Due to the broadcast nature of power line communication (PLC) channels, confidential information exchanged on the power grid is prone to malicious exploitation by any PLC device connected to the same power grid. To combat the ever-growing security threats, physical layer security (PLS) has been proposed as a viable safeguard or complement to existing security mechanisms. In this paper, the security analysis of a typical PLC adversary system model is investigated. In particular, we derive the expressions of the corresponding average secrecy capacity (ASC) and the secrecy outage probability (SOP) of the considered PLC system. In addition, numerical results are presented to validate the obtained analytical expressions and to assess the relevant PLS performances. The results show significant impacts of the transmission distances and the used carrier frequency on the overall transmission security.