Calculation of Nodal Marginal Prices Considering Load and Generation Price Uncertainties

This paper presents the mathematical models and the solution algorithms of DC optimal power flow problems considering uncertainties represented by fuzzy numbers affecting loads as well as the elements of the cost function. The main purpose of this work corresponds to transfer the uncertainties affecting both the loads and the cost vector to the results that one usually obtain with such a DC optimal power flow model, that is, to characterize the uncertainties that affect the generations, the voltage phases, the branch flows. Apart from that, this paper also describes the algorithm to be used to calculate the uncertainties affecting the nodal marginal prices, since these prices are related with the dual variables of several constraints in the optimization problem. The developed algorithms are based in the solution of multiparametric problems in which one considers parameters both in the right hand side vector of the constraints (in order to represent load uncertainties) and in the cost function (to consider uncertainties in fuel costs, for instance). Finally, the paper includes a results of a case study designed to illustrate the application of the developed algorithms as well as results obtained for the IEEE 24 bus test system.