# Numerical Performance Investigation of a Hybrid eCVT Specialized Agricultural Tractor
## 3 Hybrid eCVT Powetrain
### Hybrid eCVT Control
#### 3.2.2 Energy Management  
For this preliminary performance analysis, the proposed energy management strategy was based on two operating modes depending on the actual SOC of the battery pack: charge depleting (CD) mode and charge sustaining (CS) mode. When the battery SOC was above a certain threshold value, namely, 30% for this work, the powertrain operated in CD mode, optimizing fuel consumption; below, it operated in CS mode aiming to maintain the current state of charge value. Existing studies suggested that this threshold value should be around 55% to preserve battery life. However, other recent studies that considered a degradation model based on solid electrolyte interphase growth in a Li-ion battery cell showed that the optimal value for the charge sustaining mode is in the range of 36-38%. However, according to the same studies, 30% of SOC is a good value for CS mode [31]. In CD mode, the EM\({}_{1}\) torque control signal was obtained as the sum of two contributions deriving from the engine actual load and the battery current value. The first contribution was based on a function of the actual engine load (load observer [22]), and it depended on the sign and value of EM\({}_{2}\) rotational speed. When EM\({}_{2}\) speed was positive, EM\({}_{1}\) was mainly actuated for high values of the engine load (load observer), providing additional power to the sun gear drive shaft if necessary; when EM\({}_{2}\) speed was negative, acting as a brake or generator, EM\({}_{1}\) exploited the recirculation of power deriving from EM\({}_{2}\). As a consequence, EM\({}_{1}\) helped the ICE with a greater contribution. The second contribution that determined the EM\({}_{1}\) torque control signal was calculated as a function of the battery discharge current index, defined as the ratio between battery discharge current and maximal instantaneous acceptable discharge current, fixed at 5C (or five times the BP rated current). This contribution was equal to zero if the system needed to charge the BP. The main goal of the powertrain in CS mode was, if allowed by a low external load, to maintain the SOC level around 30%. When the requested power was too high, the powertrain preferred to accomplish the required task, for example, an occasional peak of power at the PTO and, as soon as possible, it recharged the batteries in order to bring the SOC level back to the threshold value. The EM\({}_{2}\) was instead controlled in accordance with the speed requested at the wheels. Lastly, the ICE, since it was not kinematically linked to the vehicle speed, was controlled setting a reference rotational speed depending on the specific work the tractor was tested against. As for regenerative braking, the control system operated using the EM\({}_{2}\) to reduce vehicle speed by applying a negative torque. While braking with EM\({}_{2}\), EM\({}_{1}\) was controlled to maintain its rotational speed and, as a consequence, that of the thermal unit at the reference value. During regenerative braking, the EM\({}_{2}\) first acted as a brake, since its angular speed was positive, and it was applying a negative torque. Then, it acted as a motor when its angular  
Figure 6: Kinematic relations between vehicle speed and EM\({}_{2}\) angular speed at fixed ICE rotational speed of 2350 rpm.  
speed became negative. In this second case, the recirculation of power came from EM\({}_{1}\) acting as a brake to maintain the reference rotational speed constant. During regenerative braking, the torque of the two electric machines was controlled to not exceed the battery pack charge current limit, fixed at 1C. Figure 7 shows a schematic representation of the control strategy of the HeCVT architecture.