I have to model the behavior of an electric car. For this, I use these equations and I can observe by "playing" with parameters that, when going downhill at constant speed, the car has a negative consumption (i.e. recovers energy). I was wondering if this is realistic?
It depends on how steep the hill is. On a slight hill, the energy added by gravity is still not enough to overcome rolling friction and air resistance, so the car still needs power to maintain speed. On a steeper hill, the two may balance out, so no power is used, and no power is generated. On a hill that's steep enough to require braking to control the speed, the car recovers energy. It's called regenerative braking. If the car is going too fast, applying the brakes turns the motor into a generator and charges the battery.
Yes, it can certainly happen. To recharge the battery when going down hill, the free roll speed needs to be greater than the speed you are trying to go. That means going down the same hill may result in a different outcome depending on speed.
For example, let's say you put the car in neutral and coast down a particular hill. For most of the hill, the car settles at 45 MPH. If you were to drive down the hill at 35 MPH, then the system should be charging the battery a bit. However, if you drive down at 55 MPH, then additional power is needed than just the gravity assist of the hill, power is taken from the battery to run the motor or motors.
I have a Honda Civic Hybrid, and charging the battery when going down a hill is not unusual at all.
Some Swiss trains give back energy to the grid upon descending the mountain pass that they previously climbed. The article claims as much of 70% is recovered.
I rode the Jungfraujoch and the personnel mentioned for every 3 trips down the mountain enough electricity was recovered for a "free" trip up.
The basic equations governing an electric car are reversible, so a simple analysis would say that the battery is getting charged. In the real world, there are more complications. In the case of an electric bike, there is a ratchet that disengages the engine from the wheel when the wheel is going faster from the engine (just like how on a regular bike -- where "regular" doesn't include track bikes -- if you stop pedaling, the wheel keeps moving even though the chain isn't). In an electric car, the motor can be disengaged from wheels either mechanically or electrically. Electric motors generally can't handle as much power when being driven backwards as when going forward, so electric cars are built to limit how much power can be transferred from the wheels to the battery. Absent those modifications, any time the wheels are going faster than the motor, there's going to be electricity flowing "backwards". Whether that energy will be charging the battery or frying the motor is a different matter.
And if you include heat, all cars "recover" energy in some sense when going downhill, either through increased kinetic energy, or heating of brake pads.
Absolutely. That "recovering energy" will kill you.
Take the freight trains of yore. In the day, helper districts involved extra steam engines waiting at the bottom of a mountain to help trains up. Today, it's more important to help trains down the hill with their regenerative (dynamic) brakes. Some railroads require additional units be added for dynamic braking, even for a train that could climb the hill! Best practice is to plan to use mainly or only dynamic brake, which saves money too.
The steam trains would awkwardly drag brakes all the way down the mountain, filling the valley with gray smoke.
Automotive brakes (gas or electric) don't have enough gray smoke, so they need engine braking... except electric cars can't.
That's been a huge problem, especially for the early/homebrew DC conversions. Like the freight trains, they could go up hills they couldn't go down.
Even a regenerating car has an issue, if the owner tops up the battery at Summit.
That is to say, when an electric car loses the ability to regen because its batteries are full, its only fallback is friction brakes - and as discussed, those can't sustain a downgrade either. They're playing with locomotive-style "make heat" dynamic braking, but I don't know how far along it is. They need it.
By "don't have enough gray smoke" I mean automotive brakes are not designed nor rated to descend a continuous mountain grade.