The growing penetration of electric vehicles (EVs) represents an operational challenge to system operators, mainly at the distribution level by introducing congestion and voltage drop problems. To solve these potential problems, a two-level coordination approach is proposed in this study. An aggregation entity, i.e., an EV virtual power plant (EV-VPP), is used to facilitate the interaction between the distribution system operator (DSO) and EV owners considering the decentralized electricity market structure. In level I, to prevent the line congestion and voltage drop problems, the EV-VPP internally respects the line and voltage constraints when making optimal charging schedules. In level II, to avoid power transformer congestion problems, this paper investigates three different coordination mechanisms, or power transformer capacity allocation mechanisms, between the DSO and the EV-VPPs, considering the case of EVs charging and discharging. The three mechanisms include: (1) a market-based approach; (2) a pro-rata approach; and (3) a newly-proposed constrained market-based approach. A case study considering a 37-bus distribution network and high penetration of electric vehicles is presented to demonstrate the effectiveness of the proposed coordination mechanism, comparing with the existing ones.