The formular for the drag power is the frist one, but this is the power theoretical possible to take from the wind and that is not the power needed for the vehicle to drive. The power for the vehicle is more like the 2nd formular.
It is obvious that the first formula can not be corrent for the power of the vehicle: if the vehicle changes direction from going against the wind to going with the wind it changes from needing power to drive to gaining power from the wind. So the sign in the power has to change at around 0 vehicle speed.
Another way is to look at the force need: mechnical power is force times speed, more or less by definition. The force from the wind is limited and approaching zero speed the power this also has the approach zero.
The relevant question for the vehicle is if the motor can provide sufficient force. The power only determines how fast the vehicle can go. With low speed very little power is sufficient.
I do not think that second formula describes anything. I'm fairly certain one or more people that do not understand what power is came up with that as they were likely thinking the correct one outputs a value larger than they expected or wishing.
Yes as you see the sign changes correctly when vehicle speed is zero.
Equation contains this (wind speed-vehicle speed) so max wind power to accelerate the vehicle is proportional with (wind speed - 0)
3If vehicle drives downwind it can be powered by wind at (wind speed - vehicle speed)
3If vehicle wants to drive upwind it requires a power proportional with (wind speed - (-vehicle speed))
3 same as saying (wind speed + vehicle speed)
3So is clear from this that no vehicle can exceed wind speed powered only by the wind and can not drive at any speed upwind.
And yes all this is correct. Any wind powered vehicle that exceeds wind speed will do so with either stored energy or another energy source other than the wind and same is true for a vehicle driving upwind at any speed.
When you think at a zero speed vehicle you are wrongly thinking about a vehicle anchored to the ground. But that anchoring to ground just means vehicle is now part of earth.