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POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE Permanent Magnet Flux-Switching Machine, Optimal Design and…

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POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE Permanent Magnet Flux-Switching Machine, Optimal Design and Performance Analysis Liviu Emilian SOMESAN 1 , Ioan Adrian VIOREL 1 1 Department of Electrical Machines and Drives, Faculty of Electrical Engineering, Technical University of Cluj-Napoca, 28 Memorandumului, 400 114 Cluj-Napoca, Romania liviu.somesan@emd.utcluj.ro, ioan.adrian.viorel@emd.utcluj.ro Abstract. In this paper an analytical sizing-design pro- is developed and an optimization procedure is carried cedure for a typical permanent magnet flux-switching on to obtain the motor with the maximum torque den- machine (PMFSM) with 12 stator and respectively 10 sity. The obtained machine structure, dimensions and rotor poles is presented. An optimal design, based on characteristics were checked via two dimensions finite Hooke-Jeeves method with the objective functions of element analysis (2D-FEA). A suboptimal procedure maximum torque density, is performed. The results was carried on to obtain better performance by em- were validated via two dimensions finite element analy- ploying 2D-FEA. The influence on the machine per- sis (2D-FEA) applied on the optimized structure. The formance of the permanent magnet characteristics (re- influence of the permanent magnet (PM) dimensions manent flux density and coercive field intensity) was and type, respectively of the rotor poles’ shape on the also analysed by employing 2D-FEA. The conclusions machine performance were also studied via 2D-FEA. and the final considerations in the case of the sample of PMFSM end the paper. Keywords 2. PMFSM Structure and Optimal design, performance analysis, Dedicated Sizing-Design PMFSM. Algorithm Figure 1 shows the PMFSM structure. As it can be 1. Introduction seen, the rotor of the machine is similar to that of a switched reluctance motor. The number of rotor poles The permanent magnet flux-switching machine and stator poles differs by two, respectively 10 rotor (PMFSM) has a short history and is a relatively new poles and 12 stator poles. The concentrated windings category of electric machines. The basic model of employed in the PMFSM are similar to those of the PMFSM was described in [1], where Rauch and John- switched reluctance motor (SRM). The only difference son proposed a new type of machine with permanent compared to the SRM consists on the configuration magnets (PMs) placed in the stator in order to better of the stator which contains 12 segments of ”U” shape control their temperature, and was brought back magnetic cores, between which 12 pieces of PMs are in- to the scene, in different structures [2], [3], [4], [5], set, the direction of magnetization being reversed from due to its improved performance. PMFSM has been one magnet to the following, as in Fig. 2. The sta- receiving significant attention in the last two decades tor winding comprises concentrated coils, each coil be- thanks to the advantages of high power density, ing wound around a pole which contains two adjacent mechanical robustness and torque capability [3], [4], laminated segments and a PM. Due to the short end- [5], [6]. Furthermore, it can be used with success windings the copper losses have low values. The main in harsh operating environments, such as aerospace, designing specifications for the sample PMFSM are: automotive and wind energy applications [7], [8], [9]. This paper takes into consideration a typical three ã Rated output power Pout = 30 kW. phase structure of a permanent magnet flux-switching ã Rated phase voltage Uf = 230 V. machine with 12 stator poles and 10 rotor poles. For this structure an analytical sizing-designing algorithm ã Rated speed n = 3000 rpm. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 46 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE The number of coils turns Nt is computed with the following equation: QS E Nt = √ , (3) 2π kL NR Dg2 nBgmax 2 where the phase rms induced emf is: QR Dg E = Nt 2πn √ lst π Bgmax . (4) 2 QS The stator pole dimensions are calculated based on equations (5), (6), (7), the same ratios being valid for the rotor poles by changing QS to QR and, adequately, the pole pitch and pole width factor: Dg τS = π , (5) Fig. 1: A 3-phase 12/10 PMFSM, expanded view. QS bpS = kpS τS , (6) bslS = τS − bpS , (7) where τS is the stator pole pitch, bpS is stator pole width and kpS is stator pole width factor (6). In order to improve the torque value and to reduce the cogging torque, a suboptimal procedure was con- ducted via 2D-FEA. The optimal value of the stator PM width bP M resulted: Fig. 2: Cross-section of the PMFSM design. τS bP M = , (8) Figure 2 shows a basic layout of the proposed 5 PMFSM where some of the most important dimensions The magnetic equivalent circuits were constructed are evinced. for different situations (aligned and unaligned rotor po- The PMFSM analytical design is based on an equa- sition) to calculate the no-load main flux, the armature tion which gives the machine air-gap diameter Dg func- reaction and the most important leakage fluxes [10]. tion of the design specifications, of adopted material The maxium air-gap density Φmax in aligned rotor properties and of some sizing coefficients kL , kE . The position is: performance related values, efficiency η , power factor cosϕ, maximum air-gap flux density Bgmax and stator πDg electrical loading As must be chosen to consider the φmax = Bgmax lst . (9) existing data, the machine topology and the PM type. QS Finally, the electromagnetic torque of the three s phase PMFSM can be calculated with: Pout QS Dg = 3 √ , (1) 2π 3 QR ηkL kE cosφnBgmax AS 3 T = QR φmax If . (10) 2 where QS and QR are the number of stator and rotor poles, kL is the aspect factor (2) and kE represents the The initial peak air-gap flux density was taken ratio of the back-emf to phase voltage. B gmax = 1,55 T while the PM of NdFeB type has resid- ual flux density Br = 1,2 T and coercive field intensity The stack length is: HC = 910 kA/m. The main dimensions of the PMFSM, calculated us- lst = kL Dg . (2) ing the sizing-design algorithm, are evinced in Tab. 1. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 47 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE Tab. 1: Main geometric dimensions and parameters of ã Make an optimized variable movement with initial PMFSM. step until the objective function is increasing. Item Unit Value Number of rotor poles, QR - 10 ã Repeat the search movement and use the gradient Number of stator poles, QS - 12 to find the better direction along the new track. Machine’s outer diameter, Dout m 0,277 Shaft diameter, dax m 0,045 ã Reduce the variation increment and repeat the Air-gap diameter, Dg m 0,159 Air-gap length, g m 0,0007 previous steps. The algorithm stops when the Stator PM width, bP M m 0,008538 search movement cannot find better points even Rotor pole pitch, τR m 0,0497 with the smallest increment. The found value rep- Rotor pole width, bpR m 0,01457 resents a local maximum. Stator pole pitch, τS m 0,041832 Stator pole width, bpS m 0,011418 Stator slot height, hslS m 0,04612 In the case of the proposed PMFSM design, a set of Rotor yoke height, hyR m 0,03475 five optimization variables were selected: air-gap di- Stack length, lst m 0,159 ameter, Dg , stator and rotor pole width factor (6), Stator yoke height, hyS m 0,01249 Number of turns per phase, Nt - 36 kpS , kpR , stator pole circumferential length factor, kf S , Phase current, If A 58 and aspect ratio kL . Obviously, the sizing procedure may not conduct al- bP M kf S = . (11) ways to the best results, but it gives quite important τS information for the designer. The next step was to set the minimum and the peak limits for each variable. These limits were set based on the designer experience and it is important to set these 3. Design Optimization adequately. An advanced design optimization based on numerical Finally, the optimization initial and final step sizes algorithms is applied in order to improve the PMFSM are set to 0, 001, respectively 0, 00001 with an optimiza- design and the overall system’s performances. tion ratio equal with 1, 01. The optimization process uses these parameters as increments in the calculation In this case, the Hooke-Jeeves method was selected. process. It is a pattern search method [11], [12], [13] and starts with an exploratory move in which all optimiza- The maximum torque density was considered the ob- tion variables are changed by a predefined step. The jective function for the optimization program. The ob- pattern move then repeats all changes that were found jective function is represented by the ratio between the to be successful in the exploratory move and uses an torque and the total mass of the PMFSM. In this case, objective function to evaluate the effect of the com- a total number of 22 iterations were necessary. The bined changes. The main steps in the Hooke-Jeeves evolution of the objective function and the main pa- algorithm are: rameters are illustrated in Figs. 3, 4, 5, 6. ã Choose the optimization variables that will be modified in the optimization process. ã Impose special limitations of other variables that can be altered during the process. ã Define the objective function. ã Set the initial and final value of the global incre- ment. These values will be initially modified with a larger increment, which will be further decreased in order to refine the search space. ã Compute the geometrical dimensions, the mag- netic and the electrical values, and evaluate the objective function. ã Make a research movement in the solution space, using the initial step and recomputed the objective Fig. 3: Evolution of the optimization variable. function and its gradient. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 48 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE Fig. 6: Evolution of the objective function. Fig. 4: Evolution of the developed cogging and electromagnetic torque. timizing method can be considered a reliable one in reaching its objectives. 4. Finite Element Analysis Two dimensions finite element analysis (2D-FEA), by using the Cedrat FLUX 2D environment, was per- formed to check the electromagnetic performance of the PMFSM. It was applied on the resulted structure after the maximum torque density optimization process. The 2D-FEM calculated radial-component of the air- gap flux density is shown in Fig. 7. As it is seen, the maximum air-gap flux density exceeds 2 T and the air- gap field distribution of a PMFSM is far from sinu- soidal and exhibits significant harmonics content due Fig. 5: Evolution of efficiency and power factor. to the doubly salient structure. The 2D-FEA computed static electromagnetic and The evolution of the optimization variables is illus- cogging torque is displayed in Figs. 8 and 9 versus rotor trated in Fig. 3. The air-gap diameter Dg has reached position. The rotor was moved over an electrical period a value of 0,1587 m, while the aspect factor kL has with an increment of 1 mechanical degree, one electrical reached the maximum limit of 1. The electromag- period corresponding to 36 mechanical degrees. The netic torque value has been significantly increased from phase current is the rated one, If = 58 A, and the 70 Nm to 99 Nm, Fig. 4. In Fig. 6 it can be seen that PMs’ width is 10,4 mm. the ratio between the torque and PMFSM mass has reached the maximum value of 4,38. 