SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 3, No. 1, June 2006, 63-76 Dynamic Pefomances of Self-Excited Induction Geneato Feeding Diffeent Static Loads Ali Nesba 1, Rachid Ibtiouen 2, Oma Touhami 3 Abstact: The pape examines the dynamic pefomances of a thee-phase selfexcited induction geneato (SEIG) duing sudden connection of static loads. A dynamic flux model of the SEIG in the - axis stationay efeence fame is pesented. The main flux satuation effect in the SEIG is accounted fo by using an accuate technique. The cases of puely esistive, inductive and capacitive load ae amply discussed. Models fo all of these thee-phase load in the - axis stationay efeence fame ae also given. The analysis pesented is validated expeimentally. Keywods: Induction geneato, Self-excitation, Dynamic pefomances, Loading conditions. 1 Intoduction The induction geneato self-excitation phenomenon has been well known since the beginning of the last centuy. Bassett and Potte [1] published thei wok on this subject and explained the self-excitation pocess. They demonstated that an extenally diven induction machine can opeate as a geneato if a eactive powe souce is available to povide the machine's excitation. The selfexcitation can be achieved when a capacito bank with an appopiate value is popely connected acoss the machine teminals. In ecent yeas, self-excited induction geneato has been widely used as suitable powe souce, paticulaly in enewable powe geneating systems, such as in hydoelectic and wind enegy applications [2-8]. Robust and bushless constuction (squiel cage oto), low maintenance equiements, absence of DC powe supply fo field excitation, small seize, educed cost, bette tansient pefomance, self-potection against shot-cicuits and lage ove loads, ae some of the advantages of the induction geneato ove the synchonous and DC geneatos. The disadvantages of this type of geneato ae its elatively poo voltage and fequency egulation, and low powe facto. 1 Laboatoy of Electical Engineeing, Ecole Nationale Polytechnique, ENP, BP 182 El-Haach 16200 Algies, Algeia; E-mail: nesba@ens-kouba.dz 2 E-mail: achid.ibtiouen@enp.edu.dz 3 E-mail: oma.touhami@enp.edu.dz 63
A. Nesba, R. Ibtouen, O. Touhami The fequency and magnitude of voltage geneated by the SEIG is highly influenced by the oto speed, the excitation and the load [7,8]. The steady state analysis of the isolated SEIG has been extensively dealt with ove the last decades. Howeve, the liteatue on the analysis of the dynamic pefomance of the isolated SEIG, paticulaly unde diffeent loading conditions, appeas to be somewhat spase. The aim of this pape is to pesent an analysis of the dynamic pefomance of an isolated thee-phase SEIG feeding fou types of thee-phase static loads; esistive (R), esistive-inductive (RL), esistive-capacitive (RC) and esistiveinductive-capacitive loads (RLC). The dynamic flux models of the SEIG as well as the models of R, RL, RC and RLC loads ae given. The analysis pesented is validated by expeimental esults. 2 Induction Geneato Model The induction machine voltage equations in the axis stationay efeence fame may be expessed [9]: v v s d = si s+ 64 s d s v s= si s+ d (1) (2) = i + (3) d v = i + + (4) All oto quantities and paametes ae efeed to the stato: is the angula speed of the oto. v s, v s, v and v denote the axis components of the stato, and oto voltages efeed to the stato espectively; i s, i s, i and i epesent the axis components of the stato, and oto cuents efeed to the stato espectively; s, s, and epesent the axis components of the stato, and oto fluxes efeed to the stato espectively; and s and denote stato and oto esistances efeed to the stato. The stato and oto cuents, in tems of axis fluxes can be witten:
