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W Prtvitc Wvftllj Pete international Review ofl-Ilectiuicwtl Engineering (l. R. E. E. j, l'ol. 5, tN". 2 ri-larch-elpril 20H} Performance Analysis of a Capacitance Compensated Dual Stator Winding Synchronous Reluctance Machine A. s. 0. Ogunjuyigbc. A. A. Jimoh 2, o. v. Nicolae i. E. s. Obe 3 Abstract Synchronous relucrtanc-e tnac-hine with simple salient rotor are known to have poor power factor because they have a low effective reactant-e ratitt. This paper used a J-pltase attxiliary winding and balanced capacitance compensation to injlttence the eective reactant-e ratio of a synchronous reluctance machine with simple salient rotor structure, such that its power factor and torquetampere pierformance is improved A mathematical mtxlel and dq equivalent circuit suitable for dynamic and steady state analysis was developed and used to stuttfv the synchronous operation of this machine. rlnalytical as well as experimental results-for a 4-pole. 36 slots simple salient rotor teluc-tancc machine showed that the ective rettctance ratio increased with the capacitance size, and the machine operated at a maximum powerfactor of ft. 969 ivitl-tottt altering the geometry of the rotor. The torque per ampere of the machine also improved with the size of capacitor attached to the atailiary winding. Copyright � Zttltl Praise Worthy Prize S. r.l. - All rights reserved. Keywords: Balanced Auxiliary Winding. Capacitor (cmpensation. Dttal Winding. bynchronotts Reluctance Machine. AC A/lachines A considerable amount of research efforts devoted to synchronous reluctance machine in the past ten decades has demonstrated the machine to be an attractive alternative to other AC machines (permanent magnet, Induction and Switched reluctance machines) in high performance, variable speed applications. This is as a result of its ability to withstand harsh environment, its low inertia, case of construction. high power to weight ratio and good acceleration performance [ll-[]. Most often, these research efforts made signicant attempts to control the rcluctanccs in the cl - and q-axis of the machine. The efforts have commonly followed the geometrical trend that has led to the emergence of the following types of rotor: (i) Simple salient pole type, (ii) Segmented rotor type, (iii) Flux barrier type, (iv) Transversely laminated type and (v) Axially laminated type. 'l'he different rotor congurations have gone through different design analysis and techniques to obtain a better performance. Popular amongst these techniques, as a result of the availability of more computational power, is the nite element method. Some of the successes on the rotor congurations are wcll reported in [2], [3], [71-[1 l]. The geometric approach via rotor designs has improved the performance characteristics of reluctance machines. However. the quest is for improved performance based on a widely acceptable low cost practicable means. Some research worlt exploited the benets of multiphase machine arrangements to dcvclopa high torque performance Introduction tltlanuscrrpt received and revised lltarcli Jttl it. accepted April Btlltt 43? using S-phase, nine phase arrangements rather than the traditional three phase [|2]-[l5]. In their con-esponding works, they made use of higher order odd harmonic component of the current to achieve a better torque performance. These works reported the following achievements: A llP/o torque improvement for the synchronous reluctance with a simple salient rotor[l6]. Conversely, [l 3] reported only 4% improvement, A 24% torque improvement for the synchronous reluctance machine with a simple salient rotor and a 5% torque reduction with the axially laminated rotor [l5], and A 4% torque reduction for the ux barrier rotor [ l3]. Most of the works in this direction did not express how their arrangements inuenced the effective reactance ratio as well as the power factor of the machine, [l2]-[l4]. However. reference [l5], concluded to a fact that the power factor of the synchronous reluctance machine heavily depend on the rotor structure. This