Electrical – Driving a 12V motor with brushed ESC

Short answer:

Yes, you can use up to 15 LiFePo4 cells in series (aka 15S) at the input of the ESC without any problems.

Long answer:

LiFePo4 cells definitely work all Lipo ESCs... as long as you don't exceed the max input voltage of the ESC.

Your specific ESC lists that it can handle 12S Lipo batteries. This means, it can take an input voltage is greater than >50V (>4.2V*12). This is also the reason it states that you can use up to 36 NIHM cells, which are 1.5V peak voltage (1.5v*36 = 54v). 54V is the max input voltage for this ESC.

This means, you can use 15 LiFePo4 cells in series without exceeding the input voltage rating. The peak cell voltage for LiFePo4 cells is bit over 3.5V/cell... so 3.5v* 15 = 52.5v (which is below the max rated volatge)

More details:

The internals of an ESC are switching power regulators, which output a frequency modulated AC to the motor (except sometimes cheap BECs, are linear regulator, which get super hot). The switchers compensate for any battery sag, allowing you to pretty much put in any non-alkaline cells at the input (because alkaline batteries have way too much ESR). The only way to damage the ESC is to exceed the max input voltage. Some ESC may list the actual voltage, while most just list the max number of LiPo cells that the ESC can take.

Does changing the throttle change the duration of the trapezoids?

Not directly. The duration of the 'trapezoids' is determined by commutation, which is synchronized to the rotor position. The motor will rotate at the speed it wants to, determined by the applied voltage and torque load. The controller must respond to this by commutating at the same speed and phase.

The throttle controls effective motor voltage by applying high frequency 0-100% PWM, so you could say that it indirectly affects commutation timing because motor speed is proportional to applied voltage. However motor speed is also affected by loading, which may vary independently of throttle level.

How does the ESC maintain unity power factor?

The ESC may adjust commutation timing to compensate for the lagging current caused by winding inductance. Some ESCs do it automatically, others have fixed timing advance settings. With fixed timing unity power factor is rarely achieved, and the best setting is usually a compromise between power and efficiency.

Does changing the throttle setting below a certain point change the kt of a motor?

The controller relies on winding inductance to smooth out the current. However in most ESCs the PWM frequency is barely high enough to maintain continuous current flow. As the throttle is lowered (and PWM ratio reduced) current ripple increases until the current waveform becomes a discontinuous sawtooth. Since torque is proportional to average current this lowers the effective torque constant. At higher loading the current becomes smoother so the effective torque constant increases, causing the torque/rpm curve to become nonlinear.

do the similar sinusoidally-driven BLACs (aka PMSM?) energize all 3 phases at once?

Yes, or no - depending on the controller. There is no fundamental difference between BLDC and PMSM. It is possible to power a BLDC motor with 3 phase AC, but with all 3 phases continuously powered you can't extract back-emf for zero-crossing detection. However the PWM can be modulated to shape the trapezoid waveforms into a 'saddle' profile, which becomes a sine wave when the two driven phases are combined.

How to Sinusoidally Control Three-Phase Brushless DC Motors