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various generator-load configurations that accurately

determine the conditions for self-excitation and performance

characteristics of an isolated , three-phase, self-excited

induction generator operating under balanced or unbalanced

conditions .These models are derived using symmetrical

component theory along with the generator sequence

equivalent circuits. Using this technique a 4.5kW, 400/440V,

four poles, three-phase induction motor operated as a SEIG is

analysed under different balanced or unbalanced

configuration.

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- 1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 Analysis of Self-Excited Induction Generator under Balanced or Unbalanced Conditions Shakuntla BOORAYMCA University of Science and Technology, Department of Electrical Engineering, Faridabad -121002, INDIA Email:shaku_boora@yahoo.comAbstract: This paper presents mathematical models for three-phase SEIG under balanced or unbalanced excitationvarious generator-load configurations that accurately [13].determine the conditions for self-excitation and performancecharacteristics of an isolated , three-phase, self-excited II. PROPOSED MODELSinduction generator operating under balanced or unbalancedconditions .These models are derived using symmetrical Consider a 3-φ induction machine connected to a 3-φcomponent theory along with the generator sequence network consisting of excitation capacitors with or withoutequivalent circuits. Using this technique a 4.5kW, 400/440V, a parallel load. The machine may have star or deltafour poles, three-phase induction motor operated as a SEIG isanalysed under different balanced or unbalanced connected windings. Similarly, the network may be connected in either star or delta. Further, this network mayconfiguration. be either balanced or unbalanced. For a given configurationKey Words: Induction generator, self-excited, steady state (star or delta) of the generator & the load, the method of symmetrical components can be used to analyze theanalysis, unbalanced. performance of the system. 1. INTRODUCTION Sequence equivalent circuits The positive and negative sequence equivalent network The self-excited induction generator (SEIG) has of a SEIG [14] is shown below in fig. (1)attracted considerable recent attention due to itsapplicability as a stand-alone generator using differentconventional and non-conventional energy resources withits advantage over the conventional synchronous generator..Due to the research of renewable energy resources andisolated power systems, the SEIG become one of the mostimportant renewable sources in developing countries [1-4].Besides application as a generator, the principle of self-excitation can also be used for dynamic braking of threephase induction motors [5]. Many papers have discussed (a) Positive Sequenceanalysis of three-phase balanced operation of isolated andparallel operated self-excited induction generator [6-10].However, the unbalanced operations of such generatorshave been given comparatively little attention. This modeof operation may sometimes be of interest for varioussmall-scale applications where either balanced conditionsare not necessary or difficult to achieve. Certain specificcases of unbalanced conditions in a SEIG have beendiscussed in several papers [4& 9-11]. However, no general (b) Negative Sequencemethod of analysis for the unbalanced mode of operation ofthe SEIG is available. For single-phase system, the single – Figure 1 Sequence equivalent circuits of a SEIGphase SEIG could be used with advantage. However, whenthe power requirements of the remote area are higher than A Delta Connected Generatorthe normal available ratings of single-phase induction Let us assume that a 3-φ delta connected inductionmachine have to be constructed to tailor made needs and machine is connected across a 3-φ delta connected networkthis may prove to be expensive .As an alternative, the having admittances Yab, Ybc & Yca as shown in fig (2). Eachthree-phase SEIG can be used as a single-phase generator branch of the delta network may consist of an excitation[11&12]. Used thus, the system may work out to be lesser capacitor in parallel with a general load as shown in figin cost than the specially designed single-phase SEIG of (3.3) for a-b branch.equivalent capacity. This paper presents general .mathematical models that determine the conditions of self-excitation and performance characteristics of an isolated, 59© 2010 ACEEEDOI: 01.IJEPE.01.03.535
