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Chapter 9: Single- and Two-Phase Motors*

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Chapter 9: Single- and Two-Phase Motors* OpenStax-CNX module: m28327 1 Chapter 9: Single- and Two-Phase Motors* NGUYEN Phuc This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 Single- and Two-Phase Motors This lecture note is based on the textbook # 1. Electric Machinery - A.E. Fitzgerald, Charles Kingsley, Jr., Stephen D. Umans- 6th edition- Mc Graw Hill series in Electrical Engineering. Power and Energy • This chapter discusses single-phase motors. While focusing on induction motors, synchronous-reluctance, hysteresis, and shaded-pole induction motors are also discussed. • Most induction motors of fractional-kilowatt (fractional horsepower) rating are single-phase motors. In residential and commercial applications, they are found in a wide range of equipment including refrigerators, air conditioners and heat pumps, fans, pumps, washers, and dryers. • Most single-phase induction motors are actually two-phase motors with unsymmetrical windings; the two windings are typically quite dierent, with dierent numbers of turns and/or winding distributions. • 9.1 SINGLE-PHASE INDUCTION MOTORS: QUALITATIVE EXAMINATION • Structurally, the most common types of single-phase induction motors resemble polyphase squirrel-cage motors except for the arrangement of the stator windings. An induction motor with a squirrel-cage rotor and a single-phase stator winding is represented schematically in Fig. 9.1. • Instead of being a concentrated coil, the actual stator winding is distributed in slots to produce an approximately sinusoidal space distribution of mmf. A single-phase winding produces equal forward- and backward-rotating mmf waves. By symmetry, it is clear that such a motor inherently will produce no starting torque since at standstill, it will produce equal torque in both directions. *Version 1.1: Jul 8, 2009 3:55 am -0500 http://creativecommons.org/licenses/by/3.0/ http://cnx.org/content/m28327/1.1/ OpenStax-CNX module: m28327 2 • If it is started by auxiliary Figure 9.1 Schematic view of a single-phase induction motor. means, the result will be a net torque in the direction in which it is started, and hence the motor will continue to run. • We will discuss the basic properties of the schematic motor of Fig. 9.1. If the stator current is a cosinusoidal function of time, the resultant air-gap mmf is given by Fagl = Fmaxcos (θae) cos!et(9.1) which, can be written as the sum of positive- and negative traveling mmf waves of equal magnitude. The positive-traveling wave is given by + 1 cos (9.2) Fagl = 2 Fmax (θae − !et) and the negative-traveling wave is given by − 1 cos (9.3) Fagl = 2 Fmax (θae + !et) • Each of these component mmf waves produces induction-motor action, but the corresponding torques are in opposite directions. With the rotor at rest, the forward and backward air-gap ux waves created by the combined mmf's of the stator and rotor currents are equal, the component torques are equal, and no starting torque is produced. If the forward and backward air-gap ux waves were to remain equal when the rotor revolves, each of the component elds would produce a torque-speed characteristic similar to that of a polyphase motor with negligible stator leakage impedance, as illustrated by the dashed curves f and b in Fig. 9.2a. The resultant torque-speed characteristic, which is the algebraic sum of the two component curves, shows that if the motor were started by auxiliary means, it would produce torque in whatever direction it was started. • The assumption that the air-gap ux waves remain equal when the rotor is in motion is a rather drastic simplication of the actual state of aairs. First, the eects of stator leakage impedance are ignored. Second, the eects of induced rotor currents are not properly accounted for. http://cnx.org/content/m28327/1.1/ OpenStax-CNX module: m28327 3 Figure 1 http://cnx.org/content/m28327/1.1/ OpenStax-CNX module: m28327 4 Figure 2 Figure 9.2 Torque-speed characteristic of a single-phase induction motor (a) on the basis of constant forward and backward ux waves, (b) taking into account changes in the ux waves. • When the rotor is in motion, the component rotor currents induced by the backward eld are greater than at standstill, and their power factor is lower. Their mmf, which opposes that of the stator current, results in a reduction of the backward ux wave. Conversely, the magnetic eect of the component currents induced by the forward eld is less than at standstill because the rotor currents are less and their power factor is higher. As speed increases, therefore, the forward ux wave increases while the backward ux wave decreases. The sum of these ux waves must remain roughly constant since it must induce