Adaptive Bayesian System Identification for Long-Term Forecasting of Industrial Load and Renewables Generation

The expansion of renewables in modern power systems and the coordinated development of upstream and downstream industrial chains are promoting a shift on the utility side from traditional settlement by energy toward operation driven by data and models. Industrial electricity consumption data exhibit pronounced multi-scale temporal structures and sectoral heterogeneity, which makes unified long-term load and generation forecasting while maintaining accuracy, interpretability, and scalability a challenge. From a modern system identification perspective, this paper proposes a System Identification in Adaptive Bayesian Framework (SIABF) for medium- and long-term industrial load forecasting based on daily freeze electricity time series. By combining daily aggregation of high-frequency data, frequency domain analysis, sparse identification, and long-term extrapolation, we first construct daily freeze series from 15 min measurements, and then we apply discrete Fourier transforms and a spectral complexity index to extract dominant periodic components and build an interpretable sinusoidal basis library. A sparse regression formulation with ℓ1 regularization is employed to select a compact set of key basis functions, yielding concise representations of sector and enterprise load profiles and naturally supporting multivariate and joint multi-sector modeling. Building on this structure, we implement a state-space-implicit physics-informed Bayesian forecasting model and evaluate it on real data from three representative sectors, namely, steel, photovoltaics, and chemical, using one year of 15 min measurements. Under a one-month-ahead evaluation using one year of 15 min measurements, the proposed framework attains a Mean Absolute Percentage Error (MAPE) of 4.5% for a representative PV-related customer case and achieves low single-digit MAPE for high-inertia sectors, often outperforming classical statistical models, sparse learning baselines, and deep learning architectures. These results should be interpreted as indicative given the limited time span and sample size, and broader multi-year, population-level validation is warranted.