# What exactly is 1.x and 2.0 power scalar V/f control in VFDs?

These are terms that I have come across in multiple operating manuals for VFDs and usually, they just mention that it's used for variable torque applications. My doubt is "what exactly is it?" and is there a mathematical formula that I can use to derive this relation between voltage and frequency? I read some articles that say that this has something to do with affinity laws for pumps and fans, but am unable to understand how would one derive the V/f relationships using that.

Any help or even a general direction towards additional sources which could help me in this regard are appreciated. Thanks for your time!

• My general direction would be to start at the beginning.. That would be AC circuit theory, basic electromechanical systems, electric machinery theory etc. The affinity laws for pumps and fans explain the characteristics of those machines including the torque required to drive them at a given speed. Much of what is contained in VFD manuals is about the specific product and is of little use in understanding the basic principles of operation. – Charles Cowie Aug 6 at 15:48
• Hi Charles! I actually have been working on this for a few weeks now and I understand your advice to check the basics. Checking the basics initially was actually useful in understanding the linear V/Hz relationship that is used in general cases. It is specifically the parabolic V/Hz curves in VFDs that are bugging me. First I wanted to know why they did it, and now that I have some idea, I want to know how they do it. I'll take up on your advice and try working out the torque-speed relations and hopefully, find something there. – AdiKel97 Aug 6 at 17:35

It is about efficient operation of your pump/fan. Affinity law says load torque is proportional to square of speed for fan or pump load. If you analyse a induction motor with equivalent circuit you will find that it is slip which determines efficiency. There is a slip value band from 0.05 to 0.15 where your machine operate with highest efficiency. Your motor is designed to operate at maximum efficiency at rated operating point. Most of the time V/f relation is derived from rated operating point. But then in lower speed operating region slip goes beyond 0.05 and efficiency performance degrade. Parabolic V/f relation can tackle that problem. It can ensure high efficiency even in low speed operation maintaining the slip band. Hope this helps you.

Charles' comment is appropriate, but to simplify and give you some background:

AC machines are designed to operate at a certain flux level. Beyond that the machine can saturate which can cause damage, high currents, overtemperature, fuse/breaker trips, etc.

So to step back, consider just an inductor across the AC line. Let's say it's in the US where the frequency is 60Hz. That inductor will have an impedance proportional to the line frequency, L*jw.

Now if you were to drop the frequency in half, to 30Hz that inductor would drop to half the impedance and draw twice the current. Unless it saturates.

Since an AC induction machine (for example) is designed to operate at a particular frequency, the core utilization is designed for proper operating flux at that frequency.

Now like in the case of the inductor if I drop the frequency in half, the inductance drops in half and if I keep the same voltage I would have twice the flux. Far more than the design target of the machine.

So in order to keep the machine operating near its design target flux I have to make the voltage/frequency ratio constant. (220V/60Hz or 110V/30Hz for example) That's called scalar or V/f or volts/Hz control.

It kind of breaks down at low speed due to resistances involved, a vector control scheme is preferred.

• Hi John, thanks for your answer! I actually understood the concept behind keeping the V/Hz ratio constant over the entire frequency range in order to prevent core saturation. I have a very specific doubt regarding what changes for a fan-type load that the manufacturers of drives choose to create a parabolic V/Hz profile for them. As far as I know, there is a power-speed relation at play. I am lost in trying to understand and derive that particular relation. – AdiKel97 Aug 6 at 17:18
• Ahh, OK, I see- Yes, it has to do with the affinity laws, torque proportional to speed squared, and you can calculate the excitation needed to match it for an induction machine from the equivalent circuit of an induction machine. You can probably find the derivation online, but I haven't checked. – John D Aug 6 at 17:40