A Simple Approach to Estimate the Steady-State Performance of Self-Excited Induction Generator

Transcription

1 A Smple Approach to Estmate the Steady-State Performance of Self-Excted Inducton Generator Department of Electrcal Engneerng Natonal Insttute of Technology Kurukshetra,Haryana INDIA Abstract: Ths paper presents a new and smple model for the steady-state analyss of sngle and parallel operated self-excted nducton generators (SEIG). In ths paper an attempt has been made to ncorporate the unjustfed assumptons n an exstng (Watson s) model. Ths has resulted nto an mproved model for the estmaton of performance of SEIG. A close agreement of smulated results usng proposed modelng wth expermental values on test machnes proves the valdty and superorty of proposed model. Further proposed model s extended for the analyss of a system comprsng of number of such machnes operatng n parallel. Keywords: Parallel operaton, steady state analyss, self-excted nducton generator (SEIG), wnd energy converson. Nomenclature C at rated frequency a b C per unt frequency per unt speed termnal exctaton capactance per phase I m magnetzng current per L s r V X s X r phase load resstance per phase stator resstance per phase rotor resstance per phase load voltage per phase stator reactance per phase rotor reactance per phase, referred to stator X C capactve reactance due to Sub X m magnetzng reactance per c 1. Introducton phase at rated frequency Core loss resstance Self-excted nducton generators have attaned a lot of attracton n recent years, due to the sutablty of these machnes n many applcatons ncludng wnd energy and small hydro energy systems. Further, these machnes and specally cage nducton machnes pocesses many advantages such as low cost, brushless and rugged constructon, self protecton capablty etc. To estmate the steady-state performance of a SEIG, most of the researchers used the conventonal equvalent crcut representaton of an nducton motor [1-13]. Some of the researchers used the mpedance model, and a few used the admttance-based 08 Issue 3, Volume 3, March 008

2 model for the treatment of these crcuts. Whereas [10, 1] developed a new crcut representaton, whch ncludes an actve power source n the rotor crcut. Apart from ths, [14] developed the smple most approach to descrbe the autonomous and parallel operaton of self excted nducton generators. Smplcty s the man attracton of Watson s [14] model. Dfferent models are suggested by researchers for analyss and control of parallel operated self-excted nducton generators n steady state. Al-Bahran et al [15] suggests Newton aphson technque for voltage control of two or more parallel operated SEIG. Varous control parameters were found smultaneously. The results are better but wth lengthy and complex terms. Chakraborty et al [16,17] suggests T and nverse Γ models for the analyss and control of parallel operated SEIG. More than one teratve loops were used to fnd the varous parameters. Sandhu [18] suggests a smple model havng balanced resstve loads for the analyss of parallel operated SEIG. Methodology adopted needs an estmaton of capactance sharng by ndvdual machne. Classcal and conventonal control technques are descrbed by [19-0]. P. Haguo et al [1] presents an Fuzzy-PID based approach to control the wnd turbne system. It s found that the vector control n combnaton wth Fuzzy-PID control enhances the system stablty. Such developments are the ndcaton of current research n the area of wnd energy generaton through nducton machnes. In the present paper an attempt has been made to mprove the results of [14] wth few modfcatons but wthout loosng the smplcty of the approach. Close agreement of smulated results wth expermental results, confrms the valdty of proposed modelng. Model s found to be sutable for the steady-state analyss of sngle as well as for mult machne systems.. Steady-State Analyss Fg.1 Equvalent crcut representaton. Fg.1 shows the equvalent crcut as adopted by Watson [14]. Ths crcut representaton may be modfed as gven n Fg. wth the provson of followngs, whch were found to be mssng; Incluson of stator reactance Incluson of pu frequency to make all leakage reactances and exctaton capactance more effectve. Further magnetzng branch has been shfted to stator sde, as usually adopted n motorng case. Fg. Modfed equvalent crcut. Analyss of crcut as gven n Fg., n terms of real power gves; 09 Issue 3, Volume 3, March 008

