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Accurate quantification of uncertainty in solar photovoltaic (PV) generation forecasts is imperative for the efficient and reliable operation of the power grid. In this paper, a data-driven non-parametric probabilistic method based on the Naïve Bayes (NB) classification algorithm and Dempster–Shafer theory (DST) of evidence is proposed for day-ahead probabilistic PV power forecasting. This NB-DST method extends traditional deterministic solar PV forecasting methods by quantifying the uncertainty of their forecasts by estimating the cumulative distribution functions (CDFs) of their forecast errors and forecast variables. The statistical performance of this method is compared with the analog ensemble method and the persistence ensemble method under three different weather conditions using real-world data. The study results reveal that the proposed NB-DST method coupled with an artificial neural network model outperforms the other methods in that its estimated CDFs have lower spread, higher reliability, and sharper probabilistic forecasts with better accuracy. 

The Bayesian approach has been used for the dynamic state estimation (DSE) of a power system. However, due to the complexity of noise resources, it is difficult to quantify measurement and process noise using probability density functions (PDFs). To overcome the difficulty, the authors of this article propose a modified eigen-decomposition-based interval analysis (MEDIA) method, which employs bounds instead of PDFs to quantify the noise, and uses the eigen decomposition method to reduce the negative impact of the overestimation problem. Using the simulation data generated from IEEE 16-machine and IEEE 10-machine systems, it is shown that the proposed MEDIA method can estimate the hard boundaries of dynamic states in real time. Comparison with the forward-backward propagation method and the extended set-membership filter also shows that the proposed MEDIA method performs better by providing narrower boundaries in the DSE.