Blockchain is increasingly being used to provide a distributed, secure, trusted, and private framework for energy trading in smart grids. However, existing solutions suffer from lack of privacy, processing and packet overheads, and reliance on Trusted Third Parties (TTP). To address these challenges, we propose a Secure Private Blockchain-based (SPB) framework. SPB enables the energy producers and consumers to directly negotiate the energy price. To reduce the associated packet overhead, we propose a routing method which routes packets based on the destination Public Key (PK). SPB eliminates the need for TTP by introducing atomic meta-transactions. The two transactions that form a meta-transaction are visible to the blockchain participants only after both of them are generated. Thus, if one of the participants does not commit to its tasks in a pre-defined time, then the energy trade expires and the corresponding transaction is treated as invalid. The smart meter of the consumer confirms receipt of energy by generating an Energy Receipt Confirmation (ERC). To verify that the ERC is generated by a genuine smart meter, SPB supports authentication of anonymous smart meters which in turn enhances the privacy of the meter owner. Qualitative security analysis shows the resilience of SPB against a range of attacks.