An Interval–Probabilistic CVaR (IP-CVaR) and Modelling for Unknown Probability Distribution of Some Random Variables

Abstract

Traditionally, the uncertainty qualification is utilized with the known probability distribution function (PDF). However, in some scenarios, the PDFs of some uncertain variables are modeled inaccurately or the rough PDFs of the uncertainty are not entirely clear. To solve above problems, this paper presents a new uncertainty description method with the interval model and probabilistic model, respectively. Accordingly, a new risk method, named interval–probabilistic conditional value-at-risk (IP-CVaR) is proposed and its optimal model is firstly established. Under the condition of the interval uncertainty, two interval operators are defined, as well as the positive and negative spinning reserve models are established by the IP- CVaR, especially in the case of high penetration wind power integration. In this study, to describe the risk impact of interval uncertainty on the economic operation of the power grid, a novel risk-aware flexible joint economic dispatch model with the description of the interval and probabilistic uncertainties is established, which is the new formulation of two optimal problems, i.e., the lower and upper boundaries optimal models. Comparisons between the proposed IP-CVaR and other existing techniques are conducted, and the simulations on IEEE- 39 and 118 bus system are made to verify the superiority for the proposed IP- CVaR.