Synchronous Reluctance Machine: Combined Star-Delta Winding and Rotor Eccentricity

Transcription

1 Synchronous Reluctance Machine: Combined Star-Delta Winding and Rotor Eccentricity Bishal Silwal, Mohamed N. Ibrahim, and Peter Sergeant Φ Abstract A permanent magnet assisted synchronous reluctance machine (PMaSynRM) under static and dynamic rotor eccentricity has been studied, using the finite element method (FEM). Unlike the conventional star connected machine, a 5.5 kw machine with a combined star-delta winding configuration in the stator has been considered in this study. The impact of a combined star-delta configuration on the eccentricity forces and unbalanced magnetic pull of the PMaSynRM has been investigated, and a comparison with the conventional star connected machine has been presented. Moreover, other electromagnetic quantities of interest such as the magnetic flux density distribution and the induced back emf in the windings are also analyzed. Two prototype PMaSynRMs, having similar stator and rotor stack iron and geometrical parameters with two different stator winding, have been manufactured. The theoretical findings have been validated with measurements on the prototypes. Index Terms-- eccentricity, finite element method, force, permanent magnet assisted synchronous reluctance machine, PMaSynRM, SynRM, I. INTRODUCTION YNCHRONOUS reluctance machines (SynRMs) have S obtained an immense popularity due to their high efficiency, low cost and robust structure. In addition, the torque density is much better than that of induction machines (IMs). However, the power factor of SynRMs is rather poor. In order to enhance the torque density and power factor of SynRMs, permanent magnets are inserted in the rotor fluxbarriers, resulting in the well-known permanent magnetassisted synchronous reluctance machines (PMaSynRM) [1, 2]. Several papers in literature can be found that propose better design and control techniques to increase the overall performance of these machines [3-6]. Recently, [7] analyzed the performance of a SynRM with a combined star-delta winding and compares it with the conventional star connected winding. The results show that, for the same current, the machine s output power is increased by about 5% for the combined star-delta windings compared with the conventional star connection at the rated conditions. The B. Silwal is with the Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, Ghent 9000, Belgium ( bishal.silwal@ugent.be). M. N. Ibrahim is with the Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, Ghent 9000, Belgium, and also with Electrical Engineering Department, Kafrelshiekh University, Kafrelshiekh 33511, Egypt ( m.nabil@eng.kfs.edu.eg). P. Sergeant is with the Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, Ghent 9000, Belgium ( peter.sergeant@ugent.be). P. Sergeant is also member of EEDT, Flanders Make, the Strategic Research Centre for the Manufacturing Industry. efficiency is also increased by a slight amount (0.20%). The simulations were validated by experiments on several prototypes. In [2], the performance of conventional SynRMs and PMaSynRMs with combined star-delta windings have been presented. It is found that employing combined stardelta windings in SynRMs increases the torque density and efficiency compared to the conventional star winding. The aforementioned work only studied the performance of the SynRM for a healthy case. However, an electrical machine might be subjected to various faulty conditions. Although a phase fault has been studied in [7], other faulty conditions, for instance rotor eccentricity, that might result due to the manufacturing defects or bearing failure have not been considered together with combined star-delta windings. The non-uniform air gap caused by rotor eccentricity creates an asymmetrical flux-density distribution around the air gap, which produces forces. The eccentricity force and the unbalanced magnetic pull (UMP) in SynRMs have been studied in [8-10]. Several studies have also been performed to investigate the effect of series and parallel connected stator windings on the eccentricity forces [11-12], those suggest that the eccentricity forces and the unbalanced magnetic pull are higher when the windings are connected in series than in parallel. In case of a combined star delta winding, star-delta parallel connection is not favored because of the increased risk of the circulating currents in the delta windings, which can ultimately result in higher additional losses and thus lower efficiency. Therefore, such windings are often connected in series. In that case, it is important to know how the eccentricity forces are affected by such winding configuration. In this paper, a PMaSynRM with combined star-delta windings is studied under rotor eccentricity by using the finite element method (FEM). Both static and dynamic eccentricity has been taken into account. The main focus is on the magnetic field distribution, induced voltages in the star-delta windings and the eccentricity forces. The performance of the combined star-delta connected machine is shown in comparison to that of a conventional star connected machine. II. PMASYNRM WITH COMBINED STAR-DELTA WINDING A three-phase, four pole, 5.5 kw permanent magnet assisted synchronous reluctance machine is used in this study, the cross-sectional geometry of which is shown in Figure 1. The rotor has three flux barriers per pole and ferrite permanent magnets are inserted in the center of the flux barriers (see Figure 1). Ferrite magnets are preferred over rare earth magnets (e.g. NdFeB) because of their low cost, /18/$ IEEE 427

