## 2 Power Control and Current Sharing of DERs  
The DC nanogrid considered in this paper consists of a RES, battery and SC storage units and a variable load as shown in Figure 1. The RES employs a uni-directional boost converter, while the storage units require a bi-directional one, typically a class C DC-DC converter. The battery and SC can be controlled as a single HESS, in which case they should be co-located, or independently what is suitable for distributed energy storage units, as proposed in this paper. The single-bus DC nanogrid is controlled in a decentralized way with a hierarchical structure based on DBS and droop control. However, no communication means for energy management is considered in this paper. DBS uses the DC bus voltage itself as the communication link to coordinate the operation of DERs in a decentralized way. With droop control, the current (power) injected by each DER in the nanogrid depends on its threshold voltage (\(V_{NL}\)), where the injected current is zero, and its droop slope (factor) \(R_{d}\) as shown in Equation (1). The latter determines how the injected current varies as a function of grid voltage variations.  
\[I_{DC,}=(V_{NL}-V_{DC})\frac{1}{R_{d}}, \tag{1}\]  
where;  
\[R_{d}=\frac{\Delta V_{DC}}{\Delta I_{DC}}, \tag{2}\]  
In the hierarchical structure, DBS is the primary control level of the nanogrid. The DC nanogrid considered in this paper has a nominal voltage of 1 pu. It was conceived to operate with a voltage regulation of about \(\pm\)5%, giving an operating DC bus voltage between 0.95 pu and 1.05 pu. In the case of the RESs, the threshold voltage is often taken as \(V_{NL\_PV}\) = 1.05 pu, higher than the threshold voltage of the energy storage unit or HESS, \(V_{NL\_ST}\) = 1 pu. In the concept of DBS, it gives the RESs, if available and producing power, the highest priority to feed the loads. As shown in Figure 2, by the blue curve, the solar converter operates in three regions: droop, constant power, and constant current-limited with unidirectional power flow. When the DC bus voltage is between 1.05 pu and 1.025 pu, the solar converter operates with droop factor \(R_{HPV}\). Therefore, the solar generates the maximum power at \(V_{DC}\) = 1.025 pu and starts to operate at maximum power point tracking (MPPT) with the rated solar irradiance. When the PV has a maximum power less than the rated power, due to a lower solar irradiance, the solar converter should start to operate at MPPT before the DC bus voltage drops below 1.025 pu, what can be done by \"reprogramming\" the V-I curve of the solar converter, as shown in the dashed line in Figure 2. For instance, the solar converter should start to operate at MPPT with a DC bus voltage of 1.029 pu with a maximum power of 90% from the rated power. When the DC bus voltage drops below 0.95 pu for rated solar irradiance, the solar converter starts to operate in the constant current-limited mode.  
Figure 1: Autonomous DC nanogrid considered in this study.  
The V-I curve of the energy storage unit or HESS is the red curve in Figure 2, presenting only droop and current limiting modes. When the DC bus voltage is between 1.025 pu and 0.975 pu, the storage converter operates with droop factor \(R_{dST}\). Otherwise, it operates with a constant (rated) negative current at a DC bus voltage higher than 1.025 pu and constant positive current at a DC bus voltage lower than 0.975 pu. The storage unit charges when the DC bus voltage is higher than 1 pu, as indicated by a \"negative injected current.\" Conversely, it discharges at DC bus voltages less than 1 pu.