Marginal Uncertainty Cost Functions for Solar Photovoltaic, Wind Energy, Hydro Generators, and Plug-In Electric Vehicles

The high penetration of renewable sources of energy in electrical power systems implies an increase in the uncertainty variables of the economic dispatch (ED). Uncertainty costs are a metric to quantify the variability introduced from renewable energy generation, that is to say: wind energy generation (WEG), run-of-the-river hydro generators (RHG), and solar photovoltaic generation (PVG). On other side, there are associated uncertainties to the charge/uncharge of plug-in electric vehicles (PEV). Thus, in this paper, the uncertainty cost functions (UCF) and their marginal expressions as a way of modeling and assessment of stochasticity in power systems with high penetration of smart grids elements is presented. In this work, a mathematical analysis is presented using the first and second derivatives of the UCF, where the marginal uncertainty cost functions (MUCF) and the UCF’s minimums for PVG, WEG, PEV, and RHG are derived. Further, a model validation is presented, considering comparative test results from the state of the art of the UCF minimum, developed in a previous study, to the minimum reached with the presented (MUCF) solution.