8 kap

Struja statora (r.j.)

Struja pobude (r.j.)

Karakteristika regulacije Turbogeneratora

Regulacija aktivne snageAktivna snaga P sinhronizovanog generatora moe se menjati samo promenom momenta pogonskog sredstva, npr. dovodom pare parnoj turbini. Na tek sinhronizovanom generatoru, optereenje bi dovelo do podpobudjenog reima, to bi napreglo mreu.Zato se prvo povea pobuda pa onda poveava aktivno optereenje.Ako su promene nagle, dolazie do naglih prelaznih pojava i moguih udarnih struja u svim namotajima.

Elektromehanike pojaveSinhrona maina prikljuena na mreu ima osobine oscilujueg dinamikog sistema. Kod parnih i vodnih turbina, koje su danas najee u upotrebi, obrtni moment je stalan te se kod njih javljaju samo slobodna ili sopstvena njihanja. Kod dizel generatora i kod motora koji pogone klipne kompresore, koji rade u impulsima, javljaju se i prisilne oscilacije.Treba odrediti frekvencije sistema da bi se prouila stabilnost maine.

Elektromehanike pojaveZa npr. mehaniki poremeaj, snaga e da osciluje oko radne take, tj ugao optereenja d e da osciluje.

Chart1

000

0.10460018790.11768417690.130768166

0.20848430870.23461642450.2607485403

0.31094296220.35005157850.3891601947

0.41128001240.46325793510.5152358578

0.50881904510.57352380640.6382285677

0.60290962050.68016386910.7574181177

0.69293325270.78252524010.8721172275

0.77830905580.87999321660.9816773774

0.85849899690.97199662191.0854942468

0.93301270191.05801270191.1830127019

1.00141176381.13757152261.2737312813

1.06331351041.21025982351.3572061366

1.11839419141.27572428921.4330543869

1.1663915541.33367420561.5009568572

1.20710678121.38388347651.5606601718

1.24040577321.42619197951.6119781859

1.26621976181.46050625221.6547927426

1.28454525251.48679950111.6890537497

1.29544329681.50511093881.7147785807

1.29903810571.51554445661.7320508076

1.29551502141.51826665241.7410182835

1.28511787041.51350423481.7418905992

1.26814572971.50154083631.7349359429

1.24494914241.48271327151.7204774006

1.21592582631.45740728291.6988887394

1.18151592231.42605282251.6705897226

1.14219683781.38911892291.6360410081

1.09847774081.34710821461.5957386885

1.05089376641.30055115011.5502085338

11.251.5

0.94636530311.19602268681.4456800705

0.890566051.13919652381.3878269976

0.83317984341.08010192861.3270240137

0.77477927921.01931617941.2638530796

0.71592582630.95740728291.1988887394

0.65716389010.89492801921.1326921483

0.59901512330.83241022991.0658053366

0.54197304490.77035940930.9987457737

0.4864980270.7092496580.9320012891

0.43301270190.64951905280.8660254038

0.38189783910.59156548110.8012331231

0.33348873620.53574298480.7379972334

0.28807216110.48235865150.6766451418

0.24588387780.43167008420.6174562905

0.20710678120.38388347650.5606601718

0.17186965870.33915231030.5064349619

0.14024659070.29757668840.4549067862

0.11225699410.25920330720.4061496203

0.08786630620.22402606490.3601858237

0.06698729810.19198729810.3169872981

0.04948200260.16297962750.2764772524

0.03516423030.13684839110.2385325519

0.02380264640.11339463380.2029866211

0.01512436820.09237861680.1696328654

0.00881904510.07352380640.1382285677

0.00454336930.0565212920.1084992147

0.00192596790.04103458410.0801432004

0.00057261790.02670473370.0528368495

0.00007172460.01315571370.0262397027

000

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

P i Q od delta

pobudaXdEoEoEoEoEoEoEo

1111.251.5011.251.5

Xq

0.5

ugaougaoPPPPQQQ

00000000.250.5

30.05235987760.10460018790.11768417690.1307681660.0522642316-0.00410951760.24554786610.4952052498

60.10471975510.20848430870.23461642450.26074854030.1039558454-0.01640430430.23222616960.4808566434

