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This paper uses a charging selection concept for plug-in electric vehicles (PEVs) to maximize user convenience levels while meeting predefined circuit-level demand limits. The optimal PEV-charging selection problem requires an exhaustive search for all possible combinations of PEVs in a power system, which cannot be solved for the practical number of PEVs. Inspired by the efficiency of the convex relaxation optimization tool in finding close-to-optimal results in huge search spaces, this paper proposes the application of the convex relaxation optimization method to solve the PEV-charging selection problem. Compared with the results of the uncontrolled case, the simulated results indicate that the proposed PEV-charging selection algorithm only slightly reduces user convenience levels, but significantly mitigates the impact of the PEV-charging on the power system. We also develop a distributed optimization algorithm to solve the PEV-charging selection problem in a decentralized manner, i.e., the binary charging decisions (charged or not charged) are made locally by each vehicle. Using the proposed distributed optimization algorithm, each vehicle is only required to report its power demand rather than report several of its private user state information, mitigating the security problems inherent in such problem. The proposed decentralized algorithm only requires low-speed communication capability, making it suitable for real-time implementation.