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

11111 )( EIjXRV )(21 cm IIII

2221 )( IjXRE e

res

Power flow in an induction motor

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

Par ()

Vel ()

Par Máximo (m)

Par de referencia

Vel. síncrona (s)

Curva Característica del Motor de Inducción

Deslizamiento (S)

Punto de operación

S

Torque Maximum torque (Tm)Operation point

Reference torque

Synchronous speed (s)

Slip (s)

Torque-speed profile

Speed

Par Máximo (m)

Par de referencia

Par ()

Vel. síncrona (s)

Vel ()

S

Deslizamiento (S)

Punto de operación

Curva Característica Variando Voltaje

Maximum torque (Tm)

Reference torque

Synchronous speed (s)

Slip (s)

Speed

TorqueOperation point

Torque-speed profile under input voltage variation

Vel. síncrona (s)

Deslizamiento (S)

Punto de operación

Par de referencia

Par ()

S

Par Máximo (m)

Vel ()

SS

Curva Característica variando Frecuencia

Maximum torque (Tm)

Reference torque

Torque

Synchronous speed (s)

Slip (s)

Operation point

Torque-speed profile under input frequency variation

• 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

Approximated equivalent circuit model

• Under the last assumptions, the approximated equivalent circuit model may be drawn as follows

R1 jX1 R2/s jX2

jXmV1 E1

Constant V/f control principle

• From the expressions of emf and magnetic flux

= max sin(et).

E1 = max e cos(et) = max 2f1 cos(et)

• Its RMS value is

dt

dE

1

max

11

2

2 fE

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:

11 EV

max1max1

12

2 kf

fV

max1

1 kf

V

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.

Voltaje [V]

Frecuencia [Hz]

Voltaje Boost Relación lineal

Compensación Relación no lineal

Compensación Líneal

Flujo (M)

Voltage

[V]

Boost voltage

Linear relation

Non-linear relation

Lineal compensation

Flux

Frequency [Hz]

compensation

Boost voltage

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