Mathematical modeling of a wind-electric plant with an asynchronous generator

, 621.3.049 . - . . , . - . . - . " " " - " d, q, , - s . ( ) 98 % [1]. ( , . - ) . . 1, : V– ;n– ; d sd dt d rd dt d sq , . ( ) , - s ( s s d rq dt – s=n ; us, is – r ) rq rr ird ; , dt – u sd ; rs i sd sq sd ( s rs i sq u sq ; r ) rd rr irq (1) . ; C, ic – ;L– ; r, g – ; U, I – sq . q (i q ); d (i d ); x r ird x r irq rd rq , (2) q (i q ) i d = isd + ird; i q = isq + irq – ; x s, x . . 1. r – d(i d), q(i q) , [1-3]. - , [4], . , - [5] . . (i ) a arctg (bi ) ci , a = 0,25; b = 7,6; c = 0,002. is ic = Cduc/dt, ig = gus d, q – [6] i sd C . i sq , d (i d ); x s isd x s i sq sd - , ur = ris C dusd dt du sq dt C s u sq gu sd i. id ; . C s u sd gu sq u uL = Ldi/dt, u. d, q – - (3) iq - . ISSN 2074-272X. . 2012. 5 71 u sd L u sq L did dt diq L s iq P( , U ) ud ; rid , L s id dt ud = 0; uq = –U = const – riq - uq P . ,U) P0. , P ,U) P0. u (7) P = P( ,U) – P0: u P). , d dt M ( z, ) , k (8) (4) - J u sq isq ) . 3 (u sd isd J – (5) , ; kmp – - ; - , U P0. : 3n (i sd isq q M (z ) – d); " . , (1), (3) k u , . , ( z, ) 0 ( z, ) V2 D3 . 16 z - . [7] z, . . 2, D = 3,5 = 15,7 -1, = . . 2, – M (z ) 3 1,225 - (4) isq Asq3isq M0(z ) " " - . id, iq, usd, usq, isd, isd, isq irq ) s F (.) Asu 3U ; , (9) q (isq irq )) F (.) 0 (1) – (4) (7) k,u – " . ; d dt - , (6) , z = z( ,V) = 0,5D /V; D – - s Asq q (isq s s Ar1 ( x r irq s = s – n , Aij, F – . (9) isq ,U), irq ,U) U = 220 (r = 0,02 ; L=5 ; g = 50 ; = 740 ; rr = rs = 0,09 ; x s=4 ; x r=3 ; n = 20) , . 3, (6) – . 4. rr irq M (z ) V = 20 . . 3. . 2. : ) ; ) , , , . , s = n , - . 4. , 72 ISSN 2074-272X. . 2012. 5 V, U . 2, k ( ,U) u . 4: ( z ( , V ), ) . M k– , . u , . 7, ( ,U) . , , ,V - , k = 2 . 7, – V, . . ,V P0 . , (5) – (7), (10) k = 1,5; P0 = 5 , , . 5. - " [4…85] 0 (10) . " , (8) P0 (V ))) , P arctg (k ( - A . - B , . 6. , . .6 , 1 4, . , , , C– . V1 V2 P = P( ,U) – P0>0 P0 , 2, P u - u m, Tu 3 , . [P0 – dP, P0 + dP]. - . 8, , Tu = 0,06 . 5. - Tn. . 8, – , .; Tn = 0,02 .; dP = 0,4 u . m = 50 B; , . 6. ( ) P = P . ,U) – P0<0 P0 , - . . 7. ISSN 2074-272X. . 2012. 5 73 3. . / . . : . . , i 5. 6. A // . , : . . . – . – 2008. – . 88. – . 152-156. . B - , : - , 2007. – . – .: 15.06.2012 , C – . ., . 99053, , . (0962) 435272 . , " " . . , , . - . 1. . .: 2. / " . . , . – 2008. – - ", 2008. – 196 . / 74 ]. – : : http://masters.donntu.edu.ua. . , 1957. – 195 . . , // 4. – . 29-33. Bibliography (transliterated): 1. Bezrukih P.P. Ispol'zovanie `energii vetra / P.P. Bezrukih. - M.: Izd-vo "Kolos", 2008. - 196 s. 2. Lukutin B.V. `Energo`effektivnye upravlyaemye generatory dlya vetro`elektrostancij / B.V.Lukutin, E.B. Shandarova, A.I.Muravlev // Izvestiya VUZov. Ser. `Elektromehanika. - 2008. 6. - S. 63-66. 3. Krivcov V.S. Neischerpaemaya `energiya. Kn. 2. Vetro`energetika / V.S. Krivcov, A.M. Olejnikov, A.I. Yakovlev. - Har'kov: nac. a`erokosm. un-t (HAI). - Sevastopol': Sevastop. nac. tehn. un-t, 2004. 519 s. 4. Kanov L.N. Raschet rezhima sistemy avtonomnogo `elektrosnabzheniya peremennogo toka maloj moschnosti // Elektrotehn ka i elektromehan ka. - 2011. - 4. - S. 29-33. 5. Buyal'skij V.I. Povyshenie `effektivnosti upravleniya vetroturbinoj // Vestnik SevGTU. Seriya Mehanika, `energetika, `ekologiya: sb. nauch. tr. - Sevastopol': Izd-vo SevNTU. - 2008. - Vyp. 88. - S. 152-156. 6. Garmash V.S. Modelirovanie perehodnyh rezhimov raboty vetro`elektrostancij s asinhronnymi generatorami [`Elektronnyj resurs]. - Doneck: DonNTU, 2007. - Rezhim dostupa: http://masters.donntu.edu.ua. 7. Fateev E.M. Vetrodvigateli i vetroustanovki. - M.: Sel'hozizdat, 1957. - 195 s. . 8. .– . – 2011. – : . – - . 7. , . 2. . . ( ). – , 2004. – 519 . . . 4. . , . // 6. – . 63-66. , . . . . , 33 Kanov L.N. Mathematical modeling of a wind-electric plant with an asynchronous generator. A mathematical modeling method for wind-electric asynchronous-generator plant modes is introduced. The method employs a spline approximation of the solution to nonlinear algebraic equations of the plant’s electric part and, on this basis, numerical integration of the system’s differential equations. The method is illustrated with an example of mode modeling for a wind-electric plant with continuous and pulse control of the blades turning servomotor for the power output stabilization. Key words – mathematical modeling, moment of windwheel, asynchronous generator, power stabilization, blade turning angle, algebraic equations, solution approximation. - ISSN 2074-272X. . 2012. 5  (...truncated)