## 3 Simulation Results  
The definition of the power-weighted efficiency-based methodology is then evaluated by considering a set of vehicle and powertrain parameters, as reported in Table 1.  
The ICE and the two MGs torque and efficiency characteristics are shown in Figure 5 and obtained from a commercial software usually adopted for modelling and simulating the behavior of hybrid vehicles. The MGs considered within the paper have the typical architecture adopted for hybrid vehicle powertrains, i.e., AC electric motors for the two-mode hybrid system from General Motors, whose steady-state power characteristics is a linear function of output shaft angular speed up to a specific speed limit above which the power saturates. The powertrain model presented in this paper does not include the effect of environment/external influences on powertrain components characteristics, but the methodology can be also extended to powertrain characteristics that are variable with external parameters, such as the temperature. An interesting experimental study is reported by [PERSON] et al. [40], where a complete energy flow test platform is designed and built to understand the influence of the environmental temperature on steady-state and transient plug-in hybrid electric vehicle energy transmissions at different states of charge. The powertrain architecture, shown in Figure 1, allows the activation of two modes: the Input Split mode, where the ring of the second PGS is connected to the chassis through the ground clutch 2, and the Compound Split mode, where the solar of the first PGS is linked to the ring of the second PGS through clutch 1. To evaluate the efficacy of the methodology based on the power-weighted efficiency, a simulation setup is implemented in Matlab(r) environment, by considering the following procedure:  
* Selection of a longitudinal road slope \(\alpha\) (first boundary condition);
* Definition of an operating map among the whole set of admissible vehicle speed \(V\) and acceleration \(a_{v}\) (second and third boundary conditions);
* Calculation of transmission output angular speed \(\omega_{out}=\frac{\tau_{v}}{K_{W}}V\) and acceleration \(\dot{\omega}_{out}=\frac{\tau_{v}}{K_{W}}a_{v}\);
* For 2 dofs powertrain configurations, such as the Input Split and the Compound Split modes, the angular speed of one actuator, i.e., the ICE speed \(\omega_{ICE}\), is also varied within its admissible range; \begin{table}
\begin{tabular}{c c c} \hline \hline \(M\) & 1600 & kg \\ \(R_{W}\) & 0.34 & m \\ \(f_{0}\) & 0.01 & - \\ \(C_{x}\) & 0.26 & - \\ \(S_{F}\) & 2 & m\({}^{2}\) \\ \(\rho\) & 1.2 & kg/m\({}^{3}\) \\ \hline \(\tau_{F}\) & 3.02 & - \\ \hline \(r_{r,1}\),\(r_{s,1}\),\(r_{r,2}\),\(r_{s,2}\) & 0.32, 0.2, 0.32, 0.2 & m \\ \hline \(J_{out}\),\(I_{ICE}\), \(J_{M1}\),\(J_{M2}\) & 20.28, 0.2, 0.05, 0.05 & kg m\({}^{2}\) \\ \hline \(J_{r,1}\), \(J_{c,1}\), \(J_{s,1}\), \(J_{r,2}\), \(J_{c,2}\), \(J_{s,2}\) & 0.08, 0.06, 0.05, 0.08, 0.06, 0.05 & kg m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of vehicle parameters used for the \(\eta_{PW}\) calculation. * The angular velocities of the remaining actuators, i.e., the two MGs angular speeds \(\omega_{\text{MG1}}\) and \(\omega_{\text{MG2}}\), are calculated from the two PGS kinematic relations: \[\left\{ \begin{array}{l}\omega_{s,1}r_{s,1}+\omega_{r,1}r_{r,1}=\omega_{c,1}(r _{s,1}+r_{r,1})\\ \omega_{s,2}r_{s,2}+\omega_{r,2}r_{r,2}=\omega_{c,2}(r_{s,2}+r_{r,2})\end{array}