Research on Grounding Grid Corrosion Diagnosis Based on Genetic K‐Means Algorithm

Abstract

ABSTRACT

Grounding grid corrosion is one of the main reasons that affect the stable operation of electrical equipment in substations and endanger personal safety. After many years of operation, the grounding conductors will be eroded by soil. It may even cause major accidents and economic losses. Therefore, it is of great significance to diagnose the corrosion faults of the grounding grid and find out the corroded conductors. In this paper, the genetic K‐means algorithm (GKA) is proposed to solve the mathematical model and judge the corrosion of grounding conductors. This algorithm combines GA's global searching ability and K‐means's local searching ability, which improves the diagnosis result. In the simulation experiment, compared with the single GA's diagnosis, the diagnosis results of GKA were improved, and the number of misdiagnosed branches decreased by 66.7%. The simulation results show that the proposed algorithm takes less time to run, can eliminate the misdiagnosed branches commendably, and improve the accuracy of diagnosis. The proposed method provides a new idea to evaluate the corrosion degree of the grounding grid. The clustering algorithm is used to classify branches with similar corrosion degrees to achieve the purpose of corrosion diagnosis.

Introduction

To ensure the safe operation of the power system and the personal safety of the staff, it is necessary to connect the equipment of the power system with the earth to provide discharge channels for fault current and lightening strike current [1]. Carbon steel and galvanized steel are widely used as the grounding conductor material in China; they are susceptible to factors such as acid and alkali in the soil, resulting in varying degrees of corrosion [2]. The main factors that lead to soil corrosion are the physical and chemical properties of soil, stray current, and climatic conditions, among which the physical and chemical properties of soil include moisture content, oxygen content, resistivity, soluble salt, pH value, and so on [3]. After corrosion, the conductor cross-sectional area becomes smaller, the thermal stability worsens, and the resistance value becomes larger. Severely corroded conductors will even break, which is not conducive to the evacuation of fault current and is very likely to endanger the stable operation of the power system [4]. When grounding conductors fault occurs in the power system, the fault current cannot be fully diffused into the soil. Under this condition, the grounding resistance and grounding potential increase, and the high voltage is connected to the secondary loop, which affects the stable operation of the electrical equipment, and even leads to the tripping of the substation. If the grounding of the equipment fails, when the insulation of the equipment is damaged, the live part may form a loop through the human body or other conductors, resulting in an electric shock accident. The fault of the grounding grid can easily lead to the shutdown of high-voltage substations, resulting in power grid outage, and then affect people's daily life, industrial production, transportation, and other aspects.

Therefore, it is crucial to evaluate the operation status of the grounding grid regularly, promptly identify problems, and take solutions for the maintenance of the grounding grid. In the research of grounding grids, foreign scholars usually study the grounding performance and optimal design of grounding grid [5–8]. Since the corrosion of the grounding grid of the old substation is common in China [3], most Chinese scholars focus on the study of corrosion diagnosis.

The research methods for grounding grid corrosion diagnosis mainly include the electromagnetic field method [9–11], electrochemical method [12], and electrical network method [13]. The electromagnetic field method does not require the grounding grid laying drawings, but it is susceptible to the interference of the substation magnetic field environment and requires the excitation power injection current to be large enough. The electrochemical method is relatively simple to operate, and the detection results can directly reflect the corrosion rate of the grounding conductor, but it can not diagnose the local breakpoint and corrosion degree. The diagnosis principle of the electrical network method is relatively simple, and this method can not reveal the mechanism of corrosion, but it can diagnose local breakpoints and detect the degree of corrosion, which is a relatively mature method with fruitful results.

In recent years, some emerging technologies have been applied to corrosion detection, such as ultrasonic detection [14], electromagnetic pulse time difference positioning [15], electromagnetic imaging [16], video image Recognition [17], Electrical impedance tomography technology [18], etc. Nevertheless, in the actual application and production practice of the current technology environment application, their application development is not mature enough, and they have more or less limitations.

At present, most of the research on corrosion diagnosis is based on the theory of electrical network, the grounding grid is equivalent to the pure resistance network, so as to establish the corrosion diagnosis equations. They focused on improving the optimization algorithm to solve the nonlinear and underdetermined corrosion diagnosis equations and approximated the most accurate solution set to obtain the diagnosis result but did not further combine the solution set of the equations with other fault information for secondary diagnosis to eliminate the pseudo-fault branch. If more fault information can be used, the misdiagnosis rate of the branch can be reduced to optimize the corrosion diagnosis result.

The genetic algorithm (GA) is a probability-based group search method, which has the characteristics of strong global search ability, high search efficiency, and parallel computation. In recent years, the development of GA has been relatively mature, and it has been widely used in power supply planning, reactive power optimization of power systems, transmission network planning, and other aspects [19–21]. Cluster analysis is an unsupervised learning process, which means that things are grouped into classes according to certain attributes, to minimize the similarity between clusters and maximize the similarity within clusters, so as to realize the classification of data [22]. The K-means algorithm is a basic partitioning method in cluster analysis. It is widely used because of its simple algorithm, reliable theory, fast convergence speed, and effective processing of large data [23]. By combining the above two algorithms and making full use of their respective advantages, the corrosion diagnosis model can be solved better, so as to improve the diagnosis results.

