## 3 Results
### Sizing of OESD
#### 3.5.2 Proposed EDLC (and Battery) Subsystems  
The reader should consider that the objective of this work is validating the pre-feasibility of the proposed approach from a \"common-sense\" point of view and applying the PBLM-EDLC model proposed in Section 2 to validate the main hypotheses. At this stage, searching for an optimum for the OESD system is not considered. Otherwise, methodology and models can help in this task in future research works of authors.  
With the hypotheses of Section 3.5.1, the OESD must include devices in series to define a row (for batteries \(\mathrm{S_{bat}}\) batteries/rows, for EDLC \(\mathrm{S_{EDLC}}\) units/row) according to DC bus rated voltage:  
\[U_{BUS}^{min}=S_{EDLC}\,*\,U_{d-EDLC}^{min};\,U_{BUS}^{rated}=S_{BAT}\,*\,U_{d -bat}^{rated} \tag{24}\]  
where the following is true:  
\(U_{BUS}^{min}\): is the minimum voltage at DC bus (e.g., 600 V).  
\(U_{BUS}^{rated}\): is the rated voltage at DC bus (e.g., 750 V).  
\(U_{el-EDLC}^{min}\): is the minimum voltage of elemental EDLC (500 F/16 V unit).  
\(U_{el-bat}^{rated}\): is the rated voltage of elemental battery (12.6 V/100 Ah).  
Moreover, the EDLC set of OESD integrates \(\mathrm{P_{EDLC}}\) parallel rows to reach EDLC capacity to deliver energy (in our case 28 kWh):  
\[Cap_{EDLC}=S_{EDLC}\,*\,P_{EDLC}\,*\,Cap_{el-EDLC};\,Cap_{bat}=S_{bat}\,*\,P_{bat} \,*\,Cap_{el-bat} \tag{25}\]  
where the following is true:  
\(Cap_{EDLC}\): is the proposed EDLC set rated capacity in kWh.  
\(Cap_{bat}\): is the proposed battery set rated capacity in kWh.  
\(Cap_{el-EDLC}\): is the EDLC set rated capacity (e.g., 0.018 kWh).  
\(Cap_{el-bat}\): is the elemental battery capacity (e.g., 1.28 kWh).  
According to those equations, constraints, and the parameters of the elemental device parameters, the choice for the overall OESD is summarized in Table 10. Notice that Spain and other countries do not yet have a commercial market for EDLC devices suitable for the traction of the foreseen storage capacity. For this reason, it is difficult to obtain an accurate estimate of the costs of the proposed OESD. On the other hand, it can be stated that some basic cooling equipment facilities are still available in the S269 after hybridization (i.e., equipment for the motor and electronics being removed from the original unit).  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Constraint** & **Value/Range** & **Comments** \\ \hline OESD storage limits & 500–550 kWh & Dynamic braking of the train \\ Demand peak in the route & 3.0–3.5 MW & Max. Energy deployed 85 kWh \\ Peak demand covered by OESD & 1000–1500 kW & Eq. to a single motor of S269. \\ Available volume for OESD & 21–25 m\({}^{3}\) & Rebuilt S269 locomotive \({}^{2}\) \\ Available load in 269 \({}^{1}\) & \(\approx\)20 t & Without motor of bogie-2 \({}^{2}\) \\ Supply voltage to OESD & 750 (500–900) V & Needs a PBLM of EDLC \\ OLE supply voltage & 3 (2.2–3.6) kV DC & 1668 mm and dual tracks \\ Efficiency in power conversion & 0.95 & Converters and inverters \\ Efficiency in OESD & 0.9–0.99 & Battery and EDLC \\ Battery SoC ranges & 0.2–0.9 & According to literature [52] \\ EDLC SoC ranges & (0.23–1.06) & DC bus voltage range \\ \hline \hline \end{tabular} \({}^{1}\) Maximum load in Spanish tracks (1668/1435 mm): 22.5 t/axle. \({}^{2}\) See Figure 13.  
\end{table}
Table 9: Refine and testing of OESD capacity.