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Decentralized energy production, particularly from photovoltaic (PV) systems, is becoming increasingly prevalent, leading to a rise in the number of energy producers and consumers, or ”prosumers”. These prosumers, equipped with their own energy generation and storage systems, are not just passive consumers but active participants in the energy market. They generate their own electricity, often from renewable sources, and can feed excess power back into the grid, store it for later use, or share it within a local energy community. This evolving energy paradigm presents new opportunities and challenges in terms of energy management and optimization, necessitating innovative approaches to ensure efficient and sustainable use of energy resources. This paper introduces an innovative storage management method for grid-connected photovoltaic (PV) systems. The method is designed to minimize either the economic or ecological cost, or to find an optimal balance between the two, under various tariff scenarios. This is achieved while adhering to a full self-consumption constraint imposed by the distribution system operator. The control strategy is underpinned by forecasts of electrical consumption, production, and CO2 emissions, which are developed using feedforward neural network models. These models are trained on data from a real-scale smart-grid demonstrator at the Catholic University of Lille, France. The results of the study offer a comparative analysis of the economic and ecological benefits of the three proposed strategies, demonstrating that the best compromise is achieved when considering the off-peak tariff option. Furthermore, a real-time controller was implemented on the Energy Management System (EMS) of the demonstrator and tested over a 24-hour period, yielding satisfactory results. This paper, therefore, presents a significant advancement in the field of storage management for grid-connected PV systems.