Aiming at the problem of grounding grid corrosion diagnosis, this paper combines GA and K-means algorithm to propose genetic K-means algorithm (GKA) for diagnosing grounding grid corrosion. The minimum value of the residual sum of squares between the calculated and measured node voltage is taken as the target, the hybrid algorithm first uses GA to search globally in the distribution space of the change multiple of branch current to obtain corrosion frequency and the optimal multiple of change in branch resistance, and then calculates the change multiple of branch current. Then, the above three-dimensional data (the change multiple of branch resistance, corrosion frequency, and the change multiple of branch current) are output to the K-means algorithm as the initial value. Then, the K-means algorithm is used for fast clustering. According to the final clustering results, the corrosion degree of the branch of the grounding grid can be judged.

The proposed method provides a new idea to evaluate the corrosion degree of the grounding grid. After presetting the corrosion degree level, the global optimization algorithm is used to solve the corrosion diagnosis equations, and then the change multiple of branch current is introduced as one of the corrosion characteristics information. Finally, the clustering algorithm is used to classify branches with similar corrosion degrees to achieve the purpose of corrosion diagnosis (classification).

ATP-Draw is a software for creating and editing interactive simulation models of power grids. It supports a variety of standard components and objects that users can use to construct grounding grid models to simulate actual grounding grid parameters and operation. By setting a simulated corrosion branch, the user can obtain the fault characteristics of the grounding grid after corrosion by using the components provided by the simulation platform. It is helpful for users to deeply study and analyze the corrosion fault of grounding grid without disturbing the operation of actual power system. In this paper, ATP-Draw software is used to build a grounding grid model to simulate the increase of grounding conductor resistance after corrosion.

The rest of this paper is organized as follows. The recent work related to grounding grid corrosion diagnosis is summarized in Section 2. The corrosion diagnosis model of grounding grid is established in Section 3. The proposed hybrid algorithm is depicted in Section 4. The feasibility and effectiveness of the Genetic K-means algorithm are verified in Section 5 through simulation. Finally, the conclusion is given in Section 6.

Related Work

To guarantee the safe operation of electrical equipment and personal safety, and get rid of major accidents and economic losses, some scholars propose different kinds of methods. These methods include electromagnetic field methods, electrochemical methods, electrical network methods, and some emerging technologies.

Combining the principle of electromagnetic induction and Internet of Things technology, Wang et al. [24] designed a noncontact ground gate corrosion detection and positioning system, which can be applied to the topology identification, regular detection, and real-time online monitoring of ground grid conductors. However, the accuracy, applicability, and deployment flexibility of the system need to be further studied.

Based on the electromagnetic field theory, Zhou et al. [25] proposed the vertical observation line waveform difference algorithm (WDA-uVOL) to diagnose corroded conductors in grounding grids. However, this method requires the substation to measure the magnetic induction strength of the ground gate in good condition in advance and compare it with the magnetic induction strength in the corroded state. In other words, this method is only applicable to newly built substations and has little significance for existing substations.

Wang et al. [26] proposed a fault diagnosis method based on surface potential and magnetic field distribution, the method is carried out by adding heterodyne excitation current to the grounding grid and detecting the potential and magnetic field distribution generated on the surface. In fact, the electromagnetic interference of multi-station fusion is very complex, and effective measures need to be taken to avoid these interferences.

On the basis of electrochemical detection technology, Gao et al. [27] developed a grounding grid intelligent detection device with Android software as the core. It can accurately and efficiently measure the electrochemical parameters of the grounding grid and calculate the corrosion rate and corrosion depth. However, the device needs to further improve the equivalent circuit model of the sensor to more realistically simulate the corrosion of the grounding conductors in soil.

Shou et al. [28] proposed a non-destructive testing system and method for grounding grid conductors. A certain frequency and signal emission system is injected into the grounding grid. The signal-receiving system of the remote-controlled unmanned aerial vehicle carries a signal acquisition device to quickly cruise on the ground for detection and data collection and transmits the status of the grounding grid to the terminal upper computer system, so as to evaluate the safety performance of the grounding grid. This method has a high requirement on the design performance of the system hardware.

Long et al. [29] proposed a frequency scanning method, that is, the frequency scanning impedance and amplitude frequency response testing technology of the grounding grid. In this method, the excitation current and response voltage waveforms obtained from multi-channel high-frequency sampling are used to analyze the frequency sweep impedance and amplitude frequency response curves. From the correlation coefficient analysis results, it can be seen that the sweeping voltage waveform and amplitude-frequency response curve when the conductor is broken are slightly different from those without defects. The diagnostic effect is not obvious.

According to the electrical network theory method, Yang et al. [30] proposed a cycle voltage measurement method and L-curve regularization method to locate the faults in grounding grids. The measurement method can be applied without shutting the power down, which is appropriate for evaluating grounding grids. The L-curve method was used to select the appropriate regularization parameter, which can effectively balance the error and stability of the solution to the inverse problem.

