SINGLE-PHASE INDUCTION MOTORS

Introduction

Single-phase induction motors are the most familiar of all electric motors because they are used in home appliances, businesses, and small industries. In general, they are employed when three-phase power is not available. Single-phase induction motors are usually two-pole or four-pole, rated at 2 hp or less, while slower and larger motor can be manufactured for special purposes. They are widely used in domestic appliances and for a very large number of low power drives in industry. The single phase