Dynamic Pefomances of Self-Excited Induction Geneato Feeding whee: i i s s = = s m, (5) 65 - l - s s m, (6) l - i = l - i = l s m m, (7), (8) l s and l denote stato and oto leakage inductances efeed to the stato; m and m which ae useful quantities when epesenting satuation, denote the and -axis components of the magnetizing flux: = M m ( i + i s ), (9) = M m ( i + i s ), (10) 3 M = L, (11) 2 ms and L ms epesents the stato magnetizing inductance. The use of (5)-(8) helps to eliminate the cuents in (9) and (10) as well as in the voltage equations given by (1)-(4), and if the esulting voltage equations ae solved fo the axis fluxes, the following state equations can be obtained: d d s = s v s + ( m s) (12) ls s = s v s + ( m s) (13) ls d = v + + ( ) m l d = v + + ( ) m l (14). (15) Fo a self excited induction geneato, the voltage-cuent equations of the excitation capacito ae expessed in the stationay efeence fame as:
A. Nesba, R. Ibtouen, O. Touhami dv s dv s whee C e denotes excitation capacito. 1 = i s, (16) C e 1 = i s C, (17) If the studied induction geneato is assumed to be magnetically linea, the SEIG flux model, in the stationay efeence fame, may be obtained by the use of the magnetizing flux expessions (9), (10), the set of conventional state equations (12)-(15) and the self-excitation equations (16), (17). Howeve, the modeling of the SEIG unde the assumption of magnetic lineaity leads to unealistic esults. Fig. 1 shows the influence of neglecting the satuation effect in the simulation and paticulaly the computed stato voltage duing the self-excitation pocess. It can be seen that the voltage eaches thousands of volts in less then half a second. This computed esult cannot be obtained expeimentally, because the SEIG output voltage is limited by the magnetic satuation phenomenon. The following section pesents biefly the method used in this pape, to take into account the satuation effect. e Stato voltage (V) Fig. 1 Computed stato voltage duing the self-excitation pocess when the satuation effect is neglected. 3 Satuation Model The satuation effect in the main flux path of the induction machine is accounted fo by using an accuate technique, which consists in the use of an analytical model of the magnetizing inductance M. Combination of exponential, 66
Dynamic Pefomances of Self-Excited Induction Geneato Feeding polynomial and actangent functions wee used in this model in ode to obtain a maximum of accuacy. An optimization least-squae method was applied fo the detemination of the model coefficients. This model is expessed as follow whee: Ml if I m I M = Ms if I m > I 0 0 (18) M l is the value of the magnetizing inductance of the machine in the linea egion; M s is the expession of the magnetizing inductance in the satuated egion, and is given by M = C actan( C ( I I )) + C( 1 exp( ( I I ))) + C ( I I ) + C ; m s 1 2 m 0 3 m 0 4 m 0 5 (19) I denotes the ms magnetizing cuent; I 0 is the value of I m at the uppe limit of the linea egion. The coefficients Ci ( i= 1,,5), I 0 and M l ae identified by using a leastsquae optimization method. Relative diffeence between tests data and the model of M is within exp(-6). Model-based computed values and measued values of the magnetizing inductance as a function of the magnetizing cuent ae shown in the Fig. 2. Magnetizing inductance M (H) 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 Measued Model 0 0 5 10 15 20 25 30 Magnetizing cuent Im (A) Fig. 2 Vaiation of the satuated magnetization inductance of the studied machine vesus the magnetizing cuent. The intoduction of the main flux satuation effect into the dynamic flux model of the induction machine is essentially based on the knowledge of the 67
A. Nesba, R. Ibtouen, O. Touhami and -magnetizing flux components m and m. These components may be expessed by s m = L + ls l s m = L + ls l 1 1 1 L = L = + + M ls l, (20), (21) -1. (22) Obviously,L, L and consequently m and m ae elated to the magnetizing inductance M which is a function of the ms magnetizing cuent (18), (19). This cuent is given by whee and I = ( i 2 + i 2 )/2, (23) m m m i = i + i (24) m s i = i + i (25) m s Finally, the satuated flux model of SEIG, in the stationay efeence fame, is obtained by adding the expessions of the magnetizing inductance, fluxes and cuents (18)-(25), to the equations of the linea model pesented in the pevious section. 4 Expeimental Veification In this section, expeimental and computed esults ae pesented. These esults (Figs. 3-13) descibe the dynamic esponses of the studied induction geneato duing sudden connection of thee-phase static loads onto the machine teminals. The machine used fo the tests is a wound-oto induction machine ated: 3.5kW, 220/380V, 14/8A, 50Hz, 4 poles. The self-excitation of the geneato is obtained by diving the machine at synchonous speed, and then a thee-phase 90 F capacito bank is switched on to the stato teminals of the machine. The load is connected afte the machine had eached its steady state. Fou types of static loads ae examined. 68