paper therefore present an effort which is not based on altering the geometrical structure of a simple salient rotor and yet changes the effective saliency ratio of the machine as reected in the air gap eld distribution for improved power factor and torque per ampere. The conguration, whose operation and feasibility are elaborated in this paper, has the machine furnished with two thrcc phase stator windings identied as abc and 'xyz. Unlike the doubly fed reluctance machine. these two windings, abc and xyz. have the same number of poles. The two windings occupy the ("opyrtglit it! Jlllll Praise Worthy Prize Fir. l. All rights reserved A. S. O. Ogunjrryigbe, A. A. Jimoh, D. P. Nicolae, E. S. Obe same stator slots; they are electrically isolated but magnetically coupled. The rst winding abc is connected to the utility supply thus carrying the load current, while the second winding xyz is connected to a balanced set of capacitance to uniquely inuence the effective reactance ratio of the machine such that its power factor performance is likewise enhanced. The arrangement is used in this work with a simple salient rotor design for the laboratory experimentation. An electromagnetic eld concept along with a coupled circuit approach based on an approximate equivalent circuit was used to examine the flux distribution of the conguration in [l7]. On the other hand, this paper developed mathematical models and dq equivalent circuit, useful for dynamic. steady state calculations and computer simulations of the machine. These models were utilized to investigate the inuence of the capacitance injected through the auxiliary winding on the effective axis reactance and power factor performance characteristics of the proposed synchronous reluctance machine with simple salient rotor. Calculations, experimental as well as computer simulation results conrm the usefulness of the models and the benets of the conguration. With the known advantages presented by synchronous reluctance machine, the conguration discussed in this paper is expected to extend its application area. It is also expected to create a renewed attraction to the cheap, and simple to construct salient rotor for application in the petrochemical industry where arcing within the machine is not allowed. The remainder of this paper is organized as follows: Section ll describes the general system equations and mathematical model for synchronous reluctance machine structure with an auxiliary winding attached to a balanced capacitor. The expressions for the various winding inductances are derived, and the dq equivalent circuits suitable for dynamic and steady state analysis of the machine were also developed in this section. Steady state performances of the machine based on the mathematical model and laboratory experiments, outlining the benets of the conguration are set up in section lll, while the results of transient perfonnances are discussed in section IV. The paper is concluded in section V. ll. Machine Model The conceptual diagram of the proposed machine structure discussed in this paper showing the simple salient rotor shape and the auxiliary winding connected to a balanced capacitor is illustrated in Fig. 1(a). The clock diagram of the two stator windings in the 36 stator slots, 4-pole. 3-phase machine is illustrated in Fig. 1th}. The experimental machine is wound with a full pitch; single layer winding with the number of slot per pole per phase as 3. The rst layer is occupied by the main winding abc and the second layer is occupied by the Copyright � ZEUU Praise Worthy PiriL-e $.11). AH rights reserved 43B auxiliary winding xyz. The two windings are wound with the same number of poles and have equal number of turns. The rotor of the experimental machine used for the work reported here is of the simple salient type with the dimensions as listed in Table Ill of the appendix. e Milt llllik' tln Figs. I. Synchronous reluctance machine with dual stator winding and capacitance compensation [a] Conceptual diagram of the rotor and stator {b} Clock diagram ofthe dual stator windings General and classical assumptions are taking in the analysis that follows. lt is assumed that the stator windings are sinusoidally distributed, and the iron of the stator and rotor are innitely permeable. thus saturation is not considered. The voltage equation which describes the electrical behavior ofthe machine in matrix form can be written as: _ din L. rah:- : Rsllrabr: + d: i it)" . 