Renewable energy-based Distributed Generation (DG) is the most imperative part of modern power system and offers many potential benefits. To attain maximum benefits offered by DG integration, it is important to model the time varying characteristics of both load and generation. Therefore, this paper presents a new Weibull distribution-based time-coupled Probabilistic Generation model for optimal placement and sizing of wind DG with time varying voltage dependent (TVVD) loads. At first, Probabilistic model is proposed for wind speed uncertainty modeling to calculate the hourly output power from wind DG. Afterwards, the values of output power are considered for determining optimal allocation and penetration of wind DG in distribution network to minimize the Average Multi-Objective Index (AIMO) using Particle Swarm Optimization (PSO). The strength of the proposed methodology is validated on IEEE 33 and 69-bus systems. Results depict that, proposed methodology is appropriate for wind speed modeling and is suitable for implementing in power system planning.