Uncertainties are the most significant challenges in smart power system, necessitating use of precise techniques to deal with them properly. Such problems could be effectively solved using a probabilistic optimization strategy. It is further divided into stochastic, robust, distributionally and chance-constrained optimizations. The topics systems covered this review paper. In order account for ...

The paper studies large scale mixed integer reformulation approach to stochastic programming problems containing probability and quantile functions, under assumption of discreteness of the probability distribution involved. Jointly with general sample approximation technique and contemporary mixed integer programming solvers the approach gives a regular framework to solution of practical probab...

This paper presents a fully-decentralized peer-to-peer (P2P) electricity and gas market for retailers prosumers with coupled energy units, considering the uncertainties of wholesale price prosumers’ demand. The goal is to improve overall economy proposed while increasing its flexibility. In this market, are equipped self-generation storage units can bilaterally negotiate transactions maximize t...

We develop a general methodology for deriving probabilistic guarantees solutions of robust optimization problems. Our analysis applies broadly to any convex compact uncertainty set and c...

In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general tran...