As renewable energy sources have been widely integrated into power distribution systems, alleviating power system vulnerability and reducing voltage deviation while lowering costs still remain important issues to be resolved in a power grid. For this reason, a vulnerability-aware energy storage planning framework is proposed for enhancing renewable-rich distribution networks. First, a vulnerability indicator system is established by considering both line and node operational states for vulnerability assessments. Second, an optimization model is formulated to minimize system vulnerability and life-cycle economic cost by incorporating objective functions and system operating constraints. Third, to efficiently implement the proposed model, an improved rapidly exploring random tree optimizer (IRRTO) is introduced on the basis of cubic chaotic mapping, a step-size learning factor, and a Lévy flight perturbation mechanism. Empirical validation is presented via simulations on the IEEE 33-bus system equipped with photovoltaic and wind power sources, confirming the effectiveness of the proposed methodology. Performance results verify that, compared with the case with no energy storage, the proposed model can reduce the power system vulnerability and voltage deviation up to 23.0 and 27.0%, respectively, while requiring lower investment and operating costs.