# Analysis of Non-Minimum Phase System for AC/DC Battery
## 1 Introduction  
Recently, transportation electrification had rapid growth beside the grid integration of efficient electric vehicle (EV), which is becoming exponentially essential. Geographically, China is on the top of the EV market, then Europe on the second place, followed by the United States. Automakers continue to speed up their EV production to comply with global and specific country regulations to reduce greenhouse gas effects. Until 2022, it is expected that more than 500 models of EVs will exist worldwide, making electric cars more accessible and attractive to larger amounts of people. Due to battery technology price decreases, longer driving range and availability of charging infrastructure EV sales grew from 450,000 in 2015 to 2.1 million in 2019. In addition, further increases in the market sales to 8.5 million by 2025, 26 million by 2030, and 54 million by 2040 are expected. This growing market, from the power electronics point of view, puts a huge responsibility on research and development (R&D) labs to find highly efficient, low cost, and low energy density converters for the on-board battery charging (OBC) and inverter, as well for the motor drive. In SAE Standard J1772, the system of EV battery charger is categorized into main three categories [1]. Table 1 reviews the three infrastructure and charging power levels. Level-1 is usually used for home charging overnight when the vehicle is parking. This slow charging level takes from 8-11 h to make the battery fully charged, and this is considered an OBC type. The level input voltage can be supplied with outlet 120/240 VAC without the need for dedicated facilities. The cost of infrastructure is between $500-$880 [2]. Level-2 is considered semi-fast charging [3]. A dedicated outlet is required where it can handle a higher current, and it requires electric vehicle supply equipment (EVSE). Level-2 isconsidered an on-board type. A higher current can be handled in this level, which makes it more attractive than Level-1, wherein the charging time is reduced. However, its cost is up to $3000 due to the needs of a special outlet and EVSE [4]. Level-3 is called the fast battery charger; nevertheless, it requires a special bulky infrastructure, consequently it can't be on-board, and it should be an off-board type. Therefore, its infrastructure cost is significantly high in comparison with the other two levels, between $30,000 and $160,000. Its input must be a three-phase system, so it can handle a huge amount of power to charge the battery in 20-50 min. A two-stage topology with AC-DC power factor correction (PFC) converter as the first stage then followed by an isolated DC-DC converter is nowadays the most used topology of OBCs in EV [5]. They are well known as power-factor correction converters or input current reshapes [6,7]. An extensive review of PFC topologies is addressed in [8]. Sensorless predictive control for the versatile AC-DC buck-boost converter operating as PFC is proposed in [9]. Many researchers have tried to minimize the electrolytic capacitors or eliminate them totally to increase the converter energy density aiming for low-cost solutions PFC in [10, 11, 12]. It has a simple controller with the capability of universal input voltages from 85-240 V. This approach has many advantages in the OBC application; however, the output current suffers from high ripple, which could affect badly in the next DC-DC stage or the battery itself. A detailed discussion had been made in [13] to make a comparison between different single stage isolated AC-DC OBC for EV. This paper focused on Level-2 OBC where the input voltage maximum is 240 VAC. Main important features of the OBC are higher energy density, lower cost, and less magnetic losses as well. Nowadays, the battery pack technology has input voltage from 200 V when the battery is fully discharged and 400 V when the battery is fully charged. In Level-2, OBC used the outlet voltage between 120/230 VAC RMS.