The growing adoption of electric vehicles (EVs) presents challenges for power systems, particularly due to uncontrolled charging. Such charging can lead to grid overload that requires immediate grid reinforcement. This paper proposes a planning model for an EV aggregator participating in ancillary service markets while considering the distribution grid limitations. Monte Carlo simulations capture uncertainties in mobility patterns and activations of the ancillary services. We compare uncontrolled charging with a bidirectional smart charging algorithm, which is formulated as a mixed-integer linear program. A case study focusing on the Swedish market, specifically regarding participation in the frequency containment reserve, demonstrates that smart charging benefits the EV aggregator, EV owners, and the power system. The results highlight that the flexibility of the EV can optimize the existing utilization of the grid and delay the reinforcement of the grid. The proposed planning model supports decision-making in uncertain markets, ensuring the feasibility of the EV aggregator business model.