90.15707963270.31094296220.35005157850.38916019470.1545084972-0.03678340130.21013868390.457060769

120.20943951020.41128001240.46325793510.51523585780.2033683215-0.06507967040.17945722970.4239941299

150.26179938780.50881904510.57352380640.63822856770.25-0.10106147180.14041998480.3819014413

180.31415926540.60290962050.68016386910.75741811770.2938926261-0.14443498650.09332914260.3310932716

210.36651914290.69293325270.78252524010.87211722750.3345653032-0.19484716080.03854794590.2719430525

240.41887902050.77830905580.87999321660.98167737740.3715724127-0.2518892392-0.02350287480.2048834896

270.4712388980.85849899690.97199662191.08549424680.4045084972-0.3151008497-0.09234921860.1304024124

300.52359877560.93301270191.05801270191.18301270190.4330127019-0.3839745962-0.16746824530.0490381057

330.57595865321.00141176381.13757152261.27373128130.4567727288-0.4579611105-0.2482934685-0.0386258265

360.62831853071.06331351041.21025982351.35720613660.4755282581-0.5364745084-0.3342202598-0.1319660113

390.68067840831.11839419141.27572428921.43305438690.4890738004-0.6188981931-0.4246117028-0.2303252124

420.73303828581.1663915541.33367420561.50095685720.4972609477-0.7045909429-0.5188047365-0.3330185302

450.78539816341.20710678121.38388347651.56066017180.5-0.7928932188-0.6161165235-0.4393398282

480.8377580411.24040577321.42619197951.61197818590.4972609477-0.8831336253-0.7158509737-0.5485683221

510.89011791851.26621976181.46050625221.65479274260.4890738004-0.9746354544-0.8173053566-0.6599752588

540.94247779611.28454525251.48679950111.68905374970.4755282581-1.0667232449-0.9197769318-0.7728306187

570.99483767361.29544329681.50511093881.71477858070.4567727288-1.1587292865-1.0225695278-0.886409769

601.04719755121.29903810571.51554445661.73205080760.4330127019-1.25-1.125-1

631.09955742881.29551502141.51826665241.74101828350.4045084972-1.3399021264-1.2264045015-1.1129068765

661.15191730631.28511787041.51350423481.74189059920.3715724127-1.4278286601-1.3261444993-1.2244603386

691.20427718391.26814572971.50154083631.73493594290.3345653032-1.5132044632-1.4236124758-1.3340204884

721.25663706141.24494914241.48271327151.72047740060.2938926261-1.5954915028-1.5182372542-1.4409830056

751.3089969391.21592582631.45740728291.69888873940.25-1.6741936568-1.6094888955-1.5447841342

781.36135681661.18151592231.42605282251.67058972260.2033683215-1.748861038-1.6968831153-1.6449051926

811.41371669411.14219683781.38911892291.63604100810.1545084972-1.8190937931-1.7799851768-1.7408765606

841.46607657171.09847774081.34710821461.59573868850.1039558454-1.8845453371-1.8584132213-1.8322811055

871.51843644921.05089376641.30055115011.55020853380.0522642316-1.9449249914-1.9318410024-1.9187570133

901.570796326811.251.50-2-2-2

931.62315620440.94636530311.19602268681.4456800705-0.0522642316-2.0495969039-2.062680893-2.075764882

961.67551608190.890566051.13919652381.3878269976-0.1039558454-2.0936022636-2.1197343795-2.1458664953

991.72787595950.83317984341.08010192861.3270240137-0.1545084972-2.1319627232-2.1710713394-2.2101799557

1021.7802358370.77477927921.01931617941.2638530796-0.2033683215-2.1646844196-2.2166623423-2.268640265

1051.83259571460.71592582630.95740728291.1988887394-0.25-2.191831747-2.2565365083-2.3212412695

1081.88495559220.65716389010.89492801921.1326921483-0.2938926261-2.2135254916-2.2907797402-2.3680339887

1111.93731546970.59901512330.83241022991.0658053366-0.3345653032-2.2299403623-2.3195323497-2.4091243371

1141.98967534730.54197304490.77035940930.9987457737-0.3715724127-2.2413019463-2.342986107-2.4446702678

