| Transmission lines are the important pats of power system to connect the power plants, the substations and the users. The faults of transmission lines and other electrical equipment caused by lightning strikes are deeply threatening the safe and reliable operation of the power network. So, it has important academic significance and engineering application value to establish a reasonable overhead lines model and calculate the lightning overvoltage accurately. According to the research, due to the frequency-dependent property of the wire parameters and the effect of shock corona, the lightning wave may be attenuated and distorted during the process of the propagation along the transmission lines. Skin effect in wire and the loss of soil are the main factors that lead to the overhead line parameters change with frequency. Based on the theory of fractional calculus, considering the skin effect of wire, the frequency dependent characters of soil and the effect of corona, this text established a more reasonable and concise overhead line model, and complete the research of lightning overvoltage numerical calculation. The soil impedance has been fitted by the method of vector fitting fractional system identification and particle swarm optimization. After simplifying the fitting results, we get the fraction model of frequency dependent overhead transmission line. Also, a new time domain method is presented. We improve the traditional method of FDTD, and derive the new recursion formulas and boundary conditions to solve the fractional model. On the basis of this, considering the influence of corona, we get the fractional order nonlinear model of overhead transmission lines and implemented the lightning overvoltage calculation by improving the former fractional model and its numerical method. At last an experimental example is presented to verify the correctness and effectiveness of the fractional transient calculation method. |
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