# Adaptive Leakage Protection for Low-Voltage Distribution Systems Based on SSA-BP Neural Network
## 4 Adaptive Leakage Protection Strategy  
Adaptive leakage protection is the process of adjusting the action threshold of protection adaptively, according to the change in normal leakage. For the leakage protectors of the amplitude comparison method and the phase detection method widely used in China at present, under the premise of ensuring the normal operation of the leakage protector, reducing the action setting of the current can improve the protection sensitivity.  
The basic principle of realizing adaptive leakage protection is that when the leakage current is higher than the leakage action threshold, the leakage protection is performed; when the leakage current is within the limit range, the leakage action threshold remains unchanged; and when the leakage current exceeds the specified limit range, and the duration is longer than a certain time, the leakage action threshold is adjusted.  
The operating range of the leakage protector is divided into \(n+1\) intervals, and the leakage protection action threshold \(I_{\Delta d}\) is determined according to the predicted normal leakage current \(I_{\Delta}\). The setting is adjusted according to Equation (18).  
\[I_{\Delta d}=\left\{\begin{array}{ll}I_{\Delta d0},&I_{\Delta}<I_{\Delta H0} \\ I_{\Delta d\
u},&I_{\Delta}\in[I_{\Delta L\
u},I_{\Delta H\
u}]\\ I_{\Delta d\
u},&I_{\Delta}>I_{\Delta L\
u}\end{array}\right., \tag{18}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **MIRE** & **MARE** & **MSE** \\ \hline BP & 0.0086 & 1.0053 & 0.0411 \\ SSA-BP & 0.0017 & 0.1852 & 0.0095 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of the error assessment for the different prediction models.  
where \(k=1,2,\ldots,n\), \(I_{\Delta d0}\) and \(I_{\Delta dn}\) are the lowest and highest gears, respectively, \(I_{\Delta Hk}\) and \(I_{\Delta Lk}\) are the upper and lower limits of the current in the \(k\)-th interval, respectively.  
Leakage interval switching rules should meet  
\[I_{\Delta d}=\left\{\begin{array}{ll}I_{\Delta d(p-1)},&I_{\Delta}<I_{\Delta L \
u}\ and\ t>\Delta t\\ I_{\Delta d\
u},&I_{\Delta L\
u}<I_{\Delta}<I_{\Delta H\
u}\text{, or }I_{\Delta}<I_{\Delta L\
u}\text{ and }t \leq\Delta t\text{, or }I_{\Delta d\
u}>I_{\Delta}>I_{\Delta H\
u}\text{ and }t\leq\Delta t\\ I_{\Delta d(p+1)},&I_{\Delta d\
u}>I_{\Delta}>I_{\Delta H\
u}\text{ and }t>\Delta t \end{array}\right., \tag{19}\]  
where \(v=0,1,\ldots,n\), \(t\) is the duration, when \(I_{\Delta}\geq I_{\Delta d\
u}\), the leakage protector triggered.  
When the leakage action threshold is in the maximum or minimum value range, the action threshold can only be adjusted to one side or remain unchanged; that is, when the leakage action threshold is \(I_{\Delta d0}\), the action threshold can only be increased or remain unchanged, and when the action threshold is \(I_{\Delta dn}\), the action threshold can only decrease or remain unchanged. When the action threshold is in the non-maximum or non-minimum interval, the action threshold has three possibilities: increasing, decreasing, or remaining unchanged. In order to avoid frequent switching of leakage current action intervals caused by the leakage current floating near the critical point of the interval, a partial overlapping area between adjacent intervals is set. The duration of the transient process of leakage faults is short, and they will reach a steady state within a few milliseconds. However, considering that the duration of very few faults is relatively long, without loss of generality, \(\Delta t\) is more appropriate to take 1 min as the duration.