Dong et al. [31] proposed a diagnosis method for grounding network corrosion based on branch voltage disturbance. They analyzed the sensitivity of the grounding grid branch voltage to the branch resistance, established the corresponding law between the peak voltage disturbance and the corrosion state of the branch, and judged the location and degree of corrosion by the branch voltage disturbance before and after corrosion. The corrosion characteristic information used in this method is relatively single.

Duan et al. [32] designed a ground grid corrosion detection device and corresponding measurement method based on the measurement principle of power grid theory. The location of the corrosion fault is finally completed by combining the strategy of area measurement and multiple approximate measurements. In the actual field measurement, the wiring process takes up most of the working time. It is necessary to further optimize the wiring mode and reduce the workload in the early wiring process.

For the electric network method, most scholars focus on the algorithm to solve the equation, but the equation is nonlinear, and almost can not find the exact solution. They rarely combine other fault information with a secondary diagnosis. If the solution set of the diagnostic equations is combined with other corrosion information for secondary diagnosis, more pseudo-fault branches can be eliminated and the accuracy of corrosion diagnosis can be improved.

Corrosion Diagnosis Model of Grounding Grid Based on Electrical Network Theory

Establishment of Diagnostic Equations for Grounding Grid Corrosion

The grounding grid buried underground is mainly composed of horizontal uniform conductor, which connects to each other to form a circuit network. The equivalent pure resistance network of the grounding grid is shown in Figure 1. The resistivity of soil is much larger than that of the grounding grid conductor. When constant DC excitation is added to the port between the downleads of the grounding grid, the influence of capacitance, inductance and soil is ignored, and the grounding grid can be regarded as a pure resistance network, so the corrosion diagnosis model can be established based on the electric network theory. Every conductor of the network is a branch, and every cross point of these conductors is a node. Furthermore, the points connecting the down-lead conductors and the network are considered as accessible nodes. Assume that the grounding grid has n nodes, b branches, and m accessible nodes. According to the circuit principle, the grounding network can be regarded as an N -terminal component, and the port voltage can be measured through the accessible nodes.

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First, the relationship between the port voltage and the branch resistance is established, and then the actual value of the branch resistance is obtained by solving the diagnostic equation. Finally, the corrosion of the branch is judged by comparing the actual value and the original value of the branch resistance.

Accessible nodes i and j are selected to apply DC excitation. The excitation current is I₀, which is injected by node i and discharged by node j. The potential reference point of the network is N. Among the remaining N − 1 accessible nodes, k nodes are selected to measure the node potential. The measured value of its potential is as follows: 1${\mathbf{V}}_{\mathbf{m}}=[V_{\mathrm{m}1},V_{\mathit{m}\mathit{2}},\text{…},V_{\mathit{\text{mk}}}].$

Assume that the actual values of each branch conductor resistance are as follows: 2${\mathbf{R}}_{\mathbf{b}}=[R_1,R_2,\text{…},R_{\mathit{b}}].$

According to the electrical network theory, N − 1 node potential except the reference node N can be calculated by Equations (3) and (4): 3$U_{\mathit{n}}=Y^{-1}\times I_{\mathit{n}}$ 4$Y_{\mathit{n}}=A\times \text{diag}(R-1\mathrm{b})\times A^{\mathrm{T}}\mathit{,}$where U_n is the node voltage column vector, Y_n is node admittance matrix, I_n is the column vector of node injection current, A is the reduced order correlation matrix.

Then, k calculated potential values corresponding to measured nodal voltage are selected from U_n to ich is called the calculated nodal voltage column vector, as shown in Equation (5). 5${\mathbf{V}}_{\mathbf{c}}=[V_{c1},V_{c2},\text{…},V_{\mathit{\text{ck}}}].$

The fitness function f₁ is established by the least square method as follows: 6$f_1={(V_{\mathit{m}}-V_{\mathit{c}})}^2.$

In fact, the number of nodes accessible to the grounding grid is relatively limited, so the position of DC excitation can be rotated (i.e., the position of the current injection point can be changed), and finally the total fitness function F can be obtained, as shown in Equation (7). 7$F=\sum _{i=1}^t{f}_i,$where t is the number of times that the DC excitation injection position is changed. The smaller the value of function F of the individual in the population, the more adaptive the individual will be.

Assume that the branch voltage of the grounding conductor remains constant before and after corrosion, that is, 8$I\mathit{\times }R\mathit{=}I\prime \mathit{\times }R\prime ,$where I and I^′ represent the branch current before and after the fault, respectively, R and R^′ represent the branch resistance before and after the fault, respectively.

Define the change multiple of branch resistance as R_m and the change multiple of branch current as I_m, as shown in Equations (9) and (10). 9$R_{\mathit{m}}=R\prime /R,$ 10$I_{\mathit{m}}=I\prime /\mathit{I}=R/R\prime =1/R_{\mathit{m}}\mathit{.}$

Solution of Diagnostic Equations for Grounding Grid Corrosion

In the actual grounding grid of the substation, if the resistance value of the branch is selected as the optimization variable of GA for calculation, the boundary of the variable will be difficult to determine due to the large difference in the resistance value of each conductor in the grounding grid, which will affect the convergence of the algorithm and optimization results. If the change multiple of each branch resistance is taken as the optimization variable of GA, the solution space can be easily determined.