Dynamic Pefomances of Self-Excited Induction Geneato Feeding 4.1 Resistive load The model of a thee-phase balanced esistive load in the - axis stationay efeence fame is given by: v = Ri L, (26) and v = Ri L, (27) whee: R is the load esistance (pe phase);and i and i L ae espectively the and -axis components of the load cuent. L Figs. 3 and 5 show the measued stato voltage and stato cuent following a sudden connection of the load ( R= 15 ). The computed esults ae given in Figs. 4 and 6. Both computed and measued esults show that a lage voltage dop occus when the load is connected onto the SEIG teminals. Stato voltage (V) Fig. 3 Measued stato voltage duing the connection of load. Stato voltage (V) Fig. 4 Computed stato voltage duing the connection of load. 69
A. Nesba, R. Ibtouen, O. Touhami Stato cuent (A) Fig. 5 Measued stato cuent duing the connection of load. Stato cuent (A) Fig. 6 Computed stato cuent duing the connection of load. The Fig. 7 shows the effect of the load esistance (impedance) on the ms magnetizing flux. It descibes the ms magnetizing flux duing the self-excitation pocess and the petubation povoked by the load (at 0.3s). Cases of 15 and 30 esistive loads ae examined. 4.2 Inductive load The dynamic model of a thee-phase balanced seies RL (esistive-inductive) load in the - axis stationay efeence fame is expessed by and di di L L = ( v - RiL )/ L (28) = ( v - RiL )/ L. (29) 70
Dynamic Pefomances of Self-Excited Induction Geneato Feeding R and L ae the load esistance and inductance (pe phase) espectively. The inductive loads used in this pape (in RL and RLC loads) ae magnetically linea, and pesent no magnetic coupling between phases. Rms magnetizing flux (Wb) R=30 R=15 Fig. 7 Computed ms magnetizing flux duing the connection of load. Stato voltage (V) Fig. 8 Measued stato voltage duing the connection of load. The Fig. 8 shows the measued stato voltage following a sudden connection of the inductive load (R = 47.5, L = 0.12H). The computed esult is given in Fig. 9. Although the esistive pat of this load (47.5 ) is ove than thee times geate than the esistance in the case of esistive load (15 ), computed and measued esults still showing a lage voltage dop afte the connection of the load. This poo voltage chaacteistic of the SEIG, especially when feeding an inductive load, constitutes the main disadvantage of this geneato and can be efeed to the unde excitation of the machine. In fact, the connection of the load, causes the eactive powe absobed by the load and by the leakage 71
A. Nesba, R. Ibtouen, O. Touhami eactance of the geneato to incease. On the othe hand, it engendes some voltage dop in the stato windings, which consequently causes the voltage acoss the excitation capacitos to decease, and, as a esult, the eactive powe poduced by these capacitos also decease. This diminution in the eactive powe poduced by the SEIG (capacitos), in addition to the incease of the demand of eactive powe, constain the SEIG to opeate with weak excitation and thus, with lowe output voltage Stato voltage (V) 72 Fig. 9 Computed stato voltage duing the connection of load. 4.3 Capacitive load One impovement of the SEIG output voltage chaacteistic is based on using capacitos in seies and/o in paallel with the load. In this pape, only seies connection is consideed. The dynamic pefomance of the SEIG, feeding seies connected RC and RLC loads, is examined. The dynamic model of a thee-phase balanced seies RC (esistive-capacitive) load in the - axis stationay efeence fame can be witten: and whee: dv C dv C 1 = ( v vc ), (30) RC 1 = ( v vc ), (31) RC R and C ae the load esistance and capacitance (pe phase), espectively; v and vc ae espectively, the - and -axis components of the voltage C acoss the load capacito.
