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In this section we have seen the basic control equipment that is used to start and stop induction motors. ---- An electric drive is a system consisting of one or several electric motors and of the entire electric control equipment designed to govern the performance of these motors. --- However, some industrial drives require a motor to function at various torques and speeds, both in for ward and reverse. In addition to operating as a motor, the machine often has to function for brief periods as a generator or brake. In electric locomotives, for ex ample, the motor may run clockwise or counter clockwise, and the torque may act either with or against the direction of rotation. In other words, the speed and torque may be positive or negative. In describing industrial drives, the various operating modes can best be shown in graphical form. The positive and negative speeds are plotted on a horizontal axis, and the positive and negative torques on a vertical axis. This gives rise to four operating quadrants, labeled respectively quadrants 1, 2, 3, and 4. If a machine operates in quadrant 1, both the torque and speed are positive, meaning that they act in the same direction. Consequently, a machine operating in this quadrant functions as a motor. As such, it delivers mechanical power to the load. The machine also operates as a motor in quadrant 3, except that both the torque and speed are reversed. A machine that operates in quadrant 2 develops a positive torque but its speed is negative. In other words, the torque acts clockwise while the machine turns counterclockwise. In this quadrant, the ma chine absorbs mechanical power from the load: consequently, it functions basically as a generator. The mechanical power is converted into electric power and the latter is usually fed back into the line. However, the electric power may be dissipated in an external resistor, such as in dynamic braking. Depending on the way it’s connected, a machine may also function as a brake when operating in quadrant 2. The mechanical power absorbed is again converted to electric power, but the latter is immediately and unavoidably converted into heat. In effect, when a machine functions as a brake, it absorbs electric power from the supply line at the same time as it absorbs mechanical power from the shaft. Both power inputs are dissipated as heat--often inside the machine itself. For example, whenever a machine is plugged, it operates as a brake. In larger power drives we seldom favor the brake mode of operation because it’s very inefficient. Consequently, the circuit is usually arranged so that the machine functions as a generator when operating in quadrant 2. Quadrant 4 is identical to quadrant 2, except that the torque and speed are reversed: consequently, the same remarks apply. --37 Typical torque-speed curve of a squirrel-cage induction motor operating at fixed voltage and frequency. --38 Typical torque-speed curve of a DC motor.
The torque-speed curve of a 3-phase induction motor is an excellent example of the motor-generator-brake behavior of an electrical machine. We first examined it in Section 14, Section 14.16. The reader is encouraged to take a few moments to review this section. Referring now to the solid curve, the machine acts as a motor in quadrant 1, as a brake in quadrant 2, and as a generator in quadrant 4. If the stator leads are reversed, another torque speed curve is obtained. This dash-line curve shows that the machine now operates as a motor in quadrant 3, as a generator in quadrant 2, and as a brake in quadrant 4. Note that the machine can function either as a generator or brake in quadrants 2 and 4. On the other hand, it always runs as a motor in quadrants 1 and 3. To give another example: the complete torque-speed curve of a dc shunt motor when the armature voltage is fixed. The motor-generator-brake modes are again apparent. If the armature leads are reversed, we obtain the dotted torque-speed curve. In designing variable-speed electric drives, we try to vary the speed and torque in a smooth, continuous way to satisfy the load requirements. This is usually done by shifting the entire torque-speed characteristic back and forth along the horizontal axis. For example, the torque-speed curve of the dc motor may be shifted back and forth by varying the armature voltage. Similarly, we can shift the curve of an induction motor by simultaneously varying the voltage and frequency applied to the stator. To better understand the basic principles of variable speed control, we will first show how variable frequency affects the behavior of a squirrel-cage induction motor.
--39 Torque-speed curve of a 15 hp, 460 V, 60 Hz, 3-phase squirrel-cage induction motor. --40 Torque-speed curve at three different frequencies and voltages. --41 Stator excited by dc current. The torque-speed curve of a 3-phase squirrel-cage induction motor depends upon the voltage and frequency applied to the stator. We already know that if the frequency is fixed, the torque varies as the square of the applied voltage. We also know that the synchronous speed depends on the frequency. The question now arises, how is the torque-speed curve affected when both the voltage and frequency are varied? In practice, they are varied in the same pro portion so as to maintain a constant flux in the air gap. Thus, when the frequency is doubled, the stator voltage is doubled. Under these conditions, the shape of the torque-speed curve remains the same, but its position along the speed axis shifts with the frequency. Varying the voltage and frequency in the same proportion has given rise to the "volts per hertz rule" of motor operation. By keeping the volts per hertz at the same level while the frequency is varied, we ensure that the flux in the motor is always close to its rated value. However, at frequencies be low about 20% of rated frequency, the volts per hertz ratio has to be progressively increased to compensate for the IR drop in the stator. The torque-speed curve of a 15 hp, (II kW) 3-phase, 460 V, 60 Hz squirrel-cage induction motor. The full-load speed and torque are respectively 1725 RPM and 60 N·m; the breakdown torque is 160 N m and the locked-rotor torque is 80 N·m. If we reduce both the