0 = Rrxy: + " * + he): (2) where: lube I Lahrlu-t" + Labia): Irv: Am = 1., rm + a920,. 1M. (4) gives the ux linkages ofthe windings. ti, and L, represent the self and mutual inductances of each winding, while Laban, and Lxyzx represent the mutuat as well as the coupling inductances between the two windings. lmernanfonul Review ofE-ecrrrcol Engineering. l-"bl. 5. N. 2 A. S. O. Ogtmjinligbe. A. A. Jimoh, D. l1. Nicolas. E. S. Obe i=;,,,_. = p; i, i-;.]" is) i, =[i,, i, 1,1 is} it, =[,i,, .1, 4,1 (t) t, i.,,,, t, Loin. = Lin: LN) Lbs" Lao Lcib Lac Ln. LI)" LIZ h: = L}, 1.1,. L}: (9) L11: Lev z: Lox Lop" La: Lubes}: = List-n: z Lin: Liiv Lin: L L L .. In equations (1)49), RS1, R3 are diagonal matrices which represent the stator main and auxiliary winding resistances respectively. The stator main and auxiliary winding currents are 1,1,, and i, respectively. To further illustrate the operation of the machine, the computation of the machine inductances is important. NJ. A convenient approach of determining the inductance is the winding functions method [l8]-[2l] in which inductance of the machine are calculated by an integral expression representing the placement of the winding turns along the airgap periphery. in winding functions theory, the self and mutual inductances between windings i ' and j in any electric machine can be calculated by: Stator lndttctances 2x t. -_- pa�: Ig-l{6.6,,,,]N,(9.8,,,,]N;(6.6m)d9 m) t) The effective airgap radius of the machine is given as r, i is the effective motor stack length. and the approximated inverse airgap length is represented by g" [6l.9,.,,,). The angle 6 denes a position along the stator inner surface while 6,," is the angular position of the rotor with respect to the stator reference. N, and N,- respectively indicate the winding functions of the windings i and j. lt corresponds to the mmf distribution along the airgap for unit current in winding i andj. Copyright ti? Ztilil? Praise War-airy Prize S. rJ. - Al! rights reserved 439 The winding functions for the main stator winding al-Jc is shown in Fig. 2, where C, is the number of coil per slot for the main winding. This winding function is similar for the auxiliary winding since they are wound in the same pattern and for the same number of poles. The winding function plot of Fig. 2 is seen to be a stepped- like function due to the discrete nature of the winding slots, thusa signicant space harmonic components is present. + -B i-A d. +8 -A OIIOOOIIOOIO 35C" T B Jflcn t u l 33� sac, _r "L_ " ll l y: c. __r' i 411C ~ Li I Figs. 2. Winding functions of |l1e main winding {a} Phase 'a, {b} Phase b. [c] Phase c However, to present an understanding of how the machine operates and to obtain closed form inductance equations, the stator winding function will be represented in this analysis by their fundamental component. The fundamental component has the greatest effect on the energy conversion and will be sufficient to explain the fundamental operation of the machine. Thus, the winding functions of the stator windings are expressed as: No (i9) = Na ��~'*'(P9) iv',,(9)= i\�'_.,�as(p0-1-;) (12) Ne = Nlxl Co-(pg-i 1T1) Np (9) = Nu 003L067) N}. (9) = M; cosLpB-z?) (13) iv, (9) = rig, cosi p9+23l) where N and N, are the numbers of the fundamental component turns for the main and the auxiliary winding respectively. The inverse airgap function of this kind of machine can be approximated by the expression [l9], [22]: iniemaiionnf Review ofEiectrir-ai Engineering. Vol. S. N. .2 A. S. O. Ogtmjiiyigbe, A. A. Jimoh, D. l/f Nicoiae. S. Obe g4 6.6,_,,,]=m+ncos2p(l5'6,) (l4) did; A. S. O. Ogtmjwigbe. A. A. Jimoli. D. lK Nicoloe, E. S. Obe Since the machine is assumed to be magnetically linear, the co-energy is equal to the stored magnetic energy and it is expressed as lll,, l._,__.l__.. Hence, the electromagnetic torque is expressed as: p i air. Th" I E ohcxy: 5a iihcrjr: where: l. _. t, m L z til: lx._ ) Lift-rain- {r}: From (30) and (3l), the electromagnetic torque of a synchronous reluctance machine with dual stator winding and capacitance compensation can be written as a separate sum of the torque produced by each set of the stator currents to obtain: 3L . -- 5L - . iia-liaai-Hiiis-i n: T i E 66, 66, (32) m 2 ,. 