2 and availability in the market. In addition, they can withstand high temperatures [1]. The geometrical parameters of the machine are given in Table I. coils is shown in Figure 2. As q equals 3, one slot for the star coil and two slots for the delta coils are considered. As the current of the delta coils is lower than the current of the star coils by a factor of 3, the number of turns of the delta coils has to be higher than the number of star coil turns by the same factor. This is to generate approximately the same MMF with the two coils. Consequently, the number of turns of the delta coils is 45 turn/slot. The cross-section area of the delta coils must be lower than the star coil by a factor 3. Two parallel groups are employed for both the star and combined star delta windings. A single-layer winding is employed for both star and delta coils. i c c Fig. 1. Cross-sectional geometry of the permanent magnet assisted synchronous reluctance machine used in the study (PMaSynRM). Ferrite magnets are inserted in the center of the flux-barriers. bc ab ca a TABLE I PARAMETERS OF THE MACHINE UNDER STUDY Parameter Value Number of poles 4 i b b Number of stator slots 36 Number of phases 3 Number of rotor flux barriers per pole 3 Stator outer/inner diameter Rotor outer/inner diameter Active axial length Rated power Rated voltage Rated current Rated speed 180/110 [mm] 109.3/35 [mm] 140 [mm] 5.5 kw 380 [V] [A] 3000 [rpm] The given machine has 36 slots. Two distributed winding configurations are used in this paper. The first configuration is the conventional star-connected winding and the second one consists of two three-phase winding sets connected in a combined star delta configuration. Both winding configurations result in three phases as shown in Figure 2. This means that the number of stator slots/poles/phases (q) is 3. The number of turns per slot of the star connection is 26, with a conductor cross-section area of mm 2. As shown in the literature [13-15], two possible connections of star and delta coils can be made: either the two coils are connected in series or they are connected in parallel. As mentioned already in the previous section, the star delta parallel connection is not favored because of the risk of very high circulating currents, resulting in higher losses. In addition, such parallel connection can be practically cumbersome in regards with the number of turns and the cross-section of the wire used. Therefore, the series connection of the star and delta coils is adopted. The wiring connection of the series of star delta i a Fig. 2. Combined star delta configuration with coils connected in series. III. FINITE ELEMENT MODEL A two-dimensional time-stepping method has been used in this study to compute the magnetic field solution across the cross-section of the machine. The time-stepping method is based on the magnetic vector potential formulation. The Maxwell field equations in the quasi-static state together with the constitutive material equations lead to the following equation to be solved in the cross-sectional geometry of the machine: A (1) ( υ ) = σ φ where, υ is the magnetic reluctivity and σ is the conductivity of the material, A is the magnetic vector potential and ϕ is the reduced electric scalar potential. In the stator, three-phase sinusoidal currents are enforced into the windings to simply emulate the current-controlled inverter that supplies the SynRM. For the combined stardelta connection, the three sources are connected to the star coils as shown in Figure 2. Consequently, the currents in the delta coils are not enforced; they are computed by the coupled FEM and circuit model. Notice that in the delta coils, triplen harmonics of the current may occur. These circulating currents are taken into account in the simulation. In the simulations, the rotor rotates at rated mechanical speed. The movement is done by the moving band technique. To model the static eccentricity, the stator is shifted along the negative x-axis by a distance equal to the eccentricity radius such that the shortest air gap appears along the positive x- ta428

