Download Constant V/f Control

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
V1  ( R1  jX 1 ) I 1  E1
E1  ( R2  jX 2 )I 2
I1  I 2  (I m  I c )
e  r
s
e
Power flow in an induction motor
• The power flow in an induction motor can be
appreciated in the next figure
Torque-speed
profile
Curva Característica
del
Motor de Inducción
Maximum
torque (Tm)
Par
Máximo (m)
Torque
Par
()
Operation
point
Punto
de operación
Reference
Par de referencia
torque
Synchronous
speed (s)
Vel.
síncrona (s)
Speed
Vel
()
S
Deslizamiento (S)
Slip (s)
Torque-speed profile under input
voltage
variation
Curva Característica
Variando Voltaje
Torque
Par
()
Par Máximotorque
(m) (Tm)
Maximum
Operation
point
Punto
de operación
Reference
Par de referencia
torque
Synchronous
speed (s)
Vel. síncrona (s)
Speed
Vel
()
S
Deslizamiento
(S)
Slip (s)
Torque-speed profile under input
frequency variation
Curva Característica
variando Frecuencia
Torque
Par
Maximum
Par Máximotorque
(m) (Tm)
()
Operation
point
Punto de operación
Par
de referencia
Reference
torque
Synchronous speed (s)
Vel. síncrona (s)
Vel
()
S
S
S
Deslizamiento
Slip (s)(S)
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
V1  E1
jXm
jX1
R2/s
jX2
Constant V/f control principle
• From the expressions of emf and magnetic flux
d
E1 
dt
= max sin(et).
E1 = max e cos(et) = max 2f1 cos(et)
• Its RMS value is
E1 
2f1
 max 
2
Constant V/f control principle
• From the assumption number one:
V1  E1
2f1
V1 
 max   kf1 max
2
• It is possible to maintain a constant flux, if the
relation V1/f1 does not change:
V1
 k max
f1
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
Voltaje [V]
Voltage
Flujo (  M )
Flux
[V]
Lineal
compensation
Compensación Líneal
compensation
Com pensación
Boost
Voltaje Boost
voltage
Relación no lineal
Non-linear relation
Relación lineal
Linear relation
Frequency [Hz]
Frecuencia [Hz]
Sinusoidal pulse width
modulation
Closed loop operation
• If accuracy is needed in the speed control, a closed
loop scheme must be used.
PI controller
speed
reference
V/f control
Induction
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