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This paper proposes a Multi-stage Energy Management System (MS-EMS) for power distribution in a smart microgrid comprising a photovoltaic system (PV), an Energy Storage System (ESS), and connected to an Electrical Power Grid (EPG). The proposed MS-EMS consists of two layers, the Anticipative Layer (AL) and the Reactive Layer (RL). The AL uses a Multi-objective particle swarm optimization (MOPSO) algorithm to determine the optimal power setpoints for each source over the next 24 h based on predicted energy demand and solar power generation. The RL utilizes real-time data collection and Extremum-Seeking optimization (ES) to compensate for prediction uncertainties by adjusting the ideal power setpoints in real-time. In addition, this paper addresses both the issues of management and prediction. It introduces a forecasting system that effectively predicts the next 24 h of load demand and PV power generation using actual data, by integrating a physical model with artificial neural networks (ANN). The efficiency of the proposed MS-EMS is highlighted using experimental data collected in real-time on a physical bench in Morocco. The performances of the proposed MS-EMS system are compared with those of existing EMS strategies, including an existing industrial solution. The comparison shows that the proposed MS-EMS substantially overperforms in terms of three criteria: energy bill, battery degradation cost, and peak-to-Average Ratio (PAR). Despite forecasting uncertainties, the experimental test shows a remarkable 6% gain in the reduction of the energy bill and PAR compared to an offline strategy (where uncertainties were not considered). Furthermore, it achieved a 5% and a 3% gain in the reduction of the energy bill and PAR, respectively compared to an online strategy (focused on real-time optimization). Additionally, compared to an existing industrial solution, the MS-EMS achieves a reduction in energy bill and PAR of 9% and 56% respectively while taking into account battery degradation constraints described in this study. • Multi-stage approach for Multi-Objectives Grid Management with Forecast Uncertainties. • Extremum Seeking approach for real-time energy management problem solving. • Artificial Intelligence for electrical load and PV power forecasting. • Experimental comparison of the proposed strategy with an existing industrial solution. • Experimental test shows a reduction in energy bill and PAR of 9% and 56% respectively. [ABSTRACT FROM AUTHOR]