Abstract: With the significant increase in the use of renewable power generators, future power systems face stability challenges, including subsynchronous oscillation（SSO）, which is a crucial issue. This study proposes subsynchronous damping control（SDC） strategies based on a grid-forming controlled battery energy storage system（BESS） to effectively suppress the SSOs induced by the interaction between nearby direct-drive wind farms and a weak AC grid. The BESS not only offers a range of grid services, including load shifting, peak shaving, and frequency regulation, but also provides positive damping for possible unstable SSO modes from grid-connected wind power. Different SDC structures were designed based on a low-pass filter, notch filter, and phase shifter, and their installed locations and filter/gain parameters were selected. Finally, the results were verified based on electromagnetic simulations, the damping performances of the three SDCs were compared, and the influence of the BESS capacity on oscillation damping was investigated. Specifically, the NF-SDC with a second-order notch filter and the PS-SDC based on a phase shifter exhibited superior performance under the given system conditions. The damping target SSO modes required at least 5% BESS capacity.