Frequency-Dependent Transmission Line Fractional Model and its Solution Based on Skin Effect

Abstract

Due to the continuous increasing of operating frequency in the power system and the transmission speed, under the high frequencies of the transmission line calculation and simulation process, it is necessary to consider the frequency-dependent properties. At present, the frequency-dependent transmission line modeling has a variety of methods, but in the modeling and calculation of frequency variable term, processing is relatively complicated. This article will introduce transmission line equation of fractional calculus, intuitive representation of frequency varying parameters, and by a time-domain fractional solution, simplify the operation, improve the computational efficiency. Application of this algorithm for fractional differential equations can be obtained the voltage and current responses at any point in the transmission line. Thesis also by comparison with actual example, confirmed the validity and feasibility of the algorithm. At the same time, proposed algorithm can be extended to the multiple conductor transmission lines of fractional order model, also has certain applicability.

Fractional transmission line model of oil‐immersed transformer windings considering the frequency‐dependent parameters

“…The complex frequency domain form of (7) can be obtained as follows: As can be seen from (8), fractional‐order terms appear in the impedance matrix PUL of the TWs considering the skin effect [10].…”

“…The frequency‐dependent characteristics of dielectric are described in more appropriate ways through improved Debye model with fractional‐order terms, such as Davidson–Cole, Cole–Cole [9]. In the process of modelling TWs, the fractional model can be established taking the skin effect into account simply [10].…”