Recursively Updated Probabilistic Model for Renewable Generation

The Gaussian Mixture Model (GMM) is commonly used to formulate the probabilistic model for quantifying uncertainties in renewable generation. However, traditional static probabilistic models may not efficiently adapt and learn from newly forecasted and measured data. In this paper, we propose a recursively updated probabilistic model that leverages a recursive estimation method to update the parameters of the GMM based on continuously arriving data of renewable generation. This recursive modeling approach effectively incorporates new observations while discarding outdated samples, enabling the tracking of time-varying uncertainties in renewable generation in an incremental manner. Furthermore, we introduce an extra calibration stage to enhance the long-term accuracy of the probabilistic model after a large number of incremental updates. The main contribution is to address the potential degradation of performance caused by suboptimal incremental updates accumulated over time. Numerical tests demonstrate that the proposed model achieves 5–10% higher log likelihood in characterizing renewable generation uncertainties compared to purely recursive models, while reducing computational time by three to four orders of magnitude (1000 to 10,000 times) relative to conventional EM. These results highlight the proposed model’s suitability for real-time probabilistic modeling of renewable generation, with potential applications in system operation.