This paper presents a self-scheduling framework, using risk-constrained optimization model for the home energy management system (HEMS), considering fixed, controllable, and interruptible loads, as new contribution to earlier studies. The objectives are reducing electricity bill managing risk of purchasing over on-peak hours prosumer's discomfort index (DI) due shifting load undesired hours. In...

Abstract This paper focuses on a class of variational inequalities (VIs), where the map defining VI is given by component-wise conditional value-at-risk (CVaR) random function. We focus solving using sample average approximation, solutions are estimated with that uses empirical estimates CVaRs. establish two properties for this scheme. First, under continuity and uncertainty taking values in bo...

Suppose that N is a Z+-valued random variable and that X,X1, X2, . . . is a sequence of independent and identically distributed Z+ random variables independent of N . In this paper we are interested in properties of the conditional variable Nk D =(N | ∑Nj=1 Xj = k). In particular, we want to know the asymptotic behavior of the conditional mean ENk or the conditional variance var Nk as k → ∞. We...

Introduction Algebraic speciications can be used for the speciication of var