## 1 Introduction  
The transportation sector accounts for 23% [1] of the total greenhouse gas (GHG) emissions. Electric vehicles (EVs) have emerged as a promising solution to this issue. Among the different transport sectors, public transport plays an important role in the transition to a cleaner transport industry. In particular, the electrification of bus fleets is a significant issue, as buses are the most used public transport vehicles around the world [2]. The high charging power demand of EVs can produce large voltage fluctuations and instability in grid interconnection. Moreover, economic viability is a key factor in this transport electrification transition. In this context, the EMS of EV charging stations (EVCSs) has a noteworthy influence [3] on the prosperity of these systems. In addition, BESSs are a good solution to the aforementioned fluctuations, especially with respect to increasing the flexibility of an EMS. In this way, a BESS can not only make a system more robust but also reduce greenhouse gas emissions by 24% compared with conventional grid-based charging without an energy storage system (ESS) [4]. On the other hand, even though photovoltaic (PV) installation with a vehicle-to-grid (V2G) application can result in a 50% reduction in charging cost [5], there are many cases where the installation of renewable sources is not profitable or the installation of a V2G system is not allowed by the grid operator. Inthat kind of scenario, ESS installation is still interesting. It is a central element for moving the charge of EVs over time and thus decreases the charging cost and damps the possible fluctuations, as mentioned before. Regarding the BESS converter's topology, in [6] it is concluded that a direct-current (DC) branch connection with the charging station and the BESS in parallel (Figure 1) is the best option if the aim of the ESS is to reduce the grid consumption without injecting power into the grid. Concerning the different options for ESSs, lithium-ion batteries are the best choice for energy-related applications where a high C-rate is not required [7]. With regard to EMSs, many different strategies are proposed in the scientific literature, as illustrated in [8] for an application to hybrid EVs. When it comes to optimization strategies, diverse methods are used, such as the dynamic programming approach [9], grouping genetic algorithm (GGA), and Markov decision process [10]. As far as learning-based methods are concerned [11] (reinforcement learning, neural networks, and unsupervised learning), they are very costly at the computational level [12]. A proper EMS can lead to a considerable cost reduction in the system to which it is applied; in [13], the power distribution of a microgrid was optimized using multi-objective genetic algorithms (MOGAs), which resulted in a potential cost reduction of 16%. Regarding EVCS charging schedule optimization, in [14], it was concluded that SOC-optimized managed charging can lead to a 13.5% reduction in the total charging costs of the charging station. In [15], a comprehensive analysis of a co-optimized microgrid with EVs was carried out, with the objective of applying a procrastination policy for charging the EVs. The results show that the policies can be easily implemented in real time and that they have a positive impact on cost reductions in the system. However, the need to carry out further research on a large-scale fleet, instead of a simple analysis of a single EV, is identified. In [9], the total cost of an EVCS was reduced by 50% by applying a combined approximate dynamic programming and evolution algorithm to determine the optimal charging time for each EV. For a large-scale EV charging scenario, a hybrid approach combining genetic algorithms (GAs) and dynamic programming is considered to be very effective in reducing the total cost of system operation [16]. More papers can be found on optimal charging scheduling from the grid [17; 18; 19].