CAPACITANCE REQUIRED ANALYSIS FOR SELF- EXCITED INDUCTION GENERATEUR

Transcription

1 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: CAPACITANCE REQUIRED ANALYSIS FOR SELF- ECITED INDUCTION ENERATEUR A. ABBOU,. BARARA, A. OUCHATTI,. AKHERRAZ, H. AHOUDI, ohammed V Univesity Agdal Depatment of Electical Engineeing, ohammadia School s of Enginees, Rabat, OROCCO abbou@emi.ac.ma, mohamed-baaa@hotmail.f, ouchatti_a@yahoo.f akheaz@emi.ac.ma, mahmoudi@emi.ac.ma, ABSTRACT The main dawback of induction geneato in wind eney convesion systems applications is its need fo leading eactive powe to build up the teminal voltage and to geneate electic powe. Using teminal capacito acoss geneato teminals can geneate this leading eactive powe. The capacitance value of the teminal capacito is not constant but it is vaying with many system paametes like shaft speed, load powe and its powe facto. If the pope value of capacitance is selected, the geneato will opeate in selfexcited mode. This pape pesents diect methods deived fom loop and nodal analyses to obtain diffeent citeia fo maintaining self-excitation and pefomance chaacteistics of an isolated, thee-phase, selfexcited induction geneato (SEI. Results of a detailed investigation on a conventional 3kW induction moto opeated as a SEI ae pesented to illustate the effectiveness of the poposed method. Keywods: Capacitance Requiements, Self-Excitation, Study State Analysis, Induction eneato. INTRODUCTION The self-excited induction geneato (SEI has attacted consideable ecent attention due to its applicability as a stand-alone geneato using diffeent conventional and non-conventional eney esouces with its advantage ove the conventional synchonous geneato. The eason fo the widespead populaity of induction geneato is owing to its capability to geneate the powe fom vaiable speed as well as constant speed pime moves, low unit cost, vey simple, ugged, poduces high powe pe unite mass of mateials and equies vey little maintenances. In a standalone induction geneato the majo poblem is that of guaanteeing self excitation. Self excitation of an induction machine and its sustenance depend on the appopiate combination of speed, load and teminal capacitance in elation to the magnetic non-lineaity of the machine. These in tun cause cetain limitations on the pefomance of the machine. In view of these, studies on the citeia fo self excitation of an induction geneato ae consideed to have pactical significance. The excitation equiements, of an induction geneato have been dealt with extensively in the liteatue []. Fo self excitation to occu, the following two conditions must be satisfied: i. The oto should have sufficient esidual magnetism. ii. The thee capacito bank should be of sufficient value. If an appopiate capacito bank is connected acoss the teminals of an extenally diven induction machine and if the oto has sufficient esidual magnetism an EF is induced in the machine windings due to the excitation povided by the capacito. The EF if sufficient would ciculate leading cuents in the capacitos. The flux poduced due to these cuents would assist the esidual magnetism. This would incease the machine flux and lae EF will be induced. This in tun inceases the cuents and the flux. The induced voltage and the cuent will continue to ise until the VAR supplied by the capacito is balanced by the VAR demanded by the machine, a condition which is essentially decided by the satuation of the magnetic cicuit. This pocess is thus cumulative and the induced voltage keeps on ising until satuation is eached. To stat with tansient analysis the dynamic modeling of induction moto has been used which futhe conveted into induction geneato []-[4]. agnetizing inductance is the main facto fo voltage buildup and stabilization of geneated voltage fo unloaded and loaded conditions. The dynamic odel of Self Excited Induction eneato is helpful to analyze 38

