Abstract：Magnetic saturation is one of the major challenges for all electrical machines and makes it much more difficult to design high performance electrical machines. Frozen permeability (FP) technique has recently been developed to predict the on-load components of electromagnetic qualities while considering the influence of magnetic saturation. In this paper, the FP technique and its applications in various electrical machines are comprehensively reviewed. It shows that the FP technique is able to accurately separate on-load magnetic field, flux linkage, and inductance components in all types of electrical machines. These on-load field components and parameters can be further utilized to investigate various on-load performance, such as on-load torque and torque ripple components, on-load back EMFs and voltages, flux weakening performance, radial force distribution, et al. The accurate on-load parameters can also be used to improve the machine models and controls. Hence, FP technique provides a holistic approach to the development of high performance electrical machines.
作者简介: Professor Zhu Z Q, born in 1962, Fellow IEEE, Fellow IET, PhD, Professor at the University of Sheffield, UK. Major research interests include design, control, and applications of brushless permanent magnet machines and drives for applications ranging from automotive to renewable energy.E-mail: Z.Q.Zhu@Sheffield.ac.uk ;(Corresponding author)：Dr Chu W Q, born in 1982, Principal Engineer, CSR Electric Drives Technology Research Centre, the University of Sheffield, UK. Major research interests include permanent magnet electrical machines and applications.E-mail: chu.wenqiang@gmail.com
引用本文:
诸自强, 褚文强. 冻结磁导率先进技术及其在高性能电机研发中的应用[J]. 电工技术学报, 2016, 31(20): 13-29.
Zhu Z Q, Chu W Q. Advanced Frozen Permeability Technique and Applications in Developing High Performance Electrical Machines. Transactions of China Electrotechnical Society, 2016, 31(20): 13-29.
[1] Chan C C. The state of the art of electric, hybrid, and fuel cell vehicles[J]. Proceedings of the IEEE, 2007, 95(4): 704-718. [2] Zhu Z Q, Howe D. Electrical machines and drives for electric, hybrid, and fuel cell vehicles[J]. Proceedings of the IEEE, 2007, 95(4): 746-765. [3] El-Refaie A M. Motors/generators for traction/ propulsion applications: a review[J]. IEEE Vehicular Technology Magazine, 2013, 8(1): 90-99. [4] Cao W P, Mecrow B C, Atkinson G J, et al. Overview of electric motor technologies used for more electric aircraft (MEA)[J]. IEEE Transactions on Industry Electronics, 2012, 59(9): 3523-3531. [5] Cheng M, Hua W, Zhang J, et al. Overview of stator- permanent magnet brushless machines[J]. IEEE Transactions on Industry Electronics, 2011, 58(11): 5087-5101. [6] Zhu Z Q. Switched flux permanent magnet machines- innovation continues[C]//International Conference on Electrical Machines and Systems, 2011: 1-10. [7] Eastham J F, Cox T, Proverbs J. Application of planar modular windings to linear induction motors by harmonic cancellation[J]. IET Electric Power App- lications, 2010, 4(3): 140-148. [8] Levi E, Bojoi R, Profumo F, et al. Multiphase induction motor drives—a technology status review[J]. IET Electric Power Applications, 2007, 1(4): 489- 516. [9] Bash M L, Pekarek S. Analysis and validation of a population-based design of a wound-rotor syn- chronous machine[J]. IEEE Transactions on Energy Conversion, 2012, 27(3): 603-614. [10] Vijayakumar K, Karthikeyan R, Paramasivam S, et al. Switched reluctance motor modeling, design, simulation, and analysis: a comprehensive review[J]. IEEE Transactions on Magnetics, 2008, 44(12): 4605-4617. [11] Bianchi N, Bolognani S, Bon D, et al. Torque harmonic compensation in a synchronous reluctance motor[J]. IEEE Transactions on Energy Conversion, 2008, 23(2): 466-473. [12] Amara Y, Vido L, Gabsi M, et al. Hybrid excitation synchronous machines: energy-efficient solution for vehicles propulsion[J]. IEEE Transactions on Vehicular Technology, 2009, 58(5): 2137-2149. [13] Bianchi N, Bolognani S. Magnetic models of saturated interior permanent magnet motors based on finite element