10-15 km is a bit on the low side of the range you could get with a 3000W setup, but it's not totally far off if you ride at full throttle. A new scooter should perform better in theory, but it will depend also on things such as your weight, if there is a lot of hills, if your tires are properly inflated, if your brakes are correclty set up or if you don't have a toasted bearing. So check that first.
Basically your battery can only store 960Wh in theory (marketed capacity: 48V @20Ah: 48 x 20 =960). You can probably use 80% of that, maybe less because the voltage can't just drop to zero so you end up with unusable capacity, so that's about 770Wh of usable power. If you factor in the Peukert effect (basically the Peukert effect states that riding a battery at a high discharge rate ends up in even more unusable capacity), i'ts likely that you have even less than 770Wh. Maybe around 650Wh (guesstimation, could be more, could be less, it depends on a lot of factors I cannot know).
So, let's say you ride at full power (3000W or so), 650/3000 = 0.21 hours, so that's about 12 minutes. This is just a ballpark approximation, in reality it will be more, you'll have to stop at red lights, you probably can't ride at full blast all the time and your powertrain won't draw 3000W all the time. Also I don't know if the 3000W you refer too are continuous or peak, but let's just assume they are continuous.
So let's say that your top speed is 50km/h at 3000W constant (should be around that for a 48V setup), then in 12 minutes at that pace you'll only be able to do 10 km, which is, more or less, what you experienced.
It is really a ballpark estimation, to give you a general idea of how it works, in reality it is quite a bit more complex than that, but you can't expect to do something like 50km at full blast. Not with this battery anyways.
If you want more range, then you'll either have to take it easy on the throttle, lose weight (easier said than done, I know
) or change your battery for a better one, which is probably the best solution since your batteries won't last that long anyways...
The reason why your battery won't last long is the same reason you get capacity loss with the Peukert effect: basically your battery is rated at 20Ah, which means its optimal discharge rate is 20Amps in one hour. But you're discharging it in 12 minutes in this example. If you were dischaging it in one hour, it would mean that your discharge rate is one Coulomb (or 1C). Since you're discharging it in 12 minutes, it means that you're discharging it 5 times faster, so 5C. That's five times the recommendation for this battery, and lead acid batteries don't really like to go over 3C continuously, so basically the battery heats, which progressively rises its internal resistance, eventually lowering its capacity, ending in premature death.
