A novel framework for operational infeasibility assessment of active distribution systems using improved quantile polynomial chaos expansion

This article presents an advanced two-stage statistical framework for operational infeasibility analysis (OIA) in active distribution systems operating under high uncertainties. In Stage-I, enhanced Mean and Multiple Quantile Lite-Polynomial Chaos Expansions (IMQ-Lite-PCEs) are proposed as robust meta-modeling tools for uncertainty quantification. In Stage-II, the IMQ-Lite-PCEs are leveraged to extract comprehensive statistical insights, enabling accurate estimations of key metrics such as means, variances, confidence intervals, and conditional distributions of system states, facilitating informed decision-making. The efficacy of the proposed method (PM) is rigorously validated through comparisons with state-of-the-art PCE variants for uncertainty quantification in renewable energy resource (RES)- and electric vehicle (EV)-dominated power systems. The results underline the superior accuracy of the PM, with L1 -relative errors as low as 0.22 %, 0.19 %, 0.16 %, 0.12 %, and 0.43 % for state estimations on the IEEE 33-, −69, −85, 141-, and unbalanced three-phase 37-bus systems, respectively. Moreover, the PM demonstrates exceptional capabilities in probabilistic and classification analyses, achieving 98.27 %, 98.72 %, 98.63 %, and 98.95 % classification accuracy for identifying nodal voltage violations and 91.06 %, 99.58 %, 92.94 %, and 93.11 % accuracy for detecting overloaded line power flows in the IEEE −33, −69, −85, and 141-bus networks, respectively. Additionally, comparative analysis against low-rank approximation methods, Gaussian Process Regression (GPR), and Deep Sparse GPR underscores the PM’s robust performance in handling complex probabilistic computations and classification tasks.