## 3 System Model and Problem Modeling  
### System Model  
The power transmission and distribution scenario is composed of a low earth orbit (LEO) satellite, a UAV, a ground 5G base station, and \(I\) ground PDs, as shown in Figure 1. Specifically, the PDs \(i\in\{1,\,\ldots,\,i,\,\ldots,\,I\}\) on the ground run different power services, thereby generating various power data, such as acquisition data, monitoring data, video data, etc., which need to be uploaded to the cloud server data center. In the model, the ground 5G base station is equipped with a cloud server data center, and the PDs can upload the collected data to the ground 5G base station. Due to the fixed locations of the PDs and the 5G base station, the link loss of data transmission for PDs with longer distance is large and consumes too much transmission energy; the actual amount of data transmitted to the base station will be consistently low, which seriously affects the information collection of PDs. In addition, a large number of PDs uploading data to the ground 5G base station will also lead to an excessive transmission link load on the 5G base station. Therefore, in order to reduce the link load and improve the energy efficiency of data transmission, we provide another way of data transmission, i.e., taking advantage of the UAV and the satellite. PDs upload data to the LEO satellite via the UAV. Among them, the UAV operates on a predetermined trajectory as a relay for data forwarding, and the LEO satellite, similar to the ground 5G base station, is equipped with a cloud server. The components participating in the system are summarized as follows. * Power transmission and distribution device (PD): run different power services and generate a variety of power data that need to be uploaded to the cloud server data center. * UAV: as a relay for data forwarding of PDs, which is used to forward the power data from the PDs to the cloud server data center of an LEO satellite. Figure 1: System Model. * 5G base station: equipped with a cloud server data center, which is used to receive power data from PDs that need to be uploaded to the cloud server data center. * LEO satellite: equipped with a cloud server data center to receive power data forwarded by the UAV that need to be uploaded to the cloud server data center. In addition, we show in Figure 2 how to communicate the components participating in the system according to Figure 1.  
We adopt a time-slotted model to formulate the network operation time, which is evenly divided into \(T\) time slots. Therefore, the duration of each time slot is \(\tau\) and the entire operation time can be expressed by \(\{1,\,\ldots,\,t,\,\ldots,\,T\}\). Since the UAV moves, the distance \(d_{i,u}(t)\) between the PD and the UAV changes among slots, while the distance \(d_{i,b}\) between PD and the ground 5G base station remains constant. According to the two data transmission ways of PD provided above, we use binary variables \(x_{i,u}(t)\) and \(x_{i,b}(t)\) to represent the association between the PD \(i\) and the UAV as well as the ground 5G base station, respectively. \(x_{i,u}(t)=1\) means that the PD chooses to upload data to the UAV and then forward it to the LEO satellite in the current time slot, while \(x_{i,u}(t)=0\) means that the PD does not choose to upload the data to the UAV. Similarly, \(x_{i,b}(t)=1\) means the PD in the current time slot chooses to directly forward the data to the ground 5G base station, while \(x_{i,b}(t)=0\) means PD \(i\) does not choose to forward the data to the ground 5G base station. In particular, to avoid wasting excessive resources by repeatedly forwarding data, each PD can only choose one data transmission way in each time slot, i.e.,  
\[x_{i,u}(t)+x_{i,b}(t)\leq 1. \tag{1}\]  
When the PD chooses to transmit the data via the UAV, it is assumed that the flight height \(H_{u}\) of the UAV is the minimum height that satisfies avoiding the actual terrain or buildings.