## 2 Practical Limitations of Regenerative Braking  
Most EVs are equipped with both mechanical and regenerative braking systems. The mechanical brakes generally utilize a rotating rotor and frictional disks triggered by a hydraulic pump. On the contrary, a regenerative braking system relies on the resistive torque of the electric motor and can harvest mechanical energy from the vehicle during deceleration. This is achieved by applying the resistive torque from the electric motor to the driven wheels and converting the kinetic energy of the vehicle into electric energy. During RB, the back electromotive force (EMF) of the electric motor is manipulated in such a way that the current generated by the electric motor is used to charge the battery pack [15]. Despite the fact that the procedure of harvesting braking energy and converting it into electric energy can be beneficial to the overall energy portfolio of the vehicle, there are some practical limitations of RB which can adversely affect this process. If these limitations are ignored, the energy harvesting capability could be limited, or it could even lead to an inefficient harvesting process. Therefore, to take full advantage of RB for the purpose of finding optimal speed trajectories, these constraints and limitations should be accurately identified and included in the decision-making process. Regarding the limitations associated with an electric motor, two major constraints should be considered. The first constraint is the maximum RB capability, which is determined by the maximum torque capability of the electric motor [16]. The other limitation is the inability of the controller and the electric motor to efficiently recuperate braking energy during RB at low speeds [17]. At low-speed braking, the induced EMF, which is directly proportional to the electric motor rotational speed, is insufficient, and although the electric motor can still be operated as a generator, harvesting energy is not feasible. This leads to current being drawn from the battery, which results in the discharge of the battery as opposed to charging it [18], which can negatively affect energy recuperation during RB. The focus of this study is to provide a framework to consider and integrate this low-speed limitation of electric motors during RB into the process of finding optimal speed trajectories. It is worth mentioning that other constraints that should be taken into account, which are related to RB, are the brake power distribution between RB and friction brakes and the effect of load shifting from the rear axle to the front axle during braking. These constraints potentially limit the availability of brake energy for harvesting during RB. Furthermore, the displacement of the electric motor (rear axle, front axle, or both axles) plays an important role in the energy harvesting process since only the driven axle is capable of applying RB. All these constraints have been considered in the simulation and validation stages of this study. In some studies [19; 20], a fixed low-speed boundary (LSB) during RB is proposed to address the problem of low-speed energy harvesting; however, this is not an accurate representation of an RB limitation since the LSB also varies based on the electric motor's operating point during RB [21]. This observation is detailed in the authors' previous work [21], in which a practical experiment was conducted to obtain an RB performance map of an electric motor and it was shown that the boundary defining this threshold changes as the resistive torque and operating speed of the motor change. In this study, the operation of a three-phase permanent magnet synchronous motor (PMSM) at low speeds was analyzed during RB, and its performance map was extracted, as shown in Figure 1. This graph shows a 3D plot of current variation when the motor is operated in the range of 0 to 1000 rpm under different resistive torque values of (\(-\)200) N.m. to 0 N.m. The results indicate a change in current value and direction as the motor speed and torque are varied.