This paper analyzes the modulation and the control strategy for an isolated and bidirectional two-stage DC-AC converter to interface batteries with the single-phase grid. The converter is composed of a Dual-Active-Bridge Series-Resonant (DABSR) DC-DC converter cascaded with a Voltage Source Inverter (VSI). Both converters are linked by a film capacitor. The time-variant single-phase power is decoupled on the DC-link, which allows a high ripple voltage. In the VSI control, a Notch Filter (NF) is used to filter the low-frequency ripple influence in the grid power transfer. Two different modulations are analyzed to power decoupling in the DABSR DC-DC converter: (1) 50% fixed duty ratio (FDR) with time-variant phase-shift (TVPS) modulation and (2) time-variant duty ratio (TVDR) with fixed phase-shift modulation to power transfer. The analysis for different capacitance values is made considering the ripple on the DC-Link and the THD in the grid current. The results show that 50% FDR and TVPS modulation allows ZVS mode and minimum high-frequency current. However, TVDR allows a better power decoupling in the DC current. The control strategy and modulation are validated by simulation.