2 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: all chaacteistic especially dynamic chaacteistics. Fo the past few yeas the eseaches has been developed positively in the steady state models of thee phase self excited induction geneato(sei [5] and poposed the steady state equivalent cicuit which epesents the SEI, the citical capacitance equiement and excitation balancing has been poposed [5]-[6]. Accodingly the bette applicability of induction moto as a geneato fo isolated applications has been poposed [7]. The model was found suitable fo steady state analysis but not tansient analysis. Thus fo analyzing the tansient chaacteistics, dynamic model of SEI has been developed [8] and analyzed the dynamic chaacteistics fo vaious tansient conditions and stability. As fo the dynamic and tansient opeation, it was teated fo no load and fo diffeent loads: esistive [9], inductive [], induction moto [], DC load. In this context, this wok pesents genealized statespace dynamic model of a thee phase SEI developed using d-q vaiables in stationay efeence fame fo tansient analysis and a method to finding the value of teminal capacitance equied fo self-excitation taking into account the oto speed and load impedance using a compute pogam. The poposed model fo induction geneato, load and excitation using state space appoach diving by wind tubine and supplying which is coupled to a centifugal pump in ode to optimize his pefomances. This pape is oanized as follows: section two gives the system modeling in static and a dynamic state. In this section, a simple method is also pesented and analyzed to finding the minimum value of equied capacitance fo self-excitation. Simulation esults ae discussed in section thee. Finally a conclusion esumes the developed wok and its featues. Fig. Wind Electic Pumping System The Induction oto cannot be supplied unless the SEI stato voltage build up pocess occus. Fo this eason an opeating mode switche selects fist the no load condition until the voltage build up pocess is accomplished. Subsequently the switche is tuned on as to connect the Induction oto to the SEI. In ode to analyze the pefomances of self excited induction geneato which supplies an induction moto diving pump, a system modeling is equied. Following, a steady state and dynamic modeling ae pesented.. Steady state Analysis of SEI: Figue shows the pe-phase equivalent cicuit commonly used fo SEI supplying an induction moto. A thee phase induction machine can be opeated as a SEI if its oto is extenally diven at a suitable speed and a thee-phase capacito bank of a sufficient value is connected acoss its stato teminals. When the induction machine is diven at the equied speed, the esidual magnetic flux in the oto will induce a small electomotive foce in the stato winding. The appopiate capacito bank causes this induced voltage to continue to incease until an equilibium state is attained due to magnetic satuation of the machine.. SYSTE ODELIN AND ANALYSIS. Poposed system: In the poposed system (Figue, a powe geneation system consisting of a wind tubine with SEI. The poduced powe is used to supply an induction moto coupled to a centifugal pump. As the SEI equies eactive powe fo its excitation, a thee phase capacito bank is connected acoss its stato teminals. Fig. Pe Phase Equivalent Cicuit Of Self Excited Induction eneato Feeding An Induction Pump oto We note: Index g fo Induction eneato Index m fo Induction oto All cicuit s paametes except the magnetizing inductance L ae assumed to be constant and insensitive to satuation. Fom Figue, the total cuent at node a may be given by: Vs.( Yg Yc Ym = ( 383

3 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: Whee, Yg is a total admittance induction geneato Yc is admittance capacitive Ym is a total admittance induction moto If we denote: a P.U. fequency and b P.U. speed So: The expession of admittance capacitive is giving by: a Yc = j ( c The induction geneato admittance is expessed as: Yg ( Yg Yg3 Yg = (3 Yg Yg Yg3 With: Yg = R ja Yg = (4 ja Yg3 = ar ja a b As a consequence of the symmety of pe phase equivalent cicuit, the expession of total induction moto admittance Ym can be deduced fom that of Yg by eplacing the index g by m. Theefoe, unde steady state self excitation, the total admittance must be zeo, since: Vs So ( Yg Yc Ym = (5 Equation 5 is divided into eal and imaginay pats as: (6 R( Yg Yc Ym = I( Yg Yc Ym = (7 Sepaating eal and imaginay Pats of the Yg, we obtain: R Yg = = j R j R ( R ( (8 With: a( a b R R = R (9 ( a b ( R = a a (( a b ( a b ( ( R R ( To simplify the equations and a nominal condition of the induction moto, we can wite: Ym = R j = R R ( j R ( R and ae expessed with the induction moto paametes. Equations (6 and (7 give: R R R ( R ( = ( a c R ( R ( = (3 It is noted that ( is independent of c and the only vaiable is the pe unit fequency a. Once the value of a has been detemined then c can be detemined using (3. Fo no load opeation R = and = Substituting R = and = in (: a( a b R R R ( a b ( = (4 On simplification, it yields the following: bc ( b b (5 amax = b i R ( R Whee b c is given by: R R b c = ( ms R Substituting R = and = in (3: a (( ( a b c = amax ( a b ( R R [ Hence C min is given by: C min = π 5. a max ( a (( a b ( a b ( ( ] R R Thus, C min is invesely popotional to the squae of the p.u. machine fequency. The value of Cmin detemined fom (8 is just sufficient to have selfexcitation unde steady state. If a teminal capacito C = C min is used and the geneato is stated fom est, the voltage build up will not take place. ( (6 (7 (8 384

