The performance of existing protection methods for multi-terminal direct current systems depends on the availability and sizes of boundary components. To overcome the limitation, this paper proposes a non-unit DC line protection method based on the normalized backward traveling waves (BTWs) of the 1-mode voltage. Firstly, traveling wave propagation characteristics are analyzed, and a rationalization approach based on vector fitting is proposed. Next, the analytical expressions of normalized BTWs are derived, with the negative correlation between them and fault distance proved. Then, the derivative-free conjugate gradient algorithm is utilized for amplitude fitting and normalization calculation. Finally, a non-unit protection method using the normalized BTWs is developed. The performance is validated for both electromagnetic transient PSCAD/EMTDC and real-time digital RSCAD/RTDS simulation. The results demonstrate that the proposed method can accurately identify faults with various fault resistances and locations without requiring boundary components and high sampling frequencies, and it is robust against noise disturbances.

The existing protection techniques for high-voltage direct-current (HVDC) grids suffer from several shortcomings such as high sampling frequency, poor robustness, and reliance on simulation for threshold setting. To solve these problems, this paper proposes a non-unit protection method for modular multilevel converter (MMC)-based HVDC grids using the curvatures of backward traveling waves. To this end, the propagation characteristics of traveling waves and the boundary characteristics of DC lines are first studied, then the analytical expressions of backward traveling waves are derived. Moreover, the curvatures of backward traveling waves are analyzed. On this basis, a non-unit protection method is proposed, including zone selection, disturbance identification, and pole selection. At last, with a protection platform and a real-time digital simulator (RTDS) platform of the MMC-HVDC grid, the accuracy and the robustness of the proposed protection method are verified. The results show that the protection method can correctly identify faults with different distances and resistance in 1 ms and has strong robustness against transition resistance, sampling frequency, boundary value, noise, system topology, and line parameters.