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• Proposing a new robust co-planning of AC/DC hybrid transmission network and energy storage. • Embedding BFM within the proposed co-planning model. • Using data-adaptive robust optimization to cope with uncertainties. • Validating the effectiveness of the proposed method in practical power system. This paper proposes a robust co-planning model of hybrid AC/DC transmission network and energy storage with the penetration of renewable energy to promote the accommodation of renewable energy and to avoid investment redundancy. The energy storage configured in the power grid can improve the power flow distribution and alleviate transmission congestion, postponing the investment of new devices. A deterministic co-planning model is firstly developed considering voltage fluctuation, reactive power flow and the flexibility of voltage source converter based high voltage direct current (VSC-HVDC). To address the solving complexity caused by the non-convexity of the model, second-order cone programming (SOCP) is applied to transform the proposed model into a convex problem. To cope with the uncertainty of renewable energy, the robust co-planning formulation is established, where the data-adaptive uncertainty set with the extreme scenario method is introduced to describe renewable generation uncertainty. The column-and-constraint generation (C&CG) algorithm is adopted to decompose the robust co-planning problem into a master problem and several slave problems, which reduces the calculation scale and accelerates the solving process. Two case studies on a modified Garver's 6-bus system and a practical Jiangxi province power system in China are carried out to verify the effectiveness and superiority of the proposed robust co-planning model. [ABSTRACT FROM AUTHOR]