Study on the Power-Frequency Waves Distribution Characteristics for Half-Wavelength Transmission Lines Based on the Frequency-Length Factor

To analyze the distribution characteristics of voltage and current along half-wavelength transmission lines (HWTLs) in the cases with or without short circuit in the steady state, the method based on the frequency-length factor (FLF) for lossy lines is proposed. Firstly, according to the pole condition of the FLF, the distribution characteristics of power-frequency waves along HWTLs are analyzed. Then, the comprehensive effects of the system parameters and fault resistance are explored, revealing the mechanism of the power-frequency resonance caused by nonmetallic short circuit. Meanwhile, unbalanced short-circuit fault is studied by exploiting additional impedance. The results show that the distribution of the maximum value of power-frequency resonance voltage is related to the system parameters but not to the fault impedance. When a HWTL is short circuited at 2640 km∼2930 km, the resonance voltage can reach to 21 p.u. In relation to symmetrical short circuit, the resonance voltage appears at 1469 km from the short-circuit point, while the position moves towards the short-circuit point with the increase of additional impedance in asymmetrical short-circuit conditions. Additionally, the model theoretically proves that the power-frequency overvoltage induced by short circuit does not appear on a line whose length is less than 1469 km. Finally, cases are studied on PSCAD to verify the accuracy of the model.