3 V k a P = s r a as V a L a (1) earrangement of (5) and (6) results n to the quadratc equaton n terms of unknown voltage as; ( k a C) V 0 1 V k3 = k ω (7) Where k s a fractonal value and for a sngle machne s s r k = a as s r ( X s X r ) a as In the absence of power source (1) may be wrtten as; s r = () s kl 1 Values of k 1,k and k 3 are as per Appendx 1. (1) to (7) may be used to determne the generated frequency and termnal voltage for any operatng speed and exctaton capactance. Further analyss of the generator ncludng core loss s gven n Appendx. Ths approach can be extended for N self excted nducton generators operatng n parallel as shown n Fg.3. Where N represents the number of machnes operatng n parallel. It can be also wrtten as follows; a b s = (3) a otor speed and slp determnes the frequency of the generated voltage. b a = 1 s (4) At no-load ( L ), therefore the generated frequency s same as the drven frequency. However, as evdent from above expressons, generated frequency falls wth load. For self-exctaton, magnetzng current s suppled by the capactor and s gven as; I m = VaωC (5) Further, magnetzaton characterstcs of SEIG (Appendx-I) may be expressed n the form as; 1 kv k3 I m = kv (6) 10 Issue 3, Volume 3, March 008

4 N =1 s = s r k L (9) s a b = (10) a b a = 1 s (11) N =1 and I m = VaωC (1) N = 1 I m = k1 V k V k3 (13) (8) to (13) may be used to estmate the generated voltage and frequency as gven n Appendx esults and Dscussons TABLE 1 Comparson of results for sngle machne. Fg.3. Equvalent crcut representaton of parallel operated self-excted nducton generators. Equaton (1) to (7) referred to mult machne system comprsng of N such machnes may be modfed as; P = N = 1 V k a s a as r V a a L (8) Table 1 gves the comparson of smulated results wth expermental results on a test machne, SEIG-1 (Appendx 1). Smulated results wth modfcatons as suggested n ths paper are found to be more close to expermental one n comparson to 11 Issue 3, Volume 3, March 008

5 smulated results as obtaned usng Watson model. Ths proves the valdty and superorty of the proposed modelng. Fg.4 to Fg.7 gves the varaton of termnal voltage and frequency wth load for dfferent values of exctaton capactance and operatng speed. It s observed that exctaton capactance at stator termnals and operatng speed of the machne effect the performance to a great extent and thus may be used to control the termnal condtons. Fg.5. Varaton of generated frequency wth load for dfferent exctaton capactance. Fg.4. Varaton of termnal voltage wth load for dfferent exctaton capactance. Fg.6. Varaton of termnal voltage wth load for dfferent operatng speed. 1 Issue 3, Volume 3, March 008

6 Fg.7. Varaton of termnal voltage wth load for dfferent operatng speed. Fg.8 Varaton of generated frequency and voltage wth load. TABLE Comparson of results for two machnes operatng n parallel. C=90µF, L =90Ω Table gves the comparson of smulated results wth expermental results on a set of two test machnes [Appendx-1] operatng n parallel. esults are found to be n close agreement especally for low slp operatons, justfed n case of nducton machnes. Fg.9 Varaton of load,generated frequency and voltage wth exctaton capactance. Fg. 8 to Fg. 11 shows the smulated results for a system comprsng of two self excted nducton generators. As observed termnal voltage falls sharply wth load. However fall of generated frequency wth load s small n comparson wth the termnal voltage. Ths reflects the necessacty to control the 13 Issue 3, Volume 3, March 008

7 termnal voltage wth load varatons. Fg.9 and Fg.10 shows the effect of exctaton capactance and operatng speed on the generated voltage, frequency and load suppled by two machne system operatng n parallel. Load capablty of the system ncreases wth an ncrease n exctaton capactance. However t effects the generated voltage and frequency smultaneously. of parallel operaton of two machnes. It s seen that generated voltage s greatly nfluenced due to any change of rotor resstance of one of the machnes. However varatons n generated frequency are neglgble n case both machnes are runnng at constant speeds. Ths provdes the opportunty to control the generated voltage of the system through rotor resstance, provded operatng speeds are mantaned. 4. Concluson Fg.10. Varaton of load, generated frequency and voltage wth rotor speed of machne-. Fg.11. Varaton of load, generated frequency and voltage wth rotor resstance of machne-. Fg.11 gves the effect of varatons of rotor resstance of machne- on the performance In ths paper an attempt has been made to prepare a new model to nvestgate the steady-state performance of sngle as well as parallel operated self-excted nducton generators. The man attracton of the model s ts smplcty to obtan the fnal soluton. esults obtaned are found to be close agreement to the expermental results obtaned on a test machne/set of machnes. Ths proves the valdty of model proposed for the analyss of sngle unt or number of unts operatng n parallel. Efforts are made to nclude the core loss component whch s generally neglected. Incluson of core loss branch makes the model more realstc. It s found that, to meet the power needs of the world, wnd energy s emergng s a potental canddate among renewable energy resources. Therefore future research plans of the authors n the area of wnd energy extracton usng nducton generators s as; Analyss and control of power qualty of wnd energy systems usng artfcal ntellgence. Desgn modfcatons n the nducton generators accordng to operatng constrants of a specfc area. 14 Issue 3, Volume 3, March 008

