A Diagnosis of Grounding Grid Corrosion Defects Based on Branch Voltage Disturbance

The grounding grid is the cornerstone for maintaining the safe operation of the power system. The grounding network acts as a concealed project, and its invisible characteristics make the defects difficult to be detected, which causes major safety hazards in the system. Thus accurate diagnosis of grounding grid corrosion is vital in electrical engineering. A diagnosis method for grounding grid corrosion based on branch voltage disturbance is proposed in this paper, which can judge the location and degree of corrosion through branch voltage disturbance before and after corrosion. Firstly, the sensitivity of branch voltage to branch resistance of the grounding grid is analyzed. Secondly, a diagnostic model based on branch voltage disturbance is established, and the corresponding regularity between peak voltage disturbance and the corrosion state of the grounding grid branch is developed. Finally, it is verified by experiments that this method can effectively diagnose the corrosion of the grounding grid.


I. INTRODUCTION
The grounding grid provides a reference potential for the substation and discharges dangerous currents caused by lightning and short circuit of the power system to ensure the safety and stability of the power system [1]- [4]. However, due to the non-standard construction and poor working environment of the grounding grid, the grounding grid is susceptible to electrochemical and biological corrosion [5]- [7]. The corrosion makes grounding performance unable to meet the requirements for safe operation of the power system, posing a threat to the safety of the power system and personnel [8]- [10]. The large grounding grid is buried in the soil about 0.8m deep underground, which is difficult to be excavated and replaced [11]. Therefore, it is of great engineering significance to predict the corrosion defects of the grounding grid through the accessible information above the ground surface to guide the operation and maintenance [12]- [15].
The associate editor coordinating the review of this manuscript and approving it for publication was Baoping Cai .
In the research of grounding grids, the optimal design and grounding performance of grounding grids are generally studied abroad [16], [17]. In China, many scholars are committed to the study of corrosion diagnosis, because the corrosion of the old substation grounding grid is common, and the degree of corrosion is relatively serious. Therefore, based on the electromagnetic field theory and electrical network theory, some diagnostic methods were proposed [18]. The basic idea of the former method is to inject a current into the grounding grid or excite the grounding grid with the coil current, measure the surface magnetic field, and reflect the corrosion through the magnetic field distribution [19], [20]. The magnetic field measured by this method has obvious collapse phenomenon at the breaking point of the grounding grid branch, which can diagnose the broken branch, but it is difficult to accurately diagnose the corrosion of the unbroken branch. For another method, each branch of the grounding grid is equivalent to a pure resistor, and a diagnostic model could be established by using the electrical network theory for fault prediction [21], [22]. According to the Tellegen's VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ theorem, the relationship between the down lead port resistance and branch resistance was established in reference [23] to carry out corrosion diagnosis. Besides, sensitivity relationships between branch resistance, node voltage, and port voltage were established in the study [24]. However, the diagnosis effect of this method was not satisfactory-it directly used the node potential of the grounding grid to establish a corrosion diagnosis mathematical model, lacked deep extraction of the internal relationship between the node potential data and the corrosion state, and most of the established diagnosis mathematical models were non-linear and underdetermined, which need to be solved by the optimization algorithm [25], [26]. Based on the existing research foundation, this paper proposed a method to reflect the branch corrosion by the voltage disturbance of the grounding grid branch. The characteristic of branch voltage disturbance caused by branch resistance of the grounding grid was theoretically analyzed. After injecting a current to the grounding grid, a mapping relationship between the unit distance voltage disturbance and the corrosion state could be established based on the change of each branch voltage before and after the corrosion, which reflected the location of the corrosion branch and the severity of corrosion. Finally, experiments verified the feasibility of the method, and the method could accurately diagnose the corrosion fault of the grounding grid.

A. GROUNDING GRID MODEL
The grounding grid can be equivalent to a pure resistance network [27] by injecting a small direct current into the grounding grid and ignoring the soil stray current. An equivalent physical model of the grounding grid is shown in Fig. 1.
Based on the theory of the electrical network, the mathematical model of the grounding network can be expressed as where A is the correlation matrix, U n is the node voltage matrix, U b is the branch voltage matrix, I n is the node current matrix, and Y n is the node admittance matrix.