analysis[C]//IEEE Industrial App- lication Conference, St. Louis, MO, USA, 1998: 27- 34. [14] Williamson S, Knight A M. Performance of skewed single-phase line-start permanent magnet motors[J]. IEEE Transactions on Industry Applications, 1999, 35(3): 577-582. [15] Kang G H, Hong J P, Kim G T, et al. Improved parameter modeling of interior permanent magnet synchronous motor based on finite element analysis[J]. IEEE Transactions on Magnetics, 2000, 36(4): 1867- 1870. [16] Hu J, Zou J, Liang W. Finite element calculation of the saturation dq-axes inductance for a direct drive PM synchronous motor considering cross-magneti- zation[C]//International Conference on Power Elec- tronics and Drive Systems, 2003: 677-681. [17] Walker J A, Dorrell D G, Cossar C. Effect of mutual coupling on torque production in switched reluctance motors[J]. Journal of Applied Physics, 2006, 99(10): 08R304(1-3). [18] Walker J A, Dorrell D G, Cossar C. Flux-linkage calculation in permanent-magnet motors using the frozen permeabilities method[J]. IEEE Transactions on Magnetics, 2005, 41(10): 3946-3948. [19] Chu W Q. Investigation of torque characteristics of permanent magnet and electrically excited machines[D]. UK: The University of Sheffield, 2013. [20] Kwak S Y, Kim J K, Jung H K. Characteristic analysis of multilayer-buried magnet synchronous motor using fixed permeability method[J]. IEEE Transactions on Energy Conversion, 2005, 20(3): 549-555. [21] Azar Z. Electromagnetic performance of fractional slot interior permanent magnet and synchronous reluctance brushless ac machines having non- overlapping concentrated windings[D]. UK: The University of Sheffield, 2012. [22] Azar Z, Zhu Z Q, Ombach G. Influence of electric loading and magnetic saturation on cogging torque, back-EMF and torque ripple of PM machines[J]. IEEE Transactions on Magnetics, 2012, 48(10): 2650-2658. [23] Alam F R, Abbaszadeh K. Magnetic field analysis in eccentric surface-mounted permanent-magnet motors using an improved conformal mapping method[J]. IEEE Transactions on Energy Conversion, 2016, 31(1): 333-344. [24] Schmidt E, Susic M. Parameter evaluation of permanent magnet synchronous machines with tooth coil windings using the frozen permeabilities method with the finite element analyses[C]//IEEE Canadian Conference on Electrical & Computer Engineering, Montreal, QC, 2012: 1-5. [25] Chen Q, Liu G, Zhao W, et al. Design and comparison of two fault-tolerant interior-permanent-magnet motors[J]. IEEE Transactions on Industrial Electronics, 2014, 61(12): 6615-6623. [26] Paula G T D, Monteiro J R B d A, Almeida T E P d, et al. Evaluation of surface mounted PM machine's parameters on load conditions using frozen permeabi- lity method. Part. I[C]//IEEE International Sym- posium on Industrial Electronics, Berlin, 2014: 806-811. [27] Wang Q, Zhao B, Xu Y, et al. Inductances and phase coupling analysis of tubular permanent magnet machines with transverse flux configuration[C]// International Symposium on Electromagnetic Launch Technology, 2014: 1-5. [28] Wang Q, Zhao B, Zhang J, et al. Inductances and phase coupling analysis of tubular permanent magnet machines with transverse flux configuration[J]. IEEE Transactions on Plasma Science, 2015, 43(5): 1232- 1235. [29] Sun A, Li J, Qu R. Inductance calculation in variable-flux flux-intensifying permanent magnet synchronous machines using improved frozen per- meability method[C]//IEEE Magnetics Conference, Beijing, 2015: 1-1. [30] Afinowi I, Zhu Z Q, Guan Y, et al. Electromagnetic performance of stator slot permanent magnet machines with/without stator tooth-tips and having single/double layer windings[J]. IEEE Transactions on Magnetics, 2016, 52(6): 8103410. [31] Kim D, Hwang H, Bae S, et al. Analysis and design of a double-stator flux-switching permanent magnet machine using ferrite magnet in hybrid electric vehicles[J]. IEEE Transactions on Magnetics, 2016, 52(7): 8106604. [32] Bianchi N, Alberti L. MMF harmonics effect on the embedded FE analytical computation of PM motors[J]. IEEE Transactions on Industry Applications, 2010, 46(2): 812-820. [33] Chu W Q, Zhu Z Q. Average