- 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 I a 2 = (1 − a 2 ) (Y1 Vab 1 + Y0 Vab 2 ) L (6) From the sequence networks of fig (1), the generator sequence currents are given by Is1 = – YG1Vt1 and Is2 = – YG2 Vt2 Since in fig (2), the generator is Δ-connected, the positive and negative sequence components of the generator line currents are given as: I G 1 = (1 − a ) Is 1 = −(1 − a )YG1 Vt1 Figure2. Delta connection of a SEIG & load-excitation capacitors a (7) I G 2 = (1 − a 2 ) Is 2 = −(1 − a 2 )YG 2 Vt 2 a (8) From terminal conditions, Ia 1 = IG1 & Ia 2 = IG 2 L a L a (9) Moreover, for the Δ-connected generator, the phase & the Figure3. Equivalent circuits of a-b branch line voltages are equal Z = R + jf X for R-L load ∴ Vt1 = Vab1 & Vt2 = Vab2 (10) jX From (9) & (10) Z=R- for R-C load f (Y0 + YG1) Vt1 = - Y2 Vt2 (11) The method of symmetrical components can be used toresolve the unbalanced admittances of the network of fig Y1 Vt1 = - (YG2 + Y0) Vt2 (12)(2) into a set of sequence admittances as follows: After dividing (11) by (12), we get ⎛ Yo ⎞ ⎛1 1 1⎞ ⎛ Yab ⎞ (YG1 + Y0) (YG2 + Y0) – Y1 Y2 = 0 (13) ⎜ ⎟ 1 ⎜ ⎟ ⎜ ⎟ ⎜ Y1 ⎟ = ⎜1 a a2 ⎟ ⎜ Ybc ⎟ (1) This is the equation for Δ - connected generator and Δ - ⎜ Y ⎟ 3 ⎜1 a 2 a⎟ ⎜Y ⎟ connected network. ⎝ 2⎠ ⎝ ⎠ ⎝ ca ⎠ B Star Connected Generator with No Neutral Connection In fig (2), the phase currents IabL, IbcL & IcaL can be Consider a 3-φ Y-connected induction machinerelated to the phase voltages and admittances. By using connected across a 3-φ Y-connected network as shownsymmetrical components transformations, these phase belowcurrents can be resolved into their sequence components as ⎛ L ⎞ ⎜ I abo ⎟ ⎛Y Y2 Y 1 ⎞ ⎛ V abo ⎞ ⎜ L ⎟ ⎜ 0 ⎟⎜ ⎟ (2) ⎜ I ab 1 ⎟ = ⎜ Y1 Y0 Y 2 ⎟ ⎜ v ab 1 ⎟ ⎜ L ⎟ ⎜ ⎜ I ab 2 ⎟ ⎝ Y2 Y1 Y 0 ⎟ ⎜ V ab 2 ⎠⎝ ⎟ ⎠ ⎝ ⎠ As in a delta connected passive network, there is no zerosequence voltage i.e.Vabo = 0. Thus, the positive and Figure4. Star connection of a SEIG and load-excitation capacitors.negative sequence components of the line & the phase loadcurrents are related by Let Y0, Y1, Y2 represent the sequence admittance components of Ya, Yb & Yc. The current IaL, IbL and IcL can Ia lL = (1 − a ) I ab1 (3) be related to the load phase voltages and admittances. Using symmetrical components theory, these currents can Ia L = (1 − a 2 ) I ab 2 2 (4) be resolved into their sequence components as follows: L Since, for the circuit of fig. (4), I a 0 = 0,From (2) Iab1 = Y0Vab1 + Y2Vab2, Iab2 = Y1Vab1 + Y0Vab2 Van0 = (Y2 Van1 + Y1 Van2)/Y0 (14)Therefore, Consequently, I a l = (1 − a ) (Y0 Vab 1 + Y2 Vab 2 ) L (5) 60© 2010 ACEEEDOI: 01.IJEPE.01.03.535
- 3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 ⎛ YY ⎞ ⎛ Y2 ⎞ YG1 + Y = 0 (25) I a 1 = ⎜ Y0 − 1 2 ⎟ Van1 + ⎜ Y2 − 1 ⎟ Van 2 L ⎜ Y0 ⎟ ⎜ Y0 ⎟ (15) Or YG2 + Y = 0 (26) ⎝ ⎠ ⎝ ⎠ It is noted that (25) also offers the feasible solution ⎛ Y2 ⎞ ⎛ YY ⎞ which represents the balanced operation of SEIG [2, 3]. L Ia 2 = ⎜ Y1 − 2 ⎟ Van1 + ⎜ Y0 − 1 2 ⎟ Van2 ⎜ ⎟ ⎜ Y0 ⎟ (16) Two phases open - Suppose that there is only one ⎝ Y0 ⎠ ⎝ ⎠ excitation capacitor is parallel with a load i.e. Ya = Y andHowever, the generator sequence currents are given as Yb = Yc = 0 .Therefore Y0 = Y1 = Y2 = Y/3. Hence (21) reduces to I G 1 = - YG1 Vam1 a (17) YG1 YG2 = 0 (27) The above equation can be represented by connecting IG 2 = - YG2 Vam2 a (18) positive and negative sequence equivalent circuit in It is noted that the generator and the load phase voltages parallel.may not be equal under unbalanced conditions. However,the generator and the load line voltages are equal regardless III METHOD OF SOLUTIONof the degree of unbalance. Equation (13) & (23) represent the conditions that must Sequence components of the phase and line voltages of be satisfied for the self-excitation of the induction machinethe generator and load are related as corresponding