# Analysis of Non-Minimum Phase System for AC/DC Battery
## 1 Introduction
Due to that, boost converter topologies are usually used to regulate DC-link voltage at 400 V. The DC-DC converter is only responsible to charge the battery. However, DC-DC isolated stages, resonant LLC or phase shifted full bridge topologies, decrease their efficiency due to the battery voltage variation. A buck-boost converter as PFC can adapt DC-link voltage to maintain the input/output voltage ratio constant, guaranteeing the optimal efficiency point. Nevertheless, single-switch topologies with boost and buck functions, such as SEPIC, buck-boost and Cuk converters, can comply with the battery pack voltage requirement, but the main disadvantage of those single-switch converters is the components voltage and current stresses. Thus, they are not preferable to be used in high power application where high efficiency and reliability are needed. Figure 1 shows four switches AC/DC boost/buck converter. This converter has a capability of being used as PFC with boost and buck feature in the same double line frequency cycle, wherein the first two switches (\(Q_{1}\)-D1) are working as a boost and the other two switches (\(Q_{2}\)-D2) are working as a buck. This topology has many other applications like telecommunication system, fuel-cell systems [14], power supply equipment's [15], and radio frequency amplifier applications [16]. The main disadvantage of this topology, in open loop configuration at boost mode, the duty cycle to input current and duty cycle to output current are the same. The power supply equipment is the same as the power supply equipment. The power supply equipment is the same as the power supply equipment. voltage have a right half plan zero (RHPZ), which could become unstable in closed-loop. An intuitive solution for this problem is decreasing the system dynamics by minimizing the current control loop bandwidth, and this will deteriorate the power factor, which is a vital factor in the OBC. To overcome this problem, many publications addressed this by using different control techniques such as current programmed control [17], discontinuous capacitor voltage mode control [18], voltage mode control with two different proportional-integral-derivative (PID) controllers [19], and input voltage feed-forward controllers [20]. The prior arts didn't mention the wide range of the output voltage that is necessary for the battery back specification. In [21], AC-DC CCM operation OBC was discussed to have a wide input and output voltage range with PFC controller capability. The main disadvantage of this topology as discussed earlier that it has RHPZ in the duty cycle to input inductor current transfer function \(G_{L1}d(s)\), which makes the system non-minimum phase. The paper claimed that it could achieve the minimum phase system by only using a simple proportional-integral (PI) control. A highly distorted input current appears on the experimental graphs in the paper. On top of that, the displacement factor is obvious as well. In addition, the paper ignored the high resonance peak that appears in the current control loop which could worsen the internal dynamics of the whole system. The paper contribution is solving the RHPZ problem of the previous converter. A proper modeling should be done to overcome all the previous disadvantages and increase the OBC reliability and PF. The paper is focusing on a detailed converter modeling for both boost and buck modes. This will help in solving the non-minimum problem in the converter. In addition, the paper proposes reducing or eliminating completely the resonance peak in the current control loop to maintain a high reliable system, which implying a trade off between the efficiency and system reliability. The paper is organized as sections and subsections. The first section discusses the converter modeling and supporting that with numerical analysis to show the main disadvantage of this converter. Additionally, the analysis of the obtained small-signal model of the converter allows us to obtain a minimum phase condition for the input/output transfer functions.