B. ANALYSIS OF BRANCH VOLTAGE DISTURBANCE
For a resistor network, under the same excitation condition, the disturbance capability of branch resistance changes to each branch voltage is different. To reflect the disturbance of branch resistance to branch voltage, the branch voltage is fully differentiated. Since only the current source is excited, the node current I n is independent of the branch resistance R i , so By using matrix analysis theory, the equation can be expressed as: Combining equations (1), (4) and (5), equation (6) is obtained and shown below. where S is defined as the disturbance matrix of the branch resistance to the branch voltage, where S = S (:, 1) S (:, 2) · · · S (:, b) (n−1)×b (9) where S ij represents the disturbance coefficient of the resistance of the j branch to the voltage of the i branch. The absolute value of the disturbance coefficient is generally used to characterize the disturbance capability. By analyzing the absolute value of S elements, it is found that the diagonal elements have obvious dominant phenomena in each column, indicating that the resistance of each branch has the highest voltage perturbation capability. Therefore, if one branch of the grounding grid is corroded and the resistance becomes large, the variation value of the branch voltage U fault will be significantly larger than other branches. Reasonable selection of the current excitation injection point can extract the corrosion state information of the grounding network branch from the disturbance of branch voltage.
To study the variation of the corrosion branch voltage with the corrosion degree, a branch is arbitrarily selected as the corrosion branch from a 5 * 5 resistor grid with 50 branches, and its resistance range is set to 1 ∼ 20 (the resistance value of a normal branch is 1 ). Then, the branch voltage is calculated. Voltage changes of the corrosion branch( U fault ), the branch near the corrosion branch( U near ), and the branch far from the corrosion branch ( U far ) are shown in Fig. 2.
As can be seen from Fig. 2, the variation of branch voltage before and after corrosion can be approximated as follows: After the grounding grid is corroded, the voltage change of the corroded branch is more obvious than that of other branches, which reflects the position and corrosion degree of the corroded branch.

III. THE DIAGNOSIS METHOD OF THE GROUNDING GRID CORROSION A. DIAGNOSTIC PRINCIPLE
For a grounding grid with complicated branch structures, when corrosion occurs, the proportion of the far-corrosion branch is large, and the law of equation (11) is more obvious. The voltage change of the corrosion branch is larger than that of the other branches, so this information can be used as an indirect feature to reflect the corrosion state.
For an actual grounding grid, the length of each branch is not uniform. To eliminate the interference of different initial resistances of branches with various lengths to the voltage variation, the voltage variation value per unit distance (i.e. voltage disturbance) is used as a direct feature to reflect the corrosion state of the grounding grid, which is defined below: where U i , U j , U i and U j are the potentials of adjacent nodes i and j of the grounding grid before and after corrosion under the same excitation, l ij is the distance between i and j (dimensionless value in meters). The potential difference between adjacent nodes is the voltage on each branch.
When the grounding grid is not corroded, the branch resistance is proportional to the length of the branch (i.e. R ij ∝ l ij ).
where R ij is the initial resistance of branch ij before corrosion.

B. CORROSION LOCATION AND EVALUATION 1) NODE POTENTIAL INTERPOLATION
To facilitate analysis, a coordinate grid model of the grounding grid is established according to the actual grounding grid structure. Fig. 3 shows the diagnostic model of the grounding grid with the grid size of 1 m × 1 m, and it includes 60 branches. The numbering rules for nodes and branches are first from left to right and then from top to bottom. According to the diagnosis principle, it is necessary to obtain as many node potentials as possible to calculate the voltage disturbance. For the grounding grid of the actual substation, there is no guarantee that there is sufficient down conductor to collect the potential. Therefore, the potential of the unknown node is obtained by using the Lagrangian linear interpolation.
As shown in Fig. 4, the potential of the node 5 is obtained by interpolation of the node 2, 4, 6, and 8. Formulas for calculating the interpolation are shown as follows: Horizontal interpolation U 5x Longitudinal interpolation U 5y To improve the interpolation accuracy, the average of the horizontal and longitudinal interpolation is taken as the interpolation result.
For the model in Fig. 3, a current of 1A is injected from node 1, and the current flows from node 31, and the resistance of each branch is set to 1. The comparison of the node potential calculated by theoretical calculation and interpolation calculation is shown in Fig. 5. The result shows that the difference between the theoretical data and interpolated data is small-the potential value obtained by the interpolation method has high precision.

2) EVALUATION OF CORROSION DEGREE
The magnitude change of the voltage disturbance has a corresponding relationship with the resistance of the corrosion branch so that the degree of corrosion of the grounding grid can be evaluated. It can be known from the branch voltage perturbation law that the value of the voltage disturbance increases as the resistance becomes larger.
where λ is the voltage disturbance, R is the branch resistance, I is the current injected into the grounding grid, a, b and c are fitting constants. Taking branch 23 of the model in Fig. 3 as an example, a current of 1A is injected from node 6 and flows out from node 31. The initial resistance of each branch is 1 . The corrosion degree curve can be obtained by fitting the variation law of voltage disturbance, which is shown in Fig. 6.
It can be seen that the power exponential function achieves a good fit of the corrosion law, and the fitness is R-square = 0.9998.
Then the corrosion degree formula of the branch is The specific process for corrosion positioning and evaluation of the grounding grid is shown in Fig. 7. Firstly, a diagnostic model is established according to the structural parameters of the grounding grid, and the node potential of the grounding grid before corrosion and the corrosion degree curve of the branch are obtained through theoretical calculation. Secondly, the node potential after corrosion is measured and interpolated under the same excitation. The voltage disturbance is calculated by using the potential data before and after corrosion, and it is presented in a three-dimensional graph. Finally, the corrosion state of the grounding grid can be diagnosed and evaluated by the peak position and size of the three-dimensional graph.

