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This paper presents the four-quadrant operation modes of bidirectional chargers for electric vehicles (EVs) framed in smart car parks. A cascaded model predictive control (MPC) scheme for the bidirectional two-stage off-board chargers is proposed. The controller is constructed in two stages. The model predictive direct power control for the grid side is applied to track the active/reactive power references. The model predictive direct current control is proposed to achieve constant current charging/discharging for the EV load side. With this MPC strategy, EV chargers are able to transmit the active and reactive powers between the EV batteries and the power grid. Apart from exchanging the active power, the vehicle-for-grid (V4G) mode is proposed, where the chargers are used to deliver the reactive power to support the grid, simultaneously combined with grid-to-vehicle or vehicle-to-grid operation modes. In the V4G mode, the EV battery functions as the static var compensator. According to the simulation results, the system can operate effectively in the full control regions of the active and reactive power (PQ) plane under the aforementioned operation modes. Fast dynamic response and great steady-state system performances can be verified through various simulation and experimental results. [ABSTRACT FROM AUTHOR]