To simultaneously improve the economic efficiency and resilience of distribution networks

this paper proposes a three-stage robust planning model for siting and sizing distributed wind turbines

battery storages

and dispatchable generators (e.g.

diesel generators) in distribution systems. In the first stage

these distributed energy resources (DERs) are properly planned in distribution systems. In the second stage (normal conditions)

the wind uncertainty is addressed with a robust method

and operation costs in the worst-case wind scenario are minimized by wisely scheduling the allocated DERs. In the third stage (emergency conditions)

the stochastic nature of wind energy and line outage is simultaneously considered and characterized by polyhedral uncertainty sets and

$N-K$

criteria

respectively. Moreover

a novel microgrid formation model considering master-slave DERs is proposed to improve the resilience of distribution systems during emergency conditions. Consequently

this planning model is formulated as a min-(max-min)-(max-min) optimization problem

which cannot be directly solved by commercial solvers. Hence

a novel tri-level decomposition method is p

roposed to solve this three-stage nonlinear model by decomposing it into several mixed-integer linear problems. Last

simulation results on distribution systems demonstrate the effectiveness of the planning model.