## 1 Introduction  
Battery energy storage systems (BESS) have been widely used in various applications, such as electric vehicles (EVs), consumer electronics, medical devices, smart grid, energy backup in data centers, and among others [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. For EV applications, what is referred to be as \"range anxiety\" is one of the major reasons that prohibit or slows down the adoption of EVs [9; 10; 11; 12; 13; 14]. To eliminate range anxiety in and extend the driving range of EVs, different methods have been discussed in the literature [9; 10; 11; 12; 13; 14; 15; 16; 17], such as increasing battery pack capacity, utilizing a faster charging method, utilizing a battery pack swapping method, achieving dynamic wireless charging, etc. While these methods can be effective to extend the driving range of EVs, some design challenges or drawbacks cannot be ignored. When increasing capacity, the weight, size, and cost of the battery pack inevitably increase with the increase in battery capacity [10]. Further, the needed recharge time is also increased. For faster charging, the battery state-of-health (SOH) degrades at a higher rate if faster charging is applied [11; 12]. In addition, the fast charger requires a high-power infrastructure that increases the cost of the overall system. For conventional battery swapping, specialized equipment, as well as the experienced personnel, are required to realize battery swapping [13]. For dynamic wireless charging, a large number of transmitter (Tx) coils are required with corresponding power supply units, which increases the infrastructure cost. In addition, this method might not be practical in all locations [14]. Among these methods, the battery swapping concept is a good candidate to reduce recharging time and extend the driving range with low infrastructure cost. To deal with the challenges in the conventional battery swapping concept, a new distributed and enabled battery energy storage (WEDES) system and WEDES controller for EVs are presented in [1], which allows for fast and safe exchange/swapping of smaller and lighter battery modules with wireless power transfer (WPT) technology [18,19]. An illustration of the WEDES system for EVs is shown in Figure 1b, and its example circuit diagram is shown in Figure 1c. Each of the battery modules consists of multiple battery cells, a dedicated electronics circuit, wireless power transmitter coil (Tx coil), wireless communication circuit, and client controller. While the on-board-unit (OBU) consists of a wireless power receiver coil (Rx coil), wireless communication circuit, and host controller. Different from the conventional battery swapping concept where the battery pack as a whole is exchanged at one time, in the WEDES battery system, the conventional single battery pack is divided into multiple small battery modules, which can deliver power through wireless power transfer (WPT) technology to the OBU. The distributed nature of the WEDES system combined with wireless power transfer (no physical connection between battery modules and OBU) makes the battery exchange/swapping easier, safer, and faster. The distributed WEDES battery system with the WEDES controller addresses state-of-charge (SOC) balancing, bus voltage regulation, and battery module current/voltage regulation at the same time inside the system. Therefore, an SOC balancing control loop, a bus voltage regulation control loop, and a battery module current/voltage control loop are coupled with each other within one battery module as well as between multiple battery modules. These couplings make the analysis and design of the WEDES controller complex and critical. While the initial concept of the distributed WEDES battery system is discussed in [1], the small-signal modeling and controller design analysis are not focused on. The main contributions of this paper can be summarized as follows:  
1.