Power grids are undergoing major changes due to rapid growth in renewable energy resources and improvements in battery technology. While these changes enhance sustainability and efficiency, they also create significant management challenges as the complexity of power systems increases. To tackle these challenges, decentralized Internet-of-Things (IoT) solutions are emerging, which arrange local communities into transactive microgrids. Within a transactive microgrid, ``prosumers'' (i.e., consumers with energy generation and storage capabilities) can trade energy with each other, thereby smoothing the load on the main grid using local supply. It is hard, however, to provide security, safety, and privacy in a decentralized and transactive energy system. On the one hand, prosumers' personal information must be protected from their trade partners and the system operator. On the other hand, the system must be protected from careless or malicious trading, which could destabilize the entire grid. This paper describes \emph{Privacy-preserving Energy Transactions} (PETra), which is a secure and safe solution for transactive microgrids that enables consumers to trade energy without sacrificing their privacy. PETra builds on distributed ledgers, such as blockchains, and provides anonymity for communication, bidding, and trading.