## 2 Materials and Methods  
### System Model  
Figure 2 shows the system model proposed in this paper, depicting a typical scenario of a network of LEO satellites serving tracking areas (TAs) located in remote regions on earth. The TAs here can be viewed as an entire communication user node with respect to the satellite. With a satellite ephemeris and satellite constellation design for the payload, the TAs are ensured continuous coverage by at least one satellite during switchover. This solution, proposed by 3 GPP in Release 17, addresses the key issue of \"Mobility management with large satellite coverage areas\" in non-geostationary satellite orbit (NGSO) mobility management [33]. The system model comprises three components: the satellite network, the communication relay station, and the power equipment. The satellite network comprises N LEO satellites capable of covering the grid relay station. The communication relay station receives information from the power equipment within its vicinity, and establishes communication links with the LEO satellites. Satellite coverage depends on the minimum elevation angle between the terminal and the satellite. Additionally, the grid relay station's communication duration may exceed the LEO satellites' service time. When the elevation angle of Sat1 is about to decrease below the minimum elevation angle, the relay station must select between Sat2 and Sat3 to maintain ongoing communication. Therefore, this article focuses on designing a rational satellite handover strategy to achieve seamless handover and ensure user QoS within the communication duration of power users. A single TA can be served by multiple satellites, resulting in multiple candidate satellite options during the handover process. The user's position can be determined using the Global Positioning System (GPS), while the LEO satellite orbit data can be obtained through Two-Line Element (TLE) sets using the simplified general perturbations model (SGP4), as described in [34]. The service period of each satellite to the terminal can be determined based on the satellite ephemeris information and the terminal location information as follows:  
\[T=\left\{\left(t_{s}^{1},t_{e}^{1}\right),\left(t_{s}^{2},t_{e}^{2}\right), \cdots,\left(t_{s}^{i},t_{e}^{i}\right),\cdots,\left(t_{s}^{n},t_{e}^{n}\right)\right\} \tag{1}\]  
where \((t_{s}^{i},t_{e}^{i})\) denotes the start service time and the end service time of satellite i to the power terminal. The satellite network comprises numerous satellites, and each LEO satellite can only provide coverage to the ground for a certain period due to its high-speed mobility. Different satellites have varying coverage periods. Therefore, if there are areas of overlap in the coverage periods of different satellites, it indicates that the user terminal can switch between the satellites. As shown in Figure 3, a region bounded by a dotted line represents overlapping coverage time between satellites. For example, when \(t_{s}^{1}<t_{s}^{2}<t_{e}^{1}\), it signifies that the service time of LEO Satellite 1 and LEO Satellite 2 to the terminal overlaps, allowing the terminal to switch from LEO Satellite 1 to LEO Satellite 2. It is evident that there is no overlapping coverage time between Satellite 1 and Satellite 3, thus handover cannot occur at the terminal. Based on the prediction of overlapping service cycles of satellites to terminals in the coming period, a collection of candidate satellites that can provide services during the user's communication hours can be obtained. As shown in Figure 4, the virtual start node (Sat0) is introduced, with each node representing a satellite, and the directed edges indicating handover relationships. The presence of a directed edge between two satellite nodes means that the terminal can switch between these two satellites. The satellite handover process can be represented as finding a path in the satellite handover directed graph, where the handover criterion is translated into weights applied to the directed edges [26].