An online probabilistic combination framework for power load forecasting under concept-drifting scenarios

Probabilistic load forecasting is essential for power system operators in making operational and financial decisions under uncertainty. Ensemble forecasting has emerged as a powerful approach to improve predictive performance by combining multiple individual models. However, existing ensemble methods typically assume a stationary environment and often overlook the impact of concept drift–the change in the underlying data distribution over time. Our study demonstrates that conventional combination methods, when exposed to concept drift, can underperform and in some cases yield worse results than their individual component models. We refer to this phenomenon as combination failure under concept drift. To address this issue, we develop an online probabilistic combination framework that incorporates the online learning mechanism, enabling continuous adaptation to concept drift. Kernel density estimation is integrated with Gaussian approximation of quantiles (KG) to address the ensuing quantile crossing issue. We theoretically prove the validity of KG in concept-drifting scenarios. The optimization step is then performed based on KG with the objective of minimizing continuous ranked probability score. Additionally, a trapezoidal rule-based search algorithm is proposed to extract multiform combined predictions from the combined probability density function. The efficacy of the proposed framework in handling concept drift and combination failure is substantiated through the extensive experiments on three city level datasets. Experimental results show that while traditional ensemble models exhibit a 12 % performance degradation under concept drift, the proposed framework achieves a 14 % improvement in prediction accuracy over the best individual model.