Beyond fifth-generation (B5G) communication networks and computation paradigms in the edge are expected to be integrated into power grids infrastructures over the next years. In this sense, AI technologies will play a fundamental role to efficiently manage dynamic information flows of future applications, which impacts the authorization policies applied in such a complex scenario. This article studies how Digital Twins can evolve their context-awareness capabilities and simulations technologies to anticipate faults or to detect cyber-security issues in real time, and update access control policies accordingly. Our study analyzes the evolution of monitoring platforms and architecture decentralization, including the application of machine learning and blockchain technologies in the Smart Grid, towards the goal of implementing autonomous and self-learning agents in the medium and long term. We conclude this study with future challenges on applying Digital Twins to B5G-based Smart Grid deployments.