Abstract: With the connection of large-scale renewable energy sources, the rotational inertia of modern power system decreases,and the dynamic characteristics of frequency are deteriorating. In order to support the system frequency, the power generation devices of renewable energy sources are usually required to have additional control functions, such as inertial simulation or primary frequency regulation. However, there is little research on the optimal frequency support of renewable energy sources. Based on the optimal control, this paper discusses the optimal power support trajectory and approximate optimal control structure of power electronic devices as grid-connected interfaces, when there are energy constraints on the renewable energy sources participating in frequency regulation. Firstly, the common-mode component of frequency for multi-machine system is deduced, which dominates the frequency drop characteristics of power grid. Secondly, based on the Gauss pseudospectral method, this paper studies the optimal support trajectory of power electronic devices with energy constraints when the system frequency drops. Thirdly, the optimal feedback control structure for grid-connected power electronic devices supporting power grid frequency is studied. It is shown that the control structure combined with virtual inertia control and droop control is close to the optimal control structure, and the virtual inertia control is better than the droop control when the available energy is small. Finally, the simulations verify the rationality of the theoretical analysis and the discussed optimal control structure of frequency.