The massive integration of renewable energies into the grid using fast-response converters without inertia generates issues such as inertia reduction, temporary voltage violations, and power quality reduction. The system inertia reduction is a critical problem that could lead to grid frequency exceeding the acceptable range, resulting in undesirable load-shedding or even large-scale blackouts. To overcome these issues, the use of Electric Vehicle Bidirectional Chargers (EVBCs) implementing functionalities such as distributed Virtual Inertia (VI), long-term frequency support, voltage support by reactive power, and harmonics compensation, has been proposed as a possible solution. This paper proposes a novel control strategy to manage a hybrid energy storage system (HESS) composed of DC-Link capacitors and battery, through an isolated twostage AC-DC converter (composed of a DAB resonant type DC-DC converter cascaded to a VSI), intended for off-board EVBCs. The HESS management allows decoupling of the active power dynamic response since DC-Link capacitors supply the fast dynamic response for VI support whereas the battery supplies the slower dynamic response for long-term frequency support respectively. Hence, the VI support does not affect the battery lifetime. Simulations and experimental results are presented for a 2.5 kW prototype to validate VI, frequency-voltage support along with harmonics compensation.