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The use of synchrophasor data for observation and control is expected to enhance the operation and efficiency of the next generation of power systems. However, the specific characteristics of the data generated by synchrophasors makes them particularly vulnerable to cyber attacks. This paper presents a set of strategies to protect the anonymity of synchrophasor data against passive traffic analysis attacks. Considering the periodic nature of synchrophasor data, we propose defense mechanisms based on packet concatenation and random packet drops as a countermeasure against attacks that may use the timing as well as data volume information to compromise the network. In contrast to existing defenses against traffic analysis attacks, our scheme can be easily deployed using the current networking infrastructure as it is based on end-to-end principles and does not require any specialized routers. The proposed defense mechanisms are evaluated using both analysis and simulations.