## 2 Materials and Methods
### Energy Storage Models (PBLM-EDLC and PBLM-Battery)
#### 2.3.1 Distributed Energy Resources Laboratory Facilities  
The OESD analyzed in this work includes Li-ion batteries (LiFePO\({}_{4}\)) and EDLC. In the first case, Pylontech and Victron [26] (high discharge current) batteries have been tested. EDLC devices (five BMOD0500 P016 units) are from Maxwell Capacitors [27]. The main characteristics of EDLC and batteries are shown in Tables 2 and 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristic** & **Value** \\ \hline Rated/Max. capacitance & 500/600 F \\ ESR (equivalent series resistance) & 2.1 m\(\Omega\) \\ Rated/Maximum Voltage & 16/17 V \\ Maximum/continuous current 1 & 1900/100 A \\ Maximum stored energy 2 & 18 Wh \\ Specific energy (specific power) & 3.2 Wh/kg (2700 kW/kg) \\ \hline \hline \end{tabular} \({}^{\ddagger}\) Short-circuit current 7600 A; 2 at rated voltage, i.e., 16 V.  
\end{table}
Table 2: Characteristics of EDLC.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Characteristic** & **Victron Super Pack** & **Pylontech US2000C** \\ \cline{2-3}  & **Value** & **Value** \\ \hline Chemistry & LiFePO\({}_{4}\) & LiFePO\({}_{4}\) \\ Nominal voltage & 12.8 V & 48 V \\ Voltage limits & 10–14.2 V & 46–54 V \\ Nominal capacity & 100 Ah (1.3 kWh) & 500 Ah (2.4 kWh) \\ Max. continuous current & 100 A & 25 2–50 A \\ \hline \hline \end{tabular}
\end{table}
Table 3: Characteristics of Li-ion batteries.  
To determine and tune parameters of OESD models, a broad intrusive system (both for monitoring and control) has been designed and installed in the storage devices and their environment. The demonstrator system in the laboratory (also used for load modeling [28]) measures electrical magnitudes but also some thermal and weather variables with relevance to consider device limits and overloads. These are especially important to test the performance of batteries.  
To obtain all these variables, multi-sensor devices (temperature and humidity) and thermocouples (through acquisition data cards) on the surface of OESD were installed. In addition, two specific non-commercial devices integrate protections and several switches to manage the operation of contactors and relays to accomplish charging and discharge tests and to perform measurement conditioning. They are also used to equilibrate the voltage (or discharge) of EDLCs when they are switched into series or parallel for the validation of their behavior.  
Charge and discharge can be managed manually or remotely through the IP-Symcon platform [29]. Temperatures and weather variables are monitored through this platform too. This system includes the management of several protocols (e.g., EnOcean, Zwave, and especially KNX) for the application and management of energy storage systems in PPS. With respect to voltage and current, they are monitored through several signal conditioning boards and a data acquisition card linked to the workstation.  
Figure 4 shows a picture of control devices, power sources (each one from 0 to 60 V, currents between 12 and 25 A, overall current 50 A, 3 kW), electronic loads (overall current 80-100 A, 2 kW), a signal conditioning board, and some OESD devices being used in tests.