In today's electrical power markets, due to the presence of versatile uncertain parameters such as increasing penetration rate of plug-in electric vehicles, larger portion of renewable energy resources in power production, and demand side behaviors, decision making under uncertainty is a non-separable requirement. In this context, lacks of historical data and in some cases data privacy make dealing with extracting the accurate probability distribution functions a challenging task. As a solution, the current paper applies Z-number possibilistic-probabilistic method, based on fuzzy logic principles, to deal with uncertainties in a plug-in electric aggregators-scheduling problem (PEVAgg-SSDRP)without relying on probability distribution functions of uncertain parameters with objective function of benefit maximization through optimal bidding to spinning reserve market. In the proposed model, aggregators participate in the spinning reserve market and the load reduction amount during peak hours is obtained. The uncertain parameters are PEV aggregation and demand response program's participation where the former modeled by a systematic method based on multi state Markov and to model the later, due to lack of historical data, Z-number method is utilized. In addition, because of easy implementation and fast convergence, gravitational search algorithm is used to solve the proposed mixed integer non-linear problem. (C) 2020 Elsevier Ltd. All rights reserved.
