Advances in digitalization and networking of power grids have increased the risks of cyberattacks against such critical infrastructures, where the attacks often originate from within the power grid's network. Adequate detection must hence consider both physical access violations and network anomalies to identify the attack's origin. Therefore, we propose INSIDE, combining network intrusion detection with automated facility monitoring to swiftly detect cyberattacks on power grids based on unauthorized access. Besides providing an initial design for INSIDE, we discuss potential use cases illustrating the benefits of such a comprehensive methodology.