ANALELE UNIVERSITĂłII EFTIMIE MURGU REŞIłA ANUL XV, NR., 2008, ISSN 453-7397 Ionel Dragomirescu, Cosmin Laurian Ungureanu Te Aeolian Asyncronous Generator Te production of te electric energy wit lower costs could be realized wit te elp of te aeolian electric central. In tese centrals we can use te squirrel cage asyncronous generators, because tese macines are te most safety in function and easy exploited. Tis work sow te function analyzing of te asyncronous generator aving on involving torque depending on te square wind speed, te air-density and on te construction of te wing spiral. Keywor: asyncronous generator, ortogonal model, transient regime, involving torque, function caracteristic.. Introduction Te function analyzing of asyncronous generator is made using te two axes teory, in wic te macine equations are written according wit te time, te electrical parameters being steady. In te two axes teory, te tree pase asyncronous macine is equivalent wit an asyncronous macine aving te statorical and te rotorical windings disposed in d, g electrical quaature system, figure. Te equivalent macine as te same electromagnetic torque, te same electromagnetic power canged at te terminal wit te supply every moment. 39
d u i ω i ω q i u i Figure. Te asyncronous macine in ortogonal model for te generator regime 2. Te matematical model We are considering te reference system d, q axes from te two axes teory fixed against te spinning magnetic field of te stator, wic rotated wit angular speed ω. In tis condition and for te asyncronous generator regime wit squirrel cage rotor, te equations for te stator and te rotor are te following: u u 0 0 R i + ω Ri ω R2i + ω ω R2i + + ω ω ( ) ( ) () 40
were te magnetic flows of te rotor are te following: σ i + L σ i + L i + L i i + L i ( i i ) ( i i ) ( i ) ( i ) (2) Te electric parameters involved into () and (2) equations are te following: R - te resistance of te stator pase; R 2 -te resistance of te rotor pase reduced at te stator; L σ -te dispersion inductivity of te stator pase; L -te dispersion inductivity of te rotor pase reduced at te stator; L - te main inductivity; ω, ω - te angular speed of te magnetic field of te stator, and of te rotor. At te relation () we are adding te movement equation: (3) M + M m J p dω were te electromagnetic torque is: M pl ( i i i i ) (4) and M m represents te involving torque wick can be express by te relation (3): M ρπ R 2 3 2 m C M In relations (5), ρ is te air density depending on te environment temperature, R is te lengt of te wing spiral, v is te air speed, C M is te torque factor. Terefore te matematical model wic defines te asyncronous macine function in generator regime is: di di di u R i L L + + σ ω σ v [ L i + L ( i i )] (5) 4
( ω ω )[ L i + L ( i i )] di di di 0 R i + L + L + + di di di 0 R i + L + L i + L i + i + 2 ω ω J dω pl ( ii ii ) + M m (6) p ( )[ ( )] Wit te elp of te (6) equations system we can obtain te time variation of i (t ), i (t ), i (t ), i (t ) şi ω(t), from were we can determinate te real current of te macine: i 3 2 [ i cos( ω t) i ( ω t) ] sin (7) 3. Case study For simulation we consider te case of a tree-pase squirrel cage induction macine, aving a nominal power P N 4 kw, nominal rotation n N 438 rot / min and a nominal supply tension U 380 V and a frequency 50 Hz. Te electric parameters of te macine are: R,694 Ω ; R 2,24 L σ 7,39.0-3 H, L 8,05.0-3 H, L 0,89 H, J 0,024 kg.m 2 We presume tat te asyncronous generator works in parallel wit te low-power supply energetic system. For a aeolian electric central aving R, and a wind speed equal wit 4 m/s, te involving torque M m 6,04 Nm. In fig. 2 are sown te time beavior of te stator current i, rotation n and electromagnetic torque M, considering te initial speed, te syncronous one. 42
Figure 2. Te function beavior for an asyncronous generator 4. Conclusion Te involving torque allow a load for te generator at 5.73 A. Te transient regime is lasting 0.5 s, te rotation at its low limit is 376 rot / min. After te end of te transient regime te rotation remain steady at 533 rot / min. Tis work wants to be a beginning of te aeolian central wit asyncronous macine study, were in addition to generator simulation is necessary te frequency converter simulation. 43
References [] Câmpeanu, A., Introducere în dinamica maşinilor electrice. Bucureşti, Editura Academiei Române,998. [2] Dordea, T., Maşini electrice. Partea complementară, Editura Orizonturi Universitare, Timişoara, 2002. [3]. boldea, I., Nasar, S., Induction macine Hanbook, CRC Press, Florida, 200. [4]. Kana, C., Tamodaram, M., Wolf, A., System management of a windenergy converter, IEEE Transaction on Power Electronics, vol 6, May 2000, p 375-38. Adesses: Ing. Ionel Dragomirescu, I.J.J. Caras- Severin, Str. Erou Jandarm Nicolae Marcu, Nr., Resita, dionel_r2005@yaoo.com Ing. Cosmin Laurian Ungureanu, SC Enel Distributie Banat SA, Bl. A.I. CUZA, Nr. 42, Resita, ungureanu.cosmin@enel.ro 44