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

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

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

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

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

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

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

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

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

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

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:

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.

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

Sinusoidal pulse width modulation

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

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

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

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

Results (closed loop) Speed change (819-3000 rpm) at constant load torque (1.7 Nm)

Results (closed loop) Torque change (1.9 - .2 Nm) at constant speed (3100 rpm)

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

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