考虑铁芯磁饱和的开关磁阻电机电感及转矩解析建模
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摘要
针对开关磁阻电机电感的非线性问题,提出了一种开关磁阻电机非线性电感解析计算模型,并在此基础上完成了电磁转矩的解析计算。运用分布式等效磁路法并考虑铁芯磁饱和的影响,通过分别确定各条磁路中气隙和铁芯的等效长度及磁导率,建立了含电机参数的非线性电感解析模型,并通过电感的有限元仿真结果验证了解析模型的准确性。在利用该电感解析模型求解得到磁链曲线族的基础上,使用能量法对电磁转矩进行了解析计算,并将电磁转矩的解析结果与有限元仿真结果进行了对比,结果表明:建立的非线性电感解析模型能够准确地预测出电机的动态电感,相对误差在9%以内,电磁转矩峰值处误差在6%以内,提出的电感解析模型能够获得较高精度的电感和转矩解析结果。
Aiming at the nonlinearity of inductance in switched reluctance motor, a nonlinear analytical calculation model for the inductance of switched reluctance motor is proposed, and the analytical modeling for electromagnetic torque is constructed. Adopting the distributed equivalent magnetic circuit method and considering the influence of iron core magnetic saturation, the nonlinear inductance analytical model with motor parameters is established by determining the length and permeability of the air gap and core in each magnetic circuit. The accuracy of this model is verified by the finite element analysis results of the inductance. Once the flux curve family is solved, the electromagnetic torque is analytically calculated with energy method, and the obtained electromagnetic torque is compared with that from the finite element analysis. It is indicated that the established nonlinear inductance analytical model can accurately predict the dynamic inductance of the motor, the relative error gets within 9%, and the relative error of the electromagnetic torque peak is within 6%. Therefore, high accuracy analysis results of inductance and torque can be achieved by the proposed inductance analytical model.
Aiming at the nonlinearity of inductance in switched reluctance motor, a nonlinear analytical calculation model for the inductance of switched reluctance motor is proposed, and the analytical modeling for electromagnetic torque is constructed. Adopting the distributed equivalent magnetic circuit method and considering the influence of iron core magnetic saturation, the nonlinear inductance analytical model with motor parameters is established by determining the length and permeability of the air gap and core in each magnetic circuit. The accuracy of this model is verified by the finite element analysis results of the inductance. Once the flux curve family is solved, the electromagnetic torque is analytically calculated with energy method, and the obtained electromagnetic torque is compared with that from the finite element analysis. It is indicated that the established nonlinear inductance analytical model can accurately predict the dynamic inductance of the motor, the relative error gets within 9%, and the relative error of the electromagnetic torque peak is within 6%. Therefore, high accuracy analysis results of inductance and torque can be achieved by the proposed inductance analytical model.
引文
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[14] CHEN H,YAN W,CHEN L,et al.Analytical polynomial models of nonlinear magnetic flux linkage for SRM [J].IEEE Transactions on Applied Superconductivity,2018,28(3):1-7.
[15] RADUN A.Analytical calculation of the switched reluctance motor’s unaligned inductance [J].IEEE Transactions on Magnetics,2002,35(6):4473-4481.
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[19] YU Q,WANG X,CHENG Y.Magnetic modeling of saliency effect for saturated electrical machines with a new calculation method [J].IEEE Transactions on Magnetics,2016,52(6):1-6.
[20] YAVUZ S,PARSPOUR N,LIANG M.Analytical modelling of a parametrized switched reluctance motor with adapting flux tube method [C]//Proceedings of IEEE International Conference on Industrial Technology.Piscataway,NJ,USA:IEEE,2018:335-340.
[21] YU Q,LAUDENSACK C,GERLING D.An analytical network for switched reluctance machines with highly saturated regions [C]//Proceedings of International Aegean Conference on Electrical Machines & Power Electronics & Electromotion.Piscataway,NJ,USA:IEEE,2011:250-254.