8 eferences [1] S. S. Murthy, O. P. Malk, and A.K.Tandon, Analyss of self-excted nducton generators, Proc. IEE,vol. 19,pt. C, no. 6,198,pp [] G. ana and O. P. Malk, Wnd energy converson usng a self-excted nducton generator, IEEE Trans. Power Apparatus and Systems, vol. PAS-10, no. 1,1983,pp [3] A. K. Tandon, S. S. Murthy and C. S. Jha, New method of computng steady-state response of capactor self-excted nducton generator, IE (I) Journal-EL, vol. 65,1985, pp [4] N. H. Malk and S. E. Haque, Steadystate analyss and performance of an solated self-excted nducton generator, IEEE Trans. Energy Converson, vol. EC-1, no.3, 1986,pp [5] N. H. Malk and A. H. Al-Bahran, Influence of the termnal capactor on the performance characterstcs of a self-excted nducton generator, Proc. IEE, vol.137, pt. C, no., 1990, pp [6] L. Shrdhar, B. Sngh, and C. S. Jha, A step towards mprovements n the characterstcs of self-excted nducton generator, IEEE Trans. Energy Converson, vol. 8, no. 1,1993,pp [7] T. F. Chan, Steady-state analyss of self-excted nducton generators, IEEE Trans. Energy Converson, vol. 9, no.,1994, pp [8] L. Quazene and G. McPherson, Analyss of the solated nducton generator, IEEE Trans. Power Apparatus and Systems, vol. PAS-10, no. 8, 1983, pp [9] T. F. Chan, Analyss of self-excted nducton generators usng an teratve method, IEEE Trans. Energy Converson,vol.10 no. 3,1995,pp [10] K. S. Sandhu and S. K. Jan, Operatonal aspects of self-excted nducton generator usng a new model, Electrc Machnes and Power Systems, vol. 7, no.,1999, pp [11] I. A. M. Abdel-Halm, M. A. Al- Ahmar, and M. Z. El-Sherf, A novel approach for the analyss of self-excted nducton generator, Electrc Machnes and Power Systems, vol. 7,1999, pp [1] K. S. Sandhu, Iteratve model for the analyss of self-excted nducton generators, Electrc Power Components and Systems, vol. 31, no. 10, 003, pp [13] A. K.Tandon, S. S. Murthy, and G. J. Berg, Steady-state analyss of capactor self-excted nducton generators, IEEE Trans.Power Apparatus and Systems, vol. 103, no. 3, 1984,pp [14] D.B. Watson and I.P. Mlner, Autonomous and parallel operaton of self excted nducton generator for lghtng loads n remote areas, Int. J. Elect. Engng. Educ., (), 1985, [15] A.H. Al-Bahran and N.H. Malk, Voltage Control of parallel operated selfexcted nducton generators, IEEE Trans. Energy Converson, Vol. 8, No., June 1993, pp [16] C. Chakraborty, S. N. Bhadra, S.P. Das and A.K. Chattopadhyay, Some studes on the parallel operaton of self excted nducton generators, Proc. IEE,vol. 19,pt. C, no. 6,198, pp [17] C. Chakraborty, S.N. Bhadra and A.K. Chattopadhyay, Analyss of paralleloperated self-excted nducton generator, IEEE Trans. Energy Converson, vol. 14, No., June 1999, pp Issue 3, Volume 3, March 008

