Scalable nonparametric joint chance-constrained unit commitment with renewable uncertainty

Abstract

Recent advances in modeling distributionally robust joint chance constraints (DRJCCs) include moment-based and kernel-based approaches. The computational burden of such programming increases exponentially with the dimension of DRJCCs. This paper introduces a scalable kernel-based DRJCC unit commitment approach. Network constraints are treated as chance constraints jointly over transmission lines, while reserve requirements are considered as chance constraints jointly over the scheduling horizon. DRJCCs are formulated using multivariate kernel density estimation with the integral of uniform kernel. The kernel function is linearized using a special ordered set of type 1 (SOS1) variables. Three techniques are proposed to reduce computational costs. Firstly, DRJCCs are replaced with individual chance constraints using optimized Bonferroni, and the resulting kernel-based constraints are linearized. A probability function compression technique reduces the number of constraints and SOS1 variables needed to linearize kernel density functions. Furthermore, a learning-aided technique reduces the dimensionality of optimization by removing inactive network constraints. Simulation studies demonstrate the effectiveness of the proposed techniques.