An Improved Electronc Load Controller for Self- Excted Inducton Generator n Mcro-Hydel Applcatons Abstract Ths paper descrbes the mathematcal modellng of selfexcted nducton generators (SEIGs) wth are mproved electronc load controller (IELC) for mcrohydel applcatons supplyng varety of loads. In small hydro plants, governor unt of turbne can be elmnated usng IELC, whch s smple and cost effectve. The mproved electronc load controller s a combnaton of a three-phase nsulated gate bpolar transstor (IGBT) based current controlled voltage source nverter (CC-VSI) and a hgh frequency DC chopper whch keeps the generated voltage and frequency constant n spte of change of balanced/unbalanced loads. A dynamc model of the SEIG- IELC supplng dfferent types of loads usng statonary d-q axes reference frame s developed for predctng the behavor of the system under transent condtons. The smulaton s carred out for compensaton of balanced/unbalanced loadng condtons. The smulated results show that generated frequency and voltage reman constant wth change n load. The proposed IELC acts as reactve power compensator, harmonc elmnator, load balancer and load controller. Key Words: Self-excted nducton generator, mproved electronc load controller, Mcrohydel, Voltage and Frequency Regulaton. Bhm Sngh, S. S. Murthy and Sushma Gupta I. INTRODUCTION In hlly and solated areas plenty of hydro potental s avalable. These hydro potentals can be used to drve hydro turbne to generate the electrcty. However, nducton machne can be used as a generator provded ts reactve power requrement s fulflled by capactor banks, s called self-excted nducton generator (SEIG). The SEIG has advantages lke smplcty, low cost, rugged, mantenance free, absence of DC, brushless etc. as compared to the conventonal synchronous generator. The analyss of the SEIG s complcated because ts operaton depends on the prme-mover speed, capactor and load. Capactance requrement wth load and speed for the SEIG s reported n the lterature [-3]. Consderable lterature s also reported on the transent analyss of the SEIG under balanced/unbalanced resstve, reactve and motor loads. In the lterature [4-6], d-q axes modelng are reported for the transent analyss of SEIG under balanced and unbalanced exctaton system. Jan et al. [7] have gven a generalzed model for the transent analyss of SEIG under symmetrcal and unsymmetrcal condtons. In hydro plants, a turbne s used wth governor to control power generaton. In mcro hydel applcaton, water s avalable free of cost then a turbne wthout governor can be used as prme mover and capactors are connected across the Bhm Sngh (e-mal: bsngh(aee.td,ac.n*l. S.S. Murthy (e-mal: ssmurthv(g!ee.td.ac.n and Sushma Gupta (e-mah sush gunta@vahoo.com) are wth the Department of Electrcal Engneerng, Indan Insttute of Technology, Delh, Huaz Khas New Delh-6, INDIA SEIG accordng to the rated power and the constant voltage can be mantaned by electronc load controller (ELC) [8-4]. Thus electronc load controller (ELC) keeps the load constant on the SEIG under balanced and unty pf load. But n case of unbalanced loads, SEIG currents and voltage are unbalanced and at laggng PF loads SEIG voltage drops down because SEIG and load demands the reactve power, whch s not 274 fulflled by the ELC. Most of the reported electronc load controllers are based on controlled and uncontrolled rectfer wth DC chopper, whch njects the harmoncs n the SEIG. Due to harmoncs njecton, SEIG s derated and voltage and current of SEIG are non-snusodal. In case of unbalanced load, SEIG s further derated due to presence of postve and negatve sequence component. The current controlled voltage source nverter wth self-supportng DC bus employed as statc compensator (STATCOM) can be used for flterng the harmoncs and balancng the load. In the reported lterature [5-9] STATCOM acts as a voltage regulator to mantan constant voltage