Data-driven Nonparametric Joint Chance-Constrained Programming for Power Systems Scheduling

This dissertation is dedicated to implementing data-driven nonparametric joint chance constraints (JCC) to power system optimization problems. Power generated by renewable sources, such as solar farms, is an uncertain parameter. Several approaches solve optimization under uncertainty, including stochastic programming, robust programming, and chance-constrained programming. Uncertain parameters may not belong to any parametric class of probability functions. Thus, methods that consider such uncertainty as a random variable that fits in a known probability density function (PDF) have limitations. This study focuses on chance-constrained programming under nonparametric or data-driven distributionally robust uncertainty settings. Studies based on chance-constrained programming usually focus on individual chance constraints (ICC) that lack reliability or scenario-based methods like sample average approximation with limited performance with finite samples. The data-driven nonparametric JCC models presented in this work make no assumption on the type and shape of random variable PDFs. Line flow and reserve constraints are modeled as chance constraints that are joint over transmission lines and time intervals, respectively, which significantly enhance the reliability compared to ICC models. The computational burden of high-dimensional JCCs is reduced by a convex approximation with a bi-level problem reformulation approach and an optimized Bonferroni approximation-based approach