Contents lists available at ScienceDirect Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr Stochastic robust optimization for smart grid considering various arbitrage opportunities Mohammadali Saffari a , Mohammad Saeed Misaghian a , Mohsen Kia b , Alireza Heidari c , Daming Zhang c , Payman Dehghanian d , Jamshid Aghaei e, ⁎ a Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran b Department of Electrical Engineering, Faculty of Eng., Pardis Branch, Islamic Azad University, Pardis, Tehran, Iran c School of Electrical Engineering and Telecommunications, The University of New South Wales (UNSW), Sydney, Australia d Department of Electrical and Computer Engineering, George Washington University, Washington, DC, USA e Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran ARTICLE INFO Keywords: Robust/stochastic optimization Microgrid Plug-in electric vehicles Mix-integer non-linear programming ABSTRACT Because of power electronic advancements, nowadays Plug-in Electric Vehicles (PEVs) are capable to charge/ discharge(absorb/inject) active(reactive) power. The storage capacity and the capability of bidirectional flowing active and reactive powers, lead PEVs to be contemplated as a viable option for energy arbitrage. By high penetration of PEVs, decentralized energy management of them, especially at peak hours causes serious pro- blems to the network operation and service quality. Therefore, it is important PEVs to be controlled as integrated with microgrid (MG). Besides, PEVs uncertain behavior along with the prevalent uncertainties inherent to re- newable resources and various pricing mechanism in electricity industry leaves the MG operators (MGOs) a challenging decision making. So, it is vital to be applied an efficient strategy in order to deal with this challenges. This paper proposes a centralized framework to co-optimize robust/stochastic optimization of MG with the PEVs energy arbitrage in both active and reactive powers exchange. The problem is a mix-integer non-linear pro- gramming (MINLP) problem, which is solved by GAMS software. The results of suggested model are investigated on IEEE 18-bus and IEEE 33-bus test systems. 1. Introduction Because of low emission and energy consumption, PEVs are con- templated as efficient alternative to internal-combustion-engine. Recently, there are drastically growth to use them as next generation of vehicle. Therefore, governments and energy corporations have centered their attempts to improve the development of PEVs. One of the bene- ficial merits of PEVs is the energy arbitrage opportunity which moti- vates their owners to minimize cost of energy. In Ref. [1] is investigated the arbitrage strategy of PEVs owner using stochastic optimization to estimate the potential profit from electricity price arbitrage of PEVs under three scenarios with variant electricity tariff. Reference [2] evaluates PEVs utilizing vehicle-to-grid (V2G) technology to behave as a storage system, arbitraging in the energy market and providing an- cillary services. Aforementioned references consider the arbitrage strategy from PEVs viewpoint which are seeking to maximize their profit and have not considered effects of PEVs energy arbitrage on network. High penetration of PEVs without considering efficient control strategy, brings challenges for their integration and energy manage- ment and it can make side effects on MG e.g., overload of lines or voltage drop [3]. In order to manage adverse effects of PEVs, it is es- sential energy of PEVs to be controlled as integrated with MG. In Ref. [4], a multistage droop-control mechanism has been suggested for PEVs integrated islanded MGs. The droop characteristics of the distributed generation (DG) units, load shedding of MG, and the charging and discharging behavior of PEVs have been coordinated through the pro- posed control mechanism in Ref. [4]. Reference [5] presents a hier- archical stochastic control scheme for the coordination of PEVs char- ging and wind power in a MG. In reference [6], a multi-objective optimization problem is solved to schedule power sources in a typical MG, while PEVs are viewed as a stochastic factor. Reference [7] pro- poses two energy management strategies to effectively utilize V2G potential of PEVs in managing energy imbalances in grid-connected MGs. All this works have considered only charging/discharging of ac- tive power by PEVs. In recent years, power electronic advancements give PEVs the capability of charge/discharge active power and absorb/ https://doi.org/10.1016/j.epsr.2019.04.025 Received 27 September 2018; Received in revised form 26 February 2019; Accepted 23 April 2019 ⁎ Corresponding author. E-mail address: aghaei@sutech.ac.ir (J. Aghaei). Electric Power Systems Research 174 (2019) 105847 Available online 09 May 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved. T