Mesh-constructed and radial-operated features call for elaborate consideration of co-planning for multi-energy distribution systems (MEDS). Considering a reconfiguration channel can be constructed in advance to cope with extreme

$N$

−1 contingencies

this paper proposes a hierarchical robust expansion co-planning model for MEDS. By adopting convex hull relaxation and linearization techniques

the model is cast as a mixed-integer linear programming (MILP) problem with high accuracy. Specifically

the model is divided into four parts: master investment problem

feasible load cutting subproblem in normal scenarios or

$N -1$

fault scenarios

and optimal operational subproblem. Based on defense-attack-correction methodology

a hierarchical solution incorporating adjustable

$N-1$

contingency tolerance is developed to tradeoff economy and reliability. Fur-thermore

a relaxation feedback method is applied to solve invalid feedback cuts of existing parameterization methods. Numerical test results justify the model can generate the best configuration for mesh-constructed MEDS

and the reconfiguration strategy under di

fferent adjustable

$N-1$

contingency tolerances is also given as an output of the optimization.