基于分数阶微分理论的宽频建模方法  

Wide-band Modeling Method Based on the Fractional Order Differential Theory

作　　者：刘欣[1,2] 崔翔[1] 梁贵书[2] 马龙[2] 

机构地区：[1]华北电力大学新能源电力系统国家重点实验室,北京102206 [2]华北电力大学电力工程系,保定071003

出　　处：《电工技术学报》2013年第4期20-27,共8页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金(51177048);河北省自然科学基金(E2012502009);中央高校基金(11MG36);河北省高等学校科学技术研究(Z2011220)资助项目

摘　　要：开展电力、铁路、通信系统电磁兼容以及过电压的抑制与防护等问题的研究往往需要依据电气设备、传输线路、接地系统等的网络参数建立其电磁暂态宽频计算模型。由于电磁暂态计算需要考虑的频带较宽,必须计及建模对象网络参数的频变特性,针对此问题,目前被广泛采用的方法为矢量匹配法,但该方法是利用整数阶有理函数对频变参数进行逼近,未能充分考虑网络参数频变效应固有的分数阶次幂特点,从而导致逼近结果的阶数较高,建立的模型较为复杂。本文基于分数阶微分理论,结合分数阶拟合方法和分数阶微分方程的数值解法,提出了一种通用的宽频建模方法,该方法仅需较低的拟合阶数就可以获得较好的计算精度。同时,本文对分数阶系统的无源性进行了深入讨论,提出了一种适用于分数阶电路的无源性判据,丰富了分数阶电网络理论。According to the problems of electromagnetic, overvoltage protection and insulation coordination in the power system, communication system and railway power system, et. al., the electric equipment, transmission line and grounding system, et. al. should be modeled considering their frequency dependent characteristic. The vector fitting method is a general method to be used to approximate the network parameter by the rational function, however, this method does not fully consider the fractional order characteristic of the frequency dependent effect, which will result in a relative complicate model. Based on the fractional order differential theory, this paper presents a general wide-band modeling method. In this method, the Levy＇s identification method is used to approximate the measured or calculated frequency domain network function with the irrational function, in which the powers of the Laplace operator s is non-integer and the corresponding fractional order differential equation can be obtained by the Laplace inverse transformation. Combining with the numeric solution to the fractional order differential equation, a time domain simulation can be implemented. Considering the indispensability of the passivity verification of a system for the transient simulation, the passivity verification method for the traditional state-space system is extended to the fractional order state-space system and a practical criterion is proposed in this paper.

关 键 词：分数阶微分理论 宽频建模 无源性 频变特性 

分 类 号：TM133[电气工程—电工理论与新技术]