**7. Power Balancing in ISIP-OSOP DC-DC Converters**

To guarantee stable operation in the presence of parameter variations, a control strategy that ensures power balancing is essential to provide equal power distribution among the modules. In this section, the control strategy for each multimodule configuration is studied to ensure IVS, ICS, OVS, and OCS if needed.

The possible control strategies for the four configurations have been discussed in [45]. According to the study presented in [45], for input parallel-connected systems, OCS and OVS controllers are required for IPOP and IPOS DC-DC converters, respectively. However, for input series-connected systems, IVS and OVS are required for ISOS DC-DC converters, and IVS and OCS are required for ISOP DC-DC converters. To further illustrate, active power sharing control for input parallel-connected systems is achieved by designing ICS controllers that achieve OCS and OVS for IPOP and IPOS systems or by designing OCS controllers for IPOP systems and designing OVS controllers for IPOS systems that also achieves ICS between the employed modules. However, for input-series connected systems, IVS controllers are necessary to achieve OVS and OCS for ISOS and ISOP DC-DC converters. However, in [46], Cross Feedback OCS (CFOCS) has been proposed for ISOP systems to achieve OCS without the need for IVS controllers, hence simplifying the overall control design. This control strategy has been tested for a three-module ISOP DC-DC converter considering RC in [40] to achieve IVS and OCS.

Since this paper mainly focuses on multimodule DC-DC converters designed for EV fast chargers, the control scheme designed for the four DC-DC converters is current-controlled considering an RC technique that is termed as burp charging or negative pulse charging. This charging technique is based on applying a short negative pulse or a short discharge pulse during the charging cycle. Such an algorithm offers significant advantages that can be highlighted in shortening the charging time and lowering the rise in temperature. Generally, the RC technique consists of three charging sequences, which are: a positive charging pulse, a rest period where no charging occurs, and a negative charging pulse or a discharge pulse [47]. Accordingly, the designed control schemes are based on controlling the filter inductor current of the DC-DC converters such that the output current profile is based on RC. Consequently, for IPOP and IPOS DC-DC converters, active power sharing is achieved through controlling the filter inductor currents, as shown in Figure 9a, that accordingly achieves equal output current distribution for IPOP systems and equal voltage distribution for IPOS systems. However, active power sharing in the ISOP DC-DC converter is achieved through the CFOCS presented in [40,46] and shown in Figure 9b, which eliminates the need for IVS controllers and control the output currents

of the converters. The difference between Figure 9a and b is that, in Figure 9b, the current feedback for the individual module is the summation of the other two output currents and not its output current. Unlike the three systems ISOP, IPOP, and IPOS, active power sharing in the ISOS system is achieved through the use of both IVS and OVS controllers. In other words, the control scheme for the ISOS DC-DC converter combines the control scheme presented in Figure 9a with an IVS control, resulting in Figure 9c. To clarify, three IVS controllers are designed for each module to achieve equal input voltage distribution between the employed modules. In addition, the filter inductor currents are controlled using a reference current with an RC profile to achieve equal OVS between the modules of the ISOS converter. Therefore, it can be said that the control scheme presented in Figure 9a is applicable for the four architectures with slight differences presented in Figure 9b,c.

**Figure 9.** Control schemes for the four DC-DC converters; (**a**) control scheme used for input parallel-connected systems; (**b**) control scheme used for ISOP DC-DC converter; (**c**) control scheme used for ISOS DC-DC converter.
