You don't need to change to a new motor, and if you change the motor only, you will not see an increase in power. You just need a controller that has a greater nominal amp rating than your current controller. A new controller with a nominal rating of 16+ amps. (16+amps X 48V = 768W) will give you the 750W that you want (increased power). Your "500W" motor can handle that marginal increase with no problem.
Read this article to understand that your "motor rating" is a not a real world measurement.
"There's no such thing as a rated watt!" Read here for why we don't advertise a simple power rating for the motors we sell. Also, have a look at our Youtube video where Justin talks about the power to propel bicycles in <a href="https://www.youtube.com/watch?v=ALde6zhLPs0">"School of Watts"</a>.
ebikes.ca
If you change your motor to a "750W", you are still going to be limited by the amperage limit of the stock controller. If your current controller has a nominal output of 10 amps (500W/48V =10.4amps), the new 750W motor will still only draw 500W.
Make sure the controller is compatible with the display.
The nominal and peak amperage of the controller is usually printed on the controller body.
Your battery BMS is probably OK and rated at 20 amps.
After reviewing the owner's manual, it appears they are using the KT LCD8H display? Easy to just upgrade the KT controller and it should be plug and play if you get the one with the right connectors.
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I upgraded my two "750W" Aventon levels with the KT Controllers and LCD8H displays. According to the displays the bikes are now drawing 1000W peak. Same stock motors.