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• 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]