摘要
电气设备的分数阶建模离不开分数阶电路的综合理论。针对现有W域等效正实条件的不足,对其进行了改进与说明。基于s-W变换,将有理元次分数阶导抗函数转化为W域整数阶导抗函数,在W域推导了LαCβ两种元件电路导抗函数的部分分式展开式,证明了分数阶两种元件电路导抗函数均可以福斯特实现和梯形实现。最后通过示例验证了方法的有效性,对后续W域综合研究具有一定的指导意义。
The fractional-order modeling of electrical equipment is inseparable from the synthesis theory of fractional-order circuits.This paper explains and corrects the shortcomings of the existing W-domain equivalent positive real conditions.Based on s-W transformation,this paper transforms the fractional rational order immittance function into the W-domain integer-order immittance function,and derives the partial-fraction expansion of the fractional immittance function with LαCβ two-element-kind from W-domain,thus proving that the fractional immittance function with two-element-kind can be realized by Foster circuit and ladder circuit.Finally,this paper verifies the validity of the method by a numerical example,which provides some guidance for the future research about passive synthesis in W-domain.
作者
梁贵书
李天文
LIANG Guishu;LI Tianwen(School of Electrical and Electronic Engineering,North China Electric Power University,Baoding 071003,China)
出处
《华北电力大学学报（自然科学版）》
CAS
北大核心
2019年第6期41-48,共8页
Journal of North China Electric Power University：Natural Science Edition
基金
河北省自然科学基金资助项目(E2018502121)
北京市自然科学基金资助项目(3192039)
关键词
分数阶导抗函数
s-W变换
部分分式展开
无源综合
fractional-order immittance function
s-W transformation
partial-fraction expansion
passive synthesis
