# Investigation of Regenerative Braking Performance of Brushless Direct Current Machine Drive System
## 1 Introduction  
It is essential to implement regenerative braking in all types of electric and hybrid vehicles to extend traveling distance which is hindered by a limited battery capacity [1, 2]. Mostly, regenerative braking is applied during downhill driving and when speed limitation is needed [3, 4]. Providing appropriate deceleration or braking in downhill driving, regenerative braking brings both energy regain and safety with its retarding effect [5]. Extra traveling distance due to regaining of some spent energy back is one of the solutions for \"range anxiety\" as well as for the total efficiency of an electric power train [6, 7, 8]. An optimistic guess is to provide 10% to 15% of energy back to the battery by regeneration [9]. Basically, there are some inherent limitations of regenerative braking such as the braking capability of the vehicle electric powertrain, the battery's state-of-charge (SoC), ambient temperature, etc. [10, 11]. Firstly, regenerative braking is not implemented with a fully charged battery and causes heating for some operation schemes. So, there must always be room for extra charging kept in the battery capacity. Vehicle weight distribution while cornering or braking is also a limiting factor for regeneration performance [12]. Of course, regenerative braking efficiency is highly related to operation regions of electrical machines and their power electronic systems [13]. Most of all, efficiency is limited at lower speeds due to reduced induced voltage and lowpower amount. To mitigate those disadvantages and improve the performance of regenerative braking, a number of publications are presented in the literature. In [14], a new method for regenerative braking in electric vehicles is presented. The proposed approach is a combined version of single-switch, two-switch, three-switch, and plugging operations in brushless direct current (BLDC) machines and the coordination of them according to their higher performance regions. Those operation regions are verified by means of a criteria consisting of boosting the converter ratio, braking torque, maximum conversion ratio, stopping time, and energy recovery value. In [13], an integrated fuzzy and PID (proportional-integral-derivative) controller is implemented for braking torque distribution. The proposed method brings a better performance of regenerative braking over conventional control methods related to robustness and efficiency. In addition, for fuzzified input parameters, the battery SoC, speed of vehicle, and brake force are selected. In another publication, a real-time range indicator system is developed and an on-board estimation algorithm for SoC and travel range is implemented according to real-time data captured from environmental units [15]. Weather conditions, rolling resistance, ambient temperature, power train efficiency, real-time traffic data, and regenerative-frictional braking force distribution are taken into account for the presented study. In [16], an energy optimized driving strategy is realized for heavy-duty vehicles. For model predictive control (MPC) method, regenerative braking is used as an optimization parameter. Another study is about a braking force control strategy and a sharing algorithm between regenerative braking and frictional braking for maximizing regenerative braking efficiency [12]. In [17], the maximum regenerative braking force for a vehicle is obtained by analyzing the braking capability of a PM synchronous motor. The maximum regenerative braking effort is used as a constraint for a MPC. By means of that parameter, the braking torque value is determined according to driving tendencies of user. Furthermore, the emergency braking is implemented to provide the shortest stopping distance by using a sliding mode controller. Another publication is on the regenerative braking capacity of a specific electric machine at lower speeds by analyzing the limiting factor of regeneration [18].