The third-party-invested shared energy storage operational model enables users to access energy storage services while avoiding high upfront investment costs. To address the issues of capacity mismatch and cost escalation caused by unreasonable user partitioning for shared energy storage, a shared energy storage capacity configuration method based on cluster partitioning is proposed. This approach enables partition-based management of the distribution network, optimizing shared energy storage capacity for each partition. First, a four-dimensional comprehensive evaluation index system is constructed for distribution networks with high penetration of distributed renewable energy, incorporating active/reactive power balance, modularity, and connectivity. A genetic algorithm is employed to partition the network, balancing electrical characteristics and topological structure. Second, a transaction framework for third-party-invested shared energy storage is developed. A Stackelberg leader-follower game bilevel optimization model is established between the operator and users. To address the inefficiency of solving traditional bilevel models, Karush-Kuhn-Tucker optimality conditions and complementary slackness linearization methods are introduced. Finally, case simulations are conducted on a modified IEEE 33-node distribution network. The results demonstrate that the proposed cluster partitioning indices effectively divide the network, and the bilevel model optimally configures shared energy storage capacity.