Dynamic Pefomances of Self-Excited Induction Geneato Feeding The measued and computed esults in Figs. 10 and 11 show the output voltage duing the connection of RC load onto the SEIG teminals. Although the impedance of the test RC load (15, 135 HF) is less than a half of the RL load impedance (47.5, 0.12 H), it can be clealy seen that the connection of this RC load has no significant effect on the geneato output voltage. In fact, the deficit in the SEIG eactive powe, caused by the connection of the load, and which is diectly elated to the load powe facto and impedance may be compensated by the use of seies capacitos with the load. Stato voltage (V) Fig. 10 Measued stato voltage duing the connection of load. Stato voltage (V) Fig. 11 Computed stato voltage duing the connection of load. 4.4 RLC load The dynamic model of a thee-phase balanced seies RLC (esistive-inductive-capacitive) load in the - axis stationay efeence fame is given by 73
A. Nesba, R. Ibtouen, O. Touhami 2 d vc dvc 0 2 C LC + RC + v v =, (32) 2 d vc dvc 0 2 C LC + RC + v v =, (33) whee R, L and C ae the load esistance, inductance and capacitance (pe phase), espectively. Stato voltage (V) Fig. 12 Measued stato voltage duing the connection of load. Stato voltage (V) Fig. 13 Computed stato voltage duing the connection of load. Fo the RLC load, the effect of the load on the SEIG output voltage may also be compensated by the use of seies (and/o paallel) capacitos. Howeve, it can be seen that fo the RLC load used in test (R), the SEIG output voltage is still consideably affected by the connection of the load (Figs. 12 and 13). 74
Dynamic Pefomances of Self-Excited Induction Geneato Feeding This can be efeed to the low value of the seies capacito elatively to the load impedance and powe facto. In fact, the seies capacito used with the load, must have an appopiate capacitance value, so that it can maintain sufficient excitation fo the SEIG when the load is connected. On the othe hand, a highe value capacito will oveexcite the SEIG, and the output voltage can each dangeous values. 5 Conclusion An analysis on the dynamic pefomance of an isolated thee-phase SEIG feeding fou kinds of thee-phase static loads is pesented. The cases of R, RL, RC and RLC loads ae consideed. The dynamic flux models of the SEIG as well as the models of R, RL, RC and RLC loads in the axis stationay efeence fame ae given. The main flux satuation effect in the SEIG is accounted fo by using accuate technique. The analysis pesented is validated by expeimental esults. The connection of a load onto the SEIG teminals causes its excitation to decease and thus, the SEIG to opeate at lowe magnetizing flux. The SEIG output voltage is highly influenced by the impedance and the powe facto of the load. The use of seies capacito with the load, impoves consideably the output voltage chaacteistic of the SEIG. This seies capacito must have an adequate capacitance value. The amplitudes of the signals, thei shapes as thei duation pesent pactically the same values fo both simulation and expeimentation. The coheence between computed and measued esults is vey good as well fo dynamic conditions as fo steady state. This concodance between the expeimentation and simulation confims the validity of the developed models. 6 Refeences [1] E. D. Basset, F.M. Potte: Capacitive Excitation of Induction Geneatos: Tans. Ame. Inst. Elect. Eng., 54, 1935, pp. 540 545. [2] T. Ahmed, O. Noo, E. Hiaki, M. Nakaoka: Teminal Voltage Regulation Chaacteistics by Static Va Compensato fo a Thee-Phase Self-Excited Induction Geneato: IEEE Tans. on Industy Applications, Vol. 40, No. 4, 2004, pp. 978 988. [3] S.A. Daniel, N. A.Gounden: A novel hybid isolated geneating system based on pv fed invete-assisted wind-diven induction Geneatos, Tans. on Enegy Convesion, Vol. 19, No. 2, 2004, pp. 416 422. [4] A.Tapia, G. Tapia, J.X. Ostolaza: Reactive powe contol of wind fams fo voltage contol applications, Renewable Enegy, 29, 2004, pp. 377 392. 75
A. Nesba, R. Ibtouen, O. Touhami [5] B. Palle, M.G. Simoes, F.A. Faet: Dynamic Simulation and Analysis of Paallel Self- Excited Induction Geneatos fo Islanded Wind Fam Systems, IEEE Tans. on Industy Applications, Vol. 41, No. 4, 2005, pp. 1099 1106. [6] R. Ibtiouen, A. Nesba, S. Mekhtoub, O. Touhami: An appoach fo the modeling of satuated induction machine, Poc. Intenational AEGAN Confeence on Electical Machines and Powe Electonics, ACEMP'01, Kasudasi-Tukey, 27-29 June, 2001, pp. 269 274. [7] G.K. Singh: Self-excited induction geneato eseach-a suvey, Electic Powe Systems Reseach, 69, 2004, pp. 107 114. [8] A. Nesba, R. Ibtiouen, S. Mekhtoub, O. Touhami, N. Takoabet: Rectified Self-Excited Induction Geneato as Regulated DC Powe Supply fo Hybid Renewable Enegy Systems, WSEAS Tans. on Cicuits and Systems, Issue 11, Vol. 4, Novembe 2005, pp. 1457 1463. [9] P.C. Kause: Analysis of Electic Machiney, 2 nd edition, McGaw-Hill, 1987. 76