4.1. The Influence of PMs Dimen- Tab. 2: Optimal PMFSM parameters. sions on the Machine’s Perfor- Parameter Initial value Optimal value mances Dg [m] 0,159 0,159 bpS [m] 0,01041 0,0114 The variation of the electromagnetic torque for differ- bpR [m] 0,01041 0,0145 ent dimensions of the PMs is analyzed in this section bP M [m] 0,01041 0,0084 using 2D-FEA. This aspect is an important one con- kL 1 1 sidering the significant contribution of the PMs to the total cost of the machine. Also the variation of the PM The optimal parameters of the improved PMFSM dimensions is essential in order to reduce the cogging design are given in Tab. 2. In consequence, the op- torque. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 49 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE one to the optimized one (48, 4 mm). The 2D-FEA computed cogging torque is displayed in Fig. 10. Fig. 7: Air-gap field distribution. Fig. 10: Evolution of the cogging torque for different values of PMs widths. The influence of the PM widths on the electromag- netic torque values is not an important one since there are no big changes [14]. Instead, the variation of the cogging torque is an important one. The cogging torque decreases from 14, 2 Nm (bP M = 10, 4 mm) to 7, 36 Nm (bP M = 8, 4 mm). 4.2. The Influence of PMs Character- istics on the Machine’s Perfor- mances Fig. 8: Cogging torque. The necessity of a large quantity of PMs and the high price of the permanent magnets used, respectively of NdFeB, made the PMFSM to be more expensive com- paratively with the others PM machines. Fig. 9: Electromagnetic torque. Fig. 11: PMFSM electromagnetic torque for different values of Starting from the initially adopted values, the PM Br. width bP M was modified from the initial (10, 4 mm) c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 50 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE Fig. 13: Rotor pole shape. Fig. 12: PMFSM back-emf for different values of Br . The influence of different remanent flux densities val- ues (1, 2 T ; 0, 8 T ; 0, 4 T ) on PMFSM performance is illustrated in Figs. 11 and 12. In all cases the relative permeability is the same. The variation of electromagnetic torque and back- emf for different values of Br and Hc is illustrated in the above figures. It can be seen from Figs. 11 and 12 that the obtained values for Br = 0,8 T are close to that obtained for Br = 1,2 T. There is a difference of 5 % between the results obtained in the two cases. This difference depends on the ratio of PM’s and coil Fig. 14: Cogging torque, different rotor pole shapes. mmf. 4.3. The Influence of Rotor Pole 5. Conclusion Shape on the Cogging Torque In this paper a typical structure of permanent magnet The cogging torque is relative large in the case of flux-switching machine (PMFSM) with 12 stator poles PMFSM due to the doubly-salient structure and to the and 10 rotor poles was proposed. The PMFSM design high air-gap flux density produced by PMs. It is usu- procedure is based on a specific analytical algorithm. ally undesirable because produces vibrations and noise. In order to obtain a machine with improved per- Different methods for reducing cogging torque are formance, an optimization procedure based on Hooke- available in the literature [15]. One of the well-known Jeeves method was applied with maximum torque den- methods to minimize cogging torque is to modify the sity as the objective function. shape of the rotor pole. Consequently, the shape of the rotor pole was modified from a rectangular one to 2D-FEA analysis was performed to check the electro- a trapezoidal one, as illustrated in Fig. 13. The rotor magnetic performances of the PMFSM. The 2D-FEA yoke base width is chosen in this case to be 1,4 times was also employed to check the permanent magnet and greater than the rotor pole arc. rotor pole shape influence on the motor’s performance. The results in the case of the rotor pole shape influ- The evolution of the cogging torque for two differ- ence show that the the cogging torque is reduced with ent rotor pole shapes at the optimized PM’s width approximately 35 percent when the rotor pole shape is (bP M = 10, 4 mm) is illustrated in Fig. 14. From the trapezoidal. above figure, it can be seen that the cogging torque is reduced with approximately 35 percent, from 7,37 Nm A low sensity of the PMFSM torque and back-emf to 4,8 Nm. This value represents approximately 4,75 on the permanent magnet qualities for a certain ratio percent of the developed electromagnetic torque at the of PM’s and coil mmf was proved. It is an important rated phase current. advantage and allows for an essential cost decrease. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 51 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 11 | NUMBER: 2 | 2013 | SPECIAL ISSUE References management. 2008, vol. 49, no. 8, pp. 2100–2105. ISSN 0196-8904. [1] RAUCH, S. E. and L. J. JOHNSON. Design Prin- [10] SOMESAN, L. E., K. HAMEYER, E. PADU- ciples of Flux-Switch Alternators. Transactions RARIU, I. A. VIOREL and C. MARTIS. Sizing- of the American Institute of Electrical Engineers. Designing Procedure of the Permanent Mag- Part III: Power Apparatus and Systems. 1955, net Flux-Switching Machine Based on a Sim- vol. 74, iss. 3, pp. 1261–1268. ISSN 0097-2460. plified Analytical Model. In: 13t h International DOI: 10.1109/AIEEPAS.1955.4499226. 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