This research aims to minimize the unnecessary resource consumption by intelligent Power Grid Systems (PGSs). Edge Computing (EC) technology is used to forecast PGS load and optimize the PGS load forecasting model. Following a literature review of EC and Internet of Things (IoT)-native edge devices, an intelligent PGS-oriented Resource Management Scheme (RMS) and PGS load forecasting model are proposed based on task offloading. Simultaneously, an online delay-aware power Resource Allocation Algorithm (RAA) is developed for EC architecture. Finally, comparing three algorithms corroborate that the system overhead decreases significantly with the model iteration. From the 40th iteration, the system overhead stabilizes. Moreover, given no more than 50 users, the average user delay of the proposed delay-aware power RAA is less than 13 s. The average delay of the proposed algorithm is better than that of the other two algorithms. This research contributes to optimizing intelligent PGS in smart cities and improving power transmission efficiency.