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Abstract In recent years, power system uncertainties have increased due to the growing integrations of intermittent renewable energy resources. It is imperative to introduce probabilistic load flow analysis in the study of power system operation and planning to adapt to the ever-increasing uncertainties. This paper proposes a scenario-based analytical method for the probabilistic load flow analysis, which takes advantage of both the scenario analysis method and the cumulant method. This method can not only consider various kinds of correlations among power inputs but also accurately represent the probability distributions of desired outputs with a reasonable computational burden. The performance of this method is evaluated on the IEEE 14-bus and 118-bus test systems. The accuracy and efficiency of the proposed method are validated through quantitative and graphical comparisons with Monte-Carlo simulation.

In recent years, the increasing integration of renewable energy and electric vehicles has exacerbated uncertainties in power systems. Operators are interested in identifying potential violation events such as overvoltage and overload via probabilistic power flow calculations. Evaluating the violation probabilities requires sufficient accuracy in tail regions of the output distributions. However, the conventional Monte Carlo simulation and importance sampling typically require numerous samples to achieve the desired accuracy. The required power flow simulations result in substantial computational burdens. This study addresses this challenge by proposing a surrogate-assisted importance sampling method. Specifically, a high-fidelity radial basis function-based surrogate is constructed to approximate the nonlinear power flow model. Subsequently, the surrogate is embedded in the conventional importance sampling technique to evaluate the rare probabilities with high efficiency and reasonable accuracy. The computational strengths of the proposed method are validated in the IEEE 14-bus, 118-bus, and realistic 736-bus systems through comparisons with several well-developed methods. The comparisons provide a reference for system operators to select the appropriate method for evaluating violations based on the intended applications.

Over the past decades, the deployment of distributed generations (DGs) in distribution systems has grown dramatically due to the concerns of environment and carbon emission. However, a large number of DGs have introduced more uncertainties and challenges into the operation of distribution networks. Due to the stochastic nature of renewable energy resources, probabilistic tools are needed to assist systems operators in analyzing operating states of systems. To address this issue, we develop a probabilistic framework for the assessment of systems. In the proposed framework, the uncertainties of DGs outputs are modeled using short term forecast values and errors. Moreover, an adaptive cluster-based cumulant method is developed for probabilistic load flow calculation. The performance of the proposed framework is evaluated in the IEEE 33-bus system and PG&E 69-bus system. The results indicate that the proposed framework could yield accurate results with a reasonable computational burden. The excellent performance of the proposed framework in estimating technological violations can help system operators underlying the potential risks of systems.