Nonlinear fitting method for torque-angle characteristic model of switched reluctance motor
-
摘要:
开关磁阻电机难以采用传统电机分析方法进行建模,通过分析开关磁阻电机电磁转矩生成原理,确定了不同电机饱和状态下电磁转矩与相电感导数之间的关系。用分段函数非线性拟合的方式对电感导数曲线进行建模,再进一步得到开关磁阻电机可逆矩角特性的解析模型,并基于电机的结构参数和约束条件逐一确定和优化了模型的各个参数。利用可逆矩角特性模型,可以方便地计算电机磁化曲线和瞬时磁链,给电机设计及驱动控制带来很大的方便。通过2个样机的实测数据和有限元结果对该模型解析计算结果的准确性进行了验证。
Abstract:The modeling method of the switched reluctance motor is different from the traditional motor. By analyzing the principle of electromagnetic torque generation, the relationship between electromagnetic torque and phase inductance derivatives under different motor saturation conditions is determined. The inductance derivative curve is modeled by piecewise function nonlinear fitting. And then, the analytical model for the reversible torque-angle characteristics of switched reluctance motor is obtained. The parameters of the model are determined and optimized by the structural parameters and constraint condition of the motor. The reversible torque-angle model makes the calculation of the magnetization curve and the instantaneous flux linkage possible. It brings great convenience for the design of the motor and the drive control of the motor. The accuracy of the analytical results is verified by the measured data and the finite element method with two prototypes.
-
Key words:
- switched reluctance motor /
- modeling /
- nonlinear /
- torque-angle characteristics /
- curve fitting
-
表 1 两个开关磁阻样机的主要参数
Table 1. Main parameters of two SRM prototypes
参数 SRM1 SRM2 定转子极数 6-4 6-4 定子外径/mm 150 100 定子内径/mm 95 50 定子轭高/mm 13.75 12.2 定子极弧系数 0.433 3 0.433 3 转子外径/mm 94.4 49.4 转子内径/mm 40 10 转子极弧系数 0.3 0.3 转子轭高/mm 13.6 10 轴向长度/mm 40 40 相绕组匝数 19 50 硅钢片材料 D25_50 D25_50 电机容量 7.5 kW, 270 V,
3 000 r/min200 W, 60 V,
3 000 r/min表 2 各解析模型的参数取值
Table 2. Parameter values of each analytical model
模型 m n xbo μrise α x1 μtop β xeo μfall k a 13 3 0.39 0.23 2 0.4 0.5 2 0.98 0.95 35 b 25 3 0.39 0.23 2 0.4 0.5 2 0.98 0.95 20 c 25 3 0.39 0.23 2 0.4 0.5 2 0.98 0.95 35 表 3 样机SRM1解析模型和有限元模型的Terror和TR
Table 3. Terror and TR of analytical model and finite element model for prototype SRM1
模型 误差 Is=2 A Is=4 A Is=6 A Is=8 A a Terror/(N·m) 0.24 0.97 2.07 4.26 TR/% 2.92 2.92 2.90 2.95 b Terror/(N·m) 0.38 1.56 3.16 2.81 TR/% 2.90 2.90 2.86 2.66 c Terror/(N·m) 0.10 0.42 0.73 2.97 TR/% 2.55 2.55 2.54 2.60 表 4 样机SRM2解析模型各参数值
Table 4. Parameter values of analytical model for prototype SRM2
参数 m n xbo μrise α x1 μtop β xeo μfall k 数值 40 3 0.4 0.23 2 0.41 0.5 2 0.99 0.95 20 -
[1] ARUMUGAM R, LOWTHER D A, KRISHNAN R, et al. Magnetic field analysis of a switched reluctance motor using a two-dimensional finite element method[J].IEEE Transactions on Magnetics, 1985, 21(5):1883-1885. doi: 10.1109/TMAG.1985.1063910 [2] LIN H, LOW T S, CHEN S X.Investigation on magnetic saturation in switched reluctance motor using 2D hybrid finite element method[J].IEEE Transactions on Magnetics, 1996, 32(5):4317-4319. doi: 10.1109/20.538855 [3] TORREY D A, LANG J H.Modeling a nonlinear variable-reluctance motor drive[J].IEE Proceedings B:Electric Power Applications, 1990, 137(5):314-326. doi: 10.1049/ip-b.1990.0038 [4] 邓智泉, 杨刚, 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, 25(9):139-146. doi: 10.3321/j.issn:0258-8013.2005.09.026DENG