My intuition would say you'd never have longer range driving up and down a hill compared to driving flat in a straight line (and never braking).
I would imagine that at best, you could maybe match the range. If there's any scenario where going up and down a hill would yield more range than driving flat, I'd be very interested in how/why.
There is a potential benefit, and it is not really due to regenerative braking. It would require that your traction system is more efficient at converting stored charge into kinetic energy at high loads than at medium loads and that it also has a very efficient "coasting" mode to cut losses when almost no output is required.
Cruising on level terrain is a mediocre load on the traction system to offset the rolling and aerodynamic friction. Climbing a steep grade at the same speed will increase the load significantly, but that extra kinetic output energy is being stored as gravitational potential energy rather than lost like the baseline cruising load. Then, when you descend the mountain on the other side, you recover that gravitational energy to offset the rolling and aerodynamic friction. You want to be "falling" down the mountain grade at your terminal velocity where no braking and no traction force is required to maintain your cruising speed. It will not work well for winding descents where you need to brake for turns.
I've seen this work with turbocharged ICE cars with elevation gains of 4k foot or more and hundreds of miles distance. I've repeated on many trips to prove to me that it isn't simply a fluke (such as extreme headwind or tailwind). Going over a pass yields me a better trip MPG than covering the same several hundred miles on relatively flat ground.
I could see this benefit for a hybrid car too, since I believe they mostly handle highway cruise on ICE power. However, it seems unlikely for a BEV car unless there is something about battery and power electronics that I do not understand, that would give them a significant efficiency boost at high power.
It seems possible in theory. The air is thinner at higher altitudes, and wind resistance is a big part of fuel economy, isn't it?
Suppose you're going to make a 100 mile (160 km) trip. You have two possible routes. One is a straight shot on level ground. The other is straight, too, but it takes you up a 10% grade for the first 10 miles (gaining 1 mile in altitude), then you continue on level ground for 80 miles, and then you descend a matching 10% grade at the end.
It seems like the 80 miles of cruising on level ground at high altitude would use less battery than 80 miles of cruising at sea level (if the speeds are the same).
There will be some losses due to climbing and descending. Maybe climbing and descending is a little less efficient. Also, you're definitely traveling a very slightly longer distance. But those losses might be made up for spending the bulk of your trip in thinner air.
Going up/down at 20 MPH and going flat at 80 MPH might be this scenario. If the velocity difference is big enough, wind resistance will have a bigger impact on range than the thermodynamic inefficiency of regen braking.
Yeah, rethinking it, assuming you start and end at the same spot, the milage at the beginning is the max you can achieve, full stop. Simple conservation of energy. So the question becomes, how many miles do you lose at the end?
I would imagine that at best, you could maybe match the range. If there's any scenario where going up and down a hill would yield more range than driving flat, I'd be very interested in how/why.