Hypothesis Testing for Mitigation of Operational Infeasibility on Distribution System Under Rising Renewable Penetration

High penetration of renewables and unconventional loads expose power systems to more operational infringements, which can be the bottleneck for deploying more renewables. Understanding system infeasibility characterization, in terms of the types and probability of the infeasibility occurrence at different renewable penetration levels towards 100%, is indispensable to develop suitable solutions for the seamless operation and expansion of power systems. Meanwhile, the privacy constraints, enormous scenarios, and high dimensions of variables make it impractical to access full data even through simulations. Hence, this work presents a systematic hypothesis testing framework to analyze the infeasibility characterization following the rising level of renewables with making the most of available data. Instead of making conjectures based on empirical observations. The proposed framework through p-values, Rank-biserial and Kendall's
$\tau _{b}$
coefficients, logistic and linear regressions, and Bayes factors provides sufficient statistical evidences to confirm the associations between the penetration levels and operational infringements, together with power losses. Besides, an optimal control scheme is designed to mitigate the odds ratio of violations. This logit-based control leverages logistic regression models to provide a convenient form of violation probability for convex optimization. Moreover, a nonlinear feature selection method called Feature-Wise Kernelized Lasso is the first time incorporated to select the optimal control sets to overcome the multi-collinearity and overfitting problems in Big Data. Simulation results under various IEEE test feeders with different means of renewable levels illustrate the effectiveness of the proposed methods.