After corrosion, the resistance value of the grounding conductor will increase, so the change multiple of branch resistance must be more than 1. Meanwhile, the resistance of each branch will not change remarkably and the change multiple of branch resistance is less than 2 generally. The larger the resistance increases, the more serious the corrosion is. If the change multiple of branch resistance is more than 2, it can be considered that the conductor has been broken or does not exist.

Therefore, the change multiple of branch resistance is taken as the optimization variable of GA, and the solution space of the variable is determined as [1, 2], which is convenient for GA's optimization. GA is a random adaptive global search algorithm that simulates the process of biological evolution in nature, which cannot calculate the exact value. Therefore, the calculated resistance value is set to increase by 1.1 times for the noncorrosive branch. On the other hand, the increase times of calculated resistance value of the severely corroded branch and the slightly corroded branch are 1.8 and 1.3, respectively.

GKA is composed of random algorithm and deterministic algorithm. The error of the result obtained by one or two operations is large, so it needs to be run multiple times to obtain the average value to reduce the error. In the case of 10 times of operation, the corrosion times of severe corrosion, slight corrosion, and no corrosion are set to 9, 7, and 5, respectively.

After running GA many times, the corrosion frequency (the branch with R_m > 1.1 is regarded as a corroded branch) and the average change multiple of branch resistance (R_m) can be obtained. Meanwhile, the average change multiple of branch current (I_m) can be calculated from Equation (10). Then, the 3D (R_m, corrosion frequency, I_m) data is taken as the initial data set of K-means algorithm for clustering, and the pseudo-corrosion branches are further eliminated, so as to find out the real corrosion branches. In particular, the value of k is set to 3, which are three types: no corrosion, mild corrosion, and severe corrosion.

Analysis of Genetic K-Means Algorithm for Grounding Grid Corrosion Diagnosis

GA

The working mode of the GA is derived from biology. It is a computational model of the biological evolution process simulating natural selection and the genetic mechanism of Darwinian biological evolution. It is a method to search for optimal solutions by simulating the natural evolution process. Its advantage is that it has good global search ability, it is not easy to fall into the local optimal solution, and there is potential parallelism in the search process. The mathematical model of the GA can be expressed as Equation (11). 11$\text{GA}=(\mathit{P},S,V,F,\text{Cr},\text{Mu}),$where P represents the initial population; S stands for the population size; V represents the number of variables; F is the fitness evaluation function; Se represents the selection operator; Cr represents the crossover operator; Mu represents the mutation operator.

The application of GA in grounding grid corrosion diagnosis is mainly reflected in its ability of global optimization and adaptive adjustment of search direction. In the grounding grid corrosion diagnosis, GA can be used to search the solution set of corrosion detection model or to search the optimal corrosion fault diagnosis strategy. Through the iterative process of GA, the real corrosion situation can be approximated constantly, which indirectly reflects the actual amplitude changes of current and resistance in the grounding grid.

The GA is used for the global search of corrosion diagnosis. Namely, in the feasible region of branch resistance distribution, a large number of resistance distribution vectors are randomly generated as population individuals to form the initial population. The individuals in the initial population were mutated and crossed to obtain the experimental population. Then, the better individuals of the population, that is, the individuals with the smaller objective function, are selected from the initial population and the test population, and the boundary conditions are processed to form the next-generation population. The above steps are repeated several times until the optimal individual satisfying the convergence condition is obtained as the real distribution of branch resistance, and then the corrosion condition of the grounding grid branch is judged.

K-Means Algorithm

The K-means algorithm is a typical clustering algorithm based on partition, and also an unsupervised learning algorithm. The core idea of the K-means algorithm is as follows: first, k initial clustering centers are randomly selected from the data set; second, the Euclidean distance between the remaining data objects and the clustering center is calculated; third, the clustering center nearest to the target data object is found, and then the data object is allocated to the cluster corresponding to the clustering center. Finally, the average value of data objects in each cluster is calculated as the new clustering center, and the next iteration is carried out until the clustering center no longer changes or the maximum iterations are reached. The Euclidean distance between the data object and the clustering center in the space is calculated as follows: 12$d(X,C_i)=\sqrt{\sum _{\mathrm{j}=1}^m{(X_{\mathrm{i}}-C_{\text{ij}})}^2},$where X is the data object; C_i is the ith clustering center; m is the dimension of the data object; X_j and C_ij are the jth attribute values of X and C_i, respectively.

The formula for calculating the sum of squared errors (SSEs) of the whole data set is: 13$\mathrm{SSE}=\sum _{\mathrm{i}=1}^k{\sum }_{\mathrm{X}\in {\mathrm{C}}_{\mathrm{i}}}{(C_{\mathrm{i}}-X)}^2,$where k is the number of clusters. The smaller the SSE is, the better the clustering result is.

