*2.2. Energy Consumption Model*

The simulation model calculates the power consumed at the pantograph and at the electrical substations at every time step as a function of the train speed and the engine traction or braking effort by using Equations (8) and (9)

$$P\_{puntogruph} = \frac{F\_m \upsilon}{\eta\_{lt}} + P\_{dux} - \eta\_b \min(F\_{b\prime} F\_{mux}(\upsilon)) \upsilon\_\prime \tag{8}$$

$$P\_{substativus} = P\_{puntograppl} + r(s) \left(\frac{P\_{puntograppl}}{V \cos q}\right)^2 \tag{9}$$

where η*<sup>t</sup>* is the engine traction efficiency, η*<sup>b</sup>* is the engine regenerative brake efficiency, and both are considered constant. *Paux* is the power consumed by the auxiliary systems; *Fmax*(*v*) is the maximum regenerative brake force at speed *v*. *r*(*s*) = *r*ˆ|*s* − *sss*| is the resistance of the catenary that depends on the distance between the train and the electrical substation, which is located at position *sss*. In this article the influence of the lineal resistance *r*ˆ on the energy consumption is studied. *V* is the nominal line voltage and *cos*ϕ is the power factor, and they are assumed to be constant. If a train is in a neutral zone, the power consumed at the electrical substations is zero. The energy consumption at the pantograph and substations can be obtained by integrating Equations (8) and (9) in time, respectively. This section may be divided by subheadings. It should provide a concise and precise description of the experimental results and their interpretation, and the experimental conclusions that can be drawn.

### **3. Driving Strategies and Commands**

In this work the performances of two driving strategies are compared in terms of energy savings. In particular, a holding speed without braking and final coasting phase eco-driving strategy is compared against a standard driving strategy consisting in holding a constant speed with braking. All the regenerated energy at the pantograph is assumed to be returned to the AC power grid. The dependence

of the energy consumption measured at the pantograph and electrical substations on the engine traction and brake efficiency and on the losses at the catenary is analyzed.

For the eco-driving strategy, the journey is divided in two phases. In the first phase, the driver must hold a certain speed by applying traction. If braking is necessary to maintain the constant speed, coasting is applied instead, and thus, the speed of the train will increase. In the second phase, the driver must apply coasting until the train reaches its braking curve to stop at the station.

For the standard strategy, a cruise speed is determined for the whole journey. The driver has to maintain that speed until reaching the braking curve. To drive at a constant speed, braking can be applied if necessary. Any driving strategy has to be described in easily-interpretable commands so that a driver can apply them. The driving commands are defined by using a command vector. It has two components. The first one contains the position *sc* that corresponds to the final point of the holding speed phase. The holding speed *vc* is introduced in the second component. The final coasting phase is performed starting at *sc* up to the braking curve in the holding speed without braking and the final coasting driving strategy. Notice that speed limits of the line are observed by the driving model braking the train when necessary.
