This article describes the development of an optimal and predictive energy management system (EMS) for a microgrid with a high photovoltaic (PV) power contribution. The EMS utilizes a predictive long-short-term memory (LSTM) neural network trained on real PV power and consumption data. Optimal EMS decisions focus on managing the state of charge (SoC) of the battery energy storage system (BESS) within defined limits and determining the optimal power contributions from the microgrid components. The simulation utilizes MATLAB R2023a to solve a mixed-integer optimization problem and HOMER Pro 3.14 to simulate the microgrid. The EMS solves this optimization problem for the current sampling time $(t)$ and the immediate sampling time $(t+1)$, which implies a prediction of one hour in advance. An upper-layer decision algorithm determines the operating state of the BESS, that is, to charge or discharge the batteries. An economic and technical impact analysis of our approach compared to two EMSs based on a pure economic optimization approach and a peak-shaving algorithm reveals superior BESS integration, achieving 59% in demand satisfaction without compromising the life of the equipment, avoiding inexpedient power delivery, and preventing significant increases in operating costs.

Modeling forced nonlinear multivariable dynamical systems remains challenging, particularly when first-principles models are unavailable or strong nonlinear couplings are present. In recent years, data-driven approaches grounded in the Koopman operator theory have gained attention for their ability to represent nonlinear dynamics via linear evolution in appropriately lifted spaces. This work presents a data-driven modeling framework for forced nonlinear multiple-input multiple-output (MIMO) systems based on Hankel Dynamic Mode Decomposition with control and lifting functions (HDMDc+Lift). The proposed methodology exploits Hankel matrices to encode temporal correlations and employs lifting functions to approximate the Koopman operator’s action on observable functions. As a result, an augmented-order linear state-space model is identified exclusively from input–output data, without relying on explicit knowledge of the system’s governing equations. The effectiveness of the proposed approach is demonstrated using operational data from a real multivariable tank system that was not used during the identification stage. The identified model achieves a coefficient of determination exceeding 0.87 in multi-step prediction tasks. Furthermore, spectral analysis of the resulting linear operator reveals that the dominant dynamical modes of the physical system are accurately captured. At the same time, additional modes associated with nonlinear interactions are also identified. These results highlight the HDMDc+Lift framework’s ability to provide accurate and interpretable linear representations of forced nonlinear MIMO dynamics.