for the SEIG. Larsen et al [5] have mentoned the advantage of the STATCOM. Marra and Pomlo [9] have gven the VS-PWM b-drectonal converter for SEIG, whch can regulate the frequency and voltage n case of balanced and lnear load. However, there s hardly any attempts on the voltage and frequency regulaton under unbalanced and non-lnear loads. In ths paper, an mproved electronc controller (IELC) s presented whch s the combnaton of CC-VSI and DC chopper. The IELC conssts of current controlled voltage source nverter, whch acts as a voltage regulator, and a DC chopper at DC bus of VSI keeps the rated power on the SEIG. A control technque s developed such that SEIG generates the constant power. In mcrohydel applcatons, turbne speed s kept constant and for a constant value exctaton capactor SEIG generates constant voltage, frequency and power, whch s known as sngle pont operaton. Connectng the capactor across the SEIG accordng to the balanced and unty PF power can reduce the ratng of the CC-VSI. In ths case, load balancng, reactve power compensaton and harmonc elmnaton should be provded for the load by the CC-VSI. A mathematcal model s developed for the transent analyss of IELC under the resstve, reactve and nonlnear loads wth balanced/unbalanced condtons. The mproved electronc load controller acts as a voltage and frequency regulator, harmonc elmnator, and load balancer. II. SYSTEM CONFIGURATION AND CONTROL SCHEME The schematc dagram of SEIG wth exctaton capactor, mproved electronc load controller ((CC-VSI)+DC chopper),
consumer load and control scheme s shown n Fg.l. Exctaton capactors are selected to generate the rated voltage of SEJG at no load. The reactve power requrement of SEIG and load s fulflled by the CC-VSI wth self-supportng DC bus. The SEIG generates constant power and when consumer power changes then DC chopper of IELC dumps the dfference power (generated - consumed) by consumers n the IELC. Thus, generated voltage and frequency are not affected by the applcaton and removal of the consumer load. The IELC conssts of a three-phase IGBT based current controlled voltage source nverter, DC bus capactor, DC chopper and AC nductors. The output of the nverter s connected through the AC flterng nductor to the SEIG termnals. The DC bus capactor s used as an energy storage devce and provdes self-supportng DC bus. DC Chopper s used to control dump power n IELC due to change n the consumer load. The control technque to regulate the termnal voltage, load balancng, and harmonc elmnaton of the SEIG s based on the controllng of source currents (have two components nphase and quadrature wth AC voltage). The n-phase unt vectors (u,, n, and u.) are three-phase snusodal functons, computed by dvdng the AC voltages v,, v b and v c by ther ampltude V,. Another set of quadrature unt vectors (w a, w b and w c ) s snusodal functon obtaned from n-phase vectors (u a, u b and uj. To regulate AC termnal voltage (V,) t s sensed and compared wth the reference voltage. The voltage error s processed n the PI controller. The output of the PI controller (I*,) for AC voltage control loop decdes the ampltude of reactve current to be generated by the CC-VSI. Multplcaton of quadrature unt vectors (w,, w b and w c ) wth the output of PI based AC voltage controller (r sraa ) yelds the quadrature component of the source reference currents (* saq, * sbq and V). For self-supportng DC bus of CC-VSI, ts DC bus voltage s sensed and compared wth DC reference voltage. The error voltage s processed n another PI controller. The output of the PI controller (I* md ) decdes the ampltude of actve current. Multplcaton of n-phase unt vectors (u s, Ut, and Uc) wth output of Ft controller (I*,md) yelds the n-phase component of the source reference currents (* sa(, * S bd and * SC d). The sum of quadrature and n-phase components s the total source reference currents (* M, * S