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• It concludes that the compensation circuit for HWTL is a low-pass passive filter. • The suitable type and the proper order for half-wavelength transmission lines is analyzed. • The voltage distribution is simulated to verify the feasibility of the proposed method. • Transient responses of tuned lines are compared to verify the superiority. Compensation circuit, which can increase electrical length, is the most feasible solution for flexible applications of half-wavelength transmission lines (HWTL). In previous studies, it is always assumed that the compensation circuit is structured by passive components with identical parameters to represent the distribution parameter of transmission lines. However, the structure of the traditional compensation circuit is actually equivalent to that of the constant k filter, which concludes that the compensation circuit is fundamentally a low-pass filter. In consideration of basic requirements for tuned HWTL, the Bessel filter, which has smooth group delays without waveform distortion, is selected for the calculation of compensation circuit parameters in this paper. Lastly, the Bessel-based compensation circuit is compared to natural HWTL and tuned HWTL with Butterworth filter-based and traditional compensation circuits. Comprehensive cases simulated by PSCAD are undertaken, which validate that the voltage distribution of Bessel-based compensation circuits is quite similar to that of traditional compensation circuits. Moreover, electromagnetic transients can induce significant high-frequency oscillations in tuned HWTL with traditional compensation circuits, but high-frequency oscillation is significantly reduced by Bessel-based compensation circuits. Therefore, the Bessel-based compensation circuit is verified to be a better solution for tuned HWTL. [ABSTRACT FROM AUTHOR]

• Different circuits are compared to identify the most suitable compensation circuit. • The compensation circuit is designed in the modal system. • Capacitance of the compensation circuit are simplified as the shunt reactor. • The designed compensation circuits are compared with the natural HWTL. The compensation circuits are the core to improve the flexibility of practical application of half-wavelength transmission lines (HWTL), which are restricted to the fixed transmission length due to the constant fundamental frequency. This paper proposes a mode-phase transformation based method to design the parameters of compensation circuits after comparison of frequency responses of three kinds of compensation circuits, e.g., T segments, Π segments and L segments. At first, the compensation circuit parameters are obtained in the modal system that separates the coupling multiconductor system into isolated circuits to avoid the complexity of the three-phase system. Then, the compensation circuit parameters can be transformed into multiconductor system by modal-phase transformation, which accomplishes the compensation circuit parameter design in three-phase system. Lastly, the parameters acquired by the proposed method are compared with the natural HWTL. Comprehensive simulations are undertaken which validate that the proposed method is more suitable for tuning HWTL. [ABSTRACT FROM AUTHOR]