Binary Tree Algorithm-based Fault Location Method for Tripping in Ultra-high Voltage Substations

The current conventional method for fault location in substations involves using a mathematical model to convert the problem into a parameter identification problem. However, this approach often yields poor results due to the lack of characterization of fault features. To address this, a new fault location method for tripping faults in Extra High Voltage (EHV) substations is proposed. This method utilizes a binary tree algorithm to construct a fault binary tree and encode the nodes to accurately characterize the fault characteristics. Using this information, a fault location model is developed. Experimental verification confirms the effectiveness of the proposed method, with analysis showing its ability to successfully locate tripping faults in EHV substations with high convergence and superior accuracy.


Introduction
For the fault location of tripping equipment in EHV (Extra High Voltage) substations, initially, a single piece of information was used, for example, the fault location of relay protection secondary circuits can be performed through SCD (Full title: Science Citation Database) files.The advantage of this method is simple and easy to operate, but in the actual environment, the SCD files of intelligent substations are basically not standardized, and the configuration tools of manufacturers and integrators greatly affect the working mode of intelligent substations.The recommended topology covers a variety of composition schemes, such as "direct hopping and direct picking", "network hopping and network picking", and "direct hopping and network picking".Therefore, the method of locating faults only by SCD file is not portable [1][2][3] .The advantage of this method is that it can quickly locate the fault interval, but there are many types of secondary devices in the fault interval, so it is still necessary to rely on other methods to determine the specific fault device.
Since then, some scholars have begun to study multiple information fusion methods, such as analyzing the corresponding relationship between specific communication links and secondary devices based on network partitioning and extracting some key messages to identify the operation of relay protection secondary circuits [4] .This method adds message information from other secondary devices based on fault secondary device self-inspection information, thereby improving the accuracy of secondary device fault location.However, the disadvantage is that the number of key messages extracted is limited, and only some typical fault ranges can be identified.Other fault location methods combine variable weight theory, analytic hierarchy process, and trapezoidal cloud model to establish state assessment models for most secondary equipment in intelligent substations.In addition, other fault location methods consider the correlation between historical fault data and real-time self-inspection information of secondary equipment and propose trend evaluation strategies to evaluate equipment operation based on data comparison results.However, when historical data is lost or new fault types appear, the obtained results will have significant deviations.In addition, it should be noted that although the above traditional methods consider the idea of using multiple information fusion analysis in the process of secondary equipment fault location, there are still issues such as the subjectivity of weight selection.Therefore, a binary tree algorithm-based trip fault location method for ultra-high voltage substations is proposed to achieve rapid fault diagnosis.

Faulty binary tree creation
After a detailed understanding of the working principle of an ultra-high voltage substation, the fault phenomenon of abnormal trip signal output waveform is taken as an example, and the binary tree example of abnormal trip signal output waveform fault shown in Figure 1 is obtained according to the above construction method.When dealing with binary tree sets by arrays or chained tables, node storage is complicated to retrieve and locate.To effectively solve this problem, different from the left and right value encoding methods of fault binomial tree nodes, this paper proposes a new fault binomial tree node encoding method.In other words, the encoding value of the first parent node is set to 1 without considering the root node.For the child node, if it is the left child node of a parent node, 1 is added to its parent node encoding value as its encoding value; if it is the right child node of a parent node, 2 is added to its parent node encoding value as its encoding value [5] .The fault binary tree node coding method makes each node of the fault binary tree correspond to its coding value, which is beneficial to the fault information storage and node location, as well as to the software programming design implementation.

Characterization of tripping faults in ultra-high voltage substations
Based on the previous analysis, we can accurately describe the fault state of the communication network in an Extra High Voltage (EHV) substation during a tripping fault.This description is achieved by utilizing the alarm signals from various monitoring nodes, as indicated by the equation below.
In the equation, i X represents the feature set of fault events, including a subset of abnormal state alarm information based on signaling Di X and a subset of abnormal state alarm information based on switches Mi X , N representing the total number of fault events [6][7] .The subset of abnormal state alarm information based on signaling integrates the operational status of typical equipment in the secondary system: where k and m represent the total number of components, _ MU k X denotes the status information of the th merging unit, k represents the device abnormality alarm, and STE A signifies the abnormality alarm information received by message a1.When a fault occurs, the background monitoring detects the feature information, setting the corresponding location element to 1 if detected, and 0 otherwise [8] .The subset X M , which comprises the abnormal state alarm information, is obtained by combining the operation status of all switches in the secondary system and the traffic status of messages received by each port.The expression for this subset is as follows:  

W S S S S A P P P P
where the parameter c S denotes the state of the switch.In real-world operations, if the traffic of the k th message passing through port j is below a certain threshold, the monitoring node of the switch will raise an alarm for abnormal message traffic.When the switch S undergoes self-testing and detects abnormalities, the monitoring node triggers an alarm for the device.In this case, Q is set to 1; otherwise, it is set to 0 [9][10] .By following the mentioned procedure, the tripping fault characteristics of an Extra High Voltage (EHV) substation can be effectively identified and characterized.