b and *sc), whch are compared wth the source lne current ( ra,!b and K ). These current error sgnals are amplfed and compared wth the trangular carrer wave. If the amplfed current error sgnal s equal to or greater than the trangular carrer wave, lower devce of the nverter phase lag s turned on and upper devce turned off. If the amplfed current error sgnal s equal to or less than the trangular carrer wave lower devce of the nverter phase s turned off and upper devce s turned on. The generated power by the SEIG s mantaned constant by the thrd PI controller. The generated power s compared wth the reference rated power. The PI controller processes output error of the comparator. The output of the PI controller s compared wth trangular wave. If output of PI controller s more than the trangular wave, gate pulse of chopper swtch (IGBT) s made hgh and ts current ncreases through chopper swtch so that SEIG experence same load. If controller output s less than PWM carrer trangle wave, gate pulse of IGBT s low and chopper swtch s made open. HI. MODELLING OF SEIG-IELC SYSTEM The schematc dagram s shown n Fg., whch conssts of SEIG, IELC, ts control scheme and loads. The mathematcal modellng of each component s as follows. A, Modellng of control scheme of IELC Three-phase voltages at the SEIG termnals (v a, v b and v c ) are consdered snusodal and hence ther ampltude s computed as: Fg. Schematc and power dagram of the mproved SEIG-IELC system V,= {(2/3)(v. 2 +v b '+v! )}! ' 2 () The unt vector n phase wth v a, v b and v c are derved as: u,= vyv,; u b = v l /V ; u,= v,/v... (2) The unt vectors n quadrature wth v,, v b and v c may be derved usng a quadrature transformaton of the n-phase unt vectors Ua, U*. and Uc [7] as: V V (3) 2742
(4) (5) ) Quadrature Component of Source Reference Currents: The AC voltage error V e[ at the n" samplng nstant s: V er(0) =V,, rf(nr V (n) (6) Where V m, (n) s the ampltude of reference AC termnal voltage and V w,s the ampltude of the sensed three-phase AC voltage at the SEIG termnals at n" nstant. The output of the PI controller (I*,,,,,) for mantanng AC termnal voltage constant at the n th samplng nstant s expressed as: I' ** = IW,, + K n { V cnn, - V ti(n,,} + K;, V crw (7) Where Kp, and K a are the proportonal and ntegral gan constants of the proportonal ntegral (PI) controller, V H(n) and Vt,,,,.,} are the voltage errors n n" and (n-)" nstant and I',^.,, s the ampltude of quadrature component of the source reference current at (n-)" nstant. The quadrature components of the source reference currents are estmated as: saq smq w a» * sbq smq "b, I scq BKq We \O} 2) In-Phase Component of Source Reference Currents: The DC bus voltage error V dctr at n' h samplng nstant s: y _ y _ y^ (g\ Where V dm, s the reference DC voltage and V dc(0) s the sensed DC lnk voltage of the CC-VSI. The output of the PI controller for mantanng DC bus voltage of the CC-VSI at the n * samplng nstant, s expressed as: T* = T* + K V. V +K.V (0 * smd(n) x smdn-} x *-pd \ " accrnj dccr(n-l)j Vl o ' dwr(n) V V J I*sad ( n s consdered as the ampltude of actve source current. Kpd and K d are the proportonal and ntegral gan constants of the DC bus PI voltage controller. In-phase components of source reference currents are estmated as: * s.j = I*.md u a ; 'sw = I*,mj u b ; *^ = I*,«u, () 3) Total Source Reference Currents: Total source reference currents are sum of n-phase and quadrature components of the source reference currents as: J sa sa( ' sad V,' **} *u = % +*scd (4) 4) PWM current controller: The total reference currents (* a, * sb and * K ) are compared wth the sensed source currents ( B, sb and, c ). The ON/OFF swtchng patterns of the gate drve sgnals to the IGBTs are generated from the PWM current controller. The current errors are computed as: ««,, = * B -» (5) W = * S b S b (6) w=*.