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The quasi-Z-source inverter (qZSI) with battery operation can balance the stochastic fluctuations of photovoltaic (PV) power injected to the grid/load, but its existing topology has a power limitation due to the wide range of discontinuous conduction mode during battery discharge. This paper proposes a new topology of the energy-stored qZSI to overcome this disadvantage. The operating characteristic of the proposed solution is analyzed in detail and compared to that of the existing topology. Two strategies are proposed with the related design principles to control the new energy-stored qZSI when applied to the PV power system. They can control the inverter output power, track the PV panel's maximum power point, and manage the battery power, simultaneously. The voltage boost and inversion, and energy storage are integrated in a single-stage inverter. An experimental prototype is built to test the proposed circuit and the two discussed control methods. The obtained results verify the theoretical analysis and prove the effectiveness of the proposed control of the inverter's input and output powers and battery power regardless of the charging or discharging situation. A real PV panel is used in the grid-tie test of the proposed energy-stored qZSI, which demonstrates three operational modes suitable for application in the PV power system.