[22] ZHU Z Q,LEE B,HUANG L,et al.Contribution of current harmonics to average torque and torque ripple in switched reluctance machines [J].IEEE Transactions on Magnetics,2017,53(3):1-9.
[23] 孙剑波.开关磁阻电机的减振降噪和低转矩脉动研究 [D].武汉:华中科技大学,2005:14-15.
[24] 詹琼华.开关磁阻电动机 [M].武汉:华中理工大学出版社,1992:114-116.
[25] PENG F,EMADI A.A digital PWM current controller for switched reluctance motor drives [C]//Proceedings of Transportation Electrification Conference and Expo.Piscataway,NJ,USA:IEEE,2014:1-6.
[26] GAN C,WU J,SUN Q,et al.Low-cost direct instantaneous torque control for switched reluctance motors with bus current detection under soft-chopping mode [J].IET Power Electronics,2016,9(3):482-490.
[27] SUN Q,WU J,GAN C,et al.OCTSF for torque ripple minimisation in SRMs [J].IET Power Electronics,2016,9(14):2741-2750.
[28] 朱叶盛,章国宝,黄永明.基于PWM的开关磁阻电机直接瞬时转矩控制 [J].电工技术学报,2017,32(7):31-39.ZHU Yesheng,ZHANG Guobao,HUANG Yongming.PWM-based direct instantaneous torque control of switched reluctance machine [J].Transactions of China Electrotechnical Society,2017,32(7):31-39.
[2] LEE D H,PHAM T H,AHN J W.Design and operation characteristics of four-two pole high-speed SRM for torque ripple reduction [J].IEEE Transactions on Industrial Electronics,2013,60(9):3637-3643.
[3] NABETA S I,CHABU I E,LEBENSZTAJN L,et al.Mitigation of the torque ripple of a switched reluctance motor through a multiobjective optimization [J].IEEE Transactions on Magnetics,2008,44(6):1018-1021.
[4] SANADA M,MORIMOTO S,TAKEDA Y,et al.Novel rotor pole design of switched reluctance motors to reduce the acoustic noise [C]//Conference Record of the 2000 IEEE Industry Applications Conference.Piscataway,NJ,USA:IEEE,2002:107-113.
[5] LEE D H,LIANG J,LEE Z G,et al.A simple nonlinear logical torque sharing function for low-torque ripple SR drive [J].IEEE Transactions on Industrial Electronics,2009,56(8):3021-3028.
[6] LI C,WANG G,LI Y,et al.An improved finite-state predictive torque control for switched reluctance motor drive [J].IET Electric Power Applications,2018,12(1):144-151.
[7] 牛龙涛.基于滑模变结构的开关磁阻电机转矩脉动抑制 [D].天津:天津大学,2009:28-39.
[8] 司利云,林辉,刘震.基于最小二乘支持向量机的开关磁阻电动机建模 [J].中国电机工程学报,2007(6):26-30.SI Liyun,LIN Hui,LIU Zhen.Modeling of switched reluctance motors based on LS-SVM [J].Proceedings of the CSEE,2007(6):26-30.
[9] LU W,KEYHANI A,FARDOUN A.Neural network-based modeling and parameter identification of switched reluctance motors [J].IEEE Transactions on Energy Conversion,2003,18(2):284-290.
[10] MIKAIL R,HUSAIN I,ISLAM M.Finite element based analytical model for controller development of switched reluctance machines [C]//Proceedings of Energy Conversion Congress and Exposition.Piscataway,NJ,USA:IEEE,2013:920-925.
[11] NIRGUDE A,MURALI M,CHAITHANYA N,et al.Nonlinear mathematical modeling and simulation of switched reluctance motor [C]//Proceedings of IEEE International Conference on Power Electronics,Drives and Energy Systems.Piscataway,NJ,USA:IEEE,2017:1-6.
[12] DJELLOUL-KHEDDA Z,BOUGHRARA K,DUBAS F,et al.Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines [J].IEEE Transactions on Magnetics,2017,53(7):1-11.