4 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: Thus in pactice, teminal capacito C having a value somewhat geate than C min should be selected to ensue self-excitation..3 ethod of solution: Equation (, (3 and (8 epesent the conditions that must be satisfied fo the selfexcitation of the induction machine coesponding to vaious geneato and load configuations as discussed above. Each of these equations is complex and non-linea which can be expessed as two simultaneous eal, nonlinea equations with two unknowns. Such equations can be solved using any suitable technique (Pogam compute. If the values of the machine paametes, its speed (o fequency, excitation capacitance as well as load impedances ae given, the two equations can be solved fo the magnetizing eactance and fequency (o speed. On the othe hand, if the inteest is to find the ange of teminal capacitances to sustain self excitation, the two equations can be solved fo the fequency (o speed and these capacitances by specifying the machine paametes, its speed (o fequency, load impedances and the maximum magnetizing eactance. Ou Pogam Compute gives evolution of excitation capacitance equied as function of speed and load impedance..4 SEI odeling: The model fo the SEI is simila to that of the induction moto. To model the SEI effectively, the paametes should be measued accuately. The paametes used in the SEI can be obtained by conducting tests on the induction geneato when it is used as a moto. The taditional tests used to detemine the paametes ae the open cicuit (no load test and the shot cicuit (locked oto test. In this pape the d-q model is used because it is easie to get the complete solution, tansient and steady state, of the self excitation. The paametes given in the d-q equivalent cicuit shown in Figue 3 ae obtained by conducting paamete detemination tests on the above mentioned induction machine. As it is a wound oto induction machine thee is no vaiation of oto paametes with speed. The paametes obtained fom the test at ated values of voltage and fequency ae L =L =9mH, L =7mH, R =.Ω, R =.68Ω. Fo motoing application these paametes can be used diectly. Howeve, fo SEI application the vaiation of L with voltage should be taken into consideation. (a (b Fig.3 D-Q odel Of SEI At No Load a d-axis b q-axis R pl pl pc isq = i R sd pl pl. pc i q pl ωl R pl ωl id ωl pl ωl R pl (9 The initial conditions fo self-excitation, namely the emanent magnetic flux in the oto and/o the initial chae in the capacitos ae not consideed because they will be cancelled when both sides ae diffeentiated. Deived fom Equation (9 and including initial conditions, i.e. initial voltage in the capacitos and emanent magnetic flux in the coe, one can obtain the following diffeential equation [5]: pi = A. I B ( Whee: i sq L K q L Vcq isd L K d L Vcd I = B = i q L LVcq L K q id LVcd L K d L R Lω L R L L ω Lω L R L L ω L R A = L L R L Lω L R L L ω L Lω L R L L ω L R 385

5 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: And L = L L L K d and K q ae constants which epesent the initial induced voltages along the d-axis and q-axis espectively due to emanent magnetic flux in the coe. 3. RESULTS AND DISCUSSION The induction machine used as the SEI in this investigation is a thee-phase squiel cage induction geneato with specification: 3Kw, /38V,.4/7.A, 5Hz. This late supplies an induction moto:.5kw, /38V, 8/5.6A, 5Hz. The fixed paametes of both induction machines used in this poposed system ae: R =.Ω, R =.68Ω, L =L =9mH, L =f(i m, p g = R sm =4.85Ω,R m =3.8Ω,L sm =L m =74mH,L mm = 58mH, p m =. The esidual magnetism in the machine is taken into account in simulation pocess without which it is not possible fo the geneato to self excite. Initial voltage in the capacito is consideed. Table I: Vaiation Of Fequency With Speed Base Speed=pm SPEED (PU FREQUENCY (PU SPEED (PU FREQUENCY (PU The citical speed b c Equation (6 is the speed below which the machine will not opeate. Fo the given machine paametes R, R,,, speed b and magnetizing eactance, Equation (5 was solved to obtain the p.u. fequency a max coesponding to self excitation and the citical speed b c was obtained fom Equation (6, fo each value of p.u speed, the fequency a max was be calculated. Table I. shows the vaiation of a max fo diffeent p.u speeds b with initial value of the eactance =68.38Ω. We ecall that R and ae the esistive and inductive tems of load impedance Figues 4 a, b and c espectively show the vaiation of the capacitance equied (μf with oto speed (pm fo diffeent values of R (i.e..5,, when vaies fom to infinity. It is noted that the maximum capacitance value deceases when R inceases paticulaly when appoaches zeo. In steady state, diffeent cuves tend to almost the same values of capacitance. capacitance value (uf capacitance value (uf capacitance value (uf = =.5 = = =inf speed (pm Fig.4 a- R =.5 = =.5 = = =inf speed (pm Fig.4 b- R = = =.5 = = =inf speed (pm Fig.4 c- R = Fig.4 vaiation of capacitance equied with otational speed fo seveal value of R and : a-(r =.5 b-(r = c-(r = Capacitance value (uf speed=pm speed=pm Load Resistance with = 386

6 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: Capacitance value (uf Capacitance value (uf Capacitance value (uf Fig.5 a- = speed=pm speed=pm Load Resistance with = Fig.5 b- =.6 speed=pm speed=pm Load Resistance with = Fig.5 c- = speed=pm speed=pm Load Resistance with = Fig.5 d- = Capacitance value (uf Capacitance value (uf Capacitance value (uf Effect of speed=pm speed=pm Load Reactance with R= Fig.6 a- R = speed=pm speed=pm Load Reactance with R= Fig.6 b- R =.5 speed=pm speed=pm Load Reactance with R= Fig.6 c- R = Capacitance value (uf speed=pm speed=pm Capacitance value (uf speed=pm speed=pm Load Resistance with =inf Fig.5 e- =inf Fig.5 Vaiation Of Capacitance Requied With Load Resistance Fo Seveal Value Of Speed Load Reactance with R= Fig.6 d- R = Fig.6 Vaiation Of Capacitance Requied With Load Reactance Fo Seveal Value Of Speed 387

