This article proposes a new distributed risk-limiting load restoration scheme for wind power penetrated interconnected bulk systems. The conditional value-at-risk (CVaR) is used as the risk-limiting index. The projection function based alternating direction method of multipliers algorithm (P-ADMM) is used to decouple the CVaR integrated load restoration model into a distributed form. With the proposed algorithm, the risk-limiting constraints are decomposed and the complex non-convex load restoration model with the CVaR is transformed into small-scale scenario-based QP problems. The distributed risk-limiting load restoration scheme respects the individual decision-making of regional grids and reduces the security violation risk of the interconnected bulk system under uncertain conditions. The CVaR integrated P-ADMM method can efficiently reduce the computation complexity of the load restoration optimization for the uncertain bulk system without loss of optimality. The effectiveness of the proposed method was validated using the IEEE-118 bus system connected with thirty IEEE-33 bus systems.