Regenerative Braking Calculation Help

In summary, the equation calculates the total tractive power that is required to move the vehicle at a certain speed. This power is not available for regenerative braking, as other terms in the equation consume power that would be available for the braking system.
  • #1
Ksterr
3
0
Hey everyone,

I've been a long time lurker on this forum and finally just made an account.
My final year project is in the design of a regenerative braking system for a EV. I'm reading a Modern electric vehicle design Book and came across an equation that I don't quite understand.

This equation finds power at the drive wheels:

Pd = V/1000 (Mgfr + 1/2*ρa*CD*A*V2 +M*δ*dV/dt) (kW),

The book says to integrate this equation w.r.t driving time over a given driving cycle. This will than yield energy in traction and energy in braking.

What I don't get is, aren't all these constants except for dV/dt

M = mass
g = 9.81
fr = tire rolling resistance
ρa = air density
Cd = coeffificent of drag
A = frontal area
v = speed
δ = rotational inertia factor
 
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  • #2
If the vehicle is accelerating, that is, dV/dt is not zero, then V^2 is not constant and the air drag term is thus a variable term as well.

I have some questions about the rest of the equation; I'm not quite sure where all of it comes from. I'd need to spend a while to become convinced it was all correct (if it is).
 
  • #3
I got it straight from a EV Design book.

I think it basically calculate the total tractive power?
 
  • #4
It looks like the equation is calculating the minimum required power for a given speed. This equation is basically assuming the maximum power required by a vehicle is when it is at cruising speed and accelerating. When you split the equation up:

m*g*f*r - Calculation of rolling friction (Force)

1/2*ρa*CD*A*V2 - Drag force exerted on the vehicle by air at a certain speed (Force)

M*δ*dV/dt - Required acceleration the vehicle is capable of at cruising speed. (Force)

Force multiplied by Velocity results in power (W), divide by 1000 to convert from watts (W) to kilowatts (kW).
 
  • #5
This equation from what I see equates to the total tractive force for the vehicle.

Which ends up being Power in KW. If I brake that down into positive and negative power, does that mean all the negative power would be what's available for regen braking?
 
  • #6
In a word, NO. The air drag is still going to consume power that will be unavailable for regen, as will the rolling friction. The only power available for regen is that coming from the mass*accel term, diminished by the other (parasitic) terms that are always present taking power away.
 
  • #7
Ksterr said:
This equation from what I see equates to the total tractive force for the vehicle.

Which ends up being Power in KW. If I brake that down into positive and negative power, does that mean all the negative power would be what's available for regen braking?

NO, the equation calculates the total required power for a certain cruising speed based on air drag, rolling drag, and a required amount of acceleration overhead.

You can caluclate the total energy available for regenerative braking by simply calculating the vehicle's total kinetic energy; for regenerative purposes I don't think you need to capture it with a deceleration any faster than say 0.5G. So given this acceleration and a vehicle weight THAT can be used to find your required deceleration power.
 

FAQ: Regenerative Braking Calculation Help

1. How is regenerative braking calculated?

Regenerative braking is calculated by determining the kinetic energy of the moving vehicle and the efficiency of the regenerative braking system. The formula for calculating the energy recovered is: Energy = 0.5 x Vehicle Mass x Velocity^2 x Regenerative Efficiency. This formula takes into account the weight and speed of the vehicle, as well as the efficiency of the regenerative braking system.

2. What factors affect the efficiency of regenerative braking?

The efficiency of regenerative braking can be affected by several factors, including the weight of the vehicle, the speed of the vehicle, the type of regenerative braking system, and the condition of the vehicle's batteries. Additionally, external factors such as weather conditions and road conditions can also impact the efficiency of regenerative braking.

3. How does regenerative braking save energy?

Regenerative braking saves energy by converting the kinetic energy of a moving vehicle into electrical energy that can be stored in the vehicle's batteries. This energy can then be used to power the vehicle's electrical systems, reducing the need for the vehicle to rely solely on its combustion engine. This results in reduced fuel consumption and emissions.

4. What are the benefits of regenerative braking?

There are several benefits of regenerative braking, including improved fuel efficiency, reduced emissions, and increased range for electric vehicles. Regenerative braking also helps to reduce wear and tear on the vehicle's braking system, leading to longer-lasting brake pads and rotors. It also allows for a smoother and more controlled braking experience for the driver.

5. Are there any limitations to regenerative braking?

While regenerative braking has many benefits, there are also some limitations to consider. Regenerative braking is most effective at lower speeds and during moderate braking, so it may not be as effective for sudden or emergency braking situations. Additionally, the efficiency of regenerative braking can be impacted by external factors such as temperature and battery health. It is important for drivers to be aware of these limitations and adjust their driving accordingly.

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