1172.04203522480.4864980270.7092496580.9320012891-0.4045084972-2.2478831259-2.3613807508-2.4748783758

1202.09439510240.43301270190.64951905280.8660254038-0.4330127019-2.25-2.375-2.5

1232.146754980.38189783910.59156548110.8012331231-0.4567727288-2.2480073566-2.3841671153-2.5203268741

1262.19911485750.33348873620.53574298480.7379972334-0.4755282581-2.2422937495-2.3892400626-2.5361863756

1292.25147473510.28807216110.48235865150.6766451418-0.4890738004-2.2332762365-2.3906063342-2.547936432

1322.30383461260.24588387780.43167008420.6174562905-0.4972609477-2.221394838-2.3886774896-2.5559601412

1352.35619449020.20710678120.38388347650.5606601718-0.5-2.2071067812-2.3838834765-2.5606601718

1382.40855436780.17186965870.33915231030.5064349619-0.4972609477-2.1908805938-2.3766668002-2.5624530066

1412.46091424530.14024659070.29757668840.4549067862-0.4890738004-2.173190116-2.3674766064-2.5617630968

1442.51327412290.11225699410.25920330720.4061496203-0.4755282581-2.1545084972-2.3567627458-2.5590169944

1472.56563400040.08786630620.22402606490.3601858237-0.4567727288-2.1353022464-2.3449698884-2.5546375304

1502.6179938780.06698729810.19198729810.3169872981-0.4330127019-2.1160254038-2.3325317547-2.5490381057

1532.67035375560.04948200260.16297962750.2764772524-0.4045084972-2.097113898-2.3198655291-2.5426171601

1562.72271363310.03516423030.13684839110.2385325519-0.3715724127-2.0789801545-2.3073665189-2.5357528833

1592.77507351070.02380264640.11339463380.2029866211-0.3345653032-2.0620080138-2.2954031204-2.528798227

1622.82743338820.01512436820.09237861680.1696328654-0.2938926261-2.0465480191-2.2843121482-2.5220762773

1652.87979326580.00881904510.07352380640.1382285677-0.25-2.0329131244-2.274394581-2.5158760375

1682.93215314340.00454336930.0565212920.1084992147-0.2033683215-2.0213748719-2.2659117721-2.5104486723

1712.98451302090.00192596790.04103458410.0801432004-0.1545084972-2.0121600824-2.2590821676-2.5060042527

1743.03687289850.00057261790.02670473370.0528368495-0.1039558454-2.005448095-2.2540785688-2.5027090427

1773.0892327760.00007172460.01315571370.0262397027-0.0522642316-2.0013685871-2.2510259708-2.5006833544

1803.1415926536000-0-2-2.25-2.5

P i Q od delta

Eo = 1

Eo = 1.25

Eo = 1.5

Eo = 0

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

Sheet2

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

Q (r.j.)

Reaktivna snaga hidrogeneratora

Sheet3

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

Elektromehanike pojavePromena optereenja (iz RT1 u taku RT2) ili promena pobude (u RT3), trajektorije su razliiti tranzijenti. Shematski prikazano na sledeoj slici.RT1RT2RT3

