# Simultaneous DC Railway Power System Analysis Method Using Model-Based TPS
## 4 Train Performance Simulation Results  
### Model-Based TPS Description  
Train specifications that used to express train motion using mTPS algorithm are provided in Table 1. The train set is 4 cars composed of two motor (M) cars and two train (T) cars each. The condition of track including curvature or gradient status are not provided, but included in the mTPS algorithm.  
The traction motor Table 2 and traction effort curve in Figure 7 was designed to satisfy acceleration of 3.0 km/h/s at speed 35 km/h, with only \(R_{Running}\) applied. That is, the condition validated for straight and flat (zero \(R_{Curve,i}\) and \(R_{Gradient,i}\)) conditions for the rail section. For the traction effort curve (filled in blue area), there are three sections; constant torque, constant power and characteristic section, respectively.  
In railway systems, voltage fluctuations are large due to moving train loads. So, when designing a traction substation, it is necessary to follow the voltage standards. IEC-60850 (Railway applications--Supply voltages of traction systems) proposes a range of voltage management standards specified in Table 3, which is specified in [19].  
There are also standards for the duration of both ends of voltages. The duration of voltages between the lowest non-permanent and permanent voltages shall not exceed 2 min. Additionally, the duration of voltages between highest non-permanent and permanent voltages shall not exceed 5 min. The simulation condition complies with those requirements  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quantity** & **Values** & **Quantity** & **Values** \\ \hline Weight & 191 tons &
\begin{tabular}{c} Traction and breaking \\ efficiency \\ \end{tabular} & 0.91 \\ \(M_{dy}\) & 204 tons & Nominal voltage & 1500 V \\ Set of train & 4 trains (2M-2T 1-set) & Time step & 0.5 s \\ Acceleration & 3.0 km/h/s & Speed range & 5 km/h \\ Deceleration & 3.5 km/h/s & Dwell & 30 s \\ Maximum speed & 80 km/h & Scheduled speed & 35 km/h \\ \hline \hline \end{tabular}
\end{table}
Table 1: Input vehicle data for mTPS.  
Figure 6: Circuit of moving train load using varying resistance.  
using DC breaking chopper; by setting activation voltage to 1800 V and shutdown voltage 1650 V. Additionally, the time duration for breaking mode doesn't take up to 5 min in the simulation.  
Using those specifications, the overall schematic structure for the model-based TPS is constructed as shown in Figure 8. The train moving model was partially used from previous research [20]. The program runs at multiple rates in time and distance. First, the mTPS model is represented in the top; the red box has \(\Delta\)s = 0.5 s and varying \(T_{s}\). Where the \(\Delta\)s stands for increment of distance. The cause of varying time step \(T_{s}\) has been described at Section 2.2.  
The rail, contact line and train schematic shown on the bottom; in blue box, \(T_{s2}~{}=~{}0.001\) s. Each of them represents a series of connected DC substations, with varying resistance to show mTPS applied train load moving along the entire DC metro line for 11-station, simultaneously.  
Figure 7: Traction and breaking effort curve under study.  
\begin{table}
\begin{tabular}{c c} \hline
**DC 1500 V Electrification System** & **Voltage (V)—DC (Mean Values)** \\ \hline Lowest non-permanent voltage & 1000 \\ Lowest permanent voltage & 1000 \\ Nominal voltage & 1500 \\ Highest permanent voltage & 1800 \\ Highest non-permanent voltage & 1950 \\ \hline \end{tabular}
\end{table}
Table 3: Supply voltages of DC 1500 V metro traction systems [19].