# How is "braking power" controlled with a regenerative braking set up?

As noted in the following question (How are current and voltage related to torque and speed of a brushless motor?) :

Considering a 1000W motor:

providing 100V/10A you'll be able to reach high speed but you won't be able to raise much slope.

providing 10V/100A you'll move very slowly but you'll be able to climb high-grade slopes (assuming the motor can tolerate 100A).

in motors it seems that torque is controlled by the amount of current fed into it. However for generators (i.e. in regen braking), what is the analog? How is the amount of braking power controlled? In teslas, for example, light braking results in light regen while heavy braking can result in a great amount of regen. Given that there is no gearbox or clutch pack, how is the amount of regen controlled in the generator?

• If you mean Tesla, the car brand, then it's a capital 'T'. For tesla, the unit of magnetic flux density, it's lower case when spelled out and 'T' for the symbol. Sep 25, 2018 at 19:53
• Note, all electric vehicles, including Tesla vehicles, have at least a single-stage transmission. Motors deliver power most efficiently at high speeds/low torques, but EVs typically require power at high torque/low speed. You must install a transmission if you don't want to burn out the motor with the corresponding high currents of high torque. Sep 25, 2018 at 20:46
• Another note: you don't always want to use regen braking in EVs. If a kid jumps into the street in front of you, you don't want the car to worry about re-charging battery at a safe current. You just want to stop. EV engineers have to account for this in their control algorithms, and this is why EVs still have mechanical brakes. Sep 25, 2018 at 21:03

A motor functions simultaneously as a generator. In normal operation, this "back EMF" serves to limit the current being drawn by the motor.

If you disconnect the power from a spinning motor, you can measure this back EMF directly.

If you allow this EMF to drive a current through a load, the motor will experience a braking effect, converting mechanical energy into electrical energy.

The problem with regeneration is that the voltage produced by the motor during braking is less than the battery voltage — and it drops as the motor slows down. Therefore, you need to use a boost converter (switchmode) to raise the voltage. The input to this converter is the "load" that the motor sees, and the output charges the battery.

You control the amount of current that the converter draws from the motor — the amount of braking — by changing the duty cycle of the switch in the converter. This duty cycle also needs to change as a function of the input and output voltages, so the control logic can be fairly complex.

If you're very clever, you can reuse the same switching elements that you use to drive the motor, along with the self-inductance of the motor itself, to create the regenerative braking function. In other words, you have a battery, one or more H-bridge drivers, and a motor, and you can control whether the motor is accelerating or regeneratively braking by simply changing the timing of the pulses driving the H-bridge(s).

By ignoring all of the secondary issues that can complicate the design, I hope I've created an explanation that is easy to follow.

• The converter dynamic MPPT negative impedance can matched to the positive loop resistance of the BMS to optimize braking and regernative charge but does Tesla? Is is this hypothetical? Sep 25, 2018 at 20:58
• The "Drive" logic for all of this is; The gas pedal is pressed / The brake pedal is pressed / Neither pedal is pressed / Torque-voltage-current sensors. It gets complicated.
– user105652
Sep 25, 2018 at 21:01
• I do not believe Tesla use a DC booster added design to improve kinetic energy transfer to battery, but you can link to prove me wrong. Sep 25, 2018 at 21:38
• In order to be “very clever” the voltage (hypothetical) booster must regulate its negative impedance to match the resistive load impedance and thus not draw more or less than what is available to supply in kinetic energy. The same as MPPT Solar panel regulators according to variation in solar power with a secondary converter load impedance to convert Vmpt to Vbat. They must all match for max power transfer and in this case max energy recovery from speed. Otherwise there are inefficiency losses. It would be very complex so I doubt TESLA do this. They already have over 84 MOSFETs in the original Sep 25, 2018 at 22:16

Generator and motor has a “no load” voltage proportional to speed. Rated as kV/RPM which has nothing to do with power but rather the number of poles and inductance and the voltage per rotational speed or RPM.

Torque is control by the voltage difference between applied EMF Voltage and back EMF voltage at some speed and the load resistance between source and motor load.

Winding DC resistance or DCR drops and to a lesser degree driver resistance in series and battery ESR or effective series resistance limits this current.

If a motor impedance at some speed can be said to be V/I, the usually DCR is 10% of the motor equivalent impedance. This means the start max current can be as much as 10x the rated motor current and thus 10x the rated motor power as long as you understand this also raises temperatures in everything according to each parts resistance.

Now braking at full speed is no different full acceleration at zero speed. But the amount of BEMF available of course depends on motor speed relative to max RPM.

The max speed on a well designed power train is less than 84% of the no load RPM on a lift for Maximum Power Transfer and no transmission gears. Remember this for all BLDC motors, PV MPPT chargers for Voc and Vmppt voltage.

As the motor speed changes the difference between the Vbat and the mot or gen. mode affects the max current available due to winding DCR and and other losses. You can only recover all of the kinetic energy is your braking recovery charger has a matched load impedance to the generator. In practise this never happens. It’s like shorting out a PV Solar panel and expecting to get full power to a low voltage battery. It doesn’t work this way.

MPT or maximum power transfer Theorem states max power can be transferred ( in any direction) ONLY when the impedance are matched. The generator supplies current in the opposite direction so as V drops with rising current we say that it has negative resistance according to delta V/delta I.

There is an efficiency loss too but at low speeds, the braking effect is minimal but some of the kinetic energy can be recovered as charge to the battery.

## Now to answer; how is it controlled?

Let’s assume you know what a 3 Phase Reluctance motor is and that you can rectify the AC output to a DC load including the battery by commutation get the bridge to reverse the current after some dead time.

It is controlled by the duty cycle of the MOSFET bridge and the effective series resistance of the current loop including the motor DCR, MOSFET RdsOn and battery ESR with the potential difference created by the motor now acting as a generator with the brake pedal which also controls hydraulic brake pressure.

Ohms Law=delta V/ESR=I charge recovery

Now to adjust the the current and thus resistance , let me say again as net ESR you change the average resistance with duty cycle at some switcher rate like < 30kHz for a big motor.

Net ESR= ESR/duty cycle and Electromagnetic force is proportional to V/netESR= braking recovery current.Iavg

e.g. max current = 100% at ESR=x.
10% current at 10% duty cycle at equivalent.
or average ESR = 10x Ohms

• Tony, I think the answer is correct, but I can't make it out for sure. I cannot upvote because of that. You are hard to follow. You stated it with so much tangential information it is incomprehensible to me. Sep 25, 2018 at 20:08
• Sorry Janka I’ll try to convert to eng-ease lingo but this is how we communicate to peers Sep 25, 2018 at 20:09
• I can say for sure we don't. I strive for short sentences and one single topic per sentence when I talk to other engineers about engineering topics. The main language is figures and drawings and formulas anyway. (And I'm German and we love to create coppices of German gibberish no non-native could ever think about.) Sep 25, 2018 at 20:12
• @Janka. And Germans love to run words together until it has 40 characters or more. Like one large acronym.
– user105652
Sep 25, 2018 at 20:15
• Torque is controlled by the ESR of the PWM full bridges. Limited by the DCR of the motor and the voltage difference at speed of kV/RPM and the battery voltage.. sorry ESR is usually reserved for dielectrics, I mean Rce of IGBT’s or RdsOn of MOSFETs, so I use ESR Sep 25, 2018 at 20:35