Skip to content

Induction machine drive example with a V / f scalar control

Download Simba model

This example shows a induction machine supplied with a PWM inverter and driven with a V / f scalar control, with:

  • a dc bus voltage of 600 V,
  • a switching frequency of 10 kHz,
  • a variable load torque with a square-law characteristic (such as booster pumps and centrifugal fans), with T_{load} = 0.1 + 0.003 \times \Omega^2.

Control structure

The diagram below shows the closed-loop V / f control structure.


This V / f control makes possible to drive the induction machine with a constant flux (considering the stator resistance can be neglected).

Principle of the control

The electromagnetical torque of an induction machine can be given by:

T_{em} = 3 N_{pp} \left(\frac{V_s}{\omega_s}\right)^2 \frac{R_r / \omega_r}{(R_r / \omega_r)^2 + L_r^2}

The maximum torque - when \omega_r = R_r / L_r - is then:

(T_{em})_{max} = \frac{3 N_{pp}}{2 L_r} \left(\frac{V_s}{\omega_s}\right)^2
  • N_{pp} number of pole pairs
  • V_s equivalent single-phase voltage
  • \omega_s pulsation of the stator currents
  • \omega_r pulsation of the rotor currents
  • R_r rotor resistance at the stator side
  • L_r rotor leakage inductor at the stator side

If the ratio V_s / \omega_s can be kept constant, the maximum value of the torque will be constant for different synchronous speeds \Omega_s. This principle is illustrated in the figure below:


For low speeds, the ohmic voltage drop due to the stator resistance cannot be neglected. For high speeds, when the voltage reaches this maximum, this ratio decreases leading to a flux-weakening zone and a decreasing of the torque. This makes possible to reach higher speeds than the nominal speed.

Industrial variable speed drives propose modified V / f control profiles with:

  • an adding term for low frequencies to keep a minimum torque,
  • a saturation when the voltage reaches its maximum value.

This control profile is illustrated in the global control diagram above in the V / f block. Such a control profile has not been implemented in the demo example as it was not necessary.

Torque control

The torque can then be controlled with \omega_r according to the first expression of the electromagnetical torque. For small values of \omega_r, the torque expression can even be considered linear with \omega_r:

T_{em} \approx 3 N_{pp} \left(\frac{V_s}{\omega_s}\right)^2 \frac{\omega_r}{R_r}

Speed loop

The speed loop involves a classic PI regulator.


This circuit example is issued from an example proposed by Christophe Haouy.