Optimal energy and load management in distribution networks is a key issue in power systems aimed at reducing investment and operational costs. With technological advancements, new resources such as electric vehicles (EVs) with bidirectional charging and discharging capabilities (V2G) have emerged as effective tools for reducing dependency on fossil-fuel-based generation and for managing load. In this paper, a convex optimization model is proposed to determine the optimal location and capacity of distributed generation (DG) units while accurately modeling the behavior of electric vehicles. The proposed model is formulated as a Mixed-Integer Second-Order Cone Programming (MISOCP) problem, enabling precise solutions with guaranteed global optimality. The nonlinear behavior of EVs is modeled using the Big-M linearization method. The objective function includes the total costs of investment, operation, energy procurement from the upstream grid, and energy losses. Operational constraints such as voltage limits, line flow capacities, and technical restrictions of resources are also considered. The model is simulated on the standard IEEE 33-bus distribution network, and the results of various scenarios show that the integration of V2G technology leads to significant reductions in total cost and energy losses. Moreover, sensitivity analysis with respect to key parameters confirms the structural robustness of the model. The proposed approach can serve as an effective tool for intelligent distribution network planning.