IV. EXPERIMENTAL ANALYSIS A. SIMULATION EXPERIMENT
For the grounding grid model shown in Fig. 3, a corrosion diagnosis simulation experiment was carried out by using the voltage disturbance. The two diagonal nodes 6 and 31 of the grounding grid were selected as the injection and outflow points of the current source, and node 36 was the potential reference node. A current of 1A was injected, and the initial value of each branch resistance is set to 1 .

1) SINGLE CORROSION DIAGNOSIS
When a single corrosion fault occurs, the resistance of branch 23 was set to 5 , and the voltage disturbance of each branch was calculated. The result is shown in Fig. 8.
The peak coordinate of the diagnosis result is (2.5, 4) corresponding to the branch 23 in the diagnostic model. Thus, the positioning of the corrosion branch is accurately achieved. At the same time, the peak value is substituted into Equation (20) to calculate the resistance of the corrosion branch that is 4.86 . The diagnostic error is only 2.8%, which enables accurate diagnosis of corrosion faults.

2) MULTI-CORROSION DIAGNOSIS
To simulate more complex corrosion conditions, three corrosion branches were established with different degrees of corrosion. The resistances of branch 23 and branch 7 were set to 5 and 3 , and that of branch 14 was set to 8 . The simulation result is shown in Fig. 9.
The coordinates and values corresponding to the peaks can be found in Fig. 9. Combined with the diagnosis model and the corrosion curve, resistances of three corrosion branches are 4.82 , 2.74 and 6.98 . Therefore, the fault location and the approximate judgment of the corrosion branch resistance can also be realized to meet the diagnostic requirements in the multi-corrosion diagnosis.

B. ANALOG GROUNDING GRID EXPERIMENT
The grid side length of the actual grounding grid was about 5m, and the branch resistance was about tens of milliohms. The laboratory used the same flat steel material of the grounding grid to weld the scaled analog grounding grid, and its grid side length was 1m. In the simulated grounding grid, the corrosion of the grounding grid was simulated by crimping two pieces of flat steel, and the resistance increased about 6 times as much as that of the normal branch. In the experiment, a current of 6A was injected through diagonal nodes 1 and 32 of the grounding grid, and a high-precision potential acquisition device FLUKE8845A was used to acquire the potential on the down conductor, and the potential value of the node without the down conductor was obtained through interpolation. The schematic diagram of the analog grounding grid and the experimental site diagram are shown in Fig. 10.
The voltage disturbance distribution of the analog grounding grid obtained by calculation is shown in Fig. 11. It can be determined that the corrosion branch of the grounding grid is covered by nodes 1-16. Basically, branch 1 is a corrosion branch, and the smaller peak around branch 1 may be a pseudo fault or a real fault with less corrosion.
On the basis of the first diagnosis, it was necessary to further narrow the corrosion branch range and eliminate false faults to achieve precise positioning. Thus, a current was injected from node 1, and was drawn from node 16. The potential of the grounding grid was measured for voltage disturbance calculation. The result is shown in Fig. 12.   According to the results of the above two diagnoses, there are two distinct peaks in the voltage disturbance distribution, and positions of these peaks correspond to branch 1 and branch 30 in the simulated grounding grid. This result is consistent with the corrosion point of the preset value in the  simulated grounding grid, and the resistance of the corrosion branch is about 4-6 times that of the normal branch. Therefore, the diagnose realizes the accurate positioning of the corrosion branch of the grounding grid and the rough judgment of the corrosion degree.

C. SUBSTATION FIELD EXPERIMENT
In order to verify the effect of voltage disturbance on corrosion diagnosis of the grounding grid in the actual substation, a small waste substation partition was selected in central China for on-site diagnosis experiments. The selected grounding grid partition was approximately square, and its side length was about 8m. Fig.13 presents the structural schematic diagram of substation division 1 and the grounding grid.
We injected a DC current of 1A into the grounding grid, collected the potential data of the node through the grounding grid, and obtained potential interpolation to calculate the disturbance voltage of branches. The distribution result is shown in Fig 14. Through on-site excavation, it was found that there were two branches with serious corrosion and poor welding at the corner of the grounding grid branch under the isolating switch. The specific location is shown in Fig. 15, which was close to the diagnostic result position of the voltage disturbance distribution diagram. Thus, the correctness and practical effectiveness of the method were verified.

V. CONCLUSION
A new method of the grounding grid corrosion diagnosis based on branch voltage disturbance is proposed to overcome the shortcomings of the low internal information utilization rate of down-conductor potential data set and poor diagnosis effect of the established model in the grounding grid corrosion diagnosis. Through theoretical analysis and experimental verification, the following conclusions are drawn: • Before and after corrosion of the grounding grid, the voltage disturbance caused by the increased resistance of corrosion branch is much larger than that of other branches.
• In the node potential data acquisition by measuring the grounding grid down-conductor, and the collected data is limited by the number of down-conductors. The reconstruction of the unknown node potential data can be performed by using the Lagrangian linear interpolation, which has high precision.
• Branch voltage disturbance of the grounding grid is calculated in this paper. From the distribution diagram, the corrosion branch and the corrosion degree of the grounding grid can be accurately located and evaluated through the position and value of the peak.