Research On Fractional Transmission Line Model Of Oil-immersed Transformer Windings

Establishing the precise model of the transformer windings has the vital significance for the analysis of the voltage distribution on the windings. The frequency-dependent characteristics of the impedance parameter and the admittance parameter in the transmission line model of the transformer windings are mainly caused respectively by the skin effect and the frequency-dependent characteristics of the complex permittivity of oil-immersed paper. However, the original transmission line model of the transformer windings often ignore the frequency-dependent characteristics of the permittivity of oil-paper and the skin effect, which influence the calculation of transient overvoltage distribution.Supported by National Natural Science Foundation of China under grant NO.51177048, research on the methods of passive broadband modeling for key equipment of substation, the fractional transmission line model of oil-immersed transformer windings are studied in this paper. In the paper, the measured complex permittivity of oil-immersed paper samples are fitted based on the dielectric model with two dielectric relaxation processes, the required simplified model is obtained by comparing several kinds of fitting models.Combined the simplified model with the capacitance formula of parallel plate and finite element software, the frequency-dependent parameter matrix of the fractional transmission line model is derived, based on the integer order transmission line equation of transformer windings, the fractional frequency and admittance parameters matrix are introduced.Then the fractional transmission line model of the transformer windings is established. By combining the time domain solution method of the integer order transmission line equation with fractional order differential terms under the Caputo definition, the fractional transmission line equation is discretized in time domain.Through the simulation of the fractional transmission line model of a practical continuous windings, the overvoltage waveform on the windings are obtained, at the same time, compared it with the experimental waveform and the simulation waveform of the transmission line model without considering the frequency-dependent parameters, the results confirm the validity of the fractional model.