With the increasing scale and complexity of power systems, the Security and Stability Control System (SSCS) plays a vital role in ensuring the safe operation of the grid. However, existing SSCS implementations still face many limitations in cross-regional coordination, control precision, and risk prediction. Establishing the digital simulation model is an effective way to verify the control policy of SSCS. This paper proposes a neural heuristic task scheduling method based on deep reinforcement learning (DRL) to schedule the simulation tasks. It models the task dependencies of SSCS as a directed acyclic graph (DAG) and then dynamically optimizes task priorities and resource allocation through deep reinforcement learning. The method introduces multi-head attention and heterogeneous attention mechanisms to effectively capture complex dependencies among tasks, enabling efficient multi-core task scheduling. Simulation results show that the proposed algorithm significantly outperforms traditional scheduling methods in terms of makespan, load balancing, and resource utilization. It can also adapt to dynamic changes under different task scales and multi-core environments, demonstrating strong robustness and scalability.