# Numerical Performance Investigation of a Hybrid eCVT Specialized Agricultural Tractor
## 3 Hybrid eCVT Powetrain
### Architecture and Components
However, this capability had the following constraints to preserve motor functionalities:  
* at low speed below 1100 rpm, torque could be amplified up to twice the nominal value;
* above 1100 rpm, torque amplification should be limited by the rated power value for the machine. \begin{table}
\begin{tabular}{l l} \hline EM\({}_{1}\) nominal power & 35 kW \\ EM\({}_{1}\) maximal torque & 145 Nm \\ EM\({}_{1}\) nominal efficiency & 93\% \\ EM\({}_{2}\) nominal power & 30 kW \\ EM\({}_{2}\) maximal torque & 130 Nm \\ EM\({}_{2}\) nominal efficiency & 93\% \\ \hline \end{tabular}
\end{table} 
Table 3: Main properties of proposed electric units. Figure 4: Schematic representation of HeCVT tractor architecture. The main purpose of EM\({}_{2}\) was to control the vehicle speed, while the EM\({}_{1}\):  
* helps the ICE in providing power to the PTO;
* is turned by the ICE in order to provide electric power to EM\({}_{2}\) for an electric power split;
* recirculates power when EM\({}_{2}\) acts as a brake for low vehicle speed, helping the ICE in parallel. As mentioned before, the two-stage planetary gear allowed for considering a simplified two-speed gearbox with only two speed ranges to increase torque availability at low vehicle speed. The gear ratios were chosen so that the base speed of EM\({}_{2}\) reached approximately 15 km/h in a low-speed regime, and 40 km/h in a high-speed regime, with the ICE rotating at 2350 rpm. Table 4 shows the transmission ratios of the driveline. Along with the electric machines and drives, an energy storage system consisting of a battery pack (BP) was introduced. To meet the typical compactness needs of specialized orchard tractors, the sizing of the BP capacity was chosen as a compromise between fuel consumption optimization and required volume. As in previous work [22], the proposed BP in this work had a nominal voltage of 600 V and a nominal capacity of 16 kWh. To meet the needs for a compact battery pack, lithium-ion technology was considered because of the higher energy density with respect to other chemistries available on the market. From a numerical point of view, the BP was modelled with an equivalent circuit model consisting of a voltage source and an internal resistance. The instantaneous electric power provided by the BESS was evaluated considering the power required by the EMs in accordance with a physical network (PN) modelling approach. The PN is a modular modelling approach where each element is considered to be a physical entity capable of exchanging energy with all the other subsystems to which it is connected, with the constraint that the solutions of the system must satisfy the power balance equations for each component. To evaluate the actual state of charge of the battery pack, the authors opted for a simple Coulomb \begin{table}
\begin{tabular}{l l} \hline Low speed ratio at gearbox & 22.56 \\ High speed ratio at gearbox & 8.45 \\ First-stage ring to sun teeth ratio & 2 \\ Second-stage ring to sun teeth ratio & 2 \\ \hline \end{tabular}
\end{table} 
Table 4: Transmission ratios of HeCVT powertrain. Figure 5: Torque and power characteristics for diesel engine of HeCVT tractor. counting strategy, neglecting more detailed models available in the literature. The following equations were used. \[C_{used}=\int_{t_{1}}^{t_{2}}i_{batt}\quad dt \tag{6}\]  
\[SOC=\frac{C_{nom}-C_{used}}{C_{nom}} \tag{7}\]  
where:  
* \(C_{used}\) is the used capacity;
* \(C_{nom}\) is the nominal capacity;
* \(SOC\) is the state of charge of the battery pack.