Optimal sizing of a high‐speed flywheel in an electric vehicle using the optimal control theory approach

Abstract

This study proposes an approach for finding the optimal size of a high‐speed flywheel in an energy storage system based on battery‐flywheel cooperation, called battery‐flywheel energy storage system (BFESS), supplying an electric vehicle. Considering an energy‐based model for the flywheel and battery, including the losses, the optimal control theory is utilised as a two‐dimensional Pontryagin's minimum principle for solving the problem. The objective function of the flywheel sizing problem includes two terms, in which its maximum interaction with the system from the energy and filtering aspects are taken into consideration by a desirable weighting. While energy interaction is a common task, filtering the fast dynamics of the system such as the harsh conditions for the battery is the key role of the considered lightweight and high‐speed flywheel. A trade‐off between the energy contribution and filtering is made, targetted for the long‐term and short‐term dynamics in the drive cycles, respectively. The proposed methodology is presented in detail using some simple dynamics. Also, the sizing is carried out for the ECE‐15 urban drive cycle, the WLTC class‐3 and FTP‐75 drive cycles. The results confirm that by using the determined optimal size of the flywheel energy storage system (FESS), most of the dynamics could be handled from the filtering and energy interaction aspects.

Review of Hybrid Energy Storage Systems for Hybrid Electric Vehicles

“…It is essential to note that, unlike conventional applications, the FESS employed in Electric Vehicle (EV) applications uses a low-mass inertia that rotates at exceptionally high speeds, exceeding 10,000 rpm. The energy capacity of FESS is determined by the configuration of its mass and velocity operating point [101,102]. To establish the FESS model, an energy balance approach is commonly utilized in various sizing problems.…”

“…However, it is crucial to note that the FESS's efficiency is impacted by this rate, and the leakage rate should be considered. In general, the losses observed in FESS can be separated into various components, which include windage and bearing losses in the mechanical realm, copper, hysteresis, and eddy current losses in the M/G realm, and switching and conduction losses in the power converter realm [101]. Pullen et al [103] systematically examine the application of flywheels as secondary energy storage devices in road vehicles, especially in hybrid vehicles with internal combustion engines (ICE) and hybrid energy storage (HES) systems complementing batteries.…”