## 2 Optimization Model for Network Reconfiguration Problem of Ship Power System
### Mathematical Description of Network Reconfiguration for Ship Power Systems  
The mathematical characterization of network reconfiguration in ship power systems can be viewed as an optimization process aimed at identifying the optimal value of a multi-objective constrained function [19]. The corresponding mathematical modeling is conducted based on the various established objective functions. This paper investigates a large destroyer ship, exemplified in Figure 3, which features a typical ring power system distribution network as the focus of study [20]. To facilitate a more comprehensive analysis of the grid structure, the system will be symbolically represented using specific symbols. The symbols correspond as follows: \(\xrightarrow{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text{\text{\text{\text  
2.2.1. Objective of Maximizing Load Recovery  
In the process of fault reconstruction, according to the principle of load restoration priority [21], the power supply for critical loads should be ensured first, as it is related to the safety of the ship and the lives and property of the personnel. In accordance with Section 2.1 the classification of marine load levels and rated currents is presented as shown in Table 1, where switch classification '0' indicates MBTs (Manual Bus Transfers) and '1' indicates ABTs (Automatic Bus Transfers). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Load**} & \multicolumn{2}{c}{**Electric**} & \multirow{2}{*}{**Grade**} & \multirow{2}{*}{**On/Off**} & \multirow{2}{*}{**Load**} & \multicolumn{2}{c}{**Electric**} & \multirow{2}{*}{**Grade**} & \multirow{2}{*}{**On/Off**} \\  & **Current/A** & & & & & & **Current/A** & \\ \hline L1 & 70 & 1 & 1 & L11 & 255 & 1 & 1 \\ L2 & 120 & 3 & 0 & L12 & 205 & 3 & 0 \\ L3 & 200 & 2 & 0 & L13 & 110 & 2 & 1 \\ L3 & 150 & 3 & 1 & L14 & 72 & 3 & 0 \\ L5 & 160 & 2 & 1 & L15 & 87 & 2 & 0 \\ L6 & 100 & 1 & 1 & L16 & 100 & 1 & 1 \\ L7 & 80 & 3 & 0 & L17 & 205 & 2 & 1 \\ L8 & 325 & 1 & 1 & L18 & 200 & 3 & 0 \\ L9 & 185 & 3 & 0 & L19 & 165 & 3 & 0 \\ L10 & 44 & 2 & 0 & L20 & 30 & 2 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Load attribute table. Figure 3: Symbolic diagram of loop distribution mode. While ensuring the power supply to critical loads, efforts should also be made to minimize the number of de-energized loads. Based on the classification of marine load levels, the objective function for maximizing load recovery can be formulated as Equation (1):  
\[\min f_{1}=\lambda_{1}\sum_{i=1}^{k}(1-x_{i})L_{g1i}+\lambda_{2}\sum_{j=1}^{m}( 1-x_{j})L_{g2j}+\lambda_{3}\sum_{f=1}^{n}(1-x_{f})L_{g3f}, \tag{1}\]  
where \(L_{g1i}\), \(L_{g2j}\), and \(L_{g3f}\) represent the key load, important load, and general load in the grid; \(k\), \(m\), and \(n\) denote the quantities of these three types of loads; and \(x_{i}\), \(x_{j}\), and \(x_{f}\) indicate the power supply status for different loads, where 1 signifies that power is available and 0 indicates that the power is cut off. \(\lambda_{1}\), \(\lambda_{2}\), and \(\lambda_{3}\) are the weight coefficients of the sub-three types of loads, determined based on operational experience. This paper must consider the load priority conditions, which need to satisfy the following requirement: \(\lambda_{1}>\lambda_{2}>\lambda_{3}\), where \(\lambda_{1}=\lambda_{2}=1\), \(\lambda_{3}=0.01\), representing the priority of power supply for the three types of loads.