3 axis. To model the dynamic eccentricity, the rotor is moved along the positive x-axis by a distance equal to the eccentricity radius and then the rotor is rotated around the geometrical centerline of the stator. The eccentricity radius is equal to the eccentricity expressed as a percentage of the radial air gap length. For instance, if the eccentricity is set to 33%, the whirling radius equals 33% of radial air gap length. The eccentric rotor motion produces two harmonics in the air gap flux density, hereby called as eccentricity harmonics [8,16]. It is the interaction of these two eccentricity harmonics with the fundamental component of flux-density that produces a net radial force between the stator and the rotor. This electromagnetic force is calculated using the Maxwell stress tensor method. IV. RESULT AND ANALYSIS The results of the FEM simulations are presented and discussed in this section. All the results presented in this section are obtained from the simulations when the machine is supplied with rated current at rated speed. The magnetic flux-density distribution on the cross-section of the machine under several conditions are shown in Figure 3. Figure 3(a) and Figure 3(b) show the field distributions in a healthy machine when the winding is connected in conventional star and combined star-delta configurations, respectively. It can be noticed that the core of the star-delta connected machine has slightly larger saturated regions. Figure 3(c) and Figure 3(d) show the field distributions in the star-delta connected machine, when the machine is under 33% static and 33% dynamic eccentricity, respectively. It can be seen that the flux is concentrated towards the shortest air gaps (right side in Figure 3(c) and left side in Figure 3(d)). In the case of dynamic eccentricity, unlike static eccentricity, the position of the smallest air gap is also a function of time. At t = 0.01 s when the results in Figure 3 are plotted, the position of the smallest air gap in the dynamic eccentricity case is on the left-side of the machine. The given machine is a 4-pole machine with 36 stator slots. For the given machine, the fundamental winding factors of conventional star and combined-star delta winding configuration are calculated to be and , respectively. This resulted in an about 3.5% higher fundamental component of induced emf in the combined star-delta winding compared to the conventional star. The fundamental component of the induced emf in the star-delta connected machine, in cases of static and dynamic eccentricities are shown in Figures 4 and 5. Figure 4 shows the fundamental component of the induced emfs in the star coils of phase A. It can be seen that in both static and dynamic eccentricity conditions, the induced emf is very slightly affected. The differences in the induced emfs between the healthy case and for the case of 55% static and dynamic eccentricity are 0.9% and 0.8%, respectively. A similar observation is made for the induced emfs in the delta coils of phase A. Figure 5 shows the induced emf in the delta coils of phase A for both the static and dynamic eccentricity case. The differences between the healthy case and for the case of 55% static and dynamic eccentricity are 1% and 0.9%, respectively. The fundamental and other harmonic contents of the induced emf in the star and delta coils are calculated by performing Fourier transform on the voltage waveforms. (a) (c) Fig. 3. Flux-density distribution in the cross-section of the machine for (a) healthy, star connected (b) healthy, star-delta connected (c) 33% static eccentricity, star-delta connected and (d) 33% dynamic eccentricity, stardelta connected Voltage (V) Fig. 4. Fundamental component of the induced voltages in the star coil of phase A when the machine is under static and dynamic eccentricity. Next, the eccentricity forces are studied. The asymmetrical flux-density distribution shown in Figure 3(c) and Figure 3(d) creates unbalanced force acting on the rotor. This force is mainly directed towards the shortest air gap. As already mentioned before, when the rotor is under static eccentricity, the position of the shortest air gap does not change. Therefore, the rotor experiences a radial pull in that (b) (d) 429

4 direction. But during dynamic eccentricity, the nonuniformity of the air gap is time dependent, meaning that the position of the shortest air gap changes. For this reason, the force during dynamic eccentricity is circulating in nature. The trace of the force vector for 33% dynamic eccentricity in a star-delta connected machine can be seen in Figure 6, in comparison to the same case in a conventional star connected machine. It is certain that the magnitude of the force in a combined star-delta connected machine is lower than the conventional star connected machine. difference between the force magnitude is about 8.5%. Similar observations are made in case of static eccentricity. Figure 8 shows the unbalance magnetic pull in the machine when the machine is under static eccentricity. In this case, at 55% eccentricity, the difference between the force magnitude in a conventional star