**1. Introduction**

Advances in energy storage technology and grid intelligence and increased electric vehicle (EV) ownership have greatly promoted the development of EV charging infrastructure. However, the existing charging stations are neither low-carbon nor friendly to the distribution system because they have no energy storage facilities and must obtain electric power from the distribution network [1]. In order to take advantage of the bi-directional flow between renewable energy and energy storage systems, green photovoltaic (PV)-storage charging stations, installed with both a photovoltaic power generation system and an energy storage system, were developed based on the existing traditional charging stations. A PV-storage charging station is a microgrid that integrates the technologies of photovoltaic power generation, energy storage (ES), and smart charging station (SCS). The associated operation between photovoltaic power generation and EV charging and discharging can help promote the efficient consumption of renewable energy on-site and fulfill the EV load demand. Also, the introduction of an energy storage system can effectively alleviate the impact of EV charging on the regional

distribution network. This microgrid is an organically integrated source–storage–load system and meets the requirements for new-generation power systems: clean and efficient, green and low carbon, safe and controllable. At present, many countries, such as the United States, the United Kingdom, the Netherlands, and Malaysia, have built large-scale solar-powered EV charging stations. China has also launched some PV-storage charging EV station demonstration projects in cities such as Dongguan, Shanghai, and Qingdao. PV-storage charging stations will develop rapidly with advanced PV-storage technology and decreased economic costs in the coming days.

There are currently many studies on EV charging station planning. One study [2] summarized the main theoretical methods and research directions. Traditional charging station planning mainly aims to meet the increasing EV load demand and focuses on the siting and sizing of charging stations in the distribution network. However, with the integration of renewable energy and energy storage systems, capacity allocation and operational optimization for PV-storage charging stations have become hot research topics.

The literature on PV-storage charging station planning is mainly divided into two categories. The first category focuses on exploring the location and capacity allocation of charging stations from the perspective of distribution networks [3–5] or transportation networks [6–8], in the case of already known network structure. Charging station planning in a distribution network considers factors such as the environment, power quality [3], distribution feeder layout and availability [4], and operation safety and cost optimization [5]. When it comes to the transportation network, charging station planning considers the temporal and spatial dynamics of EV movement [6] and the spatial distribution of EVs [7], and a planning model was established using queuing theory and graph theory [8]. Considering the dual factors of distribution and traffic networks, some studies [9–12] carried out charging station planning with the objective of maximizing benefits and minimizing energy loss, while other studies [13,14] evaluated the planning results.

The second category focuses on the optimization of the internal design and energy capacity of PV-storage charging stations. This kind of study focuses mainly on internal charging stations, and rarely consider the constraints of the external network, which is usually regarded as an infinite source. Internal optimization is aimed at determining the compactness of internal facilities at charging stations, including the number of facilities and photovoltaic units and the ES capacity [15]. Commonly targeted at minimizing operation cost, the optimization model was established based on constraints such as operation, cost, and equipment utilization [16] and then was solved using corresponding particle swarm optimization algorithms [17] and NSGA-II (Non-dominated Sorting Genetic II Algorithm) [18]. In addition to cost, another study [19] also considered queuing time. It can be easily seen from the above studies that current PV-storage charging station planning rarely considers uncertain factors such as distributed generation, user behavior, and electricity price.

This paper, therefore, aims to study the internal optimization of PV-storage charging stations under uncertain conditions. Taking the uncertain factors—the charging station operator (CSO) and EV users—as the upper- and lower-level problems, a user behavior-based bi-level optimization model for the PV-storage model was established to determine the capacity allocation and electricity pricing. In the upper-level model, EV charging capacity constraints are considered, and there is an assumption that each EV user charges at a charging station only during a single time period t, meaning the EV can be charged to the maximum storage capacity during that time period, in order to simplify the planning problem. In the lower-level model, the real-time electricity price is considered to calculate the expected revenue of PV-storage charging stations. The model was then converted into a single-level mixed-integer linear programming using the piecewise linear utility function, Karush–Kuhn–Tucker (KKT) conditions, and linearization methods. The obtained linear programming problem was solved to compare and analyze the quantitative influence of uncertain variables on charging station planning.
