## 3 Conventional and Proposed Control Schemes of the Battery-SC HESS  
In the conventional approach, shown in Figure 3, the battery and SC are co-located and controlled as a HESS to realize a given V-I curve or droop characteristic. The supercapacitor operates in parallel with the battery to provide short bursts of power that eliminate the high-frequency components in the transient battery current response, so that the battery current has a smooth transition. In a DC nanogrid with droop control, the DC bus voltage is sensed, and an outer voltage loop with a proportional (P) controller, which corresponds to the droop action, produces a reference current to be realized by the battery and the SC converters. The slow and fast changing components of the reference current are split, by means of either a high-pass filter (HPF) or a low-pass filter (LPF). The slow ones are used as a reference for the inner battery current control loop, while the fast ones are used for the inner SC current control loop. The bandwidth of the outer voltage loop is typically 10% of the inner current loops. It is very effective in preventing fast varying currents from flowing through the battery. The control scheme of the SC also includes a voltage loop to keep the voltage of the SC within a desired range, typically 50% to 100% of its rated value. By setting the reference voltage at 79% of the rated value, the SC has a state-of-charge with equal energy capacity to supply and absorb power before reaching the limit voltage values. Its bandwidth is typically 10% of that of the voltage (droop) loop of the HESS. Splitting the total current (\(I_{L\_Storage}\)) supplied by HESS into average components, that is the battery reference current, and the transient power component, that is the SC reference current, helps in improving the operation of the battery but it does not improve the DC bus voltage dynamics. Moreover, a common voltage loop is used to generate the total current (\(I_{L\_Storage}\)) to be supplied by the HESS, which requires  
Figure 2: V-I curves of the storage and solar (renewable energy source (RES)) converters. a communication means between the battery and the SC converters. This is not appropriate to be used in nanogrids with DERs operating in a decentralized way with droop control and DC bus signaling. In the proposed approach shown in Figure 4, the SC interface is controlled independently from the battery one, which will allow it to provide additional services to the DC nanogrid. This is achieved by selecting a droop factor for the SC interface much smaller than the battery's, which is equivalent to a higher gain for its outer DC bus voltage loop. As a result, it will provide a much larger current reference for a given DC bus voltage variation, what should improve the dynamic voltage regulation. Recall that the SC is inherently capable of providing/absorbing high bursts of power. However, due to its low energy density, the duration of the power bursts should be limited, what can be done by introducing a HPF with suitable time constant in the input of its inner current loop. On the other hand, there is no need for a LPF in the input of the inner current loop of the battery interface, assuming that the SC interface will prevent sharp variations in the DC bus voltage and consequently sharp variations in the reference current of the battery interface. The proposed control scheme has two parameters for design: the droop factor (\(R_{dSCI}\)) and the time constant (\(\tau_{F}\)) of the HPF. The first has a major impact on the peak value of the injected current, due to a sudden DC bus voltage variation, while both affect the duration of the high burst of power. Based on Equation (2), the droop factor \(R_{dSCI}\) defines how much current is injected/absorbed into/from the DC grid as a function of a voltage difference (\(V_{NL}\) and \(V_{DC}\)). If the SC unit is to provide meaningful  
Figure 4: Proposed battery-SC control diagram.