## 3 HEV Powertrain Bi-Nested Design Methodology
### Operative Cost  
Regarding the operative cost, it is correlated here with the average fuel consumption of the HEV candidate, which is assessed through different driving missions. For the purpose of this study, the considered missions are all real-world ones obtained using a global positioning System (GPS) in the city of Turin, Italy, and surrounding areas in the Piedmont region. More specifically, the three different missions are named 'urban cycle', 'uphill cycle', and 'highway cycle', and they are intended to represent diverse driving environments (i.e., urban, highway, and uphill), hence enriching the exhaustiveness of the fuel economy evaluation. 'Uphill cycle' contains not only information on vehicle velocity and acceleration over time, but also the net road altitude, which is accounted in the resistive force to be overcome by the vehicle. For the sake of clarity, in Figures 3-5, the vehicle speed profiles over time for the three missions are shown, whereas in Table 4, the main characteristics of each mission are reported. In particular, the trip duration and kilometrical lengths are given along with the minimum and maximum values of the acceleration, the highest velocity in the mission, and the variation in altitude shown only for the \"uphill\" cycle (Figure 4). This last term is to be intended as the difference between the altitude at the end of the mission and that at the starting point.  
Figure 3: Speed profile of the urban real-world drive mission.  
In order to account for typical driving habits of a person when computing the average fuel economy, the following computation was developed. The aim here is to focus on the routine of a worker, hence working days are differentiated from weekends and holidays. In the former, the person drives only in the urban environment for commuting, thus the first cycle found in Table 4 accounts for 100% of fuel economy. On the other hand, regarding weekend and holidays, an average of the simulated fuel economies obtained for the three drive missions is used where higher weights are attributed to the \"highway\" and \"uphill\" cycles. Moreover, to address the variation in FE due to the number of persons inside the vehicle, it was added to the curb weight:  
* The average mass of a person (i.e., 80 kg) when simulating the urban cycle (solo driving to work);
* The average mass of four persons when simulating the remaining cycles, thus simulating a family trip.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cycle** & **Duration** & **Length** & **Accel. Range** & **Max Speed** & **Altitude** \\  & & & & & **Variation** \\ \hline Urban & 900 s & 4.1 km & \([-1.7,1.4]\) m/s\({}^{2}\) & 66 km/h & / \\ Uphill & 931 s & 17.8 km & \([-1.7,1.3]\) m/s\({}^{2}\) & 113 km/h & 246 m \\ Highway & 1240 s & 22.9 km & \([-1.0,0.8]\) m/s\({}^{2}\) & 131 km/h & / \\ \hline \hline \end{tabular}
\end{table}
Table 4: Real-world drive mission main characteristics.  
Figure 4: Speed profile and net road altitude variation of the uphill real-world drive mission.  
Figure 5: Speed profile of the highway real-world drive mission.  
Lastly, considering 11 working months in a year and the remaining 1 as weekend or holiday, the following final average FE was computed:  
\[FE_{avg}=0.83\cdot FE_{urb}+0.09\cdot FE_{HW}+0.08\cdot FE_{uphill} \tag{16}\]  
where \(FE_{urb}\), \(FE_{HW}\), and \(FE_{uphill}\) are the fuel economy values obtained by the HEV candidate in 'urban cycle', 'highway cycle', and 'uphill cycle', respectively. As can be seen from Equation (16), the highest contribution is given by the urban cycle because of the fact that 11 months per year are spent mostly working (excluding the weekends), and thus driving in a city environment.