## 1 Introduction
An adaptive fuzzy controller with Lyapunov is proposed to manage energy and regulate voltage in island DCMGs with REs. The system optimizes energy flow, ensuring stability and efficiency, validated by simulations and experimental tests [10]. In light of the current research panorama in DCMGs, this study contributes by presenting real-time results from an operational DCMG, as well as findings from a control strategy applied to a simulation model. This combined approach provides deeper insights into the performance and operation of DCMGs and expands the scope of ongoing research in this field. One of the main technical challenges of integrating DP and DCMGs into conventional electricity distribution networks is power quality. Power quality (PQ) is a crucial issue in the contemporary global electricity infrastructure, particularly with the integration of DP and DCMG into conventional distribution networks. It refers to the ability of an electrical energy source to provide reliable, efficient, and safe power without compromising the operation of connected equipment. This implies that it is necessary to ensure that voltage and current levels in the distribution network remain within acceptable limits in order to guarantee a stable supply. Choosing the topology of an MG is a highly important step, as the choice of topology influences critical aspects of an electrical system such as flexibility, cost, reliability, controllability, robustness, resilience, and scalability. For DCMGs, three main configurations are commonly considered: radial, ring, and interconnected [11; 12]. In addition to determining the grid interface and selecting the appropriate topology for integrating all DCMG components, it is essential to define the control strategy that governs system behavior. In general, control strategies address issues such as stability, balance, and protection of the entire DCMG [9; 13]. It can be considered that the control of a DCMG is characterized in two segments, the basic control strategies, which are decentralized, centralized and distributed controls, respectively, and the multi-level strategy, which is based on a series of control stages that follow a hierarchy, as can be seen in Figure 1. At the primary level,local controllers can be divided into current control, voltage control, and droop control, implemented through PI, PID, or fuzzy controllers, source-dependent functions such as maximum power point tracking (MPPT), applicable to photovoltaic and wind systems, and reactive and active load sharing [14; 15]. The lower-level primary control consists of inner-loops, which regulate current and/or voltage, and droop control, which handles preliminary load sharing. The inner-loop control of a DC/DC power converter, regardless of its type, can be divided into two categories, voltage control mode and current control mode. The droop control concept is largely applied to the primary control layer, where the power is directly linked to the DC voltage. The following sections of the document are organized as follows: Section 2 addresses the PQ problems associated with DCMG. Section 3 describes the DCMG under investigation, outlining the methodology and equipment used in the study. Section 4 presents the main results obtained, discussing the key points in line with the conclusions. Finally, Section 5 presents the main conclusions of the work and highlights potential directions for future work.