Anti-disturbance performance reflects the core performance of cable-driven parallel robots (CDPRs) to resist external wrenches and exert wrenches to the outside world, which plays a significant role in the design and control of CDPRs. However, existing analysis methods encounter the issue of dimensional collapse when analyzing the anti-disturbance performance of redundant CDPRs, thereby failing to reflect the influence of tension distribution. In this paper, the augmented wrench space and Augmented Available Wrench Set (AAWS) are proposed for the analysis and tension distribution of redundant CDPRs, establishing the complete mapping between cable tensions and terminal wrenches of redundant CDPRs. The AAWS resolves the issue of dimensional collapse encountered in existing methods, and clarifies the comprehensive impact of tension distribution on the performance of redundant CDPRs. A tension distribution method is developed based on the AAWS to enhance the anti-disturbance performance of redundant CDPRs. Simulation indicates that the proposed AAWS-based tension distribution method effectively improves the anti-disturbance performance compared to the commonly used 2-norm-based method and the centroid method. This paper presents an efficient and universal approach for analyzing, evaluating, and improving the anti-disturbance performance of redundant CDPRs.