## 1 Introduction  
Currently, the large-scale utilization of offshore wind energy is restricted due to its development costs, which are significantly greater than the onshore wind farms. The cost of power systems accounts for 15-30% of the total development cost of offshore wind farm based on the depth of water and the seabed characteristics [1, 2]. Therefore, the realization of the optimal design of power systems is of great significance for improving the economics of the offshore wind farm. A large amount of research on the optimization of power systems in offshore wind farms has been developed. In these researches, the main idea is to reduce the one-time investment cost by improving the power calculation model, topology model, and optimization algorithm, and these advances have been well summarized in the review articles [3, 4, 5, 6]. However, the impact of energy loss on the topology and economy of power systems has not received sufficient attention or an adequate evaluation. A large amount of energy loss occurs in the medium-voltage power network, and the cost of energy loss exceeds the cable cost in the 20 years of wind farm operating life, which is revealed in a literature analysis of a small wind farm containing 25 wind turbines [7]. The magnitude of the energy loss in a medium-voltage power network is determined by the overall resistance level in its topology. The reduction of the overall resistance level in the topology requires not only a reasonable planning of the cross-section of cable but also optimal matching with its topology [7]. Therefore, it is necessary to carry out the coupling optimization of the connection topology and the cable cross-section. However, the optimization of topology and the planning of cable cross-section are performed independently in the current power system design so that the most economical power system solution is theoretically unavailable. Currently, the design of the cable cross-section is based on the maximum current-carrying criterion [8; 9; 10]. This method of design is to determine the cable cross-section after the connection topology is obtained, according to the rule that the maximum current on each cable segment in the topology should not exceed the allowable current capacity of the cable. At the same time, the safety constraints such as the voltage drop [4] and the thermal stability [10] need to be strictly met. In the solution obtained according to the principle of maximum current carrying capacity, the cross-section of each cable segment in the topology should be the smallest, and this minimizes the cost of the cable. However, the resistance increases as the cross-sectional area of the cable decreases, resulting in greater power loss during the service life of the power system for at least 20 years. According to an earlier report [11], by properly employing the large cross-section cables on cable segments with large currents in the topology, the power loss caused by the resistors was found to be greatly reduced, thereby effectively improving the economics of the power system. Another factor that has a significant impact on the overall resistance level is the topology. Currently, the minimum spanning tree (MST) derived from the graph theory is the most widely used in topology optimization of power systems [12; 13; 14; 15; 16; 17; 18]. In the MST architecture, the wind turbine and topology are treated as nodes and directed connectivity graphs, respectively, to obtain the topology with the shortest total cable length. Initially, all wind turbines are used to perform the topology generation of the MST [12; 13]. However, the topologies generated in this manner are often insufficient to meet all of the power parameter constraints [14; 15]. To solve this problem, clustering algorithms such as random combination [16], k-mean clustering [17], and fuzzy c-means clustering [18] were also applied to perform the grouping of the wind turbine groups, and then MST was used to generate connections for each group.