Regenerative Braking Efficiency

Matthew Brown
November 20, 2016

Submitted as coursework for PH240, Stanford University, Fall 2016

Everyday Driving

Fig. 1: An electric truck with regenerative braking capability, made by Smith Electric Vehicles. (Source: Wikimedia Commons)

We spend spend a huge amount of energy on transportation, and on automobiles in particular. Outside of the minor side effect of giving us unprecedented freedom of movement and enabling much of our way of life, all of that energy is "wasted". If a driver burns a tank of gasoline traveling from San Francisco to Los Angeles, 100% of the energy in the gasoline will be converted to heat and not useful for other work. Much of this energy will be converted to heat in the internal combustion engine during the combustion process, a thermodynamically required inefficiency that is the price of admission for use of heat engines. Some will be lost to friction in the drivetrain, but some of the energy in the gasoline will be converted to kinetic energy of the vehicle, the intended purpose. Whenever the driver brakes the vehicle to a stop, all of the kinetic energy of the vehicle will be converted to heat by the brakes. The idea of regenerative braking is capture some of that kinetic energy and store it, instead of discarding it as heat.

Regenerative Braking

This idea of capturing kinetic energy is not new, implementations of electrical regenerative braking have existed since at least 1906. [1] Electrical regenerative braking typically involves a vehicle propelled by an electric motor from a battery, such as the truck in Fig. 1, with the possible addition of an internal combustion engine for hybrids. If the wheels and axles of the car do work on the motor (instead of the other way around), the motor acts as a generator and energy flows back to the battery. There are other methods of recovering kinetic energy; for several years beginning in 2009, Formula One teams used flywheels to store kinetic energy. This idea has not been as popular as electrical regenerative braking, for both safety and implementation difficulty.


A conventional passenger internal combustion engine has an efficiency of about 0.12-0.20. [2] That is, only about 20% of the energy in the gasoline is converted to kinetic energy of the vehicle. This is dominated by the engine efficiency. In contrast, electric motors are quite efficient. While induction motors (IM) have an efficiency ranging from 0.65 to 0.94 (for urban vs highway driving scenarios), permanent magnet AC motors are even more efficient, reaching 0.83 to 0.95 for the same scenarios. [3] So speaking strictly of efficiency, the ratio of work out of the engine/motor to the energy in, there is a big benefit to using electric motors, which lend themselves naturally to electrical regenerative braking. While the efficiency is generally high for electric motors, it does change with both speed and torque. Fig. 2 displays the efficiency of the electric motor/inverter combination used by Sterkenburg et al, showing that efficiency can drop off when the system is operating near maximum torque at low speeds. [4]

Fig. 2: Efficiency for a given induction motor/inverter combination. Efficiency is dependent on operating conditions. (Source: M. Brown, after Van Sterkenburg et al. [5])

Limitations and Capabilities

To consider the efficiency of a vehicle including regenerative braking, we should consider its limitations. First, if the drive motor is being used as a generator, it is restricted by the same power limits as when it is acting as a motor. This is an problem because vehicles typically can brake much harder (with much more power) with conventional, friction- based brakes then they can accelerate forward; a vehicle regenerative braking alone will have less braking capability than a vehicle with friction-based brakes. It seems unlikely that vehicles will forego conventional brakes anytime soon. Braking power is not only limited by the motor's power rating, but by the charging power limit of the battery pack. This limit depends on the battery type (chemical composition) and changes with temperature. [5] This makes analyzing the braking power capability difficult, as a vehicle may be able to regen-brake at full power for a short period of time (a few seconds), but as the temperatures of the battery pack and inverter rise, the braking power will quickly fall. While real-world benefit may vary depending on the scenario, some simulations show that regen braking reduces external energy consumption by a little over 20% in urban driving situations. [4]

While it makes sense to attempt to recover kinetic energy for later driving, the exact amount of energy, and the rate of energy, that can be recovered is dependent on both the myriad of available motor, inverter, and battery types, and the driving scenario.

© Matthew Brown. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] A. Raworth, "Regenerative Control of Electric Tramcars and Locomotives," J. Inst. Electr. Eng. 38, 374 (1907).

[2] "Tires and Passenger Vehicle Fuel Economy, Transportation Research Board of the U.S. National Research Council, Special Report 286, 2006.

[3] J. W. Schultz and S. Huard, "Comparing AC Induction with Permanent Magnet Motors in Hybrid Vehicles and the Impact on the Value Proposition, Parker Motion, 2013.

[4] S. Van Sterkenburg et al., "Analysis of Regenerative Braking Efficiency - A Case Study of Two Electric Vehicles Operating in the Rotterdam Area," IEEE 6043109, 6 Sep 11.

[5] K. Smith and C.-Y. Wang, "Power and Thermal Characterization of a Lithium-Ion Battery Pack For Hybrid-Electric Vehicles," J. Power Sources 160, 662 (2006).