9 [18] K. S. Sandhu, Steady-state analyss of multmachne system wth self-excted nducton generators, Electrcal Power Components and Systems, vol. 34, Aprl 006, pp [19] K.C. Wu,.K. Joseph, N.K. Thupl, Evaluaton of classcal and fuzzy logc controllers for wnd turbne yaw control, Aerospace Control Systems, Proc. IEEE egonal Conference, vol. 1, May 5-7, 1993, pp [0] M. Namazov,. Samet,. Huseynov, Modelng and Smulaton of the fuzzy relay type controller for solvng the double ntegrator control problem, Proc. Of 9 th WSEAS Internatonal Conference on Automatc Control, Modelng & Smulaton, Istanbul, Turkey, vol.1, May 7-9, 007, pp [1] P. Haguo, W. Zhxn, Smulaton research of Fuzzy PID synthess yaw vector control system of wnd turbne, WSEAS Trans. on System and Control, Issue 10, vol., Oct. 007, pp APPENDIX 1 SPECIFICATIONS OF SEIG-1 Lne voltage=380v Lne current=1.9a atng=1.0hp Number of poles= 4 Frequency=50Hz Base speed =1500 rpm s = 9.5 ohm r = 8.04 ohm X s = X r = 8.84 ohm SPECIFICATIONS OF SEIG- Lne voltage=30v Lne current=4.96a atng=3.0hp Frequency=50Hz Number of poles= 4 Base speed =1500 rpm s = 3.35 ohm r = 1.76 ohm X s = X r = 4.85 ohm APPENDIX Fg.1. Modfed equvalent crcut ncludng core losses. Analyss of crcut as gven n Fg.1, n terms of real power gves; V V k a a P = s r c a as a V a L a Where k s a fractonal value and depends upon the desgn of the machne. In the absence of power source may be wrtten as; s = s r k 1 1 a c L 16 Issue 3, Volume 3, March 008

10 TABLE Smulated results ncludng core losses. N6=n3*d31n*d41; P6=kk*(d41*d1d31*dd1*d3d1 1*d4); Q5=M5N5P5; M5=n31*dn1*d3n11*d4; N5=n3*d1n*d31n1*d41; P5=kk*(d41*d0d31*d1d1*dd1 1*d3d01*d4); Q4=M4N4P4; APPENDIX 3 Generated frequency for two machne systems ncludng core losses may be calculated usng (8) and (10). Ths results nto the soluton of 9 th order polynomal equaton n unknown a as follows; Q9*a 9 Q8*a 8 Q7*a 7 Q6*a 6 Q5*a 5 Q4* a 4 Q3*a 3 Q*a Q1*a 1 Where Q9=P9; P9=kk*d41*d4; Q8=P8; P8=kk*(d41*d3d31*d4); Q7=M7N7P7; M7=n31*d4; N7=n3*d41; P7=kk*(d41*dd31*d3d1*d4); Q6=M6N6P6; M6=n31*d3n1*d4; M4=n31*d1n1*dn11*d3; N4=n3*d11n*d1n1*d31; P4=kk*(d31*d0d1*d1d11*dd0 1*d3); Q3=M3N3P3; M3=n31*d0n1*d1n11*d; N3=n3*d01n*d11n1*d1; P3=kk*(d1*d0d11*d1d01*d); Q=MNP; M=n1*d0n11*d1; N=n*d01n1*d11; P=kk*(d11*d0d01*d1); Q1=M1N1P1; M1=n11*d0; N1=n1*d01; P1=k*d01*d0; kk=(1/ L )(1/ c1 )(1/ c ); 17 Issue 3, Volume 3, March 008

11 n31= s1 r1 ; n1=-b 1 *(* s1 r1 ); n11=b 1 *b 1 * s1 ; d41=(x s1 X r1 )^; d31=-*b 1 *d41; d1= s1 r1 * s1 * r1 b 1 *b 1 *d41; d11=-*b 1 * s1 -*b 1 * s1 * r1 ; d01=b 1 *b 1 * s1 ; n3= s r ; K1c=K1b*K1b; K1d=a*a*(a-b 1 )*(a-b 1 )*(X s1 X r1 )^; K1e=K1cK1d; Ka=a*(a-b )*(a-b )*(X s X r ); Kb= s *(a-b )a* r ; Kc=Kb*Kb; Kd=a*a*(a-b )*(a-b )*(X s X r )^; Ke=KcKd; n=-b *(* s r ); n1=b *b * s ; d4=(x s X r )^; d3=-*b *d4; d= s r * s * r b *b *d4; d1=-*b * s -*b * s * r ; d0=b *b * s ; (1) and (13) may be used to develop the quadratc expresson n terms of V as gven below; *V -(0.0753w*a*C-K1- K)*V Where K1=K1a/K1e; and K=Ka/Ke; K1a=a*(a-b 1 )*(a-b 1 )*(X s1 X r1 ); K1b= s1 *(a-b 1 )a* r1 ; 18 Issue 3, Volume 3, March 008