# Advances and Challenges of Corrosion and Topology Detection of Grounding Grid
## 2 Corrosion Detection Method of Substation Grounding Grid
### Electric Network Method
#### 2.1.1 Port Resistance Method  
The basic principle of the port resistance method based on [PERSON]'s theorem is described in [5; 6]. It was first proposed by [PERSON] and [PERSON] of Chongqing University in the early 1990s. The principle of the port resistance method is shown in Figure 1. Grounding grids are usually formed by the interconnection of horizontal equalizing conductors. They are buried underground. Single grids are usually rectangular, and the materials are ordinary galvanized flat steel, round steel, or flat copper. Ignoring the influence of soil and other factors, the grounding conductor is regarded as an equivalent of resistors, and the points connecting the down-line and the grid are assumed to be located at the nodes of the grid without any deviation. The grounding conductor network after the completion of grounding grid laying is set to N. According to the structural drawing, and the size and material of the laying conductor, the complete conductor resistance values of each section can be obtained. After using the grounding grid for a long time, the resistance parameters of the grounding conductor are changed due to corrosion. At this time, the network is set to \(N^{\prime}\). The network \(N\) and \(N^{\prime}\) have the same topological structure and can be applied to [PERSON]'s theorem. By injecting current \(I_{0}\) between accessible nodes \(i\) and \(j\) of network \(N\) and \(N^{\prime}\) and measuring the port voltage \(U_{ij}\), we can calculate the port resistance \(R_{ij}\) and \(R\prime_{ij}\) of network \(N\) and \(N^{\prime}\) and then obtain the change of port resistance \(\Delta R_{ij}\). If the network \(N\) and \(N^{\prime}\) have m group accessible nodes, the injected nodes can be replaced in turn, and the m group port resistance can be obtained. According to [PERSON]'s current law (KCL), [PERSON]'s voltage law (KVL), and [PERSON]'s theorem, the diagnostic equation of the electric network method can be deduced.  
\[\left\{\begin{array}{l}\Delta R_{ij|1}=\sum\limits_{k=1}^{b}\Delta R_{k}I_{k |1}I^{\prime}_{k|1}/I_{0}^{2}\\ \Delta R_{ij|2}=\sum\limits_{k=1}^{b}\Delta R_{k}I_{k|2}I^{\prime}_{k|2}/I_{0} ^{2}\\ \ldots\\ \Delta R_{ij|m}=\sum\limits_{k=1}^{b}\Delta R_{k}I_{k|m}I^{\prime}_{k|m}/I_{0} ^{2}\end{array}\right. \tag{1}\]  
In Formula (1), \(I_{0}\) is the injection current of two accessible nodes, and \(\Delta R_{ij}\) is the change of port resistance measured by injection current between two accessible nodes. \(I_{k}\) is based on the current of each branch of network \(N\) at the injection of \(I_{0}\). All three quantities are known. \(\Delta R_{k}\) is the variation of branch resistance before and after network corrosion, \(I_{k}\) is the branch current of network \(N^{\prime}\); thus, \(\Delta R_{k}\) and \(I_{k}\) are unknown.  
Formula (1) is a non-linear system of equations, and the number of equations (m) is usually less than the number of branches (b). The formula belongs to the undetermined system of equations and cannot be solved directly. Generally, an iterative algorithm is implemented to solve this equation.  
Figure 1: Schematic diagram of port resistance method [5].  
The effectiveness of port resistance method depends on the accuracy of port resistance measurements. The application of this method is restricted by instrumental error from measuring the small resistance value of grounding conductor and the influence of down-line resistance, contact resistance, and cable resistance.