**Ruifeng Shi 1,2, Penghui Zhang 1, Jie Zhang 1, Li Niu 3,\* and Xiaoting Han <sup>4</sup>**


Received: 25 March 2020; Accepted: 21 May 2020; Published: 2 June 2020

**Abstract:** With the deterioration of the environment and the depletion of fossil fuel energy, renewable energy has attracted worldwide attention because of its continuous availability from nature. Despite this continuous availability, the uncertainty of intermittent power is a problem for grid dispatching. This paper reports on a study of the scheduling and optimization of microgrid systems for photovoltaic (PV) power and electric vehicles (EVs). We propose a mathematical model to address the uncertainty of PV output and EV charging behavior, and model scheduling optimization that minimizes the economic and environmental cost of a microgrid system. A semi-infinite dual optimization model is then used to deal with the uncertain variables, which can be solved with a robust optimization algorithm. A numerical case study shows that the security and stability of the solution obtained by robust optimization outperformed that of stochastic optimization.

**Keywords:** electric vehicle; microgrid; photovoltaic; robust optimization; stochastic optimization