torque separation in permanent magnet synchronous machines using frozen permeability[J]. IEEE Transactions on Mag- netics, 2013, 49(3): 1202-1210. [34] Ionel D M, Popescu M, McGilp M I, et al. Assessment of torque components in brushless permanent-magnet machines through numerical analysis of the elec- tromagnetic field[J]. IEEE Transactions on Industry Applications, 2005, 41(5): 1149-1158. [35] Abbaszadeh K, Alam F R. On-load field component separation in surface-mounted permanent- magnet motors using an improved conformal mapping method[J]. IEEE Transactions on Magnetics, 2016, 52(2): 5200112(1-12). [36] Paula G T D, Monteiro J R B d A, Almeida T E P d, et al. Evaluation of surface mounted PM machine's parameters on load conditions using frozen per- meability method. Part. II[C]//IEEE/IAS International Conference on Industry Applications, Berlin, 2014: 1-7. [37] Zhao W, Zhao F, Lipo T A, et al. Optimal design of a novel V-type interior permanent magnet motor with assisted barriers for the improvement of torque characteristics[J]. IEEE Transactions on Magnetics, 2014, 50(11): 8104504(1-4). [38] Zhao W, Chen D, Lipo T A, et al. Performance improvement of ferrite-assisted synchronous relu- ctance machines using asymmetrical rotor con- figurations[J]. IEEE Transactions on Magnetics, 2015, 51(11): 8108504(1-4). [39] Zhao W, Lipo T A, Kwon B I. Optimal design of a novel asymmetrical rotor structure to obtain torque and efficiency improvement in surface inset PM motors[J]. IEEE Transactions on Magnetics, 2015, 51(3): 8100704(1-4). [40] Fei W, Luk P C K, Miao D M, et al. Investigation of torque characteristics in a novel permanent magnet flux switching machine with an outer-rotor con- figuration[J]. IEEE Transactions on Magnetics, 2014, 50(4): 8100810(1-10). [41] Wu D, Zhu Z Q. Design tradeoff between cogging torque and torque ripple in fractional slot surface- mounted permanent magnet machines[J]. IEEE Transa- ctions on Magnetics, 2015, 51(11): 8108704(1-4). [42] Xu L, Liu G, Zhao W, et al. Analysis of new modular linear flux reversal permanent magnet motors[J]. IEEE Transactions on Magnetics, 2015, 51(11): 8109904(1-4). [43] Li G J, Zhu Z Q, Jewell G. Performance investigation of hybrid excited switched flux permanent magnet machines using frozen permeability method[J]. IET Electric Power Applications, 2015, 9(9): 586-594. [44] Tangudu J K, Jahns T M, El-Refaie A M, et al. Segregation of torque components in fractional-slot concentrated-winding interior PM machines using frozen permeability[C]//IEEE Energy Conversion Congress and Exposition, San Jose, CA, 2009: 3814- 3821. [45] Xia B, Fei W, Luk P. Analysis and design of V-spoke ferrite interior permanent magnet machine for traction applications[C]//International Conference on Power Electronics Systems and Applications, Hong Kong, 2015: 1-6. [46] Chen X, Wang J, Patel V I, et al. Reluctance torque evaluation for interior permanent magnet machines using frozen permeability[C]//IET International Conference on Power Electronics, Machines and Drives, Manchester, 2014: 1-6. [47] Popescu M, Ionel D M, Miller T J E, et al. Improved finite element computations of torque in brushless permanent magnet motors[J]. IEE Proceedings on Electrical Power Applications, 2005, 152(2): 271-276. [48] Chu W Q, Zhu Z Q. On-load cogging torque calculation in permanent magnet machines[J]. IEEE Transactions on Magnetics, 2013, 49(6): 2982-2989. [49] Pina A J, Pramod P, Islam R, et al. Extended model of interior permanent magnet synchronous motors to include harmonics in d- and q-axes flux linkages[C]// IEEE Energy Conversion Congress and Exposition, Montreal, QC, 2015: 1864-1871. [50] Seo J H, Kwak S Y, Jung S Y, et al. Investigation on EMF waveform in the interior permanent magnet synchronous machine considering load condition[C]// Biennial IEEE Conference on Electromagnetic Field Computation, Miami, FL, 2006: 321-321. [51] Paula G T D, Monteiro J R B d A, Almeida T E P d, et al. Evaluation of surface mounted PM machine's parameters on load conditions using frozen per- meability method. Part. II[C]//International Con- ference