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.

Fused filament fabrication (FFF) has been proven to be an effective additive manufacturing technique for carbon fiber reinforced polyether–ether–ketone (CFR-PEEK) due to its practicality in use. However, the relationships between the process parameters and their trade-offs in manufacturing performance have not been extensively studied for CFR-PEEK although they are essential to identify the optimal parameter settings. This study therefore investigates the impact of critical FFF parameters (i.e., layer thickness, build orientation, and printing speed) on the manufacturing performance (i.e., printing time, dimensional accuracy, and material cost) of CFR-PEEK outputs. A full factorial design of the experiments is performed for each of the three sample designs to identify the optimal parameter combinations for each performance measure. In addition, multiple response optimization was used to derive optimal parameter settings for the overall performance. The results show that the optimal parameter settings depend on the performance measures regardless of the designs, and that the layer thickness plays a critical role in the performance trade-offs. In addition, lower layer thickness, horizontal orientation, and higher speed form the optimal settings to maximize the overall performance. The findings from this study indicate that FFF parameter settings for CFR-PEEK should be identified through multi-objective decision making that involves conflicts between the operational objectives for the parameter settings.