Despite its many advantages, the non-controllable and intermittent nature of renewable energy sources is adding further stress to the energy networks and hence, grid operators are often forced to curtail RES generation or to limit its further penetration in the most congested areas. Smart tri-generation districts (electricity, gas, heat) can be key to mitigate these issues and increase the renewable hosting capacity of the grid, provided their feature an optimal use of their energy conversion and storage capabilities. This paper presents a district energy management approach based on Multi-Agent System (MAS) that takes into consideration the tri-energy vectors (electricity, gas, thermal). The optimization problem is solved in a distributed way based on the Alternating Direction Method of Multipliers with the objective of minimizing district costs and preliminary results show the efficiency of our approach to achieve this objective.