Chart1

000

0.10460018790.11768417690.130768166

0.20848430870.23461642450.2607485403

0.31094296220.35005157850.3891601947

0.41128001240.46325793510.5152358578

0.50881904510.57352380640.6382285677

0.60290962050.68016386910.7574181177

0.69293325270.78252524010.8721172275

0.77830905580.87999321660.9816773774

0.85849899690.97199662191.0854942468

0.93301270191.05801270191.1830127019

1.00141176381.13757152261.2737312813

1.06331351041.21025982351.3572061366

1.11839419141.27572428921.4330543869

1.1663915541.33367420561.5009568572

1.20710678121.38388347651.5606601718

1.24040577321.42619197951.6119781859

1.26621976181.46050625221.6547927426

1.28454525251.48679950111.6890537497

1.29544329681.50511093881.7147785807

1.29903810571.51554445661.7320508076

1.29551502141.51826665241.7410182835

1.28511787041.51350423481.7418905992

1.26814572971.50154083631.7349359429

1.24494914241.48271327151.7204774006

1.21592582631.45740728291.6988887394

1.18151592231.42605282251.6705897226

1.14219683781.38911892291.6360410081

1.09847774081.34710821461.5957386885

1.05089376641.30055115011.5502085338

11.251.5

0.94636530311.19602268681.4456800705

0.890566051.13919652381.3878269976

0.83317984341.08010192861.3270240137

0.77477927921.01931617941.2638530796

0.71592582630.95740728291.1988887394

0.65716389010.89492801921.1326921483

0.59901512330.83241022991.0658053366

0.54197304490.77035940930.9987457737

0.4864980270.7092496580.9320012891

0.43301270190.64951905280.8660254038

0.38189783910.59156548110.8012331231

0.33348873620.53574298480.7379972334

0.28807216110.48235865150.6766451418

0.24588387780.43167008420.6174562905

0.20710678120.38388347650.5606601718

0.17186965870.33915231030.5064349619

0.14024659070.29757668840.4549067862

0.11225699410.25920330720.4061496203

0.08786630620.22402606490.3601858237

0.06698729810.19198729810.3169872981

0.04948200260.16297962750.2764772524

0.03516423030.13684839110.2385325519

0.02380264640.11339463380.2029866211

0.01512436820.09237861680.1696328654

0.00881904510.07352380640.1382285677

0.00454336930.0565212920.1084992147

0.00192596790.04103458410.0801432004

0.00057261790.02670473370.0528368495

0.00007172460.01315571370.0262397027

000

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

P i Q od delta

pobudaXdEoEoEoEoEoEoEo

1111.251.5011.251.5

Xq

0.5

ugaougaoPPPPQQQ

00000000.250.5

30.05235987760.10460018790.11768417690.1307681660.0522642316-0.00410951760.24554786610.4952052498

60.10471975510.20848430870.23461642450.26074854030.1039558454-0.01640430430.23222616960.4808566434

90.15707963270.31094296220.35005157850.38916019470.1545084972-0.03678340130.21013868390.457060769

120.20943951020.41128001240.46325793510.51523585780.2033683215-0.06507967040.17945722970.4239941299

150.26179938780.50881904510.57352380640.63822856770.25-0.10106147180.14041998480.3819014413

180.31415926540.60290962050.68016386910.75741811770.2938926261-0.14443498650.09332914260.3310932716

210.36651914290.69293325270.78252524010.87211722750.3345653032-0.19484716080.03854794590.2719430525

240.41887902050.77830905580.87999321660.98167737740.3715724127-0.2518892392-0.02350287480.2048834896

270.4712388980.85849899690.97199662191.08549424680.4045084972-0.3151008497-0.09234921860.1304024124

300.52359877560.93301270191.05801270191.18301270190.4330127019-0.3839745962-0.16746824530.0490381057

330.57595865321.00141176381.13757152261.27373128130.4567727288-0.4579611105-0.2482934685-0.0386258265

360.62831853071.06331351041.21025982351.35720613660.4755282581-0.5364745084-0.3342202598-0.1319660113

390.68067840831.11839419141.27572428921.43305438690.4890738004-0.6188981931-0.4246117028-0.2303252124

420.73303828581.1663915541.33367420561.50095685720.4972609477-0.7045909429-0.5188047365-0.3330185302

450.78539816341.20710678121.38388347651.56066017180.5-0.7928932188-0.6161165235-0.4393398282

480.8377580411.24040577321.42619197951.61197818590.4972609477-0.8831336253-0.7158509737-0.5485683221

510.89011791851.26621976181.46050625221.65479274260.4890738004-0.9746354544-0.8173053566-0.6599752588

540.94247779611.28454525251.48679950111.68905374970.4755282581-1.0667232449-0.9197769318-0.7728306187

570.99483767361.29544329681.50511093881.71477858070.4567727288-1.1587292865-1.0225695278-0.886409769

601.04719755121.29903810571.51554445661.73205080760.4330127019-1.25-1.125-1

631.09955742881.29551502141.51826665241.74101828350.4045084972-1.3399021264-1.2264045015-1.1129068765

661.15191730631.28511787041.51350423481.74189059920.3715724127-1.4278286601-1.3261444993-1.2244603386