Construction of the EHV substation tripping fault location model
The conversion function of the Min-Max method is shown in Equation ( 4).This method performs a linear transformation of the original data, mapping an original value It is assumed that the hidden state of the substation trip at time t is h , and the relationship between h and the input t X at that time and the hidden state   where  represents the activation function, and W and n are network parameters.The final prediction output t Y is as follows: ( ) where the activation function  uses the softmax function, and V and c are network parameters.
The performance of the current model can be evaluated by measuring the mean square error (MSE) between the target output y and the predicted output t Y at a given time t .This MSE serves as the loss function M , providing a quantitative measure for assessing the effectiveness of the model.
To overcome the limitation of a fixed learning rate in the iterative process of traditional gradient descent methods, this study integrates the Adam algorithm and exponential decay algorithm to dynamically adjust the learning rate.This enhancement accelerates the convergence of the model.Consequently, the updated equation for the parameter B is as follows: where t g represents the gradient of the network parameter  ,   denotes the computed gradient sign, t m signifies the exponential shift value of the corrected gradient,  represents the exponential decay rate for the shift value,  stands for the learning rate correction value, 0  represents the initial value of the learning rate, E denotes the training number, and B represents the batch parameter.The specific process for locating tripping faults in ultra-high voltage substations is as follows: Input denotes characteristic information set of communication network fault status, and output denotes trip fault location result of ultra-high voltage substation.
Step 1: A discrimination process is used to activate the fault positioning module, aiming to reduce the impact of inaccurate information.This process is triggered when the total number of detected feature information exceeds a predetermined threshold.The threshold value is determined based on the minimum recorded total number of feature information from previous fault occurrences.
Step 2: The feature information and sampling values from the secondary equipment fault are retrieved and represented as the feature set for the fault section.
Step 3: The obtained feature collection is then inputted into the trained substation tripping fault location model to obtain the fault location results.

Test preparation
Two groups of traditional fault location methods are selected for comparison in this experiment: the genetic algorithm-based substation fault location method and the particle swarm optimization algorithm-based substation fault location method.
A simulation experiment system was established by using Matlab software.The system consists of an RT-LAB real-time simulator with a model of OP5600, a DSP processor with a model of TMS320F28335, and a host computer.The following table shows some simulation parameters in the corresponding terminal system.In the genetic algorithm, the search dimension for the population parameter is set to 4 as there are 4 parameters to determine.These parameter values range from 0 to 1.The unit length line route value is multiplied by the total field length of the line.Typically, the size is recommended to be 5 to 10 times the dimension.However, in consideration of the high-speed requirements of the fault location algorithm, a population size of 20 is chosen.Additionally, when sampling the voltage after a fault occurs, it is important to consider 22 points.

Results
In this test, the convergence of the algorithm serves as the evaluation criterion to assess the effectiveness of different fault location methods.By examining and comparing the convergence speeds across various iteration numbers, the experimental results provide visual evidence of the findings.Please refer to the accompanying figure for a graphical representation of the specific results.Based on the experimental results, it is evident that different fault location algorithms show different convergence effects based on various iteration settings.The analysis of convergence curves highlights the significantly superior performance of the proposed fault location method, which utilizes the binary tree algorithm for tripping faults in EHV substations.This indicates that the proposed method surpasses traditional fault location methods in terms of accuracy and precision.

Conclusion
The proposed fault location method for tripping faults in EHV substations, based on a binary tree algorithm, significantly improves accuracy.This model constructs fault binary trees and encodes fault nodes, resulting in fast convergence and reliable detection of substation operations.Future research should focus on enhancing the model's robustness and resistance to information errors during sampling, ensuring reliable performance in the presence of interference.

Figure 1 .
Figure 1.Binary tree structure diagram of abnormal faults of the trip signal output waveform and minimum values in the dataset, respectively.

1 th
 at the previous time is shown in the following equation.