Non-Parametric Joint Chance Constraints for Economic Dispatch Problem with Solar Generation

Uncertainty modeling has a significant role in power system scheduling and operation. This paper presents a data-driven non-parametric joint chance-constrained programming model for the economic dispatch problem. Solar generation uncertainties are taken into consideration. Kernel density estimator is used to find non-parametric probability density functions (PDFs) of the solar generation in each scheduling interval without imposing any assumption on the classes of PDFs. A joint chance constraint is formulated for the whole considered scheduling horizon to take into account solar generation uncertainty in the generation reserve constraint. A φ -divergence tolerance is calculated based on the point-wise error of the estimated non-parametric PDFs, and an increased confidence level (or reduced risk level) is calculated. The joint chance constraint is approximated with a set of individual constraints. A conservative upper bound for the confidence level of the individual chance constraints is calculated from the joint chance constraint confidence level. The chance constrained are converted into their linear equivalent forms to make the optimization problem solvable by standard solvers. The proposed ED model is applied to a six-bus system, and promising results are obtained.