The specific steps of the K-means clustering algorithm are as follows: (1) randomly select k samples as the mean vector of the initial cluster class; (2) divide each sample data set into the closest cluster; (3) update the mean vector of the cluster class according to the cluster to which each sample belongs; (4) repeat steps (2) and (3). When the maximum iterations are reached or the mean vector of the cluster class is no longer changed, the result of the clustering algorithm will be output.

The application of K-means algorithm in the corrosion diagnosis of grounding grid is mainly reflected in the data clustering and analysis. In the grounding grid corrosion diagnosis, a large amount of detection data can be collected, including current, voltage, and other parameters. These data often show certain distribution rules, and K-means algorithm can divide these data into several clusters, each cluster represents a specific corrosion state. By comparing the characteristics of different clusters, the corrosion areas or fault points that may exist in the grounding grid can be identified.

The K-means clustering algorithm is used for local search of corrosion diagnosis. First, according to the corrosion severity of the grounding grid, the initial clustering centers were determined, which were three corrosion degree clustering centers: no corrosion, slight corrosion, and severe corrosion. Second, the Euclidean distance between the initial data object and the three corrosion degree clustering centers is calculated. Third, the clustering center of the corrosion degree nearest to the target data object is found, and the data object is assigned to the corresponding cluster of the clustering center. Finally, the average of the data objects in each cluster is calculated as the new cluster center, and the next iteration is performed until the cluster center no longer changes or the maximum iteration is reached. So as to determine which kind of corrosion degree the grounding conductors belong to.

Genetic K-Means Algorithm

If the advantages of GA and K-means algorithm are organically combined, the problem of grounding grid corrosion diagnosis equations can be better solved. Therefore, a GA-based K-means clustering algorithm, namely, GKA, is proposed in this paper for the corrosion diagnosis of ground grid. The hybrid algorithm is combined in a series manner, and the sum of fitness functions F of the diagnostic equations is used as the objective function of the GA.

The flow chart of the genetic K-means algorithm for corrosion diagnosis of the grounding grid is shown in Figure 2. First, Equation (7) is taken as the objective function, and the global search capability of GA was used to carry out the initial optimization calculation. Then, the calculated results combined with the change multiple of branch current were used as the initial data object of the K-means algorithm for clustering, and branches with different corrosion degrees were distinguished. This serial optimization strategy fully combines GA's excellent global searching ability and K-means's local searching ability and has low computational complexity and fast convergence speed, which improves algorithm performance.

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Simulation Results and Analysis

Simulation Experiment of Grounding Grid Corrosion in 110 kV Substation

To verify the effectiveness of the Genetic K-means algorithm in the corrosion diagnosis of the grounding grid, this paper selects an actual grounding grid of a 110 kV substation in Chongqing, China, for a simulation experiment. As shown in Figure 3, the grounding grid consists of 41 nodes and 61 branches, among which nodes 1, 2, 3, 5, 7, 10, 12, 15, 17, 19, 21, 23, 26, 27, 28, 29, 31, 35, 36, 39, and 41 are accessible. The grounding grid of the 110 kV substation adopts galvanized flat steel as the grounding conductor material, and its reference resistance values of each branch are shown in Table 1.

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Table 1 Reference resistance values of grounding grid.

Branch	Resistance (mΩ)	Branch	Resistance (mΩ)	Branch	Resistance (mΩ)
1	53.6	21	6.2	41	4.8
2	6.2	22	1.9	42	7.2
3	6.2	23	6.7	43	6.7
4	15.8	24	6.7	44	6.7
5	7.2	25	6.2	45	6.7
6	13.4	26	10.5	46	7.2
7	8.1	27	10.5	47	5.3
8	8.6	28	3.8	48	4.8
9	30.6	29	5.3	49	3.8
10	6.2	30	1.4	50	8.1
11	6.2	31	3.8	51	8.6
12	6.2	32	3.8	52	7.2
13	6.2	33	5.3	53	7.2
14	6.2	34	7.2	54	7.2
15	7.2	35	13.4	55	7.2
16	13.4	36	8.1	56	7.2
17	8.1	37	8.6	57	15.8
18	8.6	38	6.7	58	7.2
19	10.5	39	6.7	59	13.4
20	3.4	40	4.3	60	8.1
—	—	—	—	61	8.6

In the actual grounding grid of the substation, corrosion often presents a characteristic of regional concentration, and the corroded area is usually concentrated in the local position with low resistance and easy discharge [3]. Hence, the slightly corroded branches are set to No. 8, 14, and 18, and the severely corroded branches are set to No. 7, 12, 13, and 17. The rules for setting the change multiple of branch resistance: 1.3 indicates slight corrosion and 1.8 indicates severe corrosion.