to various generator & load configurations Vab1 = (1-a2) Van1 = (1-a2) Vam1 (19) as discussed above. Each of these equations is complex and non-linear which can be expressed as two simultaneous Vab2 = (1-a) Van2 = (1-a) Vam2 (20) real, nonlinear equations with two unknowns. SuchHence Van1 = Vam1 & Van2 = Vam2 equations can be solved using any suitable techniqueAlso, from fig (4) (Symbolic Mathematics in MATLAB). If the values of the machine parameters, its speed (or frequency), excitation I G1 = I a 1 , I G 2 = I a 2 a L a L capacitance as well as load impedances are given, the two equations can be solved for the magnetizing reactance andTherefore, frequency (or speed). On the other hand, if the interest is to ⎛ find the range of terminal capacitances to sustain self- YY ⎞ ⎛ Y2 ⎞ ⎜ YG1 + Y0 − 1 2 ⎟ Van1 = −⎜ Y2 − 1 ⎟Van 2 (21) ⎜ ⎟ ⎜ excitation, the two equations can be solved for the ⎝ Y0 ⎠ ⎝ Y0 ⎟ ⎠ frequency (or speed ) and these capacitances by specifying the machine parameters, its speed (or frequency), load ⎛ Y2 ⎞ ⎛ YY ⎞ impedances and the maximum magnetizing reactance, Xmax ⎜ Y1 − 2 ⎜ ⎟ Van1 = −⎜ YG 2 + Y0 − 1 2 ⎟Van 2 (22) ⎟ ⎜ ⎝ Y0 ⎠ ⎝ Y0 ⎟⎠ .Consequently, Xm = Xmax represents the critical conditions for self-excitation. Once Xm, f and v are known, theDividing (21) by (22) complete performance of the generator can be evaluated provided the machine magnetizing characteristics are given ⎛ Y Y ⎞⎛ YY ⎞ ⎛ Y2 ⎞⎛ Y2 ⎞ ⎜YG1 + Y0 − 1 2 ⎟⎜YG2 + Y0 − 1 2 ⎟ −⎜Y − 2 ⎟⎜Y2 − 1 ⎟ = 0 ⎜ ⎟ Y0 ⎠⎜ ⎟ Y0 ⎠ ⎜ Y0 ⎟⎜ Y0 ⎟ 1 ⎝ ⎝ ⎝ ⎠⎝ ⎠ IV EXPERIMENTAL RESULTS AND DISCUSSION (23) Fig (5) and (6) respectively show the variation of theThis is the equation for Y-connected generator & Y- terminal voltage with rotor speed (rpm) for different valuesconnected network. of capacitance (i.e. 20, 45, 80, 108µF) when the testC Special Cases machine was under no-load and star connected for balanced and unbalanced excitation (line excitation). It is noted that The above models are general and can be used for the no-load terminal voltage increases with speed for bothbalanced and for any unbalanced conditions. In this paper, balanced and unbalanced excitation. The terminal voltagethe model for a Y-connected generator will be applied for is the highest at no-load and decreases as the machine issome selected cases. However similar analysis may also be loaded with resistive load (balanced load). It is important tocarried out for Δ - connected generator and Δ - connected point out that the terminal voltage is sensitive to both C andnetwork. the machine load. Similar sets of terminal voltage versus Balanced Network - Assume that, in fig (4), the network is speed patterns for different values of C are observed inbalanced and Ya = Yb = Yc =Y from (1) Y0 = Y & Y1 = Y2 = literature also [8, 12 and 13]. Fig (7) shows the variation of0.Therefore, from (23) stator current with rotor speed for different values of excitation capacitance ( i .e 20, 45, 80, 108 µF) when the (YG1+ Y) (YG2 + Y) = 0 (24) test machine was under no load and star connected forWhich implies that either balanced excitation. It is noted that no load stator current increases with speed. Fig (8) shows that when the machine 61© 2010 ACEEEDOI: 01.IJEPE.01.03.535
- 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010is loaded with R=450Ω, the stator current decreases withincreased load. It is clear from this figure that the value ofC has to be selected carefully because certain values of Ccan result into excessive high value of Vt and stator currentwhich can cause over heating and may damage the machineinsulation. Similar sets of stator current versus speedpatterns for different values of C are observed in literaturealso [8, 12 and 13]. Fig (9) and (10) shows the variation offrequency with speed under no-load for C=80µF and108µF. It is noted that the difference in C doesn’t affect thefrequency and depends mainly on speed. When the SEIG isloaded then both speed and frequency decreases. CONCLUSIONS The performance characteristics of an isolated, three-phase, self-excited connected induction generator can bepredicted with accuracy under balanced or unbalancedconditions. In general the performance characteristics arestrongly