Electric info: this will be 52V motor with a step-down voltage converter for the 12V for the lighting as shown in the diagram.
I come from an extensive knowledge of internal combustion engines, so learning electric was a little confusing at first as I tried to think of the components as being analogous to ICE when they're really even more of a complete system than that. Most of the stuff I read on electric seem to assume an electric familiarity or were written by other ICE people who don't really get it, either. So, I am not an expert, but I've pieced stuff together over time that I think can help other people new to this understand.
At its basic, you have battery > controller > motor. The motor has a rating, usually for continuous power, meaning they can likely take more for a short amount of time. How much you find out when it melts, I guess, but I'm not messing with it. Anyway, the motor just converts electrical power to work according to load demand (in this case, either pedal assist or throttle up to its cutoff limit). What regulates how much current the motor gets is the controller. They can be external or integrated. The Bafang motor is integrated and the one I'm using is sold either as a "750W" or "offroad use only" 1500W because 750W is the legal max in much of the US. They are the same unit except that the controller limits power on the 750W to 15A and the 1500W limits it to 30. Watts is a measure of power, kind of like HP (~750 W=1 HP). W=A x V, so either more voltage or more amps will allow the motor to perform more work. Motors and controllers are rated for a particular voltage range, so that's kind of a fixed part of the equation. The Bafang I got is a 48/52V unit. Using a 52V battery like I am, that part of the equation stays the same for either the 750 or 1500W motors, so the controller's allowed upper limit on amps is the difference between the power ratings.
I am building a battery out of these:
View attachment 155719
I got them for about $1.33 each from batterysurplus.com. These are 3.7V cells with individual BMSs. That voltage rating is a nominal rating, which is an average since a fully charged pack will rate up to 4.2V. As it discharges, the voltage drops until the BMS cuts off the battery so it doesn't get damaged and/or catch fire (demanding the same power—watts—from the lower voltage of a discharged battery means a higher amp draw to meet that, which means more heat and these types of batteries are particularly sensitive to heat due to bottleneck limitations of the anode and cathode that cause more resistance, which generates more heat, which leads to thermal runaway). Battery packs are built in a sequence of series and parallel wiring. In series wiring (S), you're adding up the voltage of each cell you add, but the capacity of the finished pack doesn't increase over the single cell's. In parallel wiring (P), the voltage doesn't change, but the capacity does. With my motor rated for either "48V" or "52V", I could build the battery pack in either a 13S or 14S configuration to get the voltage at about that respective nominal rating. I'm going with 14S for 52V (though with each cell fully charged to 4.2V, that actually gives me a 58.8V pack). For capacity, each cell is rated at 4.4aH, meaning it can theoretically discharge at 4.4A for an hour. Because the pack of 14 cells is series wired, the whole pack is still only 4.4aH. To get up the capacity, I need to make multiple 14S packs and wire each of those in parallel. I'm doing 8 to get to a max of 35.2aH. This would make it a 14S8P battery and, if you've seen batteries advertised as xxSxxP and didn't know what that was, now you do (hopefully—nobody's ever accused me of being a good teacher). The BMS is like a mini controller for the cell(s). These cells are surplus from some kind of medical device, so they have integrated BMSs (battery management), but if you buy just cells to build a battery or buy a pack made up of cells alone, you'd need to include a BMS. Discharging a battery too fast or too far can generate too much heat, likewise with charging and the BMS largely regulates this (though you also want a smart charger to slow charging rates as capacity nears maximum or to even cut it off at a percentage of full capacity for the sake of longevity in terms of charging/discharging cycles). The less cells a BMS controls, the finer the battery pack can be maintained in terms of charging or discharging, which is better for performance and longevity, so these little easy-to-package flat cells are a real steal.
Now we can talk about how the battery factors into getting the power. The controller has a maximum power limit, but what about the battery? Well, the safe maximum discharge rate of a battery cell/pack wired-in-series varies and it is measured in "C". C is a multiplication of the rated capacity so 1.5C = 1.5 x the rated capacity. In this example, my 4.4aH battery would allow 6.6A discharge per cell/pack wired-in-series. Lets say I wanted to run my motor on one 14S pack, well all I'd be able to get for power out of it would be 343.2W (52V x 6.6A) and only for about 40 minutes at max power (of course, all this is ignoring losses to inefficiency, temperatures, etc), so the controller is only regulating how much power the motor puts out that the battery can provide based on the rider's demands between 0-100% throttle, but the max power is ultimately restricted by the battery being too small of a capacity to hit the controller's limit. Though my cells can handle it, I don't want to exceed 1C on my battery pack because I highly value longevity, so if I used half of the battery I'm building for 14S4P, I would be just over the controller cut off on the 750W Bafang and I would have probably just gotten that model.
This also answers a question I've heard multiple times from people thinking in internal combustion terms lamenting the price of electric cars—why don't they give me only 250hp instead of 500 and just give me more range instead? It's because, with electrics, you have either both or neither—the battery pack capacity can be used for maximum acceleration and holding top speed by using it in the shortest time allowable or to maximize range by using as little power as possible over the longest period of time. Of course, the reality is a mix of the two, but the point is that a smaller battery has less power available whether it's used for maximum distance or maximum load. A large battery pack is expensive and costs increases match capacity, so OEMs will throw in a bigger motor to make it more commercially appealing as it's a small additional cost for them in comparison to the bigger battery and they can probably tack on a bit more profit to match. The question for them becomes: how many customers would pay double the smaller battery price (a very large portion of the car's overall price) for a larger battery to get the longer range, but have the same available power as the cheaper model when they could pay only a small percentage more on top of that for a lot more available power with effectively no other penalty, especially for an expensive vehicle that sells to a decently well-off demographic? That's an answer car companies have had that predates modern electrics since cars with more expensive drivetrains, be they higher power or something like a hybrid, almost always come with more standard equipment (usually low cost/high profit to begin with) to make their higher prices more appealing to the greater number of consumers (I prefer less stuff with more power, but I'm definitely in the minority).
