Microgrids are a development trend and have attracted a lot of attention worldwide. The control system plays a crucial role in implementing these systems and, due to their complexity, artificial intelligence techniques represent some enabling technologies for their future development and success. In this paper, we propose a novel formulation of an economic model predictive control (economic MPC) applied to a microgrid designed for a faculty building with the inclusion of a predictive model to deal with the energy demand disturbance using an artificial neural network (ANN). First, we develop a framework to identify an ANN using historical data registered by a smart three-phase power quality analyzer to provide feedforward power demand predictions. Next, we present an economic MPC formulation that includes the prediction model for the disturbance within the optimization problem to be solved by the MPC strategy. We carried out simulations with different scenarios of energy consumption, available resources and simulation times to highlight the results obtained and analyze the performance of the energy management system. In all cases, we observed the correct operation of the proposed control scheme, complying at all times with the objectives and operational restrictions imposed on the system.