691.20427718391.26814572971.50154083631.73493594290.3345653032-1.5132044632-1.4236124758-1.3340204884

721.25663706141.24494914241.48271327151.72047740060.2938926261-1.5954915028-1.5182372542-1.4409830056

751.3089969391.21592582631.45740728291.69888873940.25-1.6741936568-1.6094888955-1.5447841342

781.36135681661.18151592231.42605282251.67058972260.2033683215-1.748861038-1.6968831153-1.6449051926

811.41371669411.14219683781.38911892291.63604100810.1545084972-1.8190937931-1.7799851768-1.7408765606

841.46607657171.09847774081.34710821461.59573868850.1039558454-1.8845453371-1.8584132213-1.8322811055

871.51843644921.05089376641.30055115011.55020853380.0522642316-1.9449249914-1.9318410024-1.9187570133

901.570796326811.251.50-2-2-2

931.62315620440.94636530311.19602268681.4456800705-0.0522642316-2.0495969039-2.062680893-2.075764882

961.67551608190.890566051.13919652381.3878269976-0.1039558454-2.0936022636-2.1197343795-2.1458664953

991.72787595950.83317984341.08010192861.3270240137-0.1545084972-2.1319627232-2.1710713394-2.2101799557

1021.7802358370.77477927921.01931617941.2638530796-0.2033683215-2.1646844196-2.2166623423-2.268640265

1051.83259571460.71592582630.95740728291.1988887394-0.25-2.191831747-2.2565365083-2.3212412695

1081.88495559220.65716389010.89492801921.1326921483-0.2938926261-2.2135254916-2.2907797402-2.3680339887

1111.93731546970.59901512330.83241022991.0658053366-0.3345653032-2.2299403623-2.3195323497-2.4091243371

1141.98967534730.54197304490.77035940930.9987457737-0.3715724127-2.2413019463-2.342986107-2.4446702678

1172.04203522480.4864980270.7092496580.9320012891-0.4045084972-2.2478831259-2.3613807508-2.4748783758

1202.09439510240.43301270190.64951905280.8660254038-0.4330127019-2.25-2.375-2.5

1232.146754980.38189783910.59156548110.8012331231-0.4567727288-2.2480073566-2.3841671153-2.5203268741

1262.19911485750.33348873620.53574298480.7379972334-0.4755282581-2.2422937495-2.3892400626-2.5361863756

1292.25147473510.28807216110.48235865150.6766451418-0.4890738004-2.2332762365-2.3906063342-2.547936432

1322.30383461260.24588387780.43167008420.6174562905-0.4972609477-2.221394838-2.3886774896-2.5559601412

1352.35619449020.20710678120.38388347650.5606601718-0.5-2.2071067812-2.3838834765-2.5606601718

1382.40855436780.17186965870.33915231030.5064349619-0.4972609477-2.1908805938-2.3766668002-2.5624530066

1412.46091424530.14024659070.29757668840.4549067862-0.4890738004-2.173190116-2.3674766064-2.5617630968

1442.51327412290.11225699410.25920330720.4061496203-0.4755282581-2.1545084972-2.3567627458-2.5590169944

1472.56563400040.08786630620.22402606490.3601858237-0.4567727288-2.1353022464-2.3449698884-2.5546375304

1502.6179938780.06698729810.19198729810.3169872981-0.4330127019-2.1160254038-2.3325317547-2.5490381057

1532.67035375560.04948200260.16297962750.2764772524-0.4045084972-2.097113898-2.3198655291-2.5426171601

1562.72271363310.03516423030.13684839110.2385325519-0.3715724127-2.0789801545-2.3073665189-2.5357528833

1592.77507351070.02380264640.11339463380.2029866211-0.3345653032-2.0620080138-2.2954031204-2.528798227

1622.82743338820.01512436820.09237861680.1696328654-0.2938926261-2.0465480191-2.2843121482-2.5220762773

1652.87979326580.00881904510.07352380640.1382285677-0.25-2.0329131244-2.274394581-2.5158760375

1682.93215314340.00454336930.0565212920.1084992147-0.2033683215-2.0213748719-2.2659117721-2.5104486723

1712.98451302090.00192596790.04103458410.0801432004-0.1545084972-2.0121600824-2.2590821676-2.5060042527

1743.03687289850.00057261790.02670473370.0528368495-0.1039558454-2.005448095-2.2540785688-2.5027090427

1773.0892327760.00007172460.01315571370.0262397027-0.0522642316-2.0013685871-2.2510259708-2.5006833544

1803.1415926536000-0-2-2.25-2.5

P i Q od delta

Eo = 1

Eo = 1.25

Eo = 1.5

Eo = 0

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

Sheet2

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

Q (r.j.)

