1. Eng. Alfonso Monroy Olascoaga Ph. D. Pedro Ponce Cruz ITESM-CCM
Constant V/f Control
Eng. Alfonso Monroy Olascoaga
Ph. D. Pedro Ponce Cruz
ITESM-CCM

2. Equivalent circuit model
The stationary equivalent circuit model per phase for the induction motor is shown in the figure.

3. Equivalent circuit model
The equations that describe the operation of the induction motor are

4. Power flow in an induction motor
The power flow in an induction motor can be appreciated in the next figure

5. Torque-speed profile Maximum torque (Tm) Torque Operation point
Reference torque
Synchronous speed (ws)
Speed
Slip (s)

6. Torque-speed profile under input voltage variation
Maximum torque (Tm)
Reference torque
Synchronous speed (ws)
Slip (s)
Speed
Torque
Operation point

7. Torque-speed profile under input frequency variation
Maximum torque (Tm)
Reference torque
Torque
Synchronous speed (ws)
Slip (s)
Operation point

8. Approximated equivalent circuit model
In order to obtain de approximated equivalent circuit model, we have to assume:
V1=(R1+jX1)I1+E1 E1
I1>>Im+Ic
Im+Ic k
Rc 0

9. Approximated equivalent circuit model
Under the last assumptions, the approximated equivalent circuit model may be drawn as follows R1
jX1
R2/s
jX2
jXm
V1  E1

10. Constant V/f control principle
From the expressions of emf and magnetic flux
= max sin(et).
E1 = max e cos(et) = max 2f1 cos(et)
Its RMS value is

11. Constant V/f control principle
From the assumption number one:
It is possible to maintain a constant flux, if the relation V1/f1 does not change:

12. Boost voltage
At low speeds, the assumption (R1 + jX1)I1=0 is not valid.
The voltage drop in the stator copper must be considered.
A voltage compensation is needed in low speed operation.
The voltage depends on the load conditions.

13. Boost voltage Voltage [V] Flux Lineal compensation compensation
Linear relation
Non-linear relation
Lineal compensation
Flux
Frequency [Hz]
compensation

14. Sinusoidal pulse width modulation

15. Closed loop operation
If accuracy is needed in the speed control, a closed loop scheme must be used.
speed reference
V/f control
Induction
PI controller
motor

16. Results (open loop)
Current waveforms and harmonics content at 2396 rpm (left) and 2980 rpm (right).

17. Results (open loop)
Current and voltage waveforms at 3000 rpm

18. Results (closed loop)
No load start (2500 rpm)

19. Results (closed loop)
Speed change ( rpm) at constant load torque (1.7 Nm)

20. Results (closed loop)
Torque change ( Nm) at constant speed (3100 rpm)

21. Advantages Open loop operation Simple control algorithm
Good closed loop operation
Great for high speed and constant torque applications

22. Disadvantages Boost voltage needed Poor load speed operation
Control scheme designed for steady state operation