The simulation software ATP-Draw is applied for building a network model and collecting the port voltage after simulated corrosion. The specific steps of the grounding grid corrosion simulation experiment in ATP-draw are as follows: First, the circuit diagram was drawn in ATP-Draw according to the grounding grid topology in Figure 3, the nominal resistance value was set according to Table 1, and the branches and nodes were numbered. Second, by increasing the resistance value of some grounding conductors in the grounding grid model, the corrosion of the grounding grid in different degrees is simulated. Finally, the injection position of the excitation source is changed several times, and the constant current excitation source is applied between two accessible nodes each time, and the corresponding node port voltage after simulated branch corrosion is measured and recorded.

In the electrical network method, the grounding grid is equivalent to a pure resistance network. Injecting a large current into the grounding grid can amplify the fault characteristics and improve the accuracy and efficiency of diagnosis. 10 A current is a relatively large current in daily life and some industrial production scenarios. In addition, the choice of 10 A as the injection current makes the collected data easier to analyze and compare. Therefore, a DC excitation of 10 A is selected to inject the grounding grid for the simulation experiment.

According to the principles of electric circuits, the grounding grid can be regarded as an N-terminal component, which measures the port voltage through the accessible nodes. The “port” in the grounding grid usually refers to the interface or node used to connect devices or cables in the grounding grid. Based on the theory of electric network, the resistance value between the two ends of the conductor is an important reference to judge whether the branch is corroded, followed by the resistance value between adjacent nodes.

The information containing the resistance value of the corrosion branch will decrease with the increase of the distance between the measurement port and the corrosion point. Theoretically, the data of the port adjacent to the corrosion branch should be selected as far as possible for calculation. However, the location of the corrosion branch is not known during the actual measurement, so it should be divided into blocks and gradually measured to cover the entire grounding grid. For small and medium-sized grounding grids, the preliminary measurement adopts the method of long-span measurement, that is, two nodes (long-span nodes) far apart from each other on the grounding grid are measured. At the same time, combined with the “fixed point” principle, a node is set as a fixed point, and the other node moves from near to far, which improves the measurement efficiency and reduces the workload.

According to the above steps of simulation experiment and the principle of selecting measurement port, four sets of port voltage data are tested, and the test results are shown in Tables 2 and 3.

Table 2 Test results under the condition of 10 A current injection (node 1 injection and node 39 outflow; node 2 injection and node 36 outflow).

Inject into node 1 and out from node 39	Inject into node 2 and out from node 36
Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)
1-2	133.71	39-17	−63.50	2-1	138.36	36-17	−140.62
1-3	46.53	39-21	−49.16	2-3	154.36	36-21	−176.39
1-5	141.48	39-23	−58.23	2-5	125.71	36-23	−136.73
1-7	156.07	39-26	−45.42	2-7	77.08	36-26	−171.56
1-10	149.82	39-27	−39.99	2-10	127.69	36-27	−138.29
1-12	164.76	39-28	−38.34	2-12	86.42	36-28	−139.93
1-15	157.35	39-29	−57.67	2-15	131.59	36-29	−119.05
1-17	159.58	39-31	−41.48	2-17	132.74	36-31	−136.83
1-19	171.63	39-35	−36.41	2-19	92.84	36-35	−163.23
1-21	173.93	39-36	−99.29	2-21	95.81	36-39	−143.76

Table 3 Test results under the condition of 10 A current injection (node 10 injection and node 35 outflow; node 7 injection and node 27 outflow).

Inject into node 10 and out from node 35	Inject into node 7 and out from node 27
Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)
10-1	30.59	35-17	−95.29	7-1	69.58	27-17	−74.25
10-2	55.49	35-21	−34.22	7-2	33.89	27-21	−101.51
10-3	27.71	35-23	−84.22	7-3	73.71	27-23	−68.62
10-5	12.78	35-26	−27.95	7-5	70.65	27-26	−95.85
10-7	53.78	35-27	−62.76	7-10	77.25	27-28	−15.78
10-12	63.60	35-28	−60.94	7-12	45.57	27-29	−61.62
10-15	15.79	35-29	−78.17	7-15	85.28	27-31	−28.86
10-17	20.49	35-31	−64.39	7-17	87.67	27-35	−85.43
10-19	77.69	35-36	−79.02	7-19	56.94	27-36	−71.20
10-21	81.56	35-39	−48.34	7-21	60.42	27-39	−65.32

The test data were input to the GKA diagnostic program, and set the operation parameters as follows: the roulette strategy is adopted as the selection strategy, the coding method is real-coded, the population size is 60, the crossover rate is 0.5, the mutation rate is 0.1, and the number of iterations is 1000; the k value of the clustering is 3, the initial center is C₁(9, 1.8, 1/1.8), C₂(7, 1.3, 1/1.3), and C₃(5, 1.1, 1/1.1), and the number of clustering iterations is 5.

After running the program, the GA's preliminary diagnosis results of the grounding grid in the 110 kV substation are displayed in Table 4, where the value is run 10 times to take the average.

Table 4 The preliminary diagnosis results of grounding grid in 110 kV substation calculated by GA.

