Constant V/f control of induction motor

In an induction motor, the air-gap flux is $\phi \propto \dfrac{V}{f}$ (neglecting stator drop). If frequency is reduced to lower the speed while voltage is kept constant, the flux rises and the core saturates. So below base speed, voltage is varied in proportion to frequency (constant V/f), keeping the flux and hence the maximum torque nearly constant.

Torque-speed characteristics

Synchronous speed $N_s = 120f/P$ falls with $f$; the slip speed at maximum torque, $s_m\omega_s \approx (R_2'/X_2')\,\omega_s$, is the same at every frequency because $X_2' \propto f$. Therefore the curves shift left parallel to each other with almost the same maximum torque.

 T
  |     f4    f3    f2   f1 = base
  |   _.-.  _.-.  _.-.  _.-.
  |  /   | /   | /   | /   |
  | /    |/    |/    |/    |  Tmax ~ const
  |/     /     /     /     |
  +------+-----+-----+-----+--> speed
        Ns4   Ns3   Ns2   Ns1
  (at very low f, Tmax falls - dotted -
   because stator R drop is significant;
   add voltage boost)

• From base speed down to about 10 to 15 % of base frequency, $T_{max}$ is nearly constant: constant torque region.
• At very low frequencies the stator resistance drop becomes comparable to $V$, so flux and $T_{max}$ fall; a voltage boost (offset $V_0$) is added: $V = V_0 + kf$.
• Above base speed, $V$ is held at rated and $f$ increased: field weakening (constant power).

Open-loop constant V/f control scheme

 3-ph AC ->[Diode rect]--+--[L]--+--[PWM inverter]--> IM
                         |       C       ^
                     DC link             | gate pulses
 w* (speed ref) ->[Ramp]->[f*]->[V/f  ]-->[PWM generator]
                     |          [block]  V* and f*
                     +--------->(with low-speed boost)

1. Rectifier and DC link: three-phase diode rectifier with LC filter gives a constant DC voltage.
2. Speed reference $\omega^*$ sets the frequency command $f^*$ (since $N \approx N_s$ at small slip).
3. Ramp (soft start) block limits the rate of change of $f^*$ so that slip and current stay within limits during acceleration and deceleration.
4. V/f function generator gives $V^* = V_0 + kf^*$ (boost at low frequency), saturating at rated voltage above base frequency.
5. PWM generator and voltage source inverter produce three-phase output with amplitude $V^*$ and frequency $f^*$.
6. The motor runs near synchronous speed for that frequency; speed drops slightly with load (equal to slip speed), as no speed feedback is used. Slip compensation can be added using measured current.

Features

• Simple, cheap, no speed sensor; several motors can be run from one inverter (textile mills).
• Speed accuracy limited by slip; poor dynamic response; current limit needed for protection.
• Widely used for fans, pumps, conveyors and other general-purpose drives.