Data-Driven Nonparametric Joint Chance Constraints for Economic Dispatch with Renewable Generation

This article presents data-driven nonparametric joint chance constraints (JCCs) for ramp-constrained economic dispatch. Power generated by renewable sources, such as solar farms, is modeled as an uncertain parameter that may not belong to any parametric class of probability functions. Thus, transmission line flow limitation, which time-independent constraints, are formulated as nonparametric JCCs joint over unknown cumulative distribution functions of renewable generation sources. In addition, thermal units' time-dependent spinning reserve constraints are modeled as nonparametric JCCs joint over scheduling time periods. An approach is presented based on a multivariate kernel density estimator to convert economic dispatch with data-driven nonparametric JCCs into an optimization model solvable by standard solvers. A reduced, more conservative risk level is calculated to ensure JCCs' satisfaction, given the distance between true unknown and estimated cumulative distribution functions by kernel density estimator. An initiation strategy is applied to speed up the optimization solution time. Numerical results show that using data-driven nonparametric JCCs enhances system reliability significantly as compared to using individual chance constraints and parametric JCCs.