How does VFD calculate the motor torque?

Motor torque along with speed is the most important quantity that the VFD shall control. But how does the VFD measure or calculate the motor torque? What are the necessary inputs? Are there any extra sensors needed? Can every VFD perform the calculation of motor torque? That is the subject of our short post.

Knowing the actual value of motor torque is crucial for a good performance of a variable speed drive system. Some drives are operated in a torque controlled mode, i.e. the VFD receives the torque reference signal that shall be followed. Torque regulation is considered as the fundamental task of controlled drives used in steady state and transient operation modes. Many drives are speed controlled. Also those drives rely of information about motor torque. When the actual speed is lower than the reference speed signal the VFD is commanded to increase the motor torque (to accelerate) and vice versa. There are also torque limiters and torque ramps implemented in the control algorithms. They shall protect the mechanical load from excessive torque, backlash etc. From these few lines we can already read and feel that information about motor torque is essential for optimal drive control and protection.

So how does the VFD know the amount of torque that the motor is producing? Finally, the inverter supplies voltage and current…

Measurement of motor torque is fairly complex task. We have written about it e.g. in [1]. Direct measurement would require a special sensor, usually on base of strain gauges, along with a processing unit. It is something that might be needed for demanding applications, e.g. with high requirements on accuracy or for complex shaft strings¹.

¹ In a complex shaft system the torque at a specific section of the shaft is not necessarily the same as the motor torque (especially when considering elasticity of the shaft and potential mechanical resonances).

Nonetheless, majority of drive applications works on a principle of torque calculation. The VFD can calculate the motor shaft torque, resp. the air gap torque of the machine, based on measured electric signals. According to the Beatles, ‘All you need is love’. To calculate the motor torque all you need is a measurement of motor stator current, information about stator flux and rotor position. Plus an intelligent VFD control that computes the motor torque out of those signals. That sounds quite elegant and easy, doesn’t it?

No additional hardware

The best thing is that you don’t need any extra sensors for calculation of motor torque. Stator current shall be measured anyway for other control tasks and especially for effective protection of inverter and motor. Stator flux is determined by integration of the stator voltage which is abbreviated from dc voltage. And rotor position is an integral of rotor speed which can be calculated without the need of a speed encoder. So no additional hardware, no extra signal cables – just few blocks in the VFD control software.

Equation determining the motor torque looks following:

So knowing the stator current and flux and transforming them into the d,q frame one can easily calculate the motor torque. The relationship works in steady state operation as well during transients.

Of course, there are few “details” how to get the computation more efficient and accurate. Subscribe to our premium plan and learn more about this and many other topics associated with VFDs, electric motors, converter transformers and electric drive systems.

Can every VFD calculate the motor torque?

We have described how the motor torque is principally calculated. The question is whether every VFD can perform the calculation of motor torque? Well, not necessarily… simple control, such as basic scalar control (also called ‘V/f’) does not need to calculate the motor torque for its functionality. It comes with limitations, particularly with regards to dynamic performance. However, for applications with ‘slowly changing’ trends the scalar control may be sufficient. In such case you will likely not see the information about motor torque on the panel.