constant v/f control eng. alfonso monroy olascoaga ph. d. pedro ponce cruz itesm-ccm
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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
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