Z Q, YANG G, ZHANG Y, et al.An innovative mathematical model for a bearingless switched reluctance motor[J].Proceedings of the Chinese Society for Electrical Engineering, 2005, 25(9):139-146(in Chinese). doi: 10.3321/j.issn:0258-8013.2005.09.026 [5] RADUN A V.Design considerations for the switched reluctance motor[J].IEEE Transactions on Industry Applications, 1995, 31(5):1079-1087. doi: 10.1109/28.464522 [6] VUJICIC V, VUKOSAVIC S N.A simple nonlinear model of the switched reluctance motor[J].IEEE Transactions on Energy Conversion, 2000, 15(4):395-400. doi: 10.1109/60.900499 [7] LOOP B P, SUDHOFF S D.Switched reluctance machine model using inverse inductance characterization[J].IEEE Transactions on Industry Applications, 2003, 39(3):743-751. doi: 10.1109/TIA.2003.811785 [8] RADIMOV N, BEN-HAIL N, RABINOVICI R.Simple model of switched-reluctance machine based only on aligned and unaligned position data[J].IEEE Transactions on Magnetics, 2004, 40(3):1562-1572. doi: 10.1109/TMAG.2004.827185 [9] SALMASI F R, FAHIMI B.Modeling switched-reluctance machines by decomposition of double magnetic saliencies[J].IEEE Transactions on Magnetics, 2004, 40(3):1556-1561. doi: 10.1109/TMAG.2004.826624 [10] XUE X D, CHENG K W E, HO S L.Optimization and evaluation of torque sharing functions for torque ripple minimization in switched reluctance motor drives[J].IEEE Transactions on Power Electronics, 2009, 24(9):2076-2090. doi: 10.1109/TPEL.2009.2019581 [11] VUJICIC V P.Modeling of a switched reluctance machine based on the invertible torque function[J].IEEE Transactions on Magnetics, 2008, 44(9):2186-2194. doi: 10.1109/TMAG.2008.2000663 [12] KJAER P C, GRIBBLE J J, MILLER T J E.High-grade control of switched reluctance machines[J].IEEE Transactions on Industry Applications, 1997, 33(6):1585-1593. doi: 10.1109/28.649972 [13] MIKAIL R, SOZER Y, HUSAIN I, et al.Torque ripple minimization of switched reluctance machines through current profiling[J].IEEE Transactions on Industry Applications, 2013, 49(3):1258-1267. doi: 10.1109/TIA.2013.2252592 [14] KHALIL A, HUSAIN I.A Fourier series generalized geometry-based analytical model of switched reluctance machines[J].IEEE Transactions on Industry Applications, 2007, 43(3):673-684. https://ieeexplore.ieee.org/document/4215006 [15] HOSSAIN S A, HUSAIN I.A geometry based simplified analytical model of switched reluctance machines for real-time controller implementation[J].IEEE Transactions on Power Electronics, 2003, 18(6):1384-1389. doi: 10.1109/TPEL.2003.818870 [16] VUJICIC V P.Minimization of torque ripple and copper losses in switched reluctance drive[J].IEEE Transactions on Power Electronics, 2012, 27(1):388-399. doi: 10.1109/TPEL.2011.2158447 [17] MILLER T J E.Electronic control of switched reluctance machines[M].Oxford:Newnes Press, 2001. [18] KHALIL A, HUSAIN I.A Fourier series generalized geometry-based analytical model of switched reluctance machines[J].IEEE Transactions on Industry Applications, 2007, 43(3):673-684. doi: 10.1109/TIA.2007.895737 [19] MILLER T I J, GLINKA M, MCGILP M, et al.Ultra-fast model of the switched reluctance motor[C]//IEEE Industry Applications Conference.Piscataway, NJ: IEEE Press, 1998: 319-326. https://ieeexplore.ieee.org/document/732313