The novel trend of peer-to-peer (P2P) transactions has allowed traditional consumers to become prosumers, capable of maximizing the usage of their energy production by sharing it with their neighbors. Thus, the P2P market has emerged to allow both prosumers and consumers to trade energy independently from the conventional market. However, while local energy transactions will allow for a more open and decentralized grid, they will nevertheless have a significant impact on the planning, control and operation of distribution grids. Hence, in this paper, an improved model is presented to evaluate the impact of P2P transactions on distribution grid congestion, considering its restrictions and the uncertainty associated with renewable energy sources generation and load. The objective function has been modeled to minimize the transaction costs of each prosumer/consumer. The model was tested on a branch adapted from a 119-bus IEEE test grid, in which different operational scenarios have been considered through case studies, considering the various RES technologies and energy storage systems (ESS) installed by each prosumer/consumer. Comprehensive simulation results indicate that the introduction of smart grid enabling technologies and P2P transactions has led to both technical (voltage profile and grid congestion) and economic benefits for the distribution grid and its users.