Abstract: Retired power batteries have poor parameter consistency，when they are used for energy storage

after series and parallel connections，the barrel effect is obvious and the failure rate is high. So the improved modular multilevel H-bridge converter（MMHC）distributed energy storage based on modular multilevel converter（MMC）was proposed. However，there are many sub-modules of MMHC energy storage converters，and the resistancecapacitance sensing network is complex. Using traditional grid-connected models to study them cannot accurately describe its dynamic and static behaviors. The integer-order PI controller designed based on its traditional gridconnected model cannot meet the requirements of fast dynamic response and better robustness. To solve the above problems，the fractional-order grid-connected model of the MMHC energy storage converter identified from the frequency domain was proposed in the controller. Based on the fractional-order grid-connected model，the ITAE criterion and ISE criterion were used as performance indicators，and the model matching method was used to design the fractional PIλ controller. Through simulation and experimental comparison and analysis，the fractional-order model can better reflect the behavior of the complex system. The fractional-order controller designed has fast dynamic response and better robustness，and the superior grid-connected operation of the MMHC energy storage converter is realized.

      Key words: modular multilevel H-bridge converter（MMHC）energy storage converter；fractional order grid

connected model；dynamic response；fractional order PIλ controller；robustness