In recent years, most of the research in the field of smart grids integrating renewable energy sources assumed energy efficiency as a scheduling objective. However, the aspects of energy consumption or energy demand have not been described clearly, even though they have been proven to be an effective way of reducing energy consumption. In this context, this study aimed to cover a key research challenge in the field, such as the development of an intelligent strategy for solving energy consumption scheduling problems. The added value of our proposal consists of classifying individual consumption profiles assigned to each operation cycle phase, instead of considering an average of non-varying consumption of household appliances. Within this hybrid approach, the proposed explainable system, based on self-organizing maps of neural networks, fuzzy clustering algorithm, and scheduling technics, correlates the complex interrelation between power generated from renewable energy sources in a smart grid, prosumers’ load behaviors, and the consumption profile of controllable or uncontrollable appliances. The tests were made using green energy consumption and production from real monitored data sets. The load-shifting algorithm that was used to reduce energy consumption from the national energy grid proved its effectiveness. In fact, consumers paid 25% less for the energy they used from the national energy grid during the times when the amount of electricity produced from renewable sources was reduced as a result of weather conditions.