Accurate load forecasting plays a vital role in optimizing energy distribution and integrating renewable energy sources within smart grid systems. However, traditional centralized deep learning approaches present major challenges related to data privacy, communication overhead, and scalability, particularly in scenarios involving distributed energy consumers.
To address these concerns, this study proposes a federated learning (FL) framework that leverages Gated Recurrent Unit (GRU) networks to enable decentralized and privacy-preserving load forecasting. The proposed approach is evaluated using three distinct aggregation strategies: Federated Averaging (FedAvg), Federated Proximal (FedProx), and Federated Averaging with Trimmed Mean (FedTrimmedAvg). These methods aim to alleviate data heterogeneity and client drift, which are prevalent in non-independent and identically distributed (non-IID) settings commonly encountered in smart grid environments—challenges known to limit the effectiveness of standard FedAvg and that motivate the need for more robust alternatives.
Experimental results on real-world energy consumption datasets demonstrate that the proposed FL framework achieves competitive forecasting accuracy while preserving client data privacy. A rigorous comparative analysis reveals that FedProx and FedTrimmedAvg consistently outperform FedAvg under non-IID conditions, with FedTrimmedAvg offering the highest robustness to outliers and inconsistent client behavior. These findings highlight the effectiveness of robust aggregation techniques in federated settings and present a scalable, privacy-aware solution for intelligent energy management in next-generation smart grid infrastructures.
A. Tibermacine, Ilyes Naidji, Imad Eddine Tibermacine et al.· Frontiers in Energy Research· 1 citation
State estimation for nonlinear dynamical systems remains a fundamental challenge, particularly when measurements are sparse and internal states are inaccessible. This work presents a KOOPMAN-based Linear State Observer (KOOPMAN-LSO) design framework that enables linear observer synthesis for nonlinear systems through KOOPMAN operator theory. The nonlinear dynamics are lifted into a higher-dimensional observable space using physics-informed basis functions, where a linear predictor with control is identified via extended dynamic mode decomposition with control (eDMDc). A discrete-time Luenberger observer is then constructed in the lifted space, and the observer gain is obtained through a dual linear - quadratic regulator (LQR) formulation to ensure stable and tunable estimation error dynamics. The proposed framework combines the representational capability of KOOPMAN lifting with the simplicity and computational efficiency of linear observer design, providing a systematic approach for nonlinear state estimation under limited sensing. Its effectiveness is demonstrated on a latent thermal energy storage (LTES) system based on phase-change materials (PCM), where internal temperature states are not directly measurable. Experimental results under varying operating conditions show accurate reconstruction of unmeasured states from limited output measurements, illustrating the potential of KOOPMAN-LSO design for practical nonlinear systems. The proposed approach achieves high-fidelity reconstruction with an RMSE as low as 0.0819 {\deg}C for the LTES outlet temperature and generally below 1.0 {\deg}C for observable internal PCM temperatures.
M. Habib, Dario Aguiar, Esther Kieseritzky et al.· 0 citations