voltage and frequency to one-fourth their original value (115 V and 15 Hz) the new torque-speed curve is shifted toward the left. The curve retains the same shape, but crosses the axis at a synchronous speed of 180014 = 450 RPM (Fig, 20040). Similarly, if we raise the voltage and frequency by 50 percent (690 V. 90 Hz), the curve is shifted to the right and the new synchronous speed is 2700 rpm. Even if we bring the frequency down to zero (de), the torque-speed curve retains essentially the same shape. Current can be circulated in any two lines of the stator while leaving the third line open. The motor develops a symmetrical braking torque that in creases with increasing speed, reaching a maximum in both directions. The dc current in the windings is adjusted to pro duce the rated breakdown torque. Because the shape of the torque-speed curve is the same at all frequencies, it follows that the torque developed by an induction motor is the same when ever the slip speed (in RPM) is the same. Example +++5 _______ A standard 3-phase, 10 hp, 575 V, 1750 RPM, 60 Hz NEMA class 0 squirrel-cage induction motor develops a torque of 110 N m at a speed of 1440 RPM. If the motor is excited at a frequency of 25 Hz, calculate the following: a. The required voltage to maintain the same flux in the machine b. The new speed at a torque of 110 N·m
a. To keep the same flux, the voltage must be reduced in proportion to the frequency: E = (25/60) X 575 = 240 V b. The synchronous speed of the 4-pole, 60 Hz motor is obviously 1800 RPM. Consequently, the slip speed at a torque of 110 N m is … = 1800 - 1440 = 360 RPM The slip speed is the same for the same torque, irrespective of the frequency. The synchronous speed at 25 Hz is ns (25/60) x 1800 = 750 RPM The new speed at 110 N·m is n = 750 360 = 390 RPM
--42 Current-speed curve at 60 Hz and 15 Hz. Also T-n curve at 460 V, 60 Hz. --43 The starting torque increases and the current decreases with decreasing frequency. The current-speed characteristic of an induction motor is a V-shaped curve having a minimum value at synchronous speed. The minimum current is equal to the magnetizing current needed to create the flux in the machine. Because the stator flux is kept constant, the magnetizing current is the same at all speeds. ---42 shows the current-speed curve of the 15 hp, 460 V, 60 Hz squirrel-cage induction motor mentioned previously. We have plotted the effective values of current for all speeds; consequently, the current is always positive. The locked-rotor current is 120 A and the corresponding torque is 80 N·m. As in the case of the torque-speed curve, it can be shown that if the stator flux is held constant, the current-speed curve retains the same shape, no matter what the synchronous speed happens to be. Thus, as the synchronous speed is varied, the cur rent-speed curve shifts along the horizontal axis with the minimum current following the synchronous speed. In effect, the torque-speed and current speed curves move back and forth in unison as the frequency is varied. Suppose that the voltage and frequency are reduced by 75% to 115 V, 15 Hz. The locked-rotor current decreases to 80 A, but the corresponding torque increases to 160 N·m. equal to the full breakdown torque. Thus, by reducing the frequency, we obtain a larger torque with a smaller current. This is one of the big advantages of frequency control. In effect, we can gradually accelerate a motor and its load by progressively increasing the voltage and frequency. During the start-up period, the voltage and frequency can be varied automatically so that the motor develops close to its breakdown torque all the way from zero to rated speed. This ensures a rapid acceleration at practically constant current. In conclusion, an induction motor has excellent characteristics under variable frequency conditions. For a given frequency the speed changes very little with increasing load. In many ways, the torque speed characteristic resembles that of a dc shunt motor with variable armature-voltage control. --44 Effect of suddenly changing the stator frequency. Example +++6 ______ Using the information revealed by the 60 Hz torque-speed and current-speed curves, calculate the voltage and frequency required so that the machine will run at 3200 RPM while developing a torque of 100 N·m. What is the corresponding stator current? Solution: We first have to find the slip speed corresponding to a torque of 100 N·m. Accordingly, when the motor operates at 60 Hz and a torque of 100 N·m, the speed is 1650 RPM. Consequently, the slip speed is 1800 1650 150 RPM The slip speed is the same when the motor develops 100 N·m at 3200 RPM. Consequently, the synchronous speed must be 11, 3200 ISO 3350 RPM The corresponding frequency is, therefore, f (3350/1800) x 60 111.7Hz The corresponding stator voltage is E (111.7/60) x 460 = 856V The 60Hz current-speed and torque-speed curves show that the stator current is 40A when the torque is 100 N·m. Because the current-speed curve shifts along with the torque-speed curve, the current is again 40 A at 3200 RPM and 100 N·m.
A further advantage of frequency control is that it permits regenerative braking. Suppose the motor is connected to a 460 V, 60 Hz line. It’s running at 1650 RPM, driving a load of constant torque TL 100 N m (operating point 1). If we suddenly reduce the frequency and voltage by 50 percent, the motor will immediately operate along the 30 Hz, 230 V torque-speed curve. Because the speed cannot change instantaneously (due to inertia), we suddenly find ourselves at operating point 2 on the new torque-speed curve. The motor torque is negative; consequently, the speed will drop very quickly; following the 50% curve until we reach torque (operating point 4) The interesting feature is that in moving along the curve from point 2 to point 3, energy is returned to the ac line, because the motor acts as an asynchronous generator during this interval. The ability to develop a high torque from zero to full speed, together with the economy of regenerative braking, is the main reason why frequency controlled induction motor drives are becoming so popular. These electronically-controlled drives are covered. Also see: Generating Electrical Power |

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