## 3 Proposed Distributed Secondary Control Technique
### Case One: Control Objectives Realization  
In this case study, the efficacy and robustness of the proposed FDSC in actualizing the control objectives, mentioned in Section 2.3, is examined. Different distributed communication topologies were considered, as shown in Figure 7. Topology \(X\) depicts a communication system not fully distributed (reduced communication); each DER is connected to the nearest DER close to it, while topology \(Y\) shows a communication system that is fully distributed (all-to-all communication). The overall simulation time, which is divided into two  
Considering Figures 8a and 9a, it can be discovered that the voltage at the common bus of the MG dropped to 39.9 V, which is less than its nominal DC value of 48 V during the first stage, which can be attributed to the voltage deviation resulting from the virtual resistance of the droop and line resistance expressed in (7). Similar outcomes are evident in Figures 8b and 9b, showing the voltage output of each DER in the microgrid. As depicted in the results interpreted into Table 3, a bus voltage rise to the nominal value (48 V) is observed at the activation of the proposed FDSC, \(t=2\) s, while the voltage outputs of the DERs are above the nominal value. This voltage rise above the nominal voltage can be attributed to the non-negligible line resistance between the common bus and each DER, which is determined by \(U_{i}=U_{dc}+R_{line_{i}}I_{0_{i}}\). In addition, Figures 10 and 11 show the current sharing within the microgrid. It is observed that the consensus objective for the current distribution was not realized during the first stage. However, the current sharing deviations were completely removed at the activation of the proposed FDSC in the second stage. Within 1.5 s, the current outputs of the DERs converged to a uniform value (7.2 A) to fulfil meet the requirements stated in (11). The effect of fuzzy logic on the secondary control system is shown in Figure 12, considering the control signal from one of the \(DERs\). Compared with the conventional secondary control, which involves tuning the control parameters by trial and error method, it can be observed that the response of the control system is improved with the fuzzy-logic-tuned virtual impedance \(\tau\). Figure 11: Currents output of DERs under topology \(Y\). Figure 12: Secondary control signal of \(DER\) 1 with and without fuzzy logic. Figure 9: (a) Common bus voltage; (b) Voltage output of DERs under topology \(Y\). Upon careful examination of the current and voltage responses in this case study, it is evident that activating the proposed FDSC with the communication network using Topology \(Y\) results in slightly higher transient magnitudes, with an overshoot of 2.5% in bus voltage and current output overshoot of 57%, as compared to Topology \(X\), with a bus voltage overshoot of 0.86% and current output overshoot of 31%. This indicates that the proposed FDSC effectively guarantees the attainment of voltage restoration and current distribution objectives using the distributed characteristics. Using the distributed controller with Topology \(Y\), which depicts an all-to-all communication, each controller operating within the network receives information from all sources. This necessitates a significant number of communication links, which makes the system more complex when new DERs are added due to the addition of more links, thereby reducing the scalability of the direct current MG. In addition, the resilience and reliability of the MG can also be adversely impacted by the increased number of communication links. In contrast, utilizing the distributed controller with Topology \(X\), which represents a reduced communication, each controller within the MG interacts with a subset of sources known as near-neighbors to exchange information. In this case, few communication links are required, which reduces the complexity of the system when new DERs are added due to the addition of a few links and ultimately increases the scalability of the MG.