Hello Faruk,

I had a similar confusion, when I started out my project for variable frequency drive applications. I believe I can give you a brief answer here, please read my work published in IEEE for a deeper understanding.

The answers we seek lie in the very question itself. As you have mentioned, we are looking into the most basic modulation scheme of constant V/f open loop control of and Induction Motor (say). We will spend a minute to think, why this really means?

We will maintain the ration of sinusoidal voltage amplitude to the frequency of sinusoidal voltage, a constant. (Ignore the harmonics for now)

What do we achieve by doing so? We maintain the integrated area under half cycle of the sinusoid constant. The integral of voltage is flux, so what we are really proposing, is that the peak amplitude of flux be maintained a constant value. This helps us operate at an optimal point of flux, that is neither too low for motor operation, nor too high to cause core saturation effects.

Now that we have had a closer look at the motivation behind constant V / f control, we can address the real question. How do we quickly come up with a number for V/f ratio that we can plug into the control algorithm.

Answer: Check the motor nameplate information. It usually states the max ratings, when the motor is run on the grid frequency and the 3-phase supply is directly fed to the motor. So, as a starting point, V = line voltage amplitude. F = grid frequency. Take ratio. you're done. :)

Hope this helps, please feel free to ask for further clarifications, I will try to answer at the earliest.

Hello Faruk,

In general, an induction motor requires an almost constant magnitude of the air gap flow for satisfactory motor operation. This suggests that in order to maintain a constant flu flux (to avoid saturation), the magnitude of the stator voltage must be proportional to the frequency.

In steady-state, the standard stator voltage equation is written as :

Vs = RsIs + jws Փs

If we neglect the ohmic drop in the equation above, we find :

Փs = -j (Vs/ws)

We can write the modulus of the equation above in the following form :

Փs = Vs/ws

Avec Փs = Vs / 2π.fs

On voit bien que le flux reste constant (sans saturation) dans la région des vitesses élevées lorsqu’on varie en même temps la tension et la fréquence d’une manière proportionnelle pour garder le V/f et donc le flux constant.

Induction motor working on induction principal like transformer. Induced emf at constant working flux density could be given by equation E = 4.44 fBmAN, hence to have constant flux density for given core area(A) and turns(N), E/f = KBm, must be constant. For the core, no load ironloss could be used to find hysteresis and eddy current loss constant as WI=Wh+We=Af +Bfsqr, W/f = A+Bf or y=mx + c , line equation or c=A and slop m=B constants used to separate Wh and We from total ironloss of core used, for different frequencies with constant V/f....best luck.

Thank you for your attention.

I will use vector control in the inverter I designed.

Is it still necessary to observe the V / f ratio? (to prevent motor saturation)

Hi,

For the VFD on the market, there are several variants of the V/f law.

The choice of the suitable variant is often configurable (U/f with linear characteristics, U/f with parabolic characteristics, U/f with parameterizable characteristics, dynamic U/f ...).

The major drawback of this law (V/f) is that the torque becomes low for low speed (less than 20Hz). This is not the case for the vector control which allows to supply 100% of the torque at 0Hz.

These variants of the V/f law allow to boost the torque at low speed but still remain less efficient than the vector control.

For the calculation of the ratio, it is constant only for the linear V/f law.

It is calculated by dividing the nominal voltage of the motor by the nominal frequency. For 400V-50Hz for example the ratio is 8.