Computationally efficient tail distribution-aware large-scale power system overloading risk assessment

The uncertainties and intermittency associated with renewable generation sources, such as solar and wind, can pose significant overloading risks to power systems under N - k contingencies, potentially leading to cascading outages. Accurately quantifying these risks in independent system operator scale power systems, which may include tens of thousands of buses, remains a grand challenge. This paper proposes a computationally efficient, tail-distribution-aware approach for accurate overloading risk quantification in large-scale power systems. Specifically, a deep-kernel sparse vector-valued Gaussian process is developed and serves as a surrogate model. This model incorporates generation dispatch, predefined contingencies, and uncertain inputs, such as photovoltaic power and load demand, to predict their impacts on branch power flows, which are treated as the model outputs. To improve the fidelity of overloading risk assessment, we introduce an adaptive resampling mechanism based on power flow solver, which corrects biases in surrogate model predictions near the overloading threshold. Extensive results obtained on the realistic 21k+ bus New England power system demonstrate that the proposed method accelerates the risk assessment process by 22 times compared to the benchmark Monte Carlo sampling method, while maintaining high accuracy. Additionally, we validate the robustness of the approach across a wide range of distribution types and correlation scenarios between renewable generation and load demands.