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Background: A novel fault location method of HVDC transmission line based on a concentric relaxation principle is proposed in this paper. Methods: Due to the different position of fault, the instantaneous energy measured from rectifier and inverter are different, and the ratio k between them is the relationship to the fault location d. Through the analysis of amplitude-frequency characteristics, we found that the wave attenuation characteristic of low frequency in the traveling wave is stable, and the amplitude of energy is larger, so we get the instantaneous energy ratio by using the low-frequency data. By using the method of wavelet packet decomposition, the voltage traveling wave signal was decomposed. Results: Finally, calculate the value k. By using the data fitting, the relative function of k and d can be got, that is the fault location function. Conclusion: After an exhaustive evaluation process considering different fault locations, fault resistances, and noise on the unipolar DC transmission system, four-machine two-area AC/DC parallel system, and an actual complex grid, the method presented here showed a very accurate and robust behavior.

The grid connection of wind farms affects the load flow of a power system and may introduce an unexpected threat to the power system small signal stability. This study presents an application of probabilistic eigenvalue sensitivity indices (PSIs) for optimal allocation of wind farm in a power system. For this purpose, firstly, probabilistic sensitivity indices are used to identify the strongly correlated electromechanical eigenvalues of generators and to facilitate the wind farm site selection. Two different cases are studied, wind farm replacing synchronous generators or being directly added to the power system. Afterwards, the influence of the wind farm location on power system small signal stability is examined. For this purpose, an index is proposed to measure the small signal stability of the system and is used for optimal allocation of the wind farm. Two examples, i.e. a 3-machine 9-bus and an 8-machine 24-bus power system, with a wind farm integrated based on PSIs are presented to demonstrate the proposed approach by employing the eigenvalue analysis and a dynamic time-domain simulation. Finally, the results are compared with the traditional optimal allocation of a wind farm for power loss reduction.