Branch	Frequency	Average change multiple	Branch	Frequency	Average change multiple
3	10	1.83	58	6	1.36
57	10	1.79	6	5	1.21
17	9	1.74	19	5	1.29
8	8	1.35	24	5	1.24
12	8	1.52	31	5	1.31
13	8	1.56	42	5	1.22
7	7	1.69	52	5	1.29
18	7	1.44	59	5	1.22
14	6	1.46	60	5	1.34
46	6	1.35	Others	< 5	—

As can be seen from Table 4, there are still many misdiagnosed branches, but there is no case of missed diagnosis. Among them, the occurrence frequency of branches No. 3 and 57 is ten times, and their average change multiple of branch resistance is 1.83 and 1.79, respectively.

The clustering results of the grounding grid in 110 kV substation are shown in Figure 4, where C₁, C₂, and C₃, respectively, represent clustering centers with severe corrosion, slight corrosion, and no corrosion. According to the calculation of Equation (13), the SSE of clustering is about 0.8634, indicating that the clustering result is relatively good.

[IMAGE OMITTED. SEE PDF]

The identification after the number of each branch in Figure 4 represents the type of corrosion. According to Figure 4, the corrosion category of the branch can be determined by judging where the branch is clustered near the cluster center, branches No. 6, 19, 24, 31, 42, 52, 59, and 60 are classified into the non-corrosion category. While branches No. 3, 7, 12, 13, 17, and 57 were classified as severe corrosion, and branches 3 and 57 were misdiagnosed; branches No. 8, 14, 18, 46, and 58 were classified as minor corrosion, and branches 46 and 58 were misdiagnosed.

However, compared with the results of GA's initial diagnosis, eight misdiagnosis branches were eliminated in the secondary diagnosis of clustering, and the pre-set corrosion branches were assigned to corresponding corrosion categories. Misdiagnosed branches No. 3, 46, 57, and 58 are located at the edge of the grounding grid. The reason for misdiagnosis may be that there are few accessible nodes near the branches and sufficient corrosion information cannot be obtained.

It can be seen from Table 4 that GA diagnosed 19 corrosion branches, of which 12 were misjudged as corrosion branches. As can be seen from Figure 4, GKA diagnosed 11 corrosion branches, of which four were misjudged as corrosion branches. Compared with GA, the diagnosis result of GKA reduces eight misjudged branches, so the number of misdiagnosed branches is reduced by 66.7%. The proposed hybrid algorithm has the advantages of simple implementation, short running time, and fast convergence speed. It takes about 220 s for GKA to run a diagnosis, which is acceptable in engineering applications.

Corrosion Diagnosis Experiment of 4 × 4 Simple Grounding Grid

In this subsection, a simple grounding grid model is used to conduct simulated corrosion experiments to verify the global effect of the genetic K-means algorithm in the grounding grid corrosion diagnosis. As shown in Figure 5, the 4 × 4 simple grounding grid contains 25 nodes and 40 branches, among which nodes No. 1, 4, 8, 10, 12, 14, 18, 22, 24, and 25 are accessible nodes. Assume that regional corrosion occurs in the grounding grid, and the grounding conductors in a small grid are corroded. The corroded branches are No. 12, 16, 17, and 21.

[IMAGE OMITTED. SEE PDF]

A large number of field measurement records show that the resistance value of a single horizontal grounding conductor is below tens of milliohm, so the initial resistance of the branches of the simple grounding grid is set to 10 mΩ. To simulate the grounding grid corrosion, the resistance of the corroded branch is set to increase by 1.8 times. According to the network topology in Figure 5, the corresponding pure resistance model of the 4 × 4 simple grounding grid is welded, while the down lead lines are welded and marked at the reachable nodes, as shown in Figure 6. Among them, the healthy grounding conductors and the corroded conductors use non-inductive ceramic vertical resistors of 10 and 18 mΩ, respectively.

[IMAGE OMITTED. SEE PDF]

The experimental steps and port selection principles in this section are the same as those in Section 5.1. For the sake of experimental safety, 2 A DC excitation is used to inject simple grounding grid. After injecting 2 A constant DC source excitation into the accessible nodes, four pairs of nodes are selected for multiple measurements, and 56 groups of port voltage data are collected and recorded in Tables 5 and 6.

Table 5 Physical test results under the condition of 2 A current injection (node 1 injection and node 24 outflow; node 4 injection and node 22 outflow).

Inject into node 1 and out from node 24	Inject into node 4 and out from node 22
Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)
1-4	21.8	24-4	−23.2	4-1	17.4	22-1	−20.3
1-8	20.4	24-8	−23.4	4-8	14.4	22-8	−24.4
1-10	26.7	24-10	−17.9	4-10	11.3	22-10	−28.8
1-12	22.1	24-12	−22.0	4-12	24.3	22-12	−17.2
1-14	28.7	24-14	−15.1	4-14	18.5	22-14	−20.9
1-18	28.8	24-18	−16.3	4-18	26.0	22-18	−14.1
1-22	27.6	24-22	−17.1	4-24	23.5	22-24	−14.3

Table 6 Physical test results under the condition of 2 A current injection (node 8 injection and node 18 outflow; node 12 injection and node 14 outflow).

