This paper investigates the problem of the estimation of the energy consumed by the unschedulable electric appliances in a nearly-Zero Energy Building (nZEB) and specifically, the electric appliances that their operation cannot be programmed or scheduled by a home Energy Management System (EMS). This is important for the EMS because it is mainly based on the nZEB microgrid model and hence, the exact knowledge of the electric loads is required. In this paper, a novel method to predict the energy that will be consumed by the unschedulable loads is presented that is based on the Artificial Neural Network (ANN) technique. This is accomplished, by considering the weather forecast data and the residents’ habits of the house that will be estimated by considering the history of the electric energy consumption of the unschedulable appliances that can be obtained by the smart energy meters of the house. The effectiveness and the feasibility of the proposed energy consumption estimation algorithm are validated and evaluated by several simulation results in the MATLAB/Simulink environment, using real time electric energy measurements which were obtained by a typical house-hold, located in Northern Greece.