ISSN 1905-7873 Â© 2012 - Maejo International Journal of Science ...

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16 Maejo Int. J. Sci. Technol. 2012, 6(01), 12-27 SYSTEM MODEL The complete system as shown in Figure 1 consists of SEIG, STATCOM with associated control, and loads. The dynamic model of each component is presented herewith. SEIG Model The induction generator model is developed in a stationary q-d reference frame considering the effect of both main and cross flux saturation [21, 22]. The model, i.e. the q-d axis stator and rotor currents and the rotor speed (ω r ), in state space form is expressed using equations (7) and (8) respectively: p 1 i L v r i G i P p r TP Tem (8) 2J 3P Tem Lm iqsidr idsiqr , and v , i , r , L , G and T P are defined in Appendix-II. 4 where Shunt Capacitor Model The q-d axis stator currents i qs and i ds are converted into 3- stator currents i ga , i gb and i gc using 2- to 3- transformation [22]. Kirchhoff’s current law (KCL) [22] is applied to obtain the capacitor equations governing the SEIG voltage as pv pv ab bc iga ilda ica igb ildb icb 3C sh iga ilda ica2igb ildb icb 3C sh and v ab vbc vca 0 (10) where i ga , i lda and i ca are line ‘a’ currents for the generator, load and STATCOM respectively. STATCOM Model The charging (or discharging) of the DC bus capacitor C dc using hysteresis current controller switching functions (S a , S b , S c ) is expressed as pV i S i S i S ca a cb b cc c dc (11) Cdc The DC bus voltage V dc is reflected as voltages e a , e b and e c on the AC side of the PWM inverter as ea 2 1 1Sa Vdc e b 1 2 1 S b 3 e c 1 1 2 S c (7) (9) (12)
Maejo Int. J. Sci. Technol. 2012, 6(01), 12-27 17 The AC side filter equations in state space form are expressed as vbc 2vab ebc 2eab 3Rf ica pica 3Lf vbc vab ebc eab 3Rf icb picb 3L where eab ea eb and e bc e b e c . f (13) Static R-L Load The static load is considered as delta-connected. The phase currents for static R-L load (i prla , i prlb and i prlc ) are expressed as piprla ( vab Rai prla) La piprlb ( vbc Rbi prlb) Lb (14) pi ( v R i ) L prlc ca c prlc c Correspondingly, the line currents (i rla , i rlb and i rlc ) can be obtained as follows: i ( i i ) rla prla prlc irlb ( iprlb iprla) i ( i i ) rlc prlc prlb Induction Motor Load The values for v qs and v ds are obtained from SEIG voltages (v ab , v bc , v ca ) using 3- to 2- transformation [22]. The state space model of an induction motor dynamic load is similar to the induction generator model. It is expressed using motor parameters as 1 pi m Lm v m rm im G m im (16) Pm p rm Temm TL (17) 2 J m The equations (7 _ 17) represent the model of the complete system. These equations are solved by fourth-order Runge-Kutta integration method [22] in MATLAB. (15) RESULTS AND DISCUSSION An investigation was carried out on a 3.7-kW induction machine operated as SEIG, which was loaded with a static R-L load of 0.8 pf and a 1.5-kW induction motor load. The parameters of this machine are given in Appendix III. The capacitances C NL and C FL were calculated as 16.1 F and 26.5 F respectively for the rated SEIG voltage at no load and at the rated motor load under steady state. It was observed that the motor was unable to start even with C FL and resulted in a voltage collapse because the capacitor bank was unable to meet the excessive VAR requirements of SEIG and the motor load during starting. The starting of the motor was successful with a capacitance of 36F. The performance during voltage buildup, the starting of motor at 2.0 sec., and the subsequent loading on motor at 4.0 sec. are shown in Figure 3. During starting, the terminal voltage dropped to 0.25 p.u. and the induction motor took 0.7 sec. to stabilise the start-up transients. The excessive dip in voltage level and the longer duration for start-up were of serious quality concern. In addition, the SEIG exhibited poor voltage regulation even for the static load.
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