Page 681 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 667
where each drive type operates based on varying one or more of the electrical variables,
that is voltage and current and their frequency and magnitude.
The steady-state torque-speed curve of an AC induction motor whose stator winding
phases are fed directly from an AC line is shown in Figure 8.41. The motor synchronous
speed (w syn ) is determined by the line voltage frequency (w ). The actual speed of the rotor
e
(w ) would be a little below that since there is a slip (w ) between the synchronous speed
s
rm
and actual rotor speed in steady-state. The slip speed depends on the load torque.
w e
w syn = (8.258)
(P∕2)
w rm = w syn − w s (8.259)
The maximum torque characteristic is a function of the motor design and the line voltage
magnitude. This basic relationship indicates that an AC motor driven directly from a supply
line has a speed that is largely determined by the frequency of the supply voltage. The slip
frequency is a function of the load and the type of motor design (Figure 8.40). The exact
mechanical speed of the rotor is determined by the load around the synchronous speed.

Scalar Control Drives If the drive varies the magnitude of voltage applied to the
motor, while keeping the frequency constant, the torque-speed characteristics of the motor
are as shown in Figure 8.43a. Notice that as the voltage magnitude decreases relative to
the rated voltage (V ), the torque gets smaller. It can be shown that the maximum torque is
r
proportional to the square of the applied voltage magnitude. If the load is a constant torque
load, by varying the amplitude of the voltage (variable voltage method), we can obtain
some degree of variable speed control in the vicinity of synchronous speed of the motor.
The next method of control is to vary the frequency of the applied voltage while
keeping the magnitude of the voltage constant. The steady-state torque-speed performance
of an AC motor with such a drive is shown in Figure 8.43b. Notice that the synchronous
speed of the motor is proportional to the applied frequency of the voltage, that is if the
applied frequency is 50% of the base frequency, then the synchronous speed is also 50% of
the original synchronous speed. However, the effective impedance of the motor is smaller
at lower frequencies. This leads to large currents and results in magnetic saturation in the
motor. Therefore, in order to improve the efficiency of the motor, it is better to maintain a
constant ratio of voltage magnitude and frequency.
Variable frequency (VF) drives are capable of adjusting the AC voltage frequency,
w , as well as the magnitude of the AC voltage of each phase, V . For a three-phase AC
o
e
induction motor, phase voltages may be
V = V sin(w t) (8.260)
e
a
o
V = V sin(w t + 2 ∕3) (8.261)
b
o
e
V = V sin(w t + 4 ∕3) (8.262)
e
a
o
where the VF drive can control both w and V from zero to a maximum value. Hence, the
e o
steady-state torque-speed curve of the motor can be made as shown in Figure 8.43c. The
power electronics of the VF drive are identical to that of a brushless motor drive, that is a
three-phase inverter (Figure 8.42). The only essential difference is in the real-time control
algorithm that operates the PWM circuit. The PWM circuit is controlled in such a way that
the frequency and the magnitude of each phase voltage is changed depending on where on
the torque-speed curve we want the motor to operate. Since both frequency and magnitude
of voltage is controlled, such drives are also called variable frequency and variable voltage
(VFVV) drives. Such a drive control method is also referred to as the Volts/Hertz (V/Hz)