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I want to better understand how Electronic Speed Controllers (ESC) work for BLDC motors. Specifically, I am trying to understand battery current draw.

Question 1:
When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.

Question 2:
If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that? I'm now thinking the draw will be more along the RMS value of the output pulse wave. This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.

Question 3: (slightly off topic)
To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear. I just want to understand the theory of how ESC's work at a high level.

Much thanks!

Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.

Without a datasheet we're guessing but the 500 A peak current is likely to occur during start-up and this may last one or more tenths of a second. A capacitor to supply 500 A for 0.1 s at a useful voltage will be very large.

It's much more likely that any capacitors on the DC input stage are acting as short-term filters to pass high-frequency noise to ground.

Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?

It will need to draw enough to power the motor. It completely depends on the load the motor is given.

This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.

This may be a warning sign that you have a low quality product.

Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear.

The ESC will operate using pulse-width modulation (PWM) as it results in very low losses in the switching transistors. PWM applies pulses of 100% voltage to the motor for a short period, switches off, waits and then repeats the process.

Figure 1. PWM signal transitioning from high pulse width (75%) to low (25%) and back again. Note amplitude remains constant.

All answers assume you're talking about "hobby" ESCs, as used in planes, boats, cars, robots, etc.

Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps?

No. For the most part, the ESC draws what it draws given the motor, battery and load on the motor.

Some of the better ESC's do have current limiting, but experience in the flying field is that if you dork the thing into the dirt at full throttle, chances are that you'll damage the electronics due to overcurrent.

An ESC could be designed to limit current in such a way (I've designed industrial motor controllers that do), but AFAIK ESC's don't.

Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?

See answer to question 1.

Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage?

Neither. At the level of the throttle command to motor, it supplies a fixed PWM to the motor -- essentially it chops the battery voltage and hands it to the motor.

This is complicated by the fact that some ESC's have a governor function, that servos the motor speed to the signal coming in -- but they still have an internal throttle command that works as above.

The max operating temperature or heat rise above 25'C is what limits the nominal continuous current rating. The peak is an absolute maximum which may or may not be protected and should never be exceeded, such as starting a couple of these motors below at full throttle.

One must mind the rated peak currents to prevent damage to the electronics.

Similarily, a motor full load current rating is defined by the same method of temperature rise above 25'C for the winding hot spots. However every market does not use the same hot spot temperature for a long useful life and if no standards are given or not temp rise is specified, you might guess they don't want you to know.

However it is quite common to give the peak motor current as surge, start or locked rotor current. These are all the same as is simply Ohm's Law applied to the DC resistance or DCR, so Imax= V/DCR. This is typically Imax = 8 to 12 times the rated current in modern BLDC, high-efficiency DC motors.

Here they generously rate the motor current with a 180 second limit. This would be at max internal temperature.