## 3 System Design
### Design Method Traction Load
Assuming that three trains are moving between two TPSs, (i) and (i + 1), there are voltage drops at position x\({}_{2}\), and by substituting Formulas (28) and (29) into Formula (30) [48; 52; 53], the formulae are obtained as the following:  
\[\text{T}_{\text{s-max}}=\frac{3600}{\text{H}_{\text{s-min}}} \tag{8}\]5  
From Formula (31), rewrite the kth train at point x:  
\[\text{T}_{\text{s-max}}=\frac{3600}{\text{H}_{\text{s-min}}} \tag{8}\]6  
Similar to the case in Formulas (21) and (22), the following is the voltage drop at position x < \(\mathrm{L}_{\mathrm{D}}/2\)[48; 52; 53]:  
\[\text{T}_{\text{s-max}}=\frac{3600}{\text{H}_{\text{s-min}}} \tag{8}\]7  
\[\text{T}_{\text{s-max}}=\frac{3600}{\text{H}_{\text{s-min}}} \tag{8}\]8  
For the hypothetical case where all trains consume the same value of current, the maximum value of the voltage drop \(\Delta\mathrm{U}_{\mathrm{max}}\) occurs when x = \(\mathrm{L}_{\mathrm{D}}/2\); Formula (34) becomes the following [48; 52; 53]:  
\[\text{T}_{\text{s-max}}=\frac{3600}{\text{H}_{\text{s-min}}} \tag{8}\]9  
The minimum voltage in the contact line of the train drawing current at the end section for each operating condition is rewritten as follows [48; 52; 53; 59; 60; 61; 62; 63; 64; 65]:  
\[\text{C}_{\text{L-max}}=\text{T}_{\text{s-max}}\times\text{C}_{\text{t-max}} \tag{9}\]0  
The minimum values for mean useful voltage at the pantograph under normal operating conditions \(\mathrm{U}_{\mathrm{tr-min}}^{\mathrm{f}}=\mathrm{U}_{\mathrm{mu}}\) must meet EN 50163 [68], UIC 600 [69], and IEC 60850 standards [70]. Finally, each traction substation's rated power must meet the requirements of NEMA RI9, EN 50328, and IEC 60146-1-1, and the lowest feeder voltage must meet the requirements of EN 50163, UIC 600, and IEC 60850; the characterization of the traction power supply fixed installations is according to the EN 50388 standard [71]. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value** \\ \hline \(T_{c\text{-max}}\) (i) & 28.4875 (t/h/d) \\ \hline \(T_{c\text{-max}}\) (ii) & 31.7654 (t/h/d) \\ \hline \(T_{c\text{-max}}\) (iii) & 35.9769 (t/h/d) \\ \hline \(T_{c\text{-max}}\) (iv) & 38.4129 (t/h/d) \\ \hline \(C_{L\text{-max}}\) & Phase 1 & Phase 2 \\ \hline \((\text{p/h/d})\) & (p/h/d) & (p/h/d) \\ \hline \(C_{L\text{-max}}\) (i) & 19,941 & 29,378 & 37,034 \\ \hline \(C_{L\text{-max}}\) (ii) & 22,236 & 32,758 & 41,295 \\ \hline \(C_{L\text{-max}}\) (iii) & 25,184 & 37,101 & 46,770 \\ \hline \(C_{L\text{-max}}\) (iv) & 26,889 & 39,613 & 49,937 \\ \hline \end{tabular} Note: Three-aspect fixed block (i), cab signal (ii), MVB fixed stopping distance (iii), and moving-block variable safety distance (iv).  
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c} \hline
**Component** & **Unit** & **Value** \\ \hline Headway & [s] & 100 \\ \hline Car length & [m] & 31.72 \\ \hline Train length & [m] & 126.88 \\ \hline Width & [m] & 2.5 \\ \hline Seated/standing capacity & [p] & 74/276 \\ \hline Person per square capacity (max) & [p/m\({}^{2}\)] & 7 \\ \hline Doors per side & 5 \\ \hline Weight (driving cars), empty & [ton] & 46.3 \\ \hline Weight (intermediate cars), empty & [ton] & 46.0 \\ \hline Cars per train set & 4 \\ \hline UIC & Bo’+2+2+2+Bo’ \\ \hline Axle load & [ton] & 9.4 \\ \hline Acceleration/deceleration & [m/s\({}^{2}\)] & 1.0/1.3 \\ \hline Maximum speed & [km/h] & 95 \\ \hline Maximum speed of schedule & [km/h] & 57.6 \\ \hline Power output & [kw] & 480 \\ \hline Auxiliaries + air conditioning rating & [w/person] & 132 \\ \hline Electric traction system & [V DC] & 750 \\ \hline Train rolling resistance & \(1.5+0.03\times\text{V}+0.0002\times\text{V}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Operational plan and train traction load parameters.