## 4 Case Study  
As a case study in this paper, a 48 V DC nanogrid consisting of a PV-based RES, a battery unit, a SC unit and a variable load is considered. The PV panel provides a maximum power of 213 W with 7.35 A and 29 V at rated solar irradiance. Due to converter losses, it is considered that the maximum (rated) injected power by the PV unit is 200 W. In order to comply with the voltage levels presented in Section 2, the DC bus voltage should vary between 49.2 V and 45.6 V in the MPPT region, where the solar converter would inject 4.1 A and 4.4 A, respectively.  
In the performance investigation to be conducted in the following Sections, the conventional control scheme for the HESS will be compared to the proposed one, which can also be used for non-co-located battery and SC units. The droop factor of the HESS (\(R_{d\_ST}\)) is 0.289 \(\Omega\) and the cut-off frequency of the LPF for the frequency split is 43.5 Hz. The HESS' threshold voltage (\(V_{NL\_ST}\)) is 48 V and the current limit value is the maximum current supplied by the PV converter (\(I_{ST\_c}=I_{PV\_c}=4.4\) A). Concerning the proposed scheme, the threshold voltages of the battery and SC converters, \(V_{NL\_B}\) and \(V_{NL\_SC}\), are equal to \(V_{NL\_ST}\) and their rated currents are equal to the maximum current supplied by the PV converter (\(I_{\_c}=I_{SC\_c}=I_{PV\_c}=4.4\) A). The droop factor of the battery converter is \(R_{dB}=R_{d\_ST}\) = 0.289 \(\Omega\), while that of the SC, which as discussed in Section 3 should be 20 times lower than the battery's, is \(R_{dSCI}\) = 0.0145 \(\Omega\). The cut-off frequency of the HPF for the proposed SC control loop was calculated as described in Section 3 for \(T_{s}\) = 0.22 s and is equal to 43.5 Hz.  
Regarding the power electronic interfaces, the DC-DC converters of all elements are very similar, with the exception of the unidirectional feature of the RES. They are realized with a single three-phase DC-AC converter as shown in Figure 9, for simulation studies and in the experimental set-up. The capacitor of the DC bus (nanogrid) voltage is equal to 1500 \(\upmu\)F. LC filters (100 \(\upmu\)H and 470 \(\upmu\)F) are connected between the mid-points of the three-phase inverter legs and the storage and the source elements, to create the classical class C DC-DC converters. The converters operate with pulse-width modulation (PWM) and a switching frequency of 20 kHz.  
Figure 8: The relationship between \(1/\tau\) and \(\tau_{\_F}\) for different droop factors of the SC unit (\(R_{dSCI}\)).  
The same current control loop can be used for all DERs. A PI type-III controller was designed for the same equivalent plant with a transfer function shown in (13) [6; 18]. They were designed for a crossover frequency of \(f_{x}=2\) kHz (10% of the switching frequency) and phase margin of \(PM=80^{\circ}\). The following plant parameters were assumed: \(V_{DC}=48\) V, \(I_{DC}=4.44\) A, \(R=10.8\)\(\Omega\), \(L=100\)\(\mu\)H, \(C=1500\)\(\mu\)F, and \(D=0.46\) for \(V_{PV}=V_{Bat}=V_{SC}=29\) V. \(R\) was selected as the maximum load that could be supplied by the RES alone. At the end, the PI controller parameters are computed as \(K_{PI}=0.0114\), \(\tau=171\)\(\mu\)s and \(T_{P}=37\)\(\mu\)s.  
\[G_{di}\left(s\right)=\frac{\widetilde{i}_{t}(s)}{\tilde{d}(s)}=\frac{CV_{DC}s +2I_{DC}}{LCs^{2}+\frac{L}{R}s+\left(1-D\right)^{2}} \tag{13}\]