connected and combined star-delta connected machine is about 6.2%. The current in the delta coils of the star-delta windings is seen to have higher harmonic contents than the star coils, among which the triplen harmonics are of significant order. This leads to circulating currents in the delta coils. These circulating currents induce their own counter-acting fields that dampen the eccentricity harmonics. Thus, the reason behind reduced eccentricity forces in the combined star-delta winding can be understood. In case of dynamic eccentricity, the force also has a significant tangential component. Therefore, the total force deviates a bit from the direction of the shortest air gap. For this reason, it is worth to note the difference in the unbalanced magnetic pull experienced by the rotor in the case of static eccentricity and dynamic eccentricity. The results are reported in Table II. Fig. 5. Fundamental component of the induced voltages in the delta coil of phase A when the machine is under static and dynamic eccentricity. Fig. 7. Force exerted on the rotor when the machine is under static eccentricity. Fig. 6. Trace of the force vector when the rotor is under 33% dynamic eccentricity Figure 7 shows the unbalanced magnetic force experienced by the machine under dynamic eccentricity as a function of eccentricity, for both conventional star and combined star-delta connected windings. It is seen that the unbalanced magnetic pull increases linearly as a function of eccentricity, in both cases. However, the machine experiences less magnetic pull when the windings are connected in combined star-delta configuration. The difference between the forces in both cases also seem to increase linearly. At 55% dynamic eccentricity, the Fig. 8. Force exerted on the rotor when the machine is under dynamic eccentricity. 430

5 Eccentricity (%) TABLE II AVERAGE FORCE ACTING ON THE ROTOR Force (N) Conventional Star Force (N) Combined Star-Delta Static Dynamic Static Dynamic V. EXPERIMENTAL VALIDATION A measurement set-up, see Figure 9, is built to validate the results obtained from the simulation. For this paper, the measurements are limited to a healthy case only, however, the set-up can be extended to measure during eccentricity conditions as well. In the experimental set-up, an induction machine is used to drive a 5.5 kw PMaSynRM at the desired speed. Two stators, one with a conventional star winding and another with a combined star-delta windings are tested. The dspace 1103 platform is employed to control the inverter of the PMaSynRMs. The voltages, currents and power are measured by using a three phase power analyzer Tektronicx (PA4000). Fig. 9. Experimental set-up. Figure 10 shows the comparison between the measured and simulated voltages (RMS) in the conventional star and combined star-delta connections as a function of the stator current when the machine is running at 1500 rpm and at the optimal current angle. It can be seen that in both the measurements and simulations, the voltage in the combined star-delta connection is higher than the conventional star which has already been explained as the effect of higher winding factor of the star-delta connected windings. The measured results show a close match with the simulations. Some differences can be observed between the measured and simulated results, which is due to several reasons, for instance: 1) in the simulation, the end winding effect is not considered 2) the degradation of the magnetic properties of the materials due to the stamping and punching which influences the inductances of the machines, hence the voltage and 3) in the simulation, pure sinusoidal currents are used while in the measurements, the machine is driven by a PWM inverter. Fig. 10. RMS voltage in the stator winding as a function of the RMS stator current at a speed of 1500 rpm and optimal current angles. VI. CONCLUSION The performance of a PMaSynRM with combined stardelta winding was studied under static and dynamic eccentricity conditions. A 2-D finite element method was used to compute the magnetic field in the machine. Induced voltages in the star and delta coils of the combined star-delta connected stator windings were studied and the effect of eccentricity was analyzed. It was seen that eccentricity has very small effect on the induced voltages. In addition, the eccentricity forces were calculated. It was found that the forces in both static and dynamic eccentricity conditions are reduced in a combined star-delta connected machine compared to the conventional star connected machine. Therefore, such winding configuration could improve the performance of the machine under eccentricity conditions. The induced voltages in the machine were measured and compared with the simulated voltages. The immediate next step in the future would be to measure the eccentricity forces in a star-delta connected machine through experiments. VII. REFERENCES [1] M. N. Ibrahim, P. Sergeant, and