Optimal planning of power distribution systems with local resources is crucial to meet energy demand and avoid disruptions in energy supply for consumers. This requires the system operators to manage available resources and utilize suitable risk management tools to control and study uncertainties and their potential consequences. This paper proposes an uncertainty-based optimization framework based on the robust optimization and scenario methodology for optimal sizing and siting of electrical vehicle charging stations (EVCSs). The proposed model seeks to take advantage of the flexibility introduced by EVCSs and gain financial profit for the operator of the power distribution system through reducing power losses and offering services to electricity markets. To handle the uncertainties posed by different resources, two risk measures are employed simultaneously. The uncertainty originating from the state of charge (SOC) of electric vehicles (EVs) is addressed through stochastic programming, while the robust optimization method (ROM) enables the operator of the power distribution system to be informed of the consequences of uncertainty in electricity load. Therefore, appropriate strategies can be taken to tackle the uncertainties while keeping the system operation stable and gaining financial profit. Thus, three strategies are studied in the proposed model as follows: risk-neutral, risk-averse, and risk-taker. In addition, the non-linear terms in power flow modeling were linearized through a set of linear functions which transforms the proposed model to a MILP problem. The IEEE 33-bus test system under different levels of load uncertainty and considering the uncertainty in SOC of EVs is utilized to ensure the effectiveness of the proposed model. The results highlight the efficiency of the proposed model in considering uncertainties and taking advantage of the consideration of different risk attitudes by the decision-maker that ROM provides for the optimal operation of the power distribution system.