Since the energy domain is in a transformative shift towards sustainability, the integration of new technologies and smart systems into traditional power grids has emerged. As an effective approach, Petri Nets (PN) have been applied to model and analyze the complex dynamics in Smart Grid (SG) environments. However, we are currently missing an overview of types of PNs applied to different areas and problems related to SGs. Therefore, this paper proposes four fundamental research questions related to the application areas of PNs in SGs, PNs types, aspects modelled by PNs in the identified areas, and the validation methods in the evaluation. The answers to the research questions are derived from a comprehensive and interdisciplinary literature analysis. The results capture a valuable overview of PNs applications in the global energy landscape and can offer indications for future research directions.