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

Abstract

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.

Algorithms for Optimal Power Flow Extended to Controllable Renewable Systems and Loads

“…The operation of the PSO algorithm consists of making a search for new optimal values by each particle using the expressions ( 31) and (32), where a new position of particle i, which is X (k+1) i , is generated from its old position X (k) i , taking into account the best historical position of each particle P…”

“…Scenario 1 consists of keeping the generators connected to nodes 1 and 2 as they are established in the original case, that is, with quadratic cost functions; however, the generator connected to node 3 is assumed to be a hydraulic generator with the cost functions defined in [32].…”

“…The parameters of the cost functions of the generators with cost of uncertainty and of the batteries are shown in Tables 9-12 (data from previous research: [32]): Finally, for the battery bank, an operation and maintenance cost is assumed c s = 30 MU/MW.…”