Open AccessWide‐band modelling and transient analysis of the multi‐conductor transmission lines system considering the frequency‐dependent parameters based on the fractional calculus theory
Author(s) -
Liu Xin,
Ti Chenyang,
Liang Guishu
Publication year - 2016
Publication title -
iet generation, transmission and distribution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.92
H-Index - 110
eISSN - 1751-8695
pISSN - 1751-8687
DOI - 10.1049/iet-gtd.2016.0472
Subject(s) - laplace transform , fractional calculus , computation , electric power transmission , transient (computer programming) , convolution (computer science) , ordinary differential equation , mathematics , computer science , differential equation , mathematical analysis , algorithm , engineering , electrical engineering , operating system , machine learning , artificial neural network
The transient analysis of multi‐conductor transmission lines should consider the frequency‐dependent characteristics due to the skin effect. Fully considering the inherent fractional order characteristics of the frequency‐dependent effect, a general wide‐band modelling method is proposed. The fractional order vector fitting method is adopted to approximate the frequency‐dependent parameters and the corresponding fractional differential equations can be obtained by the inverse Laplace transformation. The backward difference is a practical method to solve the fractional differential equations; however, a linear convolution must be calculated, which will lead to a heavy computation complexity. To address this issue, a new recursive convolution method for the fractional differential equations is proposed and an efficient solution is achieved. Furthermore, considering the indispensability of the passivity verification of a system for the transient simulation, the passivity verification by extending the Hamiltonian matrix for the fractional order systems is studied and a practical criterion is proposed. Three examples are considered to validate the proposed method: (i) a single underground cable, (ii) three‐phase underground cable, and (iii) an experimental transformer under very fast transient voltage. The simulation results are compared with the results obtained by power systems computer‐aided design or measurements and good agreements are achieved.