[13] 丁文,梁得亮.一种开关磁阻电机非线性磁链与转矩建模方法 [J].电机与控制学报,2008,12(6):659-665.DING Wen,LIANG Deliang.Novel method of modeling nonlinear flux linkage and torque for switched reluctance motor [J].Electric Machines and Control,2008,12(6):659-665.
[14] CHEN H,YAN W,CHEN L,et al.Analytical polynomial models of nonlinear magnetic flux linkage for SRM [J].IEEE Transactions on Applied Superconductivity,2018,28(3):1-7.
[15] RADUN A.Analytical calculation of the switched reluctance motor’s unaligned inductance [J].IEEE Transactions on Magnetics,2002,35(6):4473-4481.
[16] MAO S H,DORRELL D,TSAI M C.Fast analytical determination of aligned and unaligned flux linkage in switched reluctance motors based on a magnetic circuit model [J].IEEE Transactions on Magnetics,2009,45(7):2935-2942.
[17] 刘闯,朱学忠,刘迪吉.开关磁阻电机的非线性电感参数法仿真分析 [J].东南大学学报(自然科学版),2001,31(4):106-110.LIU Chuang,ZHU Xuezhong,LIU Diji.Simulation analysis of non-linear inductance parameters method for SRM [J].Journal of Southeast University (Natural Science Edition),2001,31(4):106-110.
[18] 邓智泉,杨钢,张媛,等.一种新型的无轴承开关磁阻电机数学模型 [J].中国电机工程学报,2005(9):139-146.DENG Zhiquan,YANG Gang,ZHANG Yuan,et al.An innovative mathematical model for a bearingless switched reluctance motor [J].Proceedings of the CSEE,2005(9):139-146.
[19] YU Q,WANG X,CHENG Y.Magnetic modeling of saliency effect for saturated electrical machines with a new calculation method [J].IEEE Transactions on Magnetics,2016,52(6):1-6.
[20] YAVUZ S,PARSPOUR N,LIANG M.Analytical modelling of a parametrized switched reluctance motor with adapting flux tube method [C]//Proceedings of IEEE International Conference on Industrial Technology.Piscataway,NJ,USA:IEEE,2018:335-340.
[21] YU Q,LAUDENSACK C,GERLING D.An analytical network for switched reluctance machines with highly saturated regions [C]//Proceedings of International Aegean Conference on Electrical Machines & Power Electronics & Electromotion.Piscataway,NJ,USA:IEEE,2011:250-254.
[22] ZHU Z Q,LEE B,HUANG L,et al.Contribution of current harmonics to average torque and torque ripple in switched reluctance machines [J].IEEE Transactions on Magnetics,2017,53(3):1-9.
[23] 孙剑波.开关磁阻电机的减振降噪和低转矩脉动研究 [D].武汉:华中科技大学,2005:14-15.
[24] 詹琼华.开关磁阻电动机 [M].武汉:华中理工大学出版社,1992:114-116.
[25] PENG F,EMADI A.A digital PWM current controller for switched reluctance motor drives [C]//Proceedings of Transportation Electrification Conference and Expo.Piscataway,NJ,USA:IEEE,2014:1-6.
[26] GAN C,WU J,SUN Q,et al.Low-cost direct instantaneous torque control for switched reluctance motors with bus current detection under soft-chopping mode [J].IET Power Electronics,2016,9(3):482-490.
[27] SUN Q,WU J,GAN C,et al.OCTSF for torque ripple minimisation in SRMs [J].IET Power Electronics,2016,9(14):2741-2750.
[28] 朱叶盛,章国宝,黄永明.基于PWM的开关磁阻电机直接瞬时转矩控制 [J].电工技术学报,2017,32(7):31-39.ZHU Yesheng,ZHANG Guobao,HUANG Yongming.PWM-based direct instantaneous torque control of switched reluctance machine [J].Transactions of China Electrotechnical Society,2017,32(7):31-39.