The photovoltaic（PV） grid-connected system with hybrid energy storage（HESS） not only effectively solves the randomness and fluctuation of traditional PV power generation

but also overcomes the contradiction between the power density and the energy density of a single energy storage system. However

the output power quality will be worse

and the overcurrent will appear on the inverter side under unbalanced grid voltage condition. This will affect the operation stability of the entire system. In order to restrain the doubling frequency pulsation of the current in the energy storage converter

and secondary pulsation in grid-connected power in order to improve the power quality; the harmonics and overcurrent problems of the grid current reference value are analyzed in the two-phase stationary coordinate system. The current-limited model predictive direct power control（MPDPC） with power compensation is proposed. The double frequency notch filter is introduced in HESS

combining with the model predictive current control

the fast-dynamic response of the system and the high-power quality are realized. The system simulation model has been built in MATLAB/Simulink and tested for different working conditions. Simulation results show that the proposed control strategy can stabilize the secondary ripple of the current in the energy storage converter

and the output power of the inverter.At the same time this can achieve the suppression of the fault overcurrent during the coordinated control of the active/reactive power

and the negative sequence current under imbalanced grid voltage.