influenced by the value of C. Because theinduction generator is isolated, its stator frequency is freeto vary with the rotor speed and the operating slip remainssmall. This in turn results in high efficiency. Due to theirsimplicity, ruggedness and low cost of construction,squirrel-cage induction machine is a relatively inexpensivealternative to ac generation using wind power for voltageand frequency insensitive loads. LIST OF SYMBOLS f,v = Frequency and speed fb = Base frequency Zb = Base impedance Rs, R r, R = Stator, Rotor (referred to stator) and load resistance respectively Xs, Xr, Xm , Xc = Stator , Rotor (referred to stator) magnetizing and excitation reactance at base frequency respectively 62© 2010 ACEEEDOI: 01.IJEPE.01.03.535
- 5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010X, Xmax = Load and maximum magnetizing induction generators,” Proc. IEE, Part C, Vol. 140, reactance at base frequency No. 1, pp. 49-55, 1993 respectively [9] AI-Bahrani, A.H; and Malik N.H., “VoltageCmin , Cmax = Minimum and maximum values of control of parallel operated self-excited excitation capacitance (μf) induction generators,” IEEE Trans. On EnergyIs1, Ir1, Im1 = Positive sequence stator, rotor Conversion, Vol.8, NO.2, pp. 236-242, 1993 [10] Bhattacharya, J.L., and Woodward, J.L. (referred to stator) and magnetizing “Excitation balancing of a self-excited induction currents resp. generator for maximum power output,” IEE Proc.Is2, Ir2, Im2 = Negative sequence stator, rotor Part C, Vol. 135, No. 2, pp. 88-97, 1988 (referred to stator) and magnetizing [11] Rahim, Y.H.A., “Excitation of isolated three- phase currents resp. induction generator by a single capacitor,” IEEVt1, Vg1 = Positive sequence per phase Proc., Pt. B., Vol. 140, No. 1, pp. 44-50, 1993 generator terminal and air-gap [12] AI-Bahrani, A.H., and Malik, N.H, “Steady state voltages resp. analysis and performance characteristics of a three-Vt2, Vg2 = Negative sequence per phase phase induction generator self-excited with a single generator terminal and air-gap capacitor,” IEEE Trans. on Energy Conversion, Vol. 5, voltage resp. No. 4, pp. 725-732, 990.YG1, YG2 = Positive and negative sequence per [13] A.H. AI-Bahrani “Analysis of self-excited phase generator terminal admittances induction generators under unbalanced conditions.” at base frequency resp Electric Machine and Power Systems. vol 24.1996, j 2π −j 2π pp 117-129a, a2 = e 3 and e 3 resp. [14] M.G.Say, “Alternating Current Machines,” Wiley, 1976All parameters except Cmin and Cmax are in p.u APPENDIX A REFERENCES Specification and parameters of Machine[1] R. Holland, “Appropriate technology - Rural electrification in developing countries,”IEE 3-φ , 4-pole , 50Hz 400/440V, 8.5A, 50Hz, 4.5/6 Review, 1989, vol. 35, no 7, pp 251-254 kW/hp, 1440 rpm, star connected stator winding induction[2] S.S. Murthy, 0.P Malik. and A.K. Tandon. “Analysis of machine RS = 0.068993, Rr = 0.012492, Xs = Xr = self excited induction generators,” IEE Proceedings, 0.074575 Part. C, vol. 129, No 6, 1982. pp.260-265.[3] G. Rains and 0 P. Malik, “Wind energy conversion Air-gap Voltage using a self-excited induction generator,” IEEE VG = 1.895-0.492 fXm for 1.8936 < fXm2.27393 Transactions on Power Apparatus and Systems. vol. 102, no. 12, 1983, pp. 3933-3936. =0 for fXm < 1.8936[4] Elder, J.M, Boys, J.T., & Woodward, J.L. “Self- excited induction machines as a small low-cost generator,” Proc. IEE, Vol. 131, Part. C, No. 2, pp. 33-41, 1984[5] AI-Bahrani, A.H., and Malik, N.H, “Selection of the excitation capacitor for dynamic braking of induction machines,” Proc. IEE, Vol. 140, Part. B, No. 1, pp. 1-6, 1993[6] Doxey, B.C., “Theory and Application of the capacitor-excited induction generator,” The Engineer, 216, pp. 893-897, 1963.[7] N.H. Malik and A.H. Al-Bahrani, “Influence of the terminal capacitance on the performance characteristics of elf-excited induction generator”, Proc. IEE, Vol. 137, Part C, No. 2, pp.168-173, 1990.[8] AI-Bahrani, A.H; and Malik N.H., “Steady-state Fiigure11. Variation of VG with fXm – a linear approximation analysis of parallel operated self-excited 63© 2010 ACEEEDOI: 01.IJEPE.01.03.535

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