Tempered Christoffel-Weighted Polynomial Chaos Expansion for Resilience-Oriented Uncertainty Quantification

Accurate and efficient uncertainty quantification is essential for resilience assessment of modern power systems under high impact and low probability disturbances. Data driven sparse polynomial chaos expansion (DDSPCE) provides a computationally efficient surrogate framework but may suffer from ill conditioned regression and loss of accuracy in the distribution tails that determine system risk. This paper studies the impact of regression weighting schemes on the stability and tail accuracy of DD-SPCE surrogates by introducing a tempered Christoffel weighted least squares (T-CWLS) formulation that balances numerical stability and tail fidelity. The tempering exponent is treated as a hyperparameter whose influence is examined with respect to distributional accuracy compared with Monte Carlo simulations. Case studies on distribution system load shedding show that the proposed method reduces 95th percentile deviation by 16%, 5th percentile deviation by 6%, and improves the regression stability index by over 130%. The results demonstrate that controlling the weighting intensity directly influences both stability index and the accuracy of tail prediction.