非正弦励磁环境磁性材料改进损耗模型的研究
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摘要
基于由意大利学者Bertotti首次提出的损耗计算三项式模型,使用非线性最小二乘原理对爱泼斯坦方圈法测得的取向电工钢在不同励磁环境的损耗数据进行多元非线性曲线拟合。鉴于Bertotti损耗模型没有考虑非正弦励磁多变量条件(如谐波阶次、含量和相位)对铁损的影响,故基于Bertotti损耗模型中引入各铁损分量的校正因子,提出一种改进的损耗三项式模型,使其可以充分考虑非正弦励磁多变量条件的影响,并对拟合结果进行处理,得到多变量条件对校正因子和损耗各分量的影响规律。结果表明,使用改进模型计算得到的取向电工钢损耗数据与实测数据有很好的一致性,验证了改进损耗模型的正确性和有效性,所得结论对进一步探索复杂励磁环境下软磁材料的损耗特性有十分重要的理论价值。
Based on the most popular loss model proposed by Italian scholar Bertotti,the loss data of oriented electrical steels under different excitation environments,which was measured by Epstein frame,can be fitted by using non-linear least square method.However,there is no explicit consideration in the Bertotti loss model that the non-sinusoidal multivariate conditions,such as harmonic order,content and phase,may influence the iron loss components,wherefore an improved loss model with the introduction of the correction factors to the Bertotti loss model is proposed in this paper.The fitting results were processed to obtain the effects of multivariate conditions on the correction factors and loss components.Then it shows a remarkably good agreement between the calculated results and experimental data points.The conclusions are of significant theoretical value for further exploring the magnetic properties of soft magnetic materials under complex excitation environments.
Based on the most popular loss model proposed by Italian scholar Bertotti,the loss data of oriented electrical steels under different excitation environments,which was measured by Epstein frame,can be fitted by using non-linear least square method.However,there is no explicit consideration in the Bertotti loss model that the non-sinusoidal multivariate conditions,such as harmonic order,content and phase,may influence the iron loss components,wherefore an improved loss model with the introduction of the correction factors to the Bertotti loss model is proposed in this paper.The fitting results were processed to obtain the effects of multivariate conditions on the correction factors and loss components.Then it shows a remarkably good agreement between the calculated results and experimental data points.The conclusions are of significant theoretical value for further exploring the magnetic properties of soft magnetic materials under complex excitation environments.
引文
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[12]张宁,李琳,魏晓光.非正弦激励下磁心损耗的计算方法及实验验证[J].电工技术学报,2016,31(17):224-232.Zhang Ning,Li Lin,Wei Xiaoguang.Calculation method and experimental verification of core losses under non-sinusoidal excitation[J].Transactions of China Electrotechnical Society,2016,31(17):224-232.
[13]Barbisio E,Fiorillo F,Ragusa C.Predicting loss in magnetic steels under arbitrary induction waveform and with minor hysteresis loops[J].IEEE Transactions on Magnetics,2004,40(4):1810-1819.
[14]罗富强.非正弦激励下异步电机铁耗计算与分析[D].天津:天津大学,2012.
[15]张冬冬.计及谐波条件下的变系数电机铁耗模型[D].北京:华北电力大学,2016.
[16]国家质量技术监督局.GB/T 3655-2008.用爱泼斯坦方圈测量电工钢片(带)磁性能的方法[S].北京:中国标准出版社,2000.
[17]范隽宏,程汉湘.MATLAB工具箱在软磁材料单位损耗曲线拟合中的应用[J].机电工程技术,2014(8):101-106.Fan Juanhong,Cheng Hanxiang.Application of matlab toolbox on unit loss curve fitting of soft ferromagnetic material[J].Mechanical&Electrical Engineering Technology,2014(8):101-106.
[2]赵小军,崔灿,李琳,等.基于定点谐波平衡法的铁心磁滞与损耗特性分析[J].电工技术学报,2014,29(7):10-18.Zhao Xiaojun,Cui Can,Li Lin,et al.Analysis of the hysteresis and loss characteristics in the laminated core by fixed-point harmonic-balanced method[J].Transactions of China Electrotechnical Society,2014,29(7):10-18.
