# Efficiency comparison between six step and FOC for a given motor

For a given PMSM motor with sinusoidal back-EMF, it can be driven by either six-step (as in drone applications) or by FOC (as in servo control). However, for a given motor and given DC link voltage, how to compare the system efficiency difference between six-step control and FOC control?

The reason to ask this question is that drone development is getting popular and majority of ESC solutions in the market are using sensorless six-step control. However, now people began to talk about sensorless FOC for drone ESC. So I would like to understand their difference in terms of efficiency because for drone, IMHO, flying longer time and longer distance is more important than acoustic noise.

• What does 'FOC' stand for? Apr 2 '16 at 6:24
• @BruceAbbott, Field Oriented Control Apr 3 '16 at 6:41
• What does IMHO stand for? Apr 3 '16 at 7:44
• PMSM = permanent magnet synchronous motor. EMF = electro magnetic force. DC = direct current. ESC = electronic speed controller. IMHO = in my humble opinion. @soosaisteven Apr 3 '16 at 19:50
• @mkeith, thank you very much for the explanations. I will try to be clearer about those abbreviations next time. Apr 4 '16 at 0:23

Field Oriented Control (also known as Vector control) of BLDC motors can improve low speed torque and reduce torque ripple at speed. Normally it uses sine wave drive. This works best when matched to motor with sine wave back-emf. However most motors used in multirotor drones are designed for 6 step trapezoid drive.

The following traces show the different back-emfs of a 2 pole coreless ironless BLDC motor and a multipole iron cored motor. The second example might actually perform worse with sine wave drive.

So to get the best out of FOC drive it needs to 'tuned' to the motor. This might explain why the only two FOC ESCs I could find for sale (DJI 1240S/X and EMAX WindTalker) are both intended to be used only with a specific motor.

The vast majority of ESCs used in multirotors don't even use synchronous rectification, so their part-throttle efficiency is already ~5% worse than it could be. Also many of them are not using the latest most powerful processors and high speed drivers, so their switching losses are higher at high frequency (this is more important when using FOC drive, because to produce an accurate waveform requires high frequency PWM).

The only one way to find out what real improvement FOC drive could make is to try it. For a fair comparison you would have to use the same ESC and only change the commutation technique.

• thanks for the explanation. Actually, I am planning to prototype the ESC with circuits ready for both six-step and FOC so that can be tested. As you mentioned, this could be the only way to tell when one has a better efficiecny. Apr 4 '16 at 0:22
• @Bruce 4 years on - Benjamin Vetter's "VESC" ESC will do FOC for many motors and n earlier was available in an earlier version "back then". I have not yet ventured into FOC, but may be about to. Or not :-). May 1 '20 at 12:30

From Hobbywing's website:

The FOC solution greatly improves the battery's sustainability, increases the flight time and effectively protects the motor and battery and prolongs their service lives via current control.

For a given PMSM motor with sinusoidal back-EMF, it can be driven by either six-step (as in drone applications) or by FOC (as in servo control)

That is true but as you point out ... what is more efficient.

If we take the motor on its own efficiency:

• Power out = $$\T\omega\$$.
• Power in = $$\VAcos\Phi\$$

If the motor is supplied with a current waveform that exactly matches that of its airgap flux & in-phase then maximum efficiency can be realised. There will still be inefficiencies due to copper losses, iron losses, bearing losses etc.

For a machine with a backEMF that is sinusoidal in profile, it would need sinusoidal currents & equally phase currents in alignment with the q-axis of the motor.

Anything that distrupts this will reduce the efficiency:

1. Harmonics in the current waveform (quasi-squarewave is rich in harmonics).

2. Angular alignment (an increase in $$\\Phi\$$ increases the amount of D-axis current)

So immediately exciting the stator via 6-step will not be the most efficient method.

However... you must view the entire system as a whole. 6-step is easy... zonal firing, simple current regulator. If you were to deploy sinusoidal excitation you would need means to measure the current (either just the DC to reconstruct or the 3phase currents for full visibility). If you wanted to go the route of FOC (and not you do not have to with sinusoidal drives, it just makes the control laws simpler) you would need a micro-controller. Likewise if you have gone to the effort to implement a FOC you might as well implement a SVM block to maximise the utilisation of your DClink voltage (sinusoidal PWM is only 50%, SVM is 86%).

All of this adds complexity, time and more importantly weight & volume & this is something of a premium in low-market drones. In the field of UAV's then the choice swings the other way as the increase in complexity is outweighed by the increase in power efficiency