Scalable Probabilistic Optimal Power Flow for High Renewables Using Lite Polynomial Chaos Expansion

This work introduces a novel polynomial chaos expansion (PCE)-based method for uncertainty quantification (UQ) in power systems, addressing probabilistic optimal power flow problem. The proposed approach leverages upon a series of transformations to overcome two main hinders to deploying POPF in practice, i.e., the vast number of random variables (RVs) and their interdependence. The proposed Lite-PCE method requires a small set of optimal power flow samples. The most important transformation is developed based on a Clayton copula to convert substantially large dimensional input variables into a single RV for efficient computing. The transformation allows Lite-PCE to be built on a single RV and offers a significant computational benefit while working with a large number of random renewable injections. The method also handles correlated random injection variables with different types of distributions in a nonparametric fashion. The Lite-PCE method is also used to develop the concept of transmission capacity sensitivity under uncertainty using coefficients of variation. The concept and nonparametric, scalable simulations are demonstrated using various IEEE test cases, up to the 1354-Bus system with 1242 random injection variables. The UQ results illustrate the efficiency and accuracy of the method for systems of considerable size and a high number of renewable injections.