# Adaptive Leakage Protection for Low-Voltage Distribution Systems Based on SSA-BP Neural Network
## 2 Principle of Normal Leakage Current Variation  
The International Electrotechnical Commission (IEC) classifies low-voltage distribution systems as the TN system, TT system, and IT system, according to whether the neutral point of the system and the load shell are effectively grounded [26]. Since the TN-C-S system is safer and more reliable, it is progressively replacing the TN-C system, and is widely used for low-voltage distribution systems in industrial and urban civil buildings. Therefore, this paper proposes a leakage protection method for the TN-C-S system. In the low-voltage distribution network, due to the distributed capacitance and ground conductance between the line and the ground, a small amount of current flows into the ground during normal operation, namely the normal leakage current. Figure 1 shows the generation of normal leakage current of a three-phase line and the principle of leakage protection. \(A\), \(B\), \(C\), and \(PEN\) are the three-phase and PEN lines. \(I_{A}\), \(I_{B}\), \(I_{C}\), and \(I_{PEN}\) are the three-phase and PEN line currents. \(Z_{Aload}\), \(Z_{Bload}\), and \(Z_{Cload}\) are the three-phase loads. \(Z_{PEN}\) and \(Z_{PE}\) are the PEN and PE line impedances. \(Z_{AG}\), \(Z_{BG}\), and \(Z_{CG}\) are the three-phase ground impedances,\(Z_{\text{G0}}\) and \(Z_{\text{G1}}\) are the impedance of the neutral point and the repeated ground point to ground, respectively. \(I_{\text{AG}}\), \(I_{\text{BG}}\), and \(I_{\text{CG}}\) are the three-phase leakage currents. When a single-phase leakage fault occurs, the leakage current of TA (current transformer) is higher than the protection action set threshold, and switch KM is opened. The leakage current can be divided into capacitive leakage current and conductance leakage current according to the cause, which can be expressed by the following equation (taking the \(A\)-phase as an example):  
\[I_{\text{AG}}=I_{\text{C\_A}}+I_{\text{G\_A}}, \tag{1}\]  
where \(I_{\text{C\_A}}\) is the capacitive leakage current of the A-phase, and \(I_{\text{G\_A}}\) is the conductance leakage current of the \(A\)-phase. Figure 2 shows the highest leakage current recorded by the leakage protector at the main switch of a 200 kVA distribution transformer somewhere at a certain period of time. The normal leakage current has a wide range of fluctuations, which are the result of a combination of factors. Specifically, the capacitive leakage is generated by the distributed capacitance between the line and the ground. The capacitive leakage current is given by (2). \[I_{\text{C\_A}}=2\pi fC\text{U}_{A}=\frac{f_{\text{E}},SU_{A}}{2 kd}, \tag{2}\]  
Figure 1: Normal leakage current generation mechanism. Figure 2: Highest normal leakage current change curve in a year. where \(f\) is the frequency of the system voltage and \(\varepsilon_{r}\) is the atmospheric dielectric constant, and its value is affected by environmental humidity, temperature, and insulation aging. \(S\) is the effective direct area of the line to the ground, which is determined by the outer diameter and length of the line. \(U_{A}\) is the \(A\)-phase voltage, and its influence is mainly reflected in the line voltage drop caused by the load current. For rural power lines and power lines with long transmission distances and excessive loads, this voltage-drop value should be considered. \(k\) is the electrostatic force constant, and \(d\) is the height of the line. In addition to the capacitance to the ground, there is a certain conductance between the line and the ground, and the conductance current generated is:  
\[I_{G\_A}=\frac{KS}{d}U_{A}, \tag{3}\]  
where \(I_{G\_A}\) is the conductance leakage current, and \(K\) is the conductivity. Considering the large changes in atmospheric humidity, temperature, line aging, and line voltage, the normal leakage current may change greatly or even double, so it is necessary to adaptively adjust the protection action threshold, by establishing a prediction model of normal leakage current and training it with the collected data.