-. (7) These current error sgnals are amplfed and then compared wth the trangular carrer wave. If the amplfed current error sgnal correspondng to phase a («n ) s greater than the trangular wave sgnal swtch S 4 (lower devce) s ON and swtch S, (upper devce) s OFF, and the value of swtchng functon SA s set to 0. If the amplfed current error sgnal correspondng to saot s less than the trangular wave sgnal swtch S, s ON and swtch S 4 s OFF, and the value of SA s set to I. Smlar logc apples to other phases. B. Modellng of DC bus chopper The generated power of the SEIG s calculated by transformng three-phase quantty (a-b-c) nto two-phase quantty (a-p axes) as follows [20]: ^=^2/3(^^2^/2) (8) v p =V2/3 (V3/2 v, -V3/2 v c ) (9) a = V2/3(h-.b -,/2) (20) P =V2/3 (V3/2 b -V3/2 c ) (2) The generated nstantaneous power of SEIG can be defned as: P K» = v a a + v p p (22) Power (PjJ s compared wth reference power accordng to rated power of generator (P ref ) as: Perln) = Pref Pgsn(n) (23) Power error s processed n the PI controller to mantan the constant generated power at the SEIG at the n* samplng nstant, s expressed as: vw, = V ml.,> + K^ } P er(n) - P*,,.,)} + Kp, P trtn) (24) Kpp and K^ are the proportonal and ntegral gan constants of the power controller. The PI controller output (V',,)) s compared wth the trangular carrer (Vm) waveform and output s fed to the gate of the chopper swtch (IGBT). when V*^,,.^ V B, SD = and when V mn,< V B, SD = 0 (25) The SD s the swtchng functon used for generatng the gatng pulse of IGBT of the chopper of ELC. C. Modellng of CC-VSI The CC-VSI s a current controlled VSI and modeled as follows: The dervatve of ts DC bus voltage s defned as: pv dt = (SA a + SB * + SC K - SD VJR$ C^ (26) Where SA, SB and SC are the swtchng functons for the ON/OFF postons of the VSI brdge swtches S r S 6 and SD s the swtchng functon of chopper. The DC bus voltage reflects at the output of the nverter n the form of the three-phase PWM AC voltage e a, e b and e c. These voltages may be expressed as: e, = v* (2 SA- SB- SC) / 3 (27) e B = Vfc (- SA+ 2 SB- SC) / 3 (28) e c = v dc (- SA- SB + 2 SC) / 3 (29) The (CC-VSI) lne voltages are gven as: e a b = e, - e b ; e fc = e b - e c ; s a = e c - e, (30) The volt-amp equatons of the output of voltage source nverter (CC-VSI) are as: v, = R r ta + Up,,, + e ab - R f d, - L f p cb (3) v b = R f * + L f p cb + e^ - R, cc - L f p re (32) o, + u + «= 0 (33) Value of K from eqn (33) s substtuted n to eqn. (32) whch results n: v b = R, cb + L f p cb + etc + r f a + L, p ca + R r sb + L f p u (34) Rearrangng the eqn. (3) and eqn. (34) t results n: Lrpo, - L r pu = v a - e, b - Rr a + Rr * (35) Lrp a + 2 L f pd, = v b - e bc -R ( a -2 R f d, (36) Hence, the CC-VSI current dervatves are obtaned by solvng the eqn (35) and (36) as: pca = {( v b - e*) + 2 (v. - e rt ) - 3 R ( a } /(3L f ) (37) pcb = {(v b - Ob.) - (v. - e lb ) - 3 R r»}/(3l f ) (38) 2743
D. Modellng of SEIG The dynamc model of the three-phase SEIG s developed usng statonary d-q axes references frame, whose voltageampere equatons are [7]: R] [] + [L] P [] +H>r [G] [] (39) From whch, current dervatves can be expressed as p[] = [L] ' { [v] - [R] [] - co^g] [] (40) Where [v] = [ Vd3 v, s v d, v, t ] T ; [] = [ d,, ldr r [R] = dag [ R s R s R r R r ] L s +L m L m "o 0 0 r r - 0 0 0 L L J~ [Uj- 0 -L mo 0 L s +L m 0 L m L m 0 L r +L m 0 0 L m 0 L r +L m 0 0 L r + L + L m L mo"l r (4) The electromagnetc torque balance equaton of SEIG s defned as: T M =T c +J(2/P)p(A (42) The dervatve of rotor speed of the SEIG from eqn. (42) s: p(h={p/(2j)}(t sm -T c ) (43) where the developed electromagnetc torque of the SEIG s expressed as [7]: T e = (3P/4) U, (,. * - * v) (44) In mcrohdel system, prme mover have droopng characterstc and may be expressed as: mo T*.