Physical Model¶
Train Dynamics¶
\[M \frac{dv}{dt} = F_{traction} - F_{resistance} - Mg \sin(\alpha)\]
Resistive Forces¶
\[F_{resistive} = A + Bv + Cv^2\]
Electrical Power¶
\[P_{electrical} =
\begin{cases}
\frac{P_{mechanical}}{\eta} & \text{if traction} \\
P_{mechanical} \cdot \eta & \text{if braking}
\end{cases}\]
Electrical Network¶
Using Thévenin equivalent:
\[V_{train}^2 - V_{sst} V_{train} + R_{eq} P = 0\]