Direct-drive wind farms (DDWF) merged into weak AC systems have the risk of sub-synchronous oscillations (SSO). Because the DDWF model has a higher order,it needs to be reduced for actual analysis. When analyzing the SSO problems,the existing balanced reduction method cannot accurately keep SSO modes of the system during the reduction process. To solve this problem,a balanced reduction method for SSO analysis is proposed. This method is based on the participation factor analysis and retains the state variables which strongly related to the SSO model. Combining with the Hankel singular value to determine the reduction order,a reduced-order system model consistent with the SSO characteristics and dynamic characteristics of the full-order system model is established. Firstly,a balanced system model by balancing the small signal model of the full-order system is established. Then,the participation factor analysis is performed on the balanced system model,combined with the Hankel singular value to ensure the set of retained state variables,and the residual order reduction method is used to establish the reduced-order system model. Finally,by comparing the full-order system model and the reduced-order system model,the results show that the proposed reduced-order method is suitable for the study of DDWF integration into weak AC system SSO.