**1. Introduction**

Energy shortages and environmental pollution are now problems that cannot be ignored. To build an environment-friendly and resource-saving society, renewable energy generation such as wind and photovoltaic (PV) power have received increasing attention [1–3]. Renewable energy accounted for approximately 18.1% of total final energy consumption in 2017 and was mainly concentrated in the field of electricity generation. According to the "Renewables (2019) Global Status Report" estimate, by the end of 2019 more than 26% of global electricity generation had come from renewable sources [4]. Renewable energy has the advantage of being inexhaustible, but its intermittent and volatile nature poses new challenges to the safe and stable operation of the power grid.

Renewable energy generation is influenced by climate and weather, and is not controlled by human factors. The electricity generation and the electricity consumption cannot match well; there will often be no electricity available at the peak of electricity consumption, or no electricity production surplus at the trough of the situation. With the increasing number of electric vehicles, the two-way energy dispatching between electric vehicles and the power grid provides the solution for renewable energy power generation and large-scale application of electric vehicles. Electric vehicles consume renewable energy when electricity consumption demand is low, and even discharge electricity into the grid when demand is high. Reasonable and flexible scheduling strategies can ensure the coordinated operation of electric vehicles and renewable energy generation.

To solve the problem of grid-connected distributed generation, the microgrid came into being. A microgrid manages the power generation units and power load dispatching within a certain range. The key to the safe and stable operation of a microgrid is to reduce the uncertainty of renewable energy generation. Currently, the main methods to solve the uncertainty problem are stochastic optimization (SO), fuzzy programming, and robust optimization (RO) [5]. The probability distribution function is used by SO to express the output of renewable energy. This method must usually collect much scene data, which increases the difficulty of the problem [6–8]. Fuzzy programming uses fuzzy variables to represent uncertainty and fuzzy sets to describe constraints. The satisfaction of constraints is represented by a membership function. This method usually depends on the activities of people, so some deviation is unavoidable [9–11]. RO uses a set approach to represent uncertainty. This method does not need to know the probability distribution of renewable energy output, nor does it depend on human activity. The results of RO can deal with worst-case scenarios. In view of this characteristic, RO is increasingly favored [12,13].

RO has good advantages in tolerating uncertainties in dispatch problems [14]. To alleviate the risk of microgrid energy trading under the uncertainty of renewable energy and transaction price, Luhao Wang et al. proposed a risk avoidance method based on RO and created a two-stage energy-trading RO model. Their results show that the model can not only achieve the optimal operating cost of the microgrid system but also ensure the robustness of energy trading between systems at various prices [15]. Yan Cao et al. used RO techniques to study the scheduling problem of electric vehicle (EV) aggregators with price uncertainty and to participate in the market with the goal of maximizing the benefits of aggregators. When they modeled market price uncertainty, they used the upper and lower limits of the upstream grid price instead of the estimated price. The output of the algorithm was used to construct various charging and discharging strategies for operators to use for robust scheduling of EV aggregators under upstream grid price uncertainty. The results show that compared with a deterministic strategy, the total profit of the EV aggregators under the optimistic strategy had increased by 69.78% [16]. Carlos D. Rodríguez-Gallegos et al. proposed an optimized configuration method for solar panels and batteries, forming a PV hybrid system. A multi-objective optimization problem was established by considering economic goals, environmental goals, and grid quality. The worst weather conditions were considered, and RO algorithm was applied. The results showed that PV hybrid power systems have the advantages of reducing costs and improving the environment and the grid quality in remote areas [17].

Considering the uncertainty of the renewable energy output and EV charging behavior, in this study the RO theory was applied to a microgrid system containing a PV power station and EVs. To reduce the running cost and environmental cost, the goal was to build a multi-objective scheduling model. Then, the scheduling objective function was optimized by minimizing the economic and environmental costs of the microgrid system. Based on the duality principle, the semi-infinite problem containing uncertain variables was converted into an easier dual problem. Finally, SO and RO were compared. RO has a high cost, but its security and stability are most important for a microgrid. The main contributions of this paper are as follows:


The paper is organized as follows: the models of PV power output and EV charging behaviors are described in Section 2. Section 3 introduces the multi-objective scheduling system and actual constraints. The theory and application of RO are presented in Section 4. A case study is used in Section 5 to show the performance of the proposed models. Conclusions are drawn in Section 6.

### **2. Uncertainty Modeling**

In this paper, the microgrid system connected to the main power grid includes PV power stations, microturbines (MTs), diesel engines (DEs), and EVs. The uncertainties of PV output power and EV charging behavior are expressed as a set.