Inject into node 8 and out from node 18	Inject into node 12 and out from node 14
Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)	Port	Voltage (mV)
8-1	8.3	18-1	−14.7	12-1	6.8	14-1	−16.6
8-4	8.6	18-4	−16.3	12-4	13.7	14-4	−10.3
8-10	10.2	18-10	−13.9	12-8	9.3	14-8	−13.2
8-12	12.7	18-12	−9.6	12-10	16.6	14-10	−7.0
8-14	14.5	18-14	−8.9	12-18	10.7	14-18	−12.5
8-22	17.7	18-22	−5.4	12-22	8.3	14-22	−14.7
8-24	18.1	18-24	−5.7	12-24	14.6	14-24	−8.7

The collected data were input to the GKA diagnostic program, and set the operation parameters as follows: the roulette strategy is adopted as the selection strategy, the coding method is real-coded, the population size is 40, the crossover rate is 0.5, the mutation rate is 0.1, and the number of iterations is 800; the k value of the clustering is 3, the initial center is C₁(9, 1.8, 1/1.8), C₂(7, 1.3, 1/1.3), and C₃(5, 1.1, 1/1.1), and the number of clustering iterations is 5.

After running the program, the GA's preliminary diagnosis results of a 4 × 4 simple grounding grid are displayed in Table 7, where the value is run 10 times to take the average.

Table 7 The preliminary diagnosis results of 4×4 simple grounding grid calculated by GA.

Branch	Frequency	Average change multiple	Branch	Frequency	Average change multiple
12	9	1.70	24	6	1.51
16	9	1.94	35	6	1.62
17	9	1.76	1	5	1.24
21	8	1.62	14	5	1.45
29	8	1.58	15	5	1.39
18	7	1.49	38	5	1.46
2	6	1.27	Others	< 5	—

As can be seen from Table 7, there are still many misdiagnosed branches, but there is no case of missed diagnosis. Among them, the occurrence frequency of branch No. 29 is eight times, and its average change multiple of branch resistance is about 1.58.

The clustering results of a 4 × 4 simple grounding grid are shown in Figure 7, where C₁, C₂, and C₃, respectively, represent clustering centers with severe corrosion, slight corrosion, and no corrosion. The SSE of clustering is about 0.4780, which indicates that the clustering effect is relatively good.

[IMAGE OMITTED. SEE PDF]

As can be seen from the clustering results in Figure 7, branches 1, 14, 15, and 38 are divided into noncorrosive branches. Branches 12, 16, 17, 21, and 29 are classified as severely corroded; Branches 2, 18, 24, and 35 are slightly corroded; Branches No. 2, 18, 24, 29, and 35 are misdiagnosed branches. Compared with the initial diagnosis result of the GA, after the secondary diagnosis of clustering, four misdiagnosis branches are eliminated, and the preset corrosion branches are classified into corresponding corrosion categories. Table 7 shows that GA diagnosed 13 corroded branches, nine of which were misjudged as corroded branches. Figure 7 shows that GKA diagnosed nine corroded branches, five of which were misjudged as corroded branches. Compared with GA, GKA reduced four misdiagnosed branches, so the number of misdiagnosed branches was reduced by 44.4%.

Compared with the diagnostic effect of the software simulation experiment, the diagnostic result of the physical simulation corrosion experiment is slightly worse, because the resistance of the non-inductive resistance itself is small, and the line between them and the down lead lines also has a small resistance. Meanwhile, there are certain errors in measuring instruments.

Conclusions

This paper mainly investigates the corrosion diagnosis of substation grounding grids, the Genetic K-means algorithm is proposed to diagnose the corroded grounding conductors. The proposed algorithm adopts the serial optimization strategy and combines the iterative results of GA with the average change multiple of branch current as the initial data of the K-means algorithm for clustering, which can better exclude the branches of misdiagnosis and improve diagnostic accuracy.

In the experimental simulation, we evaluate the performance of the Genetic K-means algorithm. Compared with the single GA diagnosis, the diagnosis results of GKA are improved, and the number of misdiagnosed branches decreased by 66.7%. Meanwhile, in the physical experiment of the 4 × 4 pure resistance grounding grid model, the number of misdiagnosed branches was reduced by 44.4%.

The proposed method provides a new idea to evaluate the corrosion degree of the grounding grid. The clustering algorithm is used to cluster branches with similar corrosion degrees to achieve the purpose of corrosion diagnosis. In other words, the clustering algorithm is used to achieve the classification of grounding conductors with different degrees of corrosion.

Author Contributions

Longsheng Huang: conceptualization, methodology, software, validation, investigation, data curation, writing – original draft preparation, writing – review and editing, project administration. Xianghui Xiao: conceptualization, methodology, investigation, resources, writing – review and editing, supervision, project administration, funding acquisition. Mingxian Huang: software, validation, investigation, resources, writing – review and editing. Zhenshan Zhang: validation, data curation. Yunhao Song: formal analysis, visualization. Luchang Guan: formal analysis, visualization. All authors have read and agreed to the published version of the manuscript.

Acknowledgments

This study was funded in part by the National Natural Science Foundation of China (52177132), in part by the National Key Research and Development Program of China (2018YFB1308203, 2017YFB1300903).

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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