The growing use of direct current (DC) load demands and distribution generations (DGs) has led to changes in the distribution network. Due to DC and alternating current (AC) loads and generators, switching to an AC/DC distribution network is an effective solution. In this paper, the AC/DC distribution network planning problem is discussed. Uncertainties in the load demand and power generation of renewable sources cause probabilistic behavior of the distribution network, which leads to risk in the network. Therefore, the technical risks related to the node voltage and the line loading constraints dominate the problem. By modeling the cost of damage due to technical risks, these risks have become economic risks. Using the conditional value at risk (CVaR) method, the economic risk assessment of planning has been addressed. In addition, the modeling of hard and soft constraints for technical constraints has been discussed. The K-means algorithm has been used to model the uncertainties in the problem. The goals of planning are: minimizing planning costs and reducing economic risk. The proposed mathematical model has been solved in MATLAB and general algebraic modeling system (GAMS) hybrid space using a non-dominated sorting genetic algorithm (NSGA-II). Numerical results are presented for a 13-node distribution network.