E. M. Rashad, Synchronous reluctance motors performance based on different electrical steel grades, in IEEE Transactions on Magnetics, vol. 51, no. 11, Nov [2] M. N. Ibrahim, E. M. Rashad, and P. Sergeant Performance comparison of conventional synchronous reluctance machine and PMassisted type with combined star-delta winding, in Energies, vol. 10, no. 1500, pp 1-18, Sept [3] N. Bianchi, S. Bolognani, D. Bon and M. Dai Pre, Rotor flux-barrier design for torque ripple reduction in synchronous reluctance and PMassisted synchronous reluctance motors, in IEEE Transactions on Industry Applications, vol. 45, no. 3, pp , May-june [4] M. N. Ibrahim, E. M. Rashad, and P. Sergeant Simple design approach for low torque ripple and high output torque synchronous reluctance motors, in Energies, vol. 9, no. 942, pp 1-14, Sept [5] C. T. Liu, H. Y. Chung and S. Y. Lin, "On the electromagnetic steel selections and performance impact assessments of synchronous reluctance motors, in IEEE Transactions on Industry Applications, vol. 53, no. 3, pp , May-June [6] M. Ferrari, N. Bianchi, A. Doria and E. Fornasiero, Design of Synchronous Reluctance Motor for Hybrid Electric Vehicles, in IEEE Transactions on Industry Applications, vol. 51, no. 4, pp , July-Aug

6 Powered by TCPDF ( [7] M. N. Ibrahim, P. Sergeant and E. E. M. Rashad, Combined star-delta windings to improve synchronous reluctance motor performance, in IEEE Transactions on Energy Conversion, vol. 31, no. 4, pp , Dec [8] A. Arkkio, B. R. Nepal and A. Sinervo, Electromechanical interaction in a synchronous reluctance machine, in SPEEDAM 2010, Pisa, pp , June [9] H. Mahmoud and N. Bianchi, Eccentricity in synchronous reluctance motors-part I: Analytical and finite-element models, in IEEE Transactions on Energy Conversion, vol. 30, no. 2, pp , June [10] H. Mahmoud and N. Bianchi, Eccentricity in synchronous reluctance motors-part II: Different rotor geometry and stator windings, in IEEE Transactions on Energy Conversion, vol. 30, no. 2, pp , June [11] M. J. DeBortoli, S. J. Salon, D. W. Burow and C. J. Slavik, Effects of rotor eccentricity and parallel windings on induction machine behavior: a study using finite element analysis, in IEEE Transactions on Magnetics, vol. 29, no. 2, pp , Mar [12] A. Arkkio, M. Antila, K. Pokki, A. Simon, and E. Lantto, Electromagnetic force on a whirling cage rotor, in IEE Proceedings - Electrical Power Application, vol. 147, no. 5, pp , Sep [13] J. Y. Chen, C. Z. Chen, Investigation of a new AC electrical machine winding, in IEE Proceedings - Electrical Power Application, vol 145, no. 2, pp , [14] Y. Lei, Z. Zhao, S. Wang, D. G. Dorrell, W. Xu, Design and analysis of star delta hybrid windings for high-voltage induction motors, in IEEE Transactions on Industrial Electronic, vol. 58, no. 9, pp , [15] M. V. Cistelecan, F. J. T. E. Ferreira, M. Popescu, Adjustable flux three-phase ac machines with combined multiple-step star delta winding connections in IEEE Transactions on Energy Conversion, vol. 25, no. 2, pp , [16] B. Silwal, P. Rasilo, A. Belahcen, A. Arkkio, Influence of the rotor eccentricity on the torque of a cage induction machine, in Archives of Electrical Engineering, vol. 66, no. 2, pp Feb VIII. BIOGRAPHIES Bishal Silwal was born in Alau, Nepal in He received the M.Sc. (Tech.) and D.Sc. (Tech.) degrees in electrical engineering from Aalto University, Espoo, Finland, in 2012 and 2017, respectively. He is currently a Post-Doctoral Assistant with the Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, Ghent, Belgium. His current research interests include the numerical modeling of electrical machines, rotordynamics, electromagnetic forces, and thermal modeling. Mohamed N. Ibrahim has received the PhD degree in Electromechancial Engineering in December 2017 from Ghent University, Belgium. He is currently working as a postdoctoral researcher at the same University. He has been working as an Assistant Lecturer in the Department of Electrical Engineering, Faculty of Engineering, Kafrelshiekh University, Egypt since His research interests include Design and Control of Electrical Machines for Sustainable Energy Applications. Mohamed received several times the Kafrelshiekh University award for his international scientific publications. Peter Sergeant received the M.Sc. degree in electromechanical engineering in 2001, and the Ph.D. degree in engineering sciences in 2006, both from Ghent University, Ghent, Belgium. In 2001, he became a researcher at the Electrical Energy Laboratory of Ghent University. He became a postdoctoral researcher at Ghent University in 2006 (postdoctoral fellow of the Research Foundation - Flanders) and at Ghent University College in Since 2012, he is associate professor at Ghent University. His current research interests include Numerical Methods in Combination with Optimization Techniques to Design Nonlinear Electromagnetic Systems, in particular, Electrical Machines for Sustainable Energy Applications. 432