# Fault Location Method of Multi-Terminal Transmission Line Based on Fault Branch Judgment Matrix
###### Abstract  
Aiming at the difficulty of fault location of multi-source transmission lines, this paper proposes a fault location method for multi-terminal transmission lines based on a fault branch judgment matrix. The fault traveling wave signal is decomposed by Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and the IMFs sensitive components that can characterize the fault characteristics of the target signals are selected by constructing a correlation-rearrangement entropy function. The arrival time of fault signals at the endpoint has been accurately calibrated by combining them with the Teager Energy Operator (TEO). To eliminate the influence of wave velocity and fault time on the location results, this paper proposes a two-terminal location method based on the line mode component to improve the location accuracy. On this basis, combined with the fault branch judgment matrix, the accurate location of multi-terminal transmission line faults is realized. This method has been shown to have high accuracy in detecting traveling wave heads, accurately judging fault branches, and producing a small error in fault location results. Compared with the existing multi-terminal transmission line fault location algorithm, it has obvious advantages and meets the needs of actual working conditions. CEEMDAN; multi-branch grid-connected line; double-ended traveling wave ranging; fault branch judgment matrix +
Footnote †: journal: Applied  
of grounding faults and has significant limitations. [PERSON] et al. propose a fault-locating method based on the natural frequency of traveling waves and VMD (Variational Mode Decomposition), which effectively overcomes the problem of spectrum aliasing [8]. However, the accuracy of line parameters and the attenuation of traveling wave reflection signal has a significant impact on locating accuracy. The structure of multi-terminal transmission lines is complex, with several branches. In the traditional double-ended traveling wave method, fault branches are not determined, resulting in an incorrect location. To address this problem, the traveling wave difference matrix to judge the feeder fault has been developed [9; 10; 11]. This method has good location performance for T-connected lines but cannot be applied to more complex multi-terminal transmission lines. [PERSON] et al. [12] use the multi-terminal traveling wave time difference and the double-terminal traveling wave principle to build a fault branch search matrix and determines the fault branch through the change characteristics of matrix elements. The positioning method has a simple principle and high reliability, but the positioning process is complicated and requires substantial computation. Further, [PERSON] et al. [13] propose a fault location method based on a distance matrix and branch coefficient, which improves the traditional two-ended traveling wave method by using zero-mode components and line-mode components to accurately select fault branches. However, the zero-mode component quickly attenuates in lines and only exists in ground faults, so the location reliability needs to be investigated. To solve the problem of wave speed uncertainty, various studies have employed the mathematical morphology method to filter and denoise the collected fault information and then used the morphological gradient method to perform local feature calculation, which improves the accuracy of traveling wave speed [14; 15; 16]. Moreover, an improved double-ended traveling wave localization algorithm, which eliminates wave speed in the formula, has also been proposed [17; 18]. However, the band method requires an accurate fault occurrence time, which is difficult to determine in practice. A traveling wave detection algorithm based on CEEMDAN-TEO is introduced in this paper in order to reduce the problem of low precision in capturing the wave head. This algorithm improves upon CEEMDAN in terms of both its algorithm and principles, solving the problem of mode confusion.