7 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: Effect of R Figues 5 a, b, c, d and e shows the vaiation of capacitance equied with load esistance when the eactance vaies fo diffeent values of oto speed ( i.e, 8,, 6 pm. It is noted that inceasing in load eactance equies deceasing capacitance value. Figues 6 a, b, c and d shows the vaiation of capacitance equied with load eactance when the esistance R vaies fo diffeent values of oto speed ( i.e, 8,, 6 pm. It is noted that inceasing load esistance equies deceasing capacitance value. In both cases, we also find that the value of the equied capacitance also inceases with oto speed. We see fom the figues 4, 5 and 6 that the value of the equied capacitance is stongly influenced by the natue of load impedance (esistive, inductive o both. 4. CONCLUSION Self excitation in induction machine depends on appopiate combination of speed, load and excitation capacitance. In this pape we have shown the elationship between the equied capacitance, the oto speed and the natue of load impedance using a compute pogam. This pogam gives typical esults without any iteation o diveence poblem. Fistly taking into account the paametes that influence the choice of equied capacitance, on the othe hand due to thei simplicity, uggedness and low cost of constuction, squiel-cage induction machine is a elatively inexpensive altenative to ac geneation using wind powe fo voltage and fequency insensitive loads. APPENDI TABLE II INDUCTION ENERATOR PARAETERS Rated powe 3 KW Voltage 38V Y Fequency 5 Hz Pai pole Rated speed pm Stato esistance. Ω Roto esistance.68 Ω Inductance stato 9 mh Inductance oto 9 mh utual inductance 7 mh oment of Inetia.46 kg.m Table III: Induction oto Paametes Rated powe.5 KW Voltage 38V Y Fequency 5 Hz Pai pole Rated speed 44 pm Stato esistance 4.85 Ω Roto esistance 3.85 Ω Inductance stato 74mH Inductance oto 74 mh utual inductance 58 mh oment of Inetia.3 kg.m REFERENCES: [] C. Chakaboty, S.N. Bhada, A.K. Chattopadhyay, Excitation equiements fo standalone thee phase induction geneato, IEEE Tansactions on Eney Convesion, Vol.3, No. 4, 998, pp []. Rains and P. alik, Wind eney convesion using a self-excited induction geneato, IEEE Tansactions on Powe Appaatus and Systems. vol., no., 983, pp [3] A.H. AI-Bahani Analysis of self-excited induction geneatos unde unbalanced conditions. Electic achine and Powe Systems. vol 4.996,pp 7-9. [4]. Radic, Z. Stajic, D. Anautovic, citical speed-capacitance equiements fo self-excited induction geneato, Automatic Contol and Robotics Vol. 8, No, 9, pp [5] A. Kishoe,. Satish Kuma, dynamic modeling and analysis of thee phase selfexcited induction geneato using genealized state-space appoach, Intenational Symposium on Powe Electonics, Electical Dives, Automation and otion, SPEEDA 6, pp [6] Dawit S Eyaum Colin antham, and uhammed Fazlu Rahman, The dynamic chaacteistics of an isolated self-excited induction geneato diven by a wind tubine, IEEE, Tansaction on Industy applications, Vol. 39.No.4, July/August 3 pp [7] R. Kuma T., V. Agawal, P.S.V. Nataaj, A Reliable and Accuate Calculation of Excitation Capacitance Value fo an Induction eneato Based on Inteval Computation Technique, Intenational Jounal of Automation and Computing 8(4, Novembe, pp [8] Li Wang, Chaing-Huei Lee, A novel analysis on the pefomance of an Isolated self excited 388

8 3 th Septembe 3. Vol. 55 No JATIT & LLS. All ights eseved. ISSN: E-ISSN: induction geneatos, IEEE Tans. on Eney convesion June 993, vol., No.. [9] Sidha, L., B. Singh, C. S. Jha, and B. P. Singh, Analysis of a self excited induction geneato feeding induction moto load, IEEE Tansaction on Eney Convesion, Vol. 9, No., June 994. [] S. Booa, On-Set Theoy of Self-Excitation in Induction eneato, Intenational Jounal of Recent Tends in Engineeing, Vol, No. 5, Novembe 9,pp []. Ouali,. Ben ali Kamoun,. Chaabene, Investigation on the Excitation Capacito fo a Wind Pumping Plant Using Induction eneato, Smat id and Renewable Eney,,, pp