[3]张长庚,杨庆新,李永建.电工软磁材料旋转磁滞损耗测量及建模[J].电工技术学报,2017,32(11):208-216.Zhang Changgeng,Yang Qingxin,Li Yongjian.Measurement and modeling of rotational hysteresis loss of electric soft magnetic material[J].Transactions of China Electrotechnical Society,2017,32(11):208-216
[4]李劲松,杨庆新,李永建,等.高频高磁通密度时叠置硅钢片的铁心损耗计算式改进[J].高电压技术,2016,42(3):994-1002.Li Jingsong,Yang Qingxin,Li Yongjian,et al.Improved calculation formula of core losses for laminated silicon steels at high frequency and high flux density[J].High Voltage Engineering,2016,42(3):994-1002.
[5]Kapeller H,Pla?negger B,Gragger J V.Iron-loss modeling based on a loss-separation approach in modelica[J].IEEE Transactions on Magnetics,2017,54(3):1-4.
[6]崔杨,胡虔生,黄允凯.任意频率正弦波条件下铁磁材料损耗计算[J].微电机,2007,40(8):1-3.Cui Yang,Hu Qiansheng,Huang Yunkai.Iron loss prediction in ferromagnetic materials with sinusoidal supply[J].Micromotors,2007,40(8):1-3.
[7]Zhao Zhigang,Cheng Zhiguang,Forghani B,et al.Analytical study and corresponding experiments for iron loss inside laminated core under ac-dc hybrid excitation[J].International Journal of Applied Electromagnetics&Mechanics,2017,55:159-167.
[8]Bertotti G.Physical interpretation of eddy current losses in ferromagnetic materials.I.theoretical considerations[J].Journal of Applied Physics,1985,57(6):2110-2117.
[9]张冬冬,赵海森,王义龙,等.用于电机损耗精细化分析的分段变系数铁耗计算模型[J].电工技术学报,2016,31(15):16-24.Zhang Dongdong,Zhao Haisen,Wang Yilong,et al.Apiecewise variable coefficient model for precise analysis on iron losses of electrical machines[J].Transactions of China Electrotechnical Society,2016,31(15):16-24.
[10]Lavers J D,Biringer P P,Hollitscher H.A simple method of estimating the minor loop hysteresis loss in thin laminations[J].IEEE Transactions on Magnetics,1978,14(5):386-388.
[11]周腊吾,胡雪婷,徐超,等.非正弦供电下的变系数铁耗模型[J].电工技术学报,2013,28(增刊1):87-90Zhou Lawu,Hu Xueting,Xu Chao,et al.Variable coefficient core loss model under non-sinusoidal power supply[J].Transactions of China Electrotechnical Society,2013,28(S1):87-90.
[12]张宁,李琳,魏晓光.非正弦激励下磁心损耗的计算方法及实验验证[J].电工技术学报,2016,31(17):224-232.Zhang Ning,Li Lin,Wei Xiaoguang.Calculation method and experimental verification of core losses under non-sinusoidal excitation[J].Transactions of China Electrotechnical Society,2016,31(17):224-232.
[13]Barbisio E,Fiorillo F,Ragusa C.Predicting loss in magnetic steels under arbitrary induction waveform and with minor hysteresis loops[J].IEEE Transactions on Magnetics,2004,40(4):1810-1819.
[14]罗富强.非正弦激励下异步电机铁耗计算与分析[D].天津:天津大学,2012.
[15]张冬冬.计及谐波条件下的变系数电机铁耗模型[D].北京:华北电力大学,2016.
[16]国家质量技术监督局.GB/T 3655-2008.用爱泼斯坦方圈测量电工钢片(带)磁性能的方法[S].北京:中国标准出版社,2000.
[17]范隽宏,程汉湘.MATLAB工具箱在软磁材料单位损耗曲线拟合中的应用[J].机电工程技术,2014(8):101-106.Fan Juanhong,Cheng Hanxiang.Application of matlab toolbox on unit loss curve fitting of soft ferromagnetic material[J].Mechanical&Electrical Engineering Technology,2014(8):101-106.