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Vehicle-to-grid (V2G) as an essential network component of smart grid, provides services by periodically collecting the charging status of a battery vehicle (BV). A BV is normally associated with a default interest group (e.g., power grid operator). When the BV accesses its default charging or communication point, it works in the home mode. The BV may move around and temporarily access other aggregators, and then it works in the visiting mode. In this paper, we first identify that, for an aggregator, BVs have different security challenges when they work in different modes. Then, we propose an aggregated-proofs based privacy-preserving authentication scheme (AP3A) to achieve simultaneous identification and secure identification for different working mode BVs. In AP3A, BVs are differentiated into either home or visiting mode, and multiple BVs can be simultaneously authenticated by an aggregator to conserve communication resources. In addition, the aggregated pseudo-status variation is presented to realize that multiple BVs' power status can be collected as a whole without revealing any individual privacy. We perform comprehensive analysis on the proposed scheme, including attack analysis, security analysis, and performance analysis. It is shown that AP3A can resist major attacks for security protection and privacy preservation, and can be an efficient authentication approach for V2G networks.