*2.3. Energy Consumption Model for BEVs*

The Virginia Tech comprehensive power-based electric vehicle energy consumption model (VT-CPEM), developed in [25], was used in the proposed Eco-CACC-I system to compute instantaneous energy consumption levels for BEVs. The model was selected here for three main reasons: (1) speed is the only required input variable for this model, so it is easy to use to solve the proposed optimization problem; (2) the model has been validated and has demonstrated its ability to produce good accuracy compared to empirical data; and (3) the model can be calibrated to a specific vehicle using publicly available data. The VT-CPEM is a quasi-steady backward highly resolved power-based model, which only requires the instantaneous speed and the electric vehicle characteristics as input to compute the instantaneous power consumed. The VT-CPEM model is summarized in the following equations.

$$EC(t) = \int\_0^t P\_B(t) \cdot dt\tag{8}$$

$$P\_B(t) = \begin{cases} \frac{P\_W(t)}{\eta\_D \cdot \eta\_{EM} \cdot \eta\_B} + P\_A & \forall \ P\_{\text{Whrels}}(t) \ge 0\\ P\_{\text{W}}(t) \cdot \eta\_{\text{D}} \cdot \eta\_{EM} \cdot \eta\_{\text{B}} \cdot \eta\_{\text{rb}}(t) + P\_A & \forall \ P\_{\text{Whrels}}(t) < 0 \end{cases} \tag{9}$$

$$P\mathbf{w}(t) = (ma(t) + \mathcal{R}(t)) \cdot \mathbf{u}(t) \tag{10}$$

$$\eta\_{rb}(t) = \left[ e^{\left(\frac{\lambda}{|\nu(t)|}\right)} \right]^{-1} \tag{11}$$

where *EC* (kWh) represents the energy consumption from time 0 to *t*; *PW* denotes the power at the wheels (kW); *PB* is the power consumed by (regenerated to) the electric motor (kW); *PA* is the power consumed by the auxiliary systems (kW); η*<sup>D</sup>* and η*EM* (unitless) are the driveline efficiency and the efficiency of the electric motor, respectively; η*<sup>B</sup>* (unitless) denotes the efficiency from a battery to an electric motor; η*rb* represents the regenerative braking energy efficiency (unitless), which can be computed using Equation (11); the parameter λ (unitless) has been calibrated (λ = 0.0411) in [25] using empirical data described in [26]; and *R*(*t*) represents the resistance force (N) computed in Equation (7).