on Electrical Machines, Berlin, 2014: 156- 161. [52] Wu D. Effect of magnetic saturation in fractional slot PM machines with particular reference to terminal voltage distortion[D]. UK: The University of Sheffield, 2015. [53] Wu D, Zhu Z Q. On-load voltage distortion in fractional slot surface-mounted permanent magnet machines considering local magnetic saturation[J]. IEEE Transactions on Magnetics, 2015, 51(8): 8106410(1-10). [54] Wu D, Zhu Z Q. Influence of slot and pole number combinations on voltage distortion in surface- mounted permanent magnet machines with local magnetic saturation[J]. IEEE Transactions on Energy Conversion, 2015, 30(4): 1460-1471. [55] Zhu Z Q, Wu D. On-load voltage distortion in fractional-slot interior permanent magnet machines[J]. IEEE Transactions on Magnetics, 2015, 51(10): 1-9. [56] Zhu Z Q, Wu D, Ge X. Investigation of voltage distortion in fractional slot interior permanent magnet machines having different slot and pole number combinations[J]. IEEE Transactions on Energy Conversion, 2016, 31(3): 1192-1201. [57] Zhu Z Q, Wu D, Wu M C, et al. Influence of on-load voltage distortion on torque-speed characteristic of interior permanent magnet machines[C]//IEEE Energy Conversion Congress and Exposition, 2015: 760- 767. [58] Qi G, Chen J T, Zhu Z Q, et al. Influence of skew and cross-coupling on flux-weakening performance of permanent-magnet brushless AC machines[J]. IEEE Transactions on Magnetics, 2009, 45(5): 2110-2117. [59] Chai S H, Lee B H, Hong J P, et al. Design of IPMSM having high power density for position sensorless operation with high-frequency signal injection and the method of calculating inductance profile[C]// International Conference on Electrical Machines and Systems, Beijing, 2011: 1-5. [60] Dajaku G, Gerling D. Magnetic radial force density of the PM machine with 12-teeth/10-poles winding topology[C]//IEEE International Electric Machines and Drives Conference, Miami, FL, 2009: 1715-1720. [61] Xia X P, Zhu Z Q, Wu L J, et al. Comparison of radial vibration forces in 10-pole/12-slot fractional slot surface-mounted and interior PM brushless AC machines[C]//International Conference on Electrical Machines, Rome, 2010: 1-6. [62] Duan S, Zhou L, Wang J. Flux weakening mechanism of interior permanent magnet synchronous machines with segmented permanent magnets[J]. IEEE Transa- ctions on Apply Superconducting, 2014, 24(3): 1-5. [63] Sprooten J, Gyselinck J, Maun J C. Local and global effect of a broken bar in induction machines using fundamental electromagnetic laws and finite element simulations[C]//IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, Vienna , 2005: 1-6. [64] Ling Z, Zhou L, Guo S, et al. Equivalent circuit parameters calculation of induction motor by finite element analysis[J]. IEEE Transactions on Magnetics, 2014, 50(2): 833-836. [65] Jia L. Equivalent circuit parameters calculation of a wound rotor brushless doubly-fed machine based on finite element analysis[C]//IEEE Magnetics Con- ference, Beijing , 2015: 1. [66] Shirai K, Tokikuni Y, Shima K, et al. Causes of increase in the terminal voltage of a permanent- magnet-assisted salient-pole synchronous machine[C]// International Conference on Electrical Machines and Systems, Tokyo, 2009: 1-6. [67] Jeong I, Kim J, Kim Y, et al. Extended MTPA with cross coupling inductances for electrically excited synchronous motors[C]//IEEE Energy Conversion Congress and Exposition, Denver, CO, 2013: 867-873. [68] Jeong I, Gu B G, Kim J, et al. Inductance estimation of electrically excited synchronous motor via polynomial approximations by least square method[J]. IEEE Transactions on Industry Applications, 2015, 51(2): 1526-1537. [69] Li G J, Zhu Z Q, Ma X Y, et al. Comparative study of torque production in conventional and mutually coupled SRMs using frozen permeability[J]. IEEE Transactions on Magnetics, 2016, 52(6): 8103509. [70] Hwang H, Bae S, Lee C. Analysis and design of a hybrid rare-earth-free permanent magnet reluctance machine by frozen permeability method[J]. IEEE Transa- ctions on Magnetics, 2016, 52(7): 8106304(1-4).
2016, Vol. 31 
