Flexible load at the demand-side has been regarded as an effective measure to cope with volatile distributed renewable generations. To unlock the demand-side flexibility, this paper proposes a peer-to-peer energy sharing mechanism that facilitates energy exchange among users while preserving privacy. We prove the existence and partial uniqueness of the energy sharing market equilibrium and provide a centralized optimization to obtain the equilibrium. The centralized optimization is further linearized by a convex combination approach, turning into a multi-parametric linear program (MP-LP) with renewable output deviations being the parameters. The flexibility requirement of individual users is calculated based on this MP-LP. To be specific, an adaptive vertex generation algorithm is established to construct a piecewise linear estimator of the optimal total cost subject to a given error tolerance. Critical regions and optimal strategies are retrieved from the obtained approximate cost function to evaluate the flexibility requirement. The proposed algorithm does not rely on the exact characterization of optimal basis invariant sets and thus is not influenced by model degeneracy, a common difficulty faced by existing approaches. Case studies validate the theoretical results and show that the proposed method is scalable.
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