# How Regenerative Braking Works

Why and where regenerative braking is used.

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A Tesla Model S can return approximately 60kW of electricity to the battery pack while braking. (Image courtesy of Wikipedia user Teslarati.)

When a normal vehicle slows down, its kinetic energy is dissipated as heat in friction brakes. In a vehicle equipped with regenerative brakes, this energy can be captured and stored in a battery or capacitors, improving the vehicle’s overall efficiency. In this article, we’ll discuss how this technology works and its limitations.

The AC Induction Motor/Generator

Before we begin, let’s briefly go over how motors work. There are two principle parts to a motor: the stator, the outside shell that stays still, and the rotor, the part that rotates. The stator is only stationary because it is bolted down. If it were free to rotate, it would. The rotation would be in accord with Newton’s Third Law: every action produces an equal and opposite reaction. A torque on the rotor must have an opposite torque on the stator.

The rotors of most alternating current (AC) induction motors have no electrical connection. Wind turbines are an exception. Their generators can synchronize their rotational velocity to the frequency of the electricity grid by “borrowing” power from the grid. However, for most induction motors, their only connection with the stator is through bearings, which allow rotation but don’t provide power. Therefore, for the rotor to turn, and the motor to provide torque, a force must be induced in the rotor by electromagnetic induction. It is this force, induced by moving electric charges, that AC induction motors use to create a torque.

Most people are aware that your house is supplied by a single phase 50/60Hz alternating current. In three-phase power, three single phases are transmitted through separate wires with each phase offset by 120 degrees. In motors, these three phases can be arranged so that the magnetic fields produced by each phase will superimpose to create a magnetic flux wave that rotates around the stator. (See gif below.)

A rotating magnetic flux wave.

Another way to visualize this is to imagine a wheel with four magnets spaced evenly around it and opposite magnets having the same pole pointing toward the center. By changing the rotational speed of the wheel, the rotational speed of the magnets will change. The magnetic flux wave on the motor works in a similar way, but instead of the stator spinning, the speed of the flux wave is varied by changing the frequency of the electricity supply.

How Regenerative Braking Works in AC Induction Motors

When an AC induction motor is working as a motor, the traveling flux wave on the stator is moving faster than the rotor. Consequently, electrical energy is lost in the motor so energy is taken from a power supply.

Regenerative braking works in exactly the opposite way. When a vehicle with forward momentum wants to slow down, the flux wave must rotate slower than the rotor. To do this, the frequency of supply to the stator is reduced so the flux wave rotates slower than the rotor. When the flux wave travels slower than the rotor, the motor runs with negative slip. Since during regeneration the rotor is traveling faster than the flux wave, the relative forces on the rotor and stator reverse. If the torques reverse, the forces reverse. The motor begins to generate. But how can this be?

The electromotive force (EMF) in a circuit is the pushing force on the electrons integrated around the entire circuit. In normal operation, this driving force comes from the power supply. Energy is used by the motor, and a voltage is across it. During generation, the motor gives the electrons a push and increases the EMF of the circuit. This extra energy must be lost, and it is lost in the battery. The battery gains energy and is charged. Alternatively, if there is no battery, it will be lost in other parts of the circuit.

It is important to realize that an AC induction motor requires a power source to regenerate because a magnetic field must be induced on the conductors of the rotor for a force to be created.

Regenerative Braking in EVs

A Tesla Model S can return approximately 60kW of electricity to the battery pack while braking. This is an electronic limit, probably to prevent battery degradation, as the motors could theoretically return more.

Basic physics tells us that a vehicle’s kinetic energy increases in proportion to the square of the velocity—doubling the speed increases the kinetic energy four-fold. Therefore, if the maximum regenerative work the Tesla can do is 60kW, the vehicle’s maximum retardation will decrease as the velocity increases.

The graph below shows how a Tesla’s deceleration rate from regenerative brakes could vary with velocity. To provide an idea of what the numbers mean, an average of 1g (9.81m/s²) of deceleration would slow a vehicle from 60mph in 2.73 seconds. These numbers are theoretical decelerations at a constant work of 60kW. The real world is different because Tesla, like other manufacturers, electronically limits the deceleration rate of its vehicles to prevent battery damage.

The peak retardation decreases exponentially with velocity. It’s interesting to note that when the vehicle has the most kinetic energy, when it’s traveling fast, the maximum deceleration from regenerative brakes is minimal. Thus, it is likely that a considerable amount of energy would be lost in friction brakes when a vehicle brakes from high speed. If one did most of their driving in slow moving traffic or towns, this problem is negated.

Regenerative braking isn’t a magic bullet. The limitations of regenerative braking are a consequence of inefficiencies in the drivetrain. The most efficient way to drive is to minimize the use of the motor and brakes. This is achieved by anticipating traffic instead of reacting to it. Audi recently added a dashboard notification to its fancier cars that tells you when traffic lights are going to change—if you’re in a city that shares this information. This system could be adapted to improve vehicle efficiency. When approaching traffic lights, the vehicle’s speed could be adjusted to avoid braking. It could stop you from accelerating toward changing lights. Alternatively, it might slow the vehicle so by the time you arrive at the lights they are changed, preserving momentum and reducing energy consumption.

Where Regenerative Braking Isnt Used

Trains have a lot to gain from recovering kinetic energy, but they typically don’t, even though they have magnetic brakes. Instead, the braking circuit disperses energy in a bank of resistors above the carriages. This energy is lost as heat into the atmosphere as current flows through the resistors. To store the energy, the trains would require capacitors or batteries. In most cases, it has been decided that their addition would be too costly and complex. When trains are directly connected to the grid through overhead cables or a third rail, they often return the recovered power to the grid.

Why use magnetic brakes if the energy isn’t being recovered? The answer is simple: magnetic brakes have virtually no mechanical wear. Normal brakes require brake pads, but electromagnetic brakes don’t. The energy is being wasted, but costs are saved by not rubbing away material and having to replace brake pads.

There is another type of magnetic brake used by trains that rely on eddy currents. In these, electromagnets are placed just above the rail. When the train wants to slow, they are turned on. This creates a magnetic field that flows into the rail. Because the magnetic field is moving, it induces an EMF in the rail, and the EMF drives eddy currents, which are small circulations of current within the rail. These create magnetic fields that interact with the field of the electromagnet. The field of the magnet and rail are disinclined to be separate, inducing a sort of viscous drag force. This heats the rail and dissipates the kinetic energy of the train. Again, this is a little trick to reduce mechanical wear, but this time there is no way to recover the energy.

If you want to know more about motors we suggest Electric Motors and Drives Fundamentals, Types and Applications, by Austin Hugues and Bill Drury.