* = (3370-0w r ) (45)' The SEIG operates n the saturaton regon and ts magenetzng characterstcs s non-lnear n nature. Therefore the magnetzng current should be calculated n each step of ntegraton n terms of stator and rotor currents as: I B = V( d,+ dr ) J + ( p +,) (46) Magnetzng nductance s calculated from the magnetzng characterstcs between L m and I m. Relaton between L m and I ra s obtaned by synchronous speed test [7] and can be wrtten as: L m = 0.407 + 0.004 L- 0.002 L 2 + 0.000048 I m 3 (47) Fg.2 shows the transent waveforms of 3-phase generator voltages (vsatc), generator currents (abe), three-phase resstve load currents ( a, )b and, c ), three-phase IELC currents (c, * and K ), generated power and ts reference (P sen ) ampltude of SEIG termnal voltage and ts reference (V,/V lltf ), DC bus voltage and ts reference (VJ V dcref ) and generator speed (w E ) demonstratng the response of IELC for regulatng the SEIG termnal voltage supplyng wth pure resstve load (7.5 kw). At 5.-sec. one and 5.2-sec. two-phase of the load are dsconnected from the SEIG. Consequently IELC currents ncrease to balance the SEIG system and chopper current ncreases to mantan the constant power on the SEIG. At 5.3- sec. one phase and at 5.4-sec. two-phase of load s reconnected S 0.3 S.I 5.5 5. S.25 5,3 535 5-4 5.45 5,5 5.53. J.I 55 2 5.25 JJ 5,35 5, S.«55 5.5S 5.6 wv < (S 5,5 5 Z 5.25 S3 5 35 54 5.4! S.S 5.55 S( E. AC lne voltage at the pont of common couplng From drect and quadrature axs currents of the SEIG (d, and qs ) are converted n to three-phase (a, b and c). The dervatve of AC termnal voltage of the SEIG s defned as: P v. = {(. -, s - Q - (u-» - *)} / (3 C) (48) p v> = {(, - lc - a ) +2 ( b -,, - ce )} / (3 C) (49) v, +v b + v c = 0. (50) where,, b and c are SEIG stator lne currents,, a, n, and lc are 3-phase load currents and a, * and «are CC-VSI currents. C s per phase no load exctaton capactor value connected parallel to SEIG. IV. RESULTS AND DISCUSSION The SEIG system wth IELC feedng resstve and reactve balanced/unbalanced loads s smulated and results are shown n Fgs. 2-4. For the smulaton, a 7.5 kw, 230V, 5.6 A, 4- pole machne has been used as a generator and parameters of the generator are gven n Appendx. f '.l SM 5.2 2< 5.}.W 5-4 5.4 5.5 5.55 5.6 'Ml? I 33. (5 I )5 5-25 5,3 5.35 5. 5.45 5.5 S.55 5.6, 5.5 5,Z 5.25 5,3 5.35. 5.4 5.45 5.5 5,55 5,6 I.I 5.IS 5.2 S.2! 5.3 5.35 5.4 5-4S _ I I I L_ 5. 5.IS 5.2 5.2! 5.3 5.35 54 MS ).5 5.55 5.6 Tme (t) A. SEIG-IELC System resstve load behavour Feedng Three-phase Fg. 2 Performance waveforms of three-phase SEIG-IELC system supplyng resstve load (7.5 kw) 2744
on SEIG. At applcaton of load and under steady state, generator speed remans constant, whch shows that generated voltage and frequency are constant. Under three-phase load on the SEIG, IELC current decreases whch shows power on the SEIG remans constant. Load currents, generator currents and voltages are snusodal and harmonc free. B. SEIG-IELC system behavor Feedng Three-phase Reactve load 5 S.I 20 0-20 AJUU 5.5 52 Wfff 5.25 MM wwx 5.3 5.35 no MUUMMM fmwm) 5.35 5. MM 5.45 WWWWWVYWWWVV ffl WMJMwmmm 5.5 5,55 5 Fg.3 shows the transent waveforms of the three-phase SEIG- IELC supplyng reactve load (0.8 PF). At 5.2-sec one phase load s dsconnected from the SEIG consequently IELC current of one-phase ncreases to balance the SEIG system. At 5.3-sec. two-phases of load s dsconnected from the load and hence IELC currents of two phases ncrease for balancng the SEIG system. At 5.4-sec. one-phase and 5.5-sec. two-phases of load are reconnected on the SEIG. In ths case, IELC "vrrents decrease because SEIG system s balanced. Chopper jrent also ncreases and decreases when consumer load creases and ncreases respectvely whch shows that the nerated power of the SEIG remans constant n spte of naton n consumer load. In reactve load, generator voltage constant and perfectly snusodal whch shows that IELC s tng as a voltage regulator and load balancer. The speed of JIG remans constant, whch shows that the generator s netatng constant voltage, frequency and power. SEIG-IELC system behavor Feedng Three-phase Non- Lnear load 5.5 2 5.25 S.J 5.35 5,4 5.45 55 S.SS 5.4 AAAAAAAAAAA 3 0 j.l 5.5 U 525. 5.S5 5.4 S.45 5,5 S.H 5.6 '" k I I I I h I I I I " 0 WAAAA^^ 5,5 5,2 5.25 5.3 5.3) 5.4 5.45 5.5 5.55 5.6 (45 S.5 6 55 6* 6.65 6.7 6 7J S 6,j.l 5.I5 52 SJ3 5,3 5,35 5,4 5.4S 5.S 5,55 S I 20 A^AAAAAAAAA/WW\AAAAA/YWWV - 7000 ;S.I 5.5 52 Ul S) 5)5 5^4 5,45 5,5 5.55 56 A/VWWWVVWWVVWWWWVXA 5.5 5 5.25 5.3 5.35 5.4 5.45 5.5 5.55 5.6 5.IS 5.2 55 5.3 5.35 5.4 5.45 5.5 S.SS S f 3M j.l 5.5 U 5.25 5.3 5.35 5,4 5,45 5.5 5.55 5.6 M^^YI^^ 6.45 ftj 6,5 6.6 6,«; A.? 6,75 6,J ^VyMv*4%W##^ k^^\0^^.73 6.8 6 4 (.4S S.5 6J5 U t. 6.7 6.75 6. 66 6_65 6_7 ^658 5 600 III 5,5 l US 5,3 5.35 5.4! 5.4! 5.5 5,55 5,6 ' 4 M 6J 6S 665 6.7 b. 6J 6 -mf J34 I S.I 5.5 J-2 l 5,3 5,55 5.4 S.45 S.5 5.55 S.6 TmtfSe) f/a 64> 6-5 S.5 6 6 6.65 6. 6 7J Fg. 3 Performance of three-phase SEIG-IELC supplyng reactve load (7.5 kw at 0.8 PF) Fg. 4 Transent waveforms of three-phase SEIG-IELC system supplyng nonlnear load 2745
Fg. 4 shows the SEIG-IELC system behavor supplyng the non-lnear load. A three-phase rectfer wth R load and capactve flter s taken as a non-lnear load. At 6.5-sec loadng on the rectfer load ncreases because of that load current ncreases. It s observed from the fgure that generator voltages and currents reman constant and snusodal. At 6.75- sec. loadng on rectfer load s decreased consequently rectfer load currents decrease however the SEIG voltages and currents reman constant and snusodal whch shows that IELC s actng as a harmonc elmnator. The SEIG speed remans constant n complete duraton, whch proofs that t s generatng constant frequency, voltage and power. V. CONCLUSION The developed mathematcal model of three-phase SEIG- IELC system has been found an approprate tool to study the behavor of SEIG wth IELC at dfferent types of loads under transent condtons. Smulatons have been carred out and smulated results show that SEIG termnal voltage and frequency reman constant whle supplyng the resstve, reactve and non-lnear loads wth balanced/unbalanced condtons. When unbalancng of load takes place then IELC generates compensatng currents and balances the generator currents and voltage thus IELC acts as load balancer. In case of varaton n consumer load, chopper of IELC operates accordngly and generated power of the generator remans constant. The SEIG generates constant voltage and frequency as t s operatng at constant power. Therefore, mproved electronc load controller acts as voltage regulator, frequency regulator, load balancer and harmonc elmnator. VI. APPENDICES A. STATCOM control parameters U=.5 rah, R f = 0.05 S and C dt = 4000u,F. AC voltage P controller: K, a =0.05, K;.= 0.04. DC bus voltage PI controller K^ = 0.04, K«=0.005 Carrer frequency = 20 khz Power PI controller K^ = 0.4 K p = 0.05 B. Machnes parameters The parameters of the nducton machnes are gven below. R»=.0Q,R, = 0.77Q,X = X, r =.0 Q, J = 0.384 kg/m 2 [7] S. K. Jan, J. D. Sharma and S. P, Sngh, "Transent performance of three-phase self-excted nducton generator durng balanced and unbalanced faults," IEE Proc. Cener. Transm. Dstrb., Vol. 49, No., pp. 50-57, January 2002. [8] S. Rajakaruna and R. Bonert, "A Technque for the steady-state analyss of a self-excted nducton generator wth varable speed," IEEE Trans. on Energy Converson, Vol. 8, No. 4, pp. 757-76, December 993. [9] R. Bonert and S. Rajakaruna, "Self-excted nducton generator wth excellent voltage and frequency control," IEE Proc. Gener. Transm. Dstrb., Vol. 45, No., pp. 33-39, January 998. [0] D. Henderson, "An advanced electronc load governor for control of mcro hydroelectrc generaon," IEEE Trans, on Energy Converson, Vol. 3, No. 3, pp. 300-304, December 998. [] S. S. Murthy, R. 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