the stator counter emf, which is approximately constant if the stator leakage-impedance voltage drop is small. http://cnx.org/content/m28327/1.1/ OpenStax-CNX module: m28327 5 • Hence, with the rotor in motion, the torque of the forward eld is greater and that of the backward eld less than in Fig. 9.2a, the true situation being about that shown in Fig. 9.2b. In the normal running region at a few percent slip, the forward eld is several times greater than the backward eld, and the ux wave does not dier greatly from the constant-amplitude revolving eld in the air gap of a balanced polyphase motor. • In the normal running region, therefore, the torque-speed characteristic of a single-phase motor is not too greatly inferior to that of a polyphase motor having the same rotor and operating with the same maximum air-gap ux density. • In addition to the torques shown in Fig. 9.2, double-stator-frequency torque pulsations are produced by the interactions of the oppositely rotating ux and mmf waves which rotate past each other at twice synchronous speed. These interactions produce no average torque, but they tend to make the motor noisier than a polyphase motor. 9.2 STARTING AND RUNNING PERFORMANCE OF SINGLE-PHASE INDUCTION AND SYNCHRONOUS MOTORS Single-phase induction motors are classied in accordance with their starting methods and are usually referred to by names descriptive of these methods. Figure 3 Figure 9.3 Split-phase motor: (a) connections, (b) phasor diagram at starting, and (c) typical torque-speed characteristic. 9.2.1 Split-Phase Motors • Split-phase motors have two stator windings, a main winding (also referred to as the run winding) which we will refer to with the subscript 'main' and an auxiliary winding (also referred to as the start winding) which we will refer to with the subscript 'aux'. As in a two-phase motor, the axes of these windings are displaced 90 electrical degrees in space, and they are connected as shown in Fig. 9.3a. The auxiliary winding has a higher resistance-to-reactance ratio than the main winding, with the result that the two currents will be out of phase, as indicated in the phasor diagram of Fig. 9.3b, Θ which is representative of conditions at starting. Since the auxiliary-winding current Iaux leads the http://cnx.org/content/m28327/1.1/ OpenStax-CNX module: m28327 6 Θ main-winding current Imain, the stator eld rst reaches a maximum along the axis of the auxiliary winding and then somewhat later in time reaches a maximum along the axis of the main winding. • The winding currents are equivalent to unbalanced two-phase currents, and the motor is equivalent to an unbalanced two-phase motor. The result is a rotating stator eld which causes the motor to start. After the motor starts, the auxiliary winding is disconnected, usually by means of a centrifugal switch that operates at about 75 percent of synchronous speed. The simple way to obtain the high resistance-to-reactance ratio for the auxiliary winding is to wind it with smaller wire than the main winding, a permissible procedure because this winding operates only during starting. Its reactance can be reduced somewhat by placing it in the tops of the slots. A typical torque-speed characteristic for such a motor is shown in Fig. 9.3c. • Split-phase motors have moderate starting torque with low starting current. Typical applications include fans, blowers, centrifugal pumps, and oce equipment. Typical ratings are 50 to 500 watts; in this range they are the lowest-cost motors available. 9.2.2 Capacitor-Type Motors • Capacitors can be used to improve motor starting performance, running performance, or both, depend- ing on the size and connection of the capacitor. The capacitor-start Figure 4 Figure 9.4 Capacitor-start motor: (a) connections, (b) phasor diagram at starting, and (c) typical torque-speed characteristic. motor is also a split-phase motor, but the time-phase displacement between the two currents is obtained by means of a capacitor in series with the auxiliary winding, as shown in Fig. 9.4a. Again the auxiliary winding is disconnected after the motor has started, and consequently the auxiliary winding and capacitor can be designed at minimum cost for intermittent service. Θ • By using a starting capacitor of appropriate value, the auxiliary-winding current Iaux at standstill can Θ be made to lead the main-winding current Imain by 90 electrical degrees, as it would in a balanced http://cnx.org/content/m28327/1.1/ OpenStax-CNX module: m28327 7 two-phase motor (see Fig. 9.4b). In practice, the best compromise between starting torque, starting current, and cost typically results with a phase angle somewhat less than 90o. A typical torque-speed characteristic is shown in Fig. 9.4c, high starting torque being an outstanding feature.
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