Hybrid energy storage systems (HESSs) have become an effective solution for smoothing the active power variations of photovoltaic (PV). In order to reduce the required capacities and costs of the HESS, a coordinated control scheme is developed to mitigate the power variations of a PV plant by using the HESS and the active power curtailment (APC) of PV. Furthermore, a multi-objective optimization model is established to dispatch the output power of batteries and supercapacitors, considering the overall losses and the state-of-charge (SOC) deviation of the supercapacitor. Based on the proposed smoothing strategy, an allocation model is developed to optimize the energy and power capacities of the HESS with the aim of maximizing the annual net income of the PV and HESS plant. The numerous simulations are carried out to verify the effectiveness of the proposed smoothing and allocation methods by using the real data of a PV plant. In addition, we also discuss the impacts of the different dispatching strategies of the HESS, grid requirements of power variations, and solution methods on the HESS allocation results.