Reaktivna snaga hidrogeneratora

Sheet3

Eo = 1

Eo = 1.25

Eo = 1.5

Ugao opterecenja

P (r.j.)

Snaga hidrogeneratora (Xd=1,Xq=0.5)

Elektromehanike pojaveZa male poremeaje i male oscilacije, uzima se nagib krive optereenja, tzv. Sinhronizaciona snaga:Ako se podeli sa brzinom, dobija se sinhronizacioni koeficijent. Ovo je mera stabilnosti za koliko e se promeniti ugao optereenja ako dodje do promene snage tj. momenta na vratilu.Smanjuje se sa poveanjem ugla d.

Elektromehanike pojavePri elektromehanikim oscilacijama rotora sinhrone maine u prigunom namotaju se indukuju naponi, pa u njemu teku struje koje stvaraju moment koji se protivi njihanju. Taj moment se naziva prigunim momentom. Pri malim odstupanjima od sinhrone brzine, priguni moment je proporcionalan brzini promene ugla optereenja (klizanju) :

Kratak spojKratak spoj generatora je najintenzivniji prelazni proces.Kratak spoj je nagla promena iz normalnog radnog stanja sa ustaljenim vrednostima P, Q, d i fluksa u zazoru u novo radno stanje sa P=Q=0, ali sa promenom fluksa u zazoru sa nominalnog nivoa na skoro nulti nivo. Nastaju znaajne udarne struje u svim namotajima.Pristup analizi je preko podele na periode prelaznog procesa:Subtranzijentni (udarni) period,Tranzijentni (prelazni) period,Ustaljeni period.

Subtranzijentni period kratkog spojaUestvuju svi namotaji.Amortizacioni namot je dominantan po amplitudi i ima najmanju vremensku konstantu.U prvom trenutku se indukuje znaajna struja jer je amortizacioni namot kratko spojen, a fluks kroz njega tei da se brzo smanji.

Subtranzijentni period kratkog spojaGledano sa statora, subtranzijentne reaktanse su :xqs

Induktivnosti kratkog spojax d - rasipna reaktansa statorskog namotaja (po d-osi),x f - rasipna reaktansa pobudnog rotorskog namotaja,x m - reaktansa magnetne sprege (meuinduktivnost) statora i pobudnog rotorskog namotaja,x a - rasipna reaktansa amortizacionog (prigunog namotaja), po d-osi.

Tranzijentni period kratkog spojaGledano sa statora, tranzijentna reaktanse xd i xq su :

Struja kratkog spojaPristup br 1:Kombinacija struja u raznim periodima daje ukupnu struju.Pristup broj 2:Reaktansa u kolu se menja tokom subtranzijentnog i tranzijentnog dela perioda

Struja kratkog spojaDodatno, prelazne struje imaju i jednosmernu komponentu, ija amplituda zavisi od nivoa magnetnog fluksa u datoj fazi u trenutku nastanka kratkog spoja.Takodje, komponenta dvostruke frekvencije je mogua.Obe opadaju po aperiodinoj vremenskoj konstanti.

Tipini podaciZavisno od vrste rotora maine, kreu se u opsezima:

Struja faze a (q je malo)

Struja faze b (q je oko 120)

Struja faze c (q je oko -120)

Struja pobude (svedena)

Udarna struja kratkog spojaUkoliko se u jednoj fazi zatekne maksimalan fluks, ima se najvia mogua udarna struja. Teoretski bi udarna struja bila 2 puta via od subtranzijentne struje, ali amplituda subtranzijentne i aperiodine opadnu.Za tipine vrednosti od Td = 0,06 s i Ta = 0,2 s ima seStoga se obino uzima