Download Equivalent circuit model

Contant V/f Control
Dr. Pedro Ponce & M. en
C. Alfonso Monroy
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
Torque
Par
Máximo (m)
Maximum
torque (Tm)
Par
Punto
de operación
()
Operation
point
Par de referencia
Reference
torque
Vel.Synchronous
síncrona (s) speed (s)
VelSpeed
()
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
Vel. síncrona (s)
Synchronous speed (s)
Speed
Vel
()
S
Deslizamiento
(S)
Slip (s)
Torque-speed profile under
input frequency variation
Curva Característica
variando Frecuencia
Torque
Maximum torque (Tm)
Par Máximo (m)
Operation point
Par
()
Punto de operación
Reference
Par de referencia
torque
Synchronous speed (s)
Vel. síncrona (s)
Vel
()
S
S
S
Slip (s)
Deslizamiento (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  t).
= E1max
sin(

e
dt
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
[V]
Voltaje
Voltage
Flujo ( 
Flux
[V]
M)
Lineal
compensati
on
Compensación Líneal
compensati
Com pensación
on
Boost
voltage
Voltaje Boost
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