6L: , lstimh +[.\'_'l': T. fr}: n: aer lube Substituting the respective inductance matrix components of equations (8)-(lt]), and simplifying, the electromagnetic torque (expressed in terms of current) is obtained as: _ 5E (Lt-fl iapifailin +(Ltif2 Lqziiiizfqz + "" 2 2 +[i. l )[i,,i_,, +i,,,i,_,,] mi rm; (33) This equation show that the total electromagnetic torque developed by the machine is as a result of three main torque components. This noticeably demonstrates the inuence of the additional winding introduced in the machine, as well as the capacitor attached to it. The rst and the second components are familiar equations which represent the reluctance torque developed by the main and the auxiliary winding respectively, while the third component is the torque developed as a result of the interaction between the main and the auxiliary winding currents. If the capacitor is not attached to the auxiliary winding, (33) will resolve to the familiar electromagnetic torque equation of a conventional synchronous reluctance machine. The size of capacitor connected to the auxiliary winding determines the torque contribution of the auxiliary winding and that of the interaction between the two winding currents. Ill. Steady state Analysis and Experimental Results Under steady state operation, with sinusoidal excitations, the derivatives of equations (23)-(26) are Copyright � Zillll Praise Worthy Prize Sal. - All riglitt reserved 441 zero and the general dynamic model given by equations (23)-(26) is transformed into the following steady state model: Vql = Riifqi +X.ii*'ii| +Xiitifa2 Vi = Rnfiii X i ll ql 0 z Rxzlsd + I�d2!!2 +.�m,dfd| +Vt3q Xmq l; (34) 0 = Raid; - xgiq, - x, 1,, + is, These resulting equations are then used to determine the steady state performance characteristic of the machine. lll. l. Constant Speed (Jperaiion When the axis currents are determined from (34) and back substituted, the steady state axis impedance of the machine is derived as: V V qid - _ L z e Zqrtl _ Iqd j V C086 Z2 Zn where: Z1 = ii n: Xiiz ' it z r Y3 - . + Z ql Yqz _ 11', =mLd|,Xu| =wl.q|.l,- =;l(;, and i) is the rotor angle. J=0, when the machine axis coincides with the axis of stator phase and all when it coincides with the quadrature axis. The effect of the capacitance attached to the auxiliary winding on the effective d-and q-axis reactance is calculated using equation (35) and compared with the experimentally obtained values in the plots of Fig. 4. The measured values of the direct axis reactance (Xd) were obtained at i500 rpm and the quadrature axis reactance (Xq) were obtained at pull-out point using the Honsinger method [24], [25]. Y t t | i _i ---c.|mam1 1:. ' --t'-|rnw-c s, _ 25� ----- arm-mi x Ill-i Measured K I _ ~ . . i i i Kr |5|-|_ . . . . . _ . .. _ at � tan-- ------- ------------ -- --; _ _ _ _-,..-m=! i 1555"- so nu I-I '.I.''.i...'.-_'f.-IT_ .. t I t 1 1-5 \ 3.5 l 1.! 5 5.! 0 Capacitance (F) m Fig. 4. Variation of the effective axis reactance as a function of capacitance lniemiiiioiiol Review ifElecuical Engineering. Vol. 5. N. .2 A. S. 0. Ogunjtqiigbe, A. A. Jimoh. D. if Nicolae. E. S. Obe The effective d-axis reactance of the machine was found to obviously increase with the size of the capacitor, while the q- axis reactance was only slightly inuenced. This situation on its own indicates that the conguration increased the effective reactance ratio of the machine. To illustrate the effect of the conguration on the power factor of the machine, the input active and reactive power of the machine is calculated using: 3 . . i; = E(Pq|fq} + I-dlldi) (36) 3 _. . Q=giiqiiut _}Ji1ql) (37) Using (36) and (37), the variation of the power factor of the synchronous reluctance machine with the conguration as a function of the size of the capacitor and load angle is evaluated using: a us) Pf+Q 603$ = and the peak current in each phase calculated using: [s] : VIIjI + rtfl where: l X Y jd|= (40) xrdl('�tflrt')_'xlmif J ix: _ Y) <41) are the axis cun-ents of the main winding and are derived from (33), i}, =Vsin5; Vql = Vcos . Plots illustrating the variation of the reactive power as a function of the capacitance (attached to the auxiliary winding) are generated using (37)-40 and displayed in Fig 5. For every load angle examined. the main winding reactive power reduces with an increase in the size of the capacitance attached to the auxiliary winding, and in some cases getting to zero. This invariably reduces the input apparent power of the machine and it indicates that the machine can be operated at very high power factor and unity power factor in some cases. While the best power factor obtainable with no capacitor attached to the auxiliary winding is about 0.55, a power factor as high as 0.99 was predicted for the machine with capacitance fitted to the auxiliary winding. Fig. 6a displays the calculated power factor against the size of the capacitor. The general trend in these plots of Fig. 6(a) is the same for all load angle. and illustrates that the inherent power factor of the machine increase Copyright Q 20H] Praise Worthy Prize Sari. All rights reserved with the increase in the size of capacitor. However, the size of the capacitor that can be attached to the auxiliary winding is well constrained by its ampere turn rating The main winding current is shown in Fig. 6(b) to increase with an increase in the load angle and for every load angle considered the points of minimum main winding currents consistently match the points where the highest power factor are obtainable. The possibility of using the capacitance attached to the auxiliary winding to inuence the power factor to either high. leading or lagging values is also evident in Fig. 6th). Load angle -_.,_ go Main inbuilt: rnoetre power-trams IIHJI 1 It It.) HA 8.! 0.8 l Capacitance (F) , m" Fig. 5. Variation of the input reactive power as a function of capacitance Load nil! 5' . . 0.0 its --------- --------- -- i is Q :01 ...--. :5: l I'm-rec factor Q 5 OJ 0.1 I D 0.2 0.4 0.6 0.8 1 Capacitance ( F] m la] Lind upln ---.__gu -.,- m. i u. ~--- zo- -- �III.III l!� i; Main winding curl-ml IA} 41.5 c 0.: 1 1.: Power [actor angkr (rad) (b) Figs. b. (a) Variation of the power factor as a function of capacitance, (h) Variation of the main winding current as a lilnction of power factor angle :3:- m lnrenmtionuf Review of Electrical Engineering. Vol. 5. N. 2 .�-I. S. O. Ogttrgittytgbe. A. A. Jimoh, D. if Nicotoe. E. S. Obe- HtYZ. flxperimetrtcrl Results The synchronous reluctance machine with dual winding and capacitance compensation was adapted and fabricated from a three phase 36 stator slots induction motor with a frame size DZIIZM. The conventional stator of the machine was rewound following the practical arrangement of the stator windings shown in Fig. lib). The main winding of the machine is supplied directly from the mains utility supply. However. since the experimental machine is not equipped with a damper winding, it cannot start on its own even with this configuration. The machine was synchronized in the laboratory using a DC machine operated in the motoring regime. A labeled pictorial representation of the experimental set up is shown in Fig. 7. Measured power factor, current and torque with different capacitor sizes (l5 pF. 45 uF, 60 uF. 75 pF,) attached to the auxiliary winding are respectively displayed in Tables l and ll. While the machine is able to deliver its rated load, table I clearly showed that the machine operates at a comparatively higher power factor. Similarly, Table ll show that for every load point considered, the torque per ampere of the machine increased with the size of the capacitor, thereby justifying the fact that the conguration discussed in this paper improved the torque per ampere without varying the rotor geometry of the machine. The effective axis reactances of the machine were measured using the Honsinger methods [25]. and the results were closely compared to the ones analytically calculated in Fig. 4. The no-load current of the machine as recorded in table Il is found to drop with the increase in the size of the capacitor; consequently. the effective direct axis reactance of the machine also increased with the size of the capacitor. On the other hand. the quadracture axis reactance is only slightly inuenced by the conguration, therefore, the effective reactance ratio of the machine as viewed from the source increased with the size of the capacitor. Consequently. the power factor and torque per ampere performance characteristics ofthe machine is improved. Dill: acquisition w ca? (or equipments hank DC Experimental machine Machine Fig. l. Pictorial view ofthe experimental setup Copyrtgtltt f) 2010 Praise ilhrtlti Prat� 51:11. .40 rtgrltts reset/Teri TABLE l MEASURED Power: FACIOR PERFORMANHECliAR.~\C']'[ER1S'l'|{" AT Vnxtous Loan, AND C APALTFITJR SIZE Load Power Power Power Power [pul factor with factor with factor with factor with T5 pF 60pF 45 uF l5 pF capacitor capacitor capatcittir capacitor 0.0 0.932 0. 8'07 �1.68 0.41 0.1 0.95? 0.84 0.739 0.494 0.2 0.963 0.902 0.li|5 0.604 0 3 0 96? 0.909 0.84 0.6? 0.4 0.969 0.92 086 0306 0.5 0.969 0.924 0.862 0.725 0.? 0.967 0.91 0.86 0 T39 0.8 0.963 0.9|5 (1.85 0J4 0.3 �1.95? (1.905 0.85 0.72 0.9 0.949 0 906 0.83 0.68 I 0 0.939 0.906 0.8 0.62 TABLE ll MEASURED MAIN WINIIIING CURRENT AT VARIOUS LOAD AND CAPACITOR SIZES Load Main Main Main Main (pu) winding winding winding winding Current with Current Current with Current with T5 pl with 60pF 45 uF l5 pF capacitor capacitor capacitor capacitor 0.0 2.00 1.99 2.28 3i 0| 2.33 2.33 2.34 3 3 0.2 2.9? 2 {l4 3.00 3.? 0.3 3.4? 3.29 3.30 4 I 0.4 3 S6 3.68 3.80 4.5 0.5 4.20 4.02 4.50 4 S 0.? 4.54 4 34 5.00 5.2 0.8 4.92 4 33 5.40 5TH 0.8 5 39 5.29 6.20 6J6 0.9 5.99 6. I9 6.90 6.04 1.0 6T8 T.6l 7.13 The nature of the current and voltage waveforms in the main and auxiliary winding of the motor with 8 Nm load applied to the motor is shown for different sizes of capacitor in Fig. 8{a)-(d). The presence of harmonic in the phase current is obvious; and the measured THD showed that the harmonics of the machine with compensation is better than the conventional machine, particularly and improved with the size of the load as well as the size of capacitor. A typical distribution of the THD measured for a 60 pF capacitance and with a load of 8 Nm is displayed in Fig. 9. As expected from the winding conguration used for the experimental machine, apart from the fundamental the phase belt harmonics are the most prominent. The experimental trace of Fig. Std) displays that a leading current flows in the auxiiiary winding. This leading current inuences and directly shift the main winding current along the axis as the size ofthe capacitor is increased. The shift in the phase ofthe current (evident in Fig. 9(a)-(c) is such that the power factor is inuenced from lagging towards a leading power factor. fntertruttotttti Review 0fEfet.tt'frttt' Engtncewttrg. i191. 5. N. Z A. S. U. Ogtmjuyigbe. A. A. Jimoh. D. P. Nicoloe, E. S. Obe W l" T hhinwiarlingclrrus - m m, JFK _' . . ._. _ lllll -\ w .. / J i/ h t! run {I I m m n ___ Main-dug ' voltage m LEM 1-0- v - (i!) $ MHI .-|..-,[.....-. s m: Slab winding current II Jon III lllll QU ill IIE Gk J5 Si: ' uihwiiliiiiYell-II! ~$ tilt! HIII IQOn (b) V-lw ,,, c. m U Mam I'm ' gclrnll i IQ .[l.'- K I IE ltl- I .. .4 I in m. _. .. kl .. . IB a-I i- - ma " " _ _ Mlinwilldingvoltage II qt. ..., I||- .....| .i..-... I I'm-g Jimiu (C) .. 1-1:.� (d) Figs. 8. Steady state waveforms of the motor on S Nm load; Red; peak value ofthe main winding current ( ltlaidiv}; Black: peak value ofthe main winding voltage [I00 Vidiv). Machine tted with (a) l5 pF [b] 45 pF_ (c) 60 |.iF capacitor, and (d) Auxiliary winding voltage and current with 6i] pF capacitor Copyright D 20H] Praise Worthy Prize Sm. - All rights resented 444 I - a a t r e Hum-enume- Figs. 9. (a) Total Harmonic distortion ofthe main winding current with the application of8 Nm load and 60 pF capacitor IV. Conclusion The use of auxiliary winding and capacitance compensation to improve the effective reactance ratio of a synchronous reluctance machine with simple salient rotor is presented and discussed in this paper. By the application of winding functions and the transformation theory, a mathematical model and equivalent circuit suitable for dynamic, transient and steady state analysis was developed for a synchronous reluctance machine with an auxiliary winding for capacitance compensation. The developed model was used to conduct an investigation of the effect of the conguration on the etTective reactance ratio, power factor and torque per ampere of a simple salient rotor synchronous reluctance machine. Validating experimental results of the analytical developments are provided showing perfonnancc characteristics of a 4~p0le 36 slots experimental machine adapted -om an induction motor. The experiments as well as the analytical study clearly showed that the effective reactance ratio of a synchronous reluctance machine is improved without altering the geometry of the rotor as it is conventionally done. With this improvement of the effective reactance ratio, synchronous reluctance machine with a simple salient rotor was operated at a better power factor and torque per ampere for all operational loads. A maximum power factor of 0.969 as against the 0.55 for the uncompensated was obtained. References [l] T. Lipo. Novel reluctance concepts for variable speed drives." in bfeditei-ronean Eiectrotechmcol conference. MIELECOAL l99l. pp. 34-43. M. .I. Karnper and A. F. Volschenk, "Effect ol Rotor dimensions and cross magnetisation on Ld and Lq inductances of Reluctance Synchronous machine with cageless Flux Barrier rotor. IEE Proceeding- Electrical Power Application. vol. 30, pp. 2l3-22U. I994. 1. Boldea. X. Fu. and S. Nasar. "Performance evaluation of axially laminated anisotropic [ALA] rotor reluctance synchronous motors, IEEE Transactions on industry Applications. voi. 30. pp. QTl-JSS, I994. F. Patasitili. M. Villani. and A. Tassi, "Dynamic Analysis of Synchronous Reluctance Motor drives Based on Simulink and l1] [3] l4] international Review of Electrical Engineering. Fol. S. N. 2 A. S. O. Ognnjuyigbe, .4. A. Jinioli. D. V. Nicolae, E. S. Obe Finite Element Model." in lEEE 32nd Annual conference on industrial Electronics. lECON 2006, 2006. pp. lSl-l S20. A. Vagati. "The synchronous reluctance solution: a rtew alternative in ac drives, in 20th lmernational conference on industrial electronics. control and iiistriinientations. IECONW-l. vol. I. I994, pp. i-iz. E. Obe and T. Senjyu. "Analysis of a polyphase synchronous reluctance machine with two identical windings." Electric PiJIi-Ei System Research vol. i6. pp. S 15-524. 2006. A. Chiba, T. Fultao. and M. Matsui. "Test Results on a Super High Speed Amorphous Iron Reluctance Motor. lEEE Transactions on industry Applications. vol. 25. pp. I I9-I25. I989 T. Matsuo and T. A. Lipo. "Rotor design optimization of synchronous reluctance machine." lEEE Transactions on Energy Conversion. vol. 9. pp. 359-365. I994. D. A. Staton, T. .I. E. Milier. and S.E.Wo0d. "Maximising the Saliency Ratio of the Synchronous Reluctance Motor," lEE Proceedings-B. vol. I40. pp. 249-259. I993. A. Vagtli. A. Canova. M. Chiampi. M. Pastorelli. and M. Repetto. "Design Refinement of Synchronous Reluctance Motors through Finite Element Analysis." iEEE Transactions on industry Applications. vol. 36. Pp. l094-l I02, 2000. [I I] I. Boldea, Reluctance Synchronous ilvlacltines and Drives. Oxtbrd: Claderon Press. 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"A ve-phase reluctance motor with high specic torque, lEEE Transactions on industry Applications. vol. 23. pp. 659-662. I992. A. S. O. Dgunjuyigbe. E. S. Obe, A. A. Jimoh, and D. V. Nicolae. Synchronous Reluctance machine with magnetically coupled Double three-phase windings. in ELECTROMOTlON 2009 EPE Chapter Electric iJrives' Joint Symposium. Lille. France. 2009. D. W. Novotny and T. A. Lipo. Vector control and Dynamics qr AC Drives. Oxford: Claderon press. 2000. [I9] [I9] O. Ojo. G. Dong, and M Omoigui. "Analysis of a synchronous reluctance machine with an auxiliary single phase winding. iEEE Transactions on industry Applications. vol. 39. pp. ll07-l3l3. 2003. [20] O. Ojo. A. Girtart. O. Omozusi, and A. A. Jimoh. "Modelling and Analysis of a Single-phase Synchronous Reluctance Machine including Saturation EiTect." lEiilf industry Application Society Annual General Meeting. Louisiana. pp. 294-30]. I997. [2]] L. Xu. F. Liang, and T. A. Lipo. "Transient Model of a Doubly Excited Reluctance Motor. lit-TEE Transactions on Energy Conversion. vol. 6. pp. [26-133. I99]. [22] R. E. Bert: and M G Joriavic. "Control of Synchronous Reluctance Machines. utwwnewcastleeduau, I993. [23] P. Krause. ainalysris of Electric Mocliiirery: McGraw-Hill Book Company. I986. [24] C. A. M. D. Ferraz and C. R. d. Souza. "Measuring the Parameters of a Cage-Rotor Reluctance Motor." in Canadian Conrence on Electrical and Computer Engineering Toronto. 200]. pp. 7T5- T30. [25] V. Honsinger. "The inductances Ld and Lq of reluctance machines. lEEE Transactions on Power Apparatus oml Systems. vol. PnS-90. pp. 293-304. JanlFeb I97]. l5] [5] l7] l3] l9] [l9] H3] [l4] [l5] [l6] I17] [l3] Copyright � 20 l 0 Praise Horthy' Prize S. r. l. - All riglus reserved 445 Appendix TABLE A I PARAMETERS OF THE EXPERIMENTAL MACHINE Voltage _.I" I50 V Frequency] 50H: Rated main winding current. 8.8 A Number of poles. P 4 Unsaturated direct axis reactance . .'t'.i 43.3] t1 Unsaturated quadracttire reactance . X, I260 t1 Air-gap at the pole Face. g| 0.25 mm Aiigap between pole. g; I2 mm Stack length ]48.5mm Number of stator slots 36 Main winding resistance. R,,| 414i) Auxiliary winding. Rn 14.90 Pole arcipole pitch ratio =05 Authors information 'ElectricaliE-Ilectionic Engineering department. University of lbadan . lbdw- Nissan Electrical Engineering department. Tswane University of Technology, Pretoria. Emails: iimhm�iltui-aiam; Electrical Enginering Department. University ofNigcria ,Nsultka.. Nigeria. oggnngh ahoocom Ogunjuyighe Ayodeji Samson received B.Eng degree in I99] from the Bendel state University, an M.Sc with distinction in I995 from the University of Lagos. Lagos. Nigeria. and a D.Tech from the Tshwane University of Technology. Pretoria. South Africa. Since I998, Ayodeji has lectured in the ElectricallElectronic Engineering department of the University of Ibadtin. Nigeria. He is a corporate member of the Nigeria Society of engineer His research interests are in the eld of performance improvement oi Electric Machines. and contingency planning in power systems. Adina A. Jimoh (MIEEE I986} received Sling degree in I97? and M.Eng. degree in I980. both from Ahmadu Hello University (ABU) Zaria. Nigeria and Ph.D. degree Iiom McMastei University. Hamilton, Canada in I936. He was with Ahmadu Bello University up till I992, when he moved to the Research & Development unit of the National Electric Power Authority (NEPAJ Nigeria. Adisa was with NEPA up till I996 when he relocated to University oi Durban-Westville. Durban, South Africa where he taught courses and carried out research in high performance energy efficient electric machines and power systems. and power electronics. In 200] he joined Tshwane University of Technology. Pretoria. where, as a full professor, he leads and coordinate the research and doctorate programs of the Graduate School of Electrical and Electronic Engineering. He is a registered engineer in South Africa. His research interests are in the eld of Electric Machines. Drives and Power Electronics application in Power Systems. Dan Valenlin Nicola: [MIEEEJ was born in I943. in Bticharest. Romania. lie graduated the Polytechnic University of Bucharest. Romania in .|iily I97] with Msc degree and got his doctorate degree in 2004 at Vaal University of Technology, South Aica. Aer graduation he worked as researcher in the Institute for Nuclear Technologies. National c litter-national Review ofi-Ilectrical Engineering. Ibl. .5. N. 2