## 1 Introduction  
With the innovation of communication and computing technology, the power grid is developing towards intelligence. For the purpose of providing a stable power supply, smart grids are usually equipped with intelligent functions, such as video monitoring and power line monitoring, to facilitate the adjustment of control commands. Analyzing these intelligent functions inevitably brings about tremendous computational tasks, which are challenging to execute locally. Thanks to edge computing technology [1], some computational tasks can be handed over to nearby edge servers for execution to alleviate the local computing pressure of grids. Despite great promise, computational tasks for grids in remote regions (e.g., mountains, deserts, and oceans) are still difficult to be executed on account of lacking edge servers and network service. To provide computing power for remote grids, satellites are considered to be an effective solution. The computational tasks of remote grids can be offloaded to urban terrestrial cloud (TC) servers for executing through satellite forwarders. But the long propagation distance between terminals in remote grids and urban TC via satellite links will lead to high delays. In response to this problem, researchers proposed satellite edge computing (SatEC) architecture [2; 3; 4] by referring to mobile edge computing (MEC) [5]. Through deploying edge computing servers on satellites, SatEC allows the computational tasks of remote grids to be directly executed by nearby visible satellites. Since the process of transferring tasks from satellites to urban TC is eliminated, existing works that focus on task offloading in SatEC networks can achieve relatively satisfactory performance. However, they still have the following defects that limit their effectiveness in remote grids:  
Firstly, there still are large queuing delays when heavy computational tasks of remote grids are offloaded simultaneously. Though novel works [6; 7; 8; 9] allow the direct processing of computational tasks by satellites to reduce transmission latency, they introduce higher processing latency caused by the lower processing capabilities of satellites. Specifically, since the energy capacity of satellites is limited [10], SatEC servers deployed on satellites usually tend to obtain low energy overhead at the cost of processing efficiency. This means that when multiple tasks are offloaded to the same SatEC server, later tasks must enter the queue to wait for former tasks to be slowly executed. Thus, the queuing delay of smart grids with heavy computational tasks will be extremely high, which may cause the untimely adjustment of control commands and untimely fault monitoring in smart grids. As an infrastructure with considerable service coverage, this untimely task execution will affect the power consumption of massive devices or even further crash charging devices by unstable currents without timely regulation. Secondly, although some works allow offloading tasks within satellite-air integrated networks to alleviate queuing delay of pure SatEC, they require some predefined models and complex offloading decision processes. For example, the movement trajectories of aerial users are required in [11], and the flight trajectory of unmanned aerial vehicles is required in [12]. Nonetheless, such information is difficult to obtain in practice. Additionally, solving offloading decisions that optimize the delay and energy consumption is usually formulated as a mixed-integer programming (MIP) problem [13; 14]. Some advanced methods, such as 3D hypergraph matching [11], the game-theoretic approach [7], and a multiple-satellite offloading method [15] have been proposed to solve the hard MIP problem. However, all of them require a considerable number of iterations to reach satisfying optima. This complex offloading decision process likewise leads to the untimely execution of computational tasks in smart grids, especially under the fast fading satellite channels [16].