Xem mẫu

ENGNG3070 Power Electronics Devices, Circuits and Applications 6. POWER ELECTRONIC CONTROL OF INDUCTION MOTORS 6.1 Introduction Three-phase induction motors are the most frequently utilised electric machines in industry. They are characterised with low cost, high reliability, high efficiency, simple construction and, in the case of squirrel-cage induction motors, with virtually maintenance-free operation. If operated with stator three-phase voltage supply of fixed frequency and fixed rms value, induction motors will run at a speed that very slightly depends on loading. In contrast to DC machines, where choice of methods of speed control and associated power electronic converters that are nowadays in use is rather limited, there exists a variety of both speed control techniques and appropriate power electronic converters that are used in conjunction with three-phase induction motor drives. A three-phase induction machine requires three-phase AC supply at stator side. In a squirrel-cage type of induction machines this is simultaneously the only approachable winding. However, in slip-ring induction machines the three-phase rotor winding may be approached as well. Thus the speed of an induction machine may be controlled by controlling the stator AC supply for both types of induction machines; additionally, speed may be controlled in slip-ring machines from the rotor winding side as well. Squirrel-cage induction machines are by far the most frequently used machines. It is for this reason that the following discussion will be predominantly devoted to speed control methods associated with alteration of the stator supply, that are equally applicable for both types of induction machines. Only one method, specifically aimed at slip ring machines, will be looked at. If an induction machine is supplied with a voltage of frequency f then the so-called synchronous speed is determined with the frequency and the number of pole pairs P and is expressed in rpm as ns =60f/P (6.1) However, an induction motor will run at a speed n that differs from the synchronous. The difference between actual speed of rotation and the synchronous speed is characterised by the quantity called slip. Slip s is expressed in per unit as ratio of the speed difference normalised with respect to the synchronous speed, i.e., s = (ns − n) / ns (6.2) Thus zero speed of rotation indicates unity slip and synchronous speed of rotation corresponds to zero slip. Torque-speed characteristic of an induction machine can be derived for steady-state operation with sinusoidal supply from the per-phase equivalent circuit, given in Fig. 6.1. Is Rs jXss jXsr Ir Vn jXm Im Rr /s Fig. 6.1: Steady-state per-phase equivalent circuit of an induction machine for purely sinuso-idal supply voltage.  E Levi, Liverpool John Moores University, 2002 74 ENGNG3070 Power Electronics Devices, Circuits and Applications All the parameters of the rotor winding in Fig. 6.1 are referred to the stator winding, by means of the transformation ratio. Symbols in bold denote phasors. Variable resistor in the rotor circuit represents both rotor copper loss and power converted into mechanical. Recall that stator winding of the machine can be connected in either star or delta; the equivalent circuit is valid for phase rather than line values, regardless of the winding connection. Thus Vn stands for rated phase to neutral voltage of the stator. All the reactances are given at fixed, rated frequency. Torque-slip characteristic of a three-phase induction machine follows from power flow considerations in Fig. 6.1, in the form T (s) = 3P V2 Rr s = 3P V 2 Rr s (6.3) Rs + Rr s + Xss + Xsr Rs +Rr s + X while stator current phasor can be expressed directly from Fig. 6.1 as Is =Vn Ze Ze = Rs + jXss + jXs+Rr s+ jXXm) (6.4) Torque is a rather complicated function of motor parameters, supply voltage and slip and its typical appearance is given in Fig. 6.2 for rated supply conditions. The operating region is restricted to slips up to typically 10%, indicating that speed of rotation changes with load but remains within rather narrow boundaries from zero load up to rated load. Maximum (pull-out) torque, rated torque and starting torque, as well as corresponding slips, are indicated in Fig. 6.2 and can be calculated from the following expressions: Te maximum (pull-out) torque Ten Test operating region slip 1 sm sn 0 s 0 ns speed Fig. 6.2: Torque-speed characteristic of a three-phase induction machine for rated supply conditions. sm = Rr R2 + X2 T m = T (s = sm) = 3P Vn (Rs + Rr r ss)2 + X2 = 3P Vn Rs + T st = T (s = ) = 2πf Vn (Rs + Rr )2 + X 2 en = e(s = sn) = 3P Vn (Rs + Rr r ss)2 + X 2 1 R2 + X2 (6.5)  E Levi, Liverpool John Moores University, 2002 75 ENGNG3070 Power Electronics Devices, Circuits and Applications Equations (6.1)-(6.5) enable discussion of all the relevant methods of speed control, applicable to an induction machine. It follows from (6.1) that synchronous speed can be altered by changing the number of pole pairs. Assuming that load torque is constant, if pole pair number is doubled during operation of the machine, synchronous speed will be halved, leading to operation at essentially one half of the rated speed. This method of speed control is used in drives that typically require operation at two distinctly different operating speed (say, a washing machine; spinning is done at high speed, while normal washing cycle takes place at low speed). Speed control by pole pair changing requires special construction of the stator winding. It is usually realised for two different speeds of operation and pole pair changing is performed by mechanical reconnection of the stator winding from one pole pair number to another. Illustration of torque-speed characteristics is shown in Fig. 6.3 for change-over from one pole pair to two pole pairs. Power electronics converters are not involved in this speed control method, and its applicability is restricted to the cases when two speeds, rather than continuous speed variation, are needed. Therefore speed control by pole pair changing will not be considered further on. Te load torque A B 1500 3000 speed (rpm) Fig. 6.3: Speed control by change of pole pair number: drive operates either in point A or in B. The two methods of speed control, that are universally applicable to all the three-phase induction machines and that will be elaborated, are the speed control by stator voltage variation and speed control by simultaneous stator voltage and frequency variation. The former, although very simple, has restricted applicability for the reasons that will be explained; the latter is the most widely used method of speed control of induction machines. Finally, a method valid for slip-ring machines only, insertion of a resistance in the rotor circuit, will be considered as well. 6.2 Speed Control by Stator Voltage Variation Equation (6.3) shows that electromagnetic torque developed by an induction machine is proportional to the square of the applied rms stator phase voltage. Thus, given the load torque to be, say, a constant, reduction of voltage will lead to operation with increased slip, i.e., with decreased speed. As voltage is not allowed to exceed rated value, this method of speed control can be utilised only for reducing the speed below rated. Torque-speed (slip) characteristics for this speed control technique are shown in Fig. 6.4. Note that, according to (6.5), pull-out slip is not function of the applied voltage. Hence the motor develops maximum torque at constant slip (speed), determined with (6.5), regardless of the applied voltage. However, both maximum (pull-out) and starting torque are functions of voltage squared. Hence, when voltage is reduced, maximum torque and starting torque reduce as well, proportionally to the voltage reduction squared. This is one of the major drawbacks of this speed control method: reduction in starting torque means that the motor will be able to start only loads that are of small torque  E Levi, Liverpool John Moores University, 2002 76 ENGNG3070 Power Electronics Devices, Circuits and Applications at low speeds; reduction in maximum torque means that overloading capability of the motor reduces with reduction in voltage. Te rated voltage reducing voltage operating region slip 1 sm 0 s Fig. 6.4: Torque-slip characteristics of an induction machine with speed control by stator voltage variation. Additional drawback of this method is that, when voltage is reduced and speed therefore reduces as well, additional copper loss in rotor winding takes place. Regardless of these two serious shortcomings, this method of speed control is widely used in two distinct cases. When the load torque is proportional to the speed squared (pumps, ventilators, compressors, etc.) then even a small reduction in speed means significant reduction in the output power, which is proportional to the cube of the speed. For a number of applications with load torque of this type it is sufficient to vary the speed in this narrow region. The second application is in drives that run for prolonged periods of time with very light loads. In such a situation it is advantageous to reduce the voltage for light load operation as this improves the efficiency of the drive. In other words, considerable saving in electricity consumption may be achieved in this way. Example: A three-phase squirrel-cage induction motor drives a load of rated torque, with rated slip of 3%. Stator and rotor resistance (referred to stator) are both equal to 0.015 Ω. Sum of stator and rotor leakage reactance is X =0.09Ω. Calculate the necessary reduction in stator supply voltage if the induction motor is to drive the same load with slip equal to 15%. Solution: Pull-out slip of the motor is, from given parameters, equal to s = Rr = 0.015 0.0152 + 0.092 = 0.164 = 16.4% R2 + X2 The motor is required to operate at slip of 15%. As load torque is constant, this indicates that in new operating point motor torque will be very close to maximum torque, so that overloading capability will be almost non-existent. The necessary reduction of the voltage, that will yield operation with 15% slip, can be calculated as follows:  E Levi, Liverpool John Moores University, 2002 77 ENGNG3070 Power Electronics Devices, Circuits and Applications TL = T n at all speeds; hence 3P 2 Rr sn en 2πf n (Rs + Rr sn)2 + X2 3P 2 Rr s e1 en 2πf 1 (Rs + Rr s )2 + X2 sn = 0.03 s = 015 3P 2 Rr s 2 Rr s e1 = 1= 2πf 1 (Rs + Rr s )2 + X2 = 1 (Rs + Rr s )2 + X2 2 r n 2 r n 2πf n (Rs + Rr sn)2 + X2 n (Rs + Rr sn)2 + X2 V 2 1 (Rs + Rr s )2 + X2 0.15 (0.015+ 0.015/ 0.15 2 + 0.092 Vn sn (Rs + Rr sn)2 + X2 0.03(0.015+ 0.015/ 0.03 2 + 0.092 V = 0.624Vn Necessary voltage reduction is 37.6%. Situation is illustrated in accompanying Figure. Te rated voltage TL = Ten 62.4% of rated voltage 0.16 0.03 slip 0.15 Let us examine, using this example, increase in rotor losses that takes place with this speed control method. Taking power transferred from stator to rotor to be Psr , for these two operating conditions one has n = (1− sn) srn curn = sn srn srn = 1Psn = .03 n curn = 0.031 n P = enω1 = en(1−s1)ωs = enωn 1− s1 = 0. 76 n 1 = (1− s1) sr1 sr1 = 1−1 1 = 0876 n / 085= 103 n º srn cur1 = s1 sr1 = 015x103 n = 01545 n This consideration shows that power transferred from stator to rotor is the same for the two cases. Hence reduction in output power reflects itself directly as an increase in rotor copper loss, which goes up from 3% of the rated power to more than 15% of the rated power. As this loss takes place in the motor, it will essentially cause overheating. Needless to say, efficiency is sharply reduced. Starting problem with reduced voltage and this increase in loss are the two major reasons why this speed control method is not used with constant load torques. Situation is much improved in both respects when load torque is proportional to the square of the speed. Speed control by stator voltage variation is therefore applied in conjunction with this type of load in practice. Speed control by stator voltage variation is realised by using AC-AC voltage controller in each stator phase of the machine. Voltage controller is of the same structure as in Chapter 4 on reactive power compensation. Figure 6.5 illustrates the connection of the power electronic  E Levi, Liverpool John Moores University, 2002 78 ... - tailieumienphi.vn
nguon tai.lieu . vn