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The use of the conventional dual closed-loop control strategy by photovoltaic (PV) plants with grid-connected inverters may weaken the damping of a power system, which may aggravate low-frequency oscillations (LFOs). This influence will become more severe as the penetration of PV plants increases. Therefore, it is necessary to incorporate damping controls into PV plants to suppress LFOs. This paper proposed an additional compound damping control (ACDC) system that combines additional damping control (ADC) for the inverter with ADC-based dynamic power compensation control (DPCC), allowing hybrid energy storage systems (HESSs) to suppress LFOs. First, the feasibility of suppressing low-frequency oscillations in PV plants is demonstrated by the torque method and a small signal model. Then, an additional damping controller is added to the active power control link of the PV inverter to enhance the damping abilities of the system. However, given that the damping performance of PV plants with only ADC is limited by the compensated power, PV plants require devices that can rapidly compensate for the damping power. Therefore, we added the HESS to the DC bus and proposed DPCC. Finally, a three-machine nine-node system for a PV plant was modeled and simulated in the PSCAD platform. The simulation results showed that the proposed control strategy could provide effective damping for interarea oscillation.