To realize the coordination of economic performance and reliability in multi-stage planning

the explicit expression is used to explicitly linearize the typical reliability indicators of distribution networks. The reliability-related costs calculated by each indicator are introduced into the objective function of the distribution network planning model

which is combined with the linearization constraints based on binary variables for construction investment

operation

and maintenance

to establish a multi-stage expansion planning model for active distribution networks. Concerning the uncertainty of the growth of distributed generations (DGs) and loads during the planning period

this study uses the expectation value of random variables and the maximum fluctuation deviation interval to transform the multi-stage expansion planning model into a “max-min” robust planning problem considering the growth uncertainties. The problem is constructed based on the power balance relationship between the DG and the load power as well as the power injected by the substation and solved by Gurobi solver called by YALMIP to maximize the set of uncertainty variables and minimize the costs. Finally

the effectiveness in addressing the uncertainty of source-load growth and the improvement of the overall economic efficiency and reliability of the planning results are verified on a 24-bus distribution network.