## 1 Introduction  
Modern DC electrical distribution systems have recently been investigated owing to various advantages, including improved effectiveness and reliability, fewer conversion steps, and an uninterrupted electricity supply compared to traditional alternative systems [1, 2]. Furthermore, in developing nations where public distribution systems are still scarce, access to electricity is seen as a critical facet for facilitating the fulfillment of various human everyday needs [3]. To attain sustainable development and minimize climate change, district heating must move from traditional fossil fuels to renewable energy sources (RES) with fewer carbon emissions. DC-based RES and charging points of electric vehicles (EV) must be connected to DC distribution systems to ensure more efficient operation than when connected to conventional AC distribution systems. Considering these benefits, the implementation of DC systems in housing complexes, buildings, and other structures is projected to expand. As a result, the requirements for DC system applications have surged [4, 5, 6, 7]. In recent decades, many studies on DC systems have analyzed the details of DC distribution systems. In Finland, a low-voltage direct current network was set up in 2005 as a preliminary step toward the development of 1 kV intermediate LVDC distribution systems [8]. DC source feasibility in low- and medium-voltage distribution networks has been investigated to demonstrate that employing an LVDC system can significantly reduce the conversion stage losses caused by converters [9]. The results showed that the overall system losses were lower than in the case of a conventional AC grid. In [10], the viability of an LVDC distribution for utilization in commercial establishments was investigated. Their analysis results indicate that the implementation of an LVDC distribution system is preferable to an AC distribution system. The most suitable voltage from a technical and financial standpoint is a DC voltage level between 300 V and 400 V. Several investigations into genuine testbed systems have been conducted at Lappeenranta University. A viable LVDC distribution network architecture, incorporating fault analysis and a grounding mechanism, was established by [8; 11]. In [10; 12; 13], LVDC network designs with relatively comparable features and similar purposes were presented. The smart grid could address energy issues if there were more DC loads in the LVDC distribution, as was investigated in [14]. It is interesting to note that a nonlinear network employing a chaotic circuit can effectively manage the flow energy in linear electrical networks. Currently, most consumers are supplied with AC [15]. With the evolution of DC distribution, it is preferable to use DC energy sources to minimize power losses. The growing integration of renewable energy into the electric grid necessitates the development of new and efficient technologies to interconnect these sources. A smart transformer (ST) is a viable option for shifting grid conditions [16]. Currently, it is difficult to convince consumers to use DC because their equipment is designed to work with AC. Therefore, it will be interesting to integrate DC and AC distributions to encourage customers to use both AC and DC loads in the future. Moreover, a parallel power supply from photovoltaic modules and a power grid have been described in an LED lighting system [17]. In other words, we must begin by combining these two types of distributions. Depending on the load consumption, DC distribution can be either an LVDC or an HVDC distribution system. In previous research, LVAC and LVDC were designed for a platform supply vessel (PSV) with supply voltages of 690 V AC, 60 Hz, and 1000 V DC. The performance of both designs was quantified for a PSV in light of fuel usage, weight, gas emissions, volume, and dependability [18].