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Constant V/f Control
Eng. Alfonso Monroy Olascoaga
Ph. D. Pedro Ponce Cruz
ITESM-CCM
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Equivalent circuit model
• The stationary equivalent circuit model per phase for the induction motor is shown in the figure.
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Equivalent circuit model
• The equations that describe the operation of the induction motor are
11111 )( EIjXRV )(21 cm IIII
2221 )( IjXRE e
res
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Power flow in an induction motor
• The power flow in an induction motor can be appreciated in the next figure
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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
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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
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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
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• 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
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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
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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
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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
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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.
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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
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Sinusoidal pulse width modulation
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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
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Results (open loop)
• Current waveforms and harmonics content at 2396 rpm (left) and 2980 rpm (right).
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Results (open loop)
• Current and voltage waveforms at 3000 rpm
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Results (closed loop)
• No load start (2500 rpm)
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Results (closed loop)
• Speed change (819-3000 rpm) at constant load torque (1.7 Nm)
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Results (closed loop)
• Torque change (1.9 - .2 Nm) at constant speed (3100 rpm)
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Advantages
• Open loop operation
• Simple control algorithm
• Good closed loop operation
• Great for high speed and constant torque applications
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Disadvantages
• Boost voltage needed
• Poor load speed operation
• Control scheme designed for steady state operation