## 1 Introduction  
Electric vehicles (EVs) have been presented as a promising solution for reducing fossil fuel consumption and air pollution worldwide [1; 2; 3; 4]. The market penetration of EVs has rapidly increased in populated cities in recent years. In Beijing, China, the government has strongly pushed the application and development of pure electric vehicles to lessen the impact of vehicle exhaust emissions on air quality. The program states that more than 30,000 fossil fuel public buses will be completely replaced by zero-emission pure electric buses (PEBs), and an appropriate number of fast-charging stations will be built for the PEBs' recharging. As for the developing trends, the EVs' charging power and voltage should be higher, so as to reduce the recharging time and to allow the owners to obtain the benefits of low electricity, compared to conventional internal combustion engine vehicles [5]. Based on the rapid development of charging technologies, high power direct current (DC) fast-charging has become available and popular Compared with normal alternating current (AC) charging and battery-swapping charging, it has a shorter recharging duration and lower investment for different types of spare battery packs [6; 7]. Depending on the battery and vehicle type, a recharge range of greater than 100 km in less than 10 min is easily achievable in fast-charging mode [8]. Compared with the private EVs, the PEB has its own characteristics, namely, a larger onboard battery capacity, operation according to the route schedule, and charging according to the driver's will at a fixed station within limited intervals. All of these factors bring a new challenge, that is, that the distribution capacity demand and the charging load fluctuation will be higher [9]. However, the current distribution capacity only considers the traditional load in the design process, so the extra megawatt level distribution capacity demand of fast-charging station construction cannot be satisfied. As the onboard battery is more than 120 kWh and the charging duration is less than 15 min, the fast-charging power of one PEB is high, up to 230 kW. Thus, the cost of the expansion of the power grid capacity is nearly 10,000 Chinese Yuan per kVA (CNY/ kVA) in Beijing. The construction locations of the charging stations will be limited in some areas where they are necessary. Furthermore, there is a large industrial electricity tariff standard that is applied to fast-charging stations in Beijing and other cities in China, where a 32 CNY/kVA (4.8421 USD/kVA) per month basic capacity price (BEP) is charged according to the capacity of the distribution transformer, in addition to the time-of-use (TOU) electricity cost. For this, the operation cost may be further increased in the stations with a large distribution capacity. So, the suppression of the peak charging power is a critical issue for the design and operation of PEB fast-charging stations. In the existing literature, the charging optimization of electric vehicles (EVs) has been widely researched. The authors of [10] proposed a charging schedule planning method based on an actual electric bus system, which effectively reduced the electricity cost with three-level TOU tariffs. While the scenario was one bus line, ten electric buses, and a charging power at 50 kW, the cost of the distribution capacity was not considered. An optimal charging strategy to minimize the demand charges was presented based on the simulation of charging and running an electric bus (EB) fleet. Research into charging thresholds and charging schedules have developed, and the electricity cost comparison and economic fleet size have been given in [11]. However, the charging schedule used for the EBs operating in a route with one 500 kW catenary arm fast charger was not suitable for an integrated fast-charging station with several routes and charging piles.