Open loop and closed loop V/f inverter-fed drive

Open-loop V/f control

A voltage source (PWM) inverter feeds the induction motor. The speed command sets the inverter frequency $f$; a function generator sets the voltage so that $V/f$ is constant (with a small boost at low frequency for the $I_1R_1$ drop). The air-gap flux is then nearly constant and the motor runs close to $N_s = 120f/P$.

 speed   +------+  f*  +----------+  V*  +---------+    +----+
 ref --->| ramp |--+-->| V/f      |----->| PWM VSI |--->| IM |
         +------+  |   | function |      +---------+    +----+
                   |   +----------+        ^     ^
                   +-----------------------+     |
                              f*                 | dc link
                         ac -> rectifier --------+

• Simple, cheap, no speed sensor; good for fans, pumps, and many motors on one inverter.
• A ramp (soft start) limits the rate of change of $f$ so that the slip stays small.

Problems of open-loop operation

1. Speed error with load: the motor speed $N = N_s(1-s)$ falls as the load increases; there is no correction, so speed regulation is poor.
2. Pull-out/instability: if the frequency changes too fast, or a sudden load is applied, the slip exceeds the breakdown slip and the motor stalls or draws very high current.
3. No current limit: overcurrent during fast acceleration or braking.
4. Low-speed weakness: at low frequency the stator drop reduces flux and torque; a fixed boost may over- or under-flux the motor.
5. Poor dynamic response; the drive may oscillate at light load.

Closed-loop operation (slip regulation)

Speed is measured by a tachogenerator/encoder and compared with the reference. The speed error, through a PI controller, sets the slip speed $\omega_{sl}^*$, which is limited to a safe value. The inverter frequency is

$$\omega_e^* = \omega_r + \omega_{sl}^*$$

Since torque $\propto \omega_{sl}$ at constant flux, limiting the slip limits the torque and current.

 w_r* +    +----+  w_sl*  +-----+ +   w_e*   +-----+  V*  +-----+
 ---->(O)->| PI |-------->|limit|-->(O)------>| V/f |----->| PWM |-> IM
      -|   +----+         +-----+    ^ +      +-----+  f*  | VSI |   |
       |                             |                     +-----+   |
       +-------------------- w_r ---+---------- tacho <--------------+

• On a load increase, the speed falls, the error rises, and the slip and frequency increase until the speed is restored, so speed regulation is very good.
• The slip limit keeps the motor below breakdown slip, giving fast acceleration and braking at the maximum allowed torque without stalling.
• The voltage is taken from $\omega_e^*$ through the V/f function, so the flux stays constant.
• A negative slip limit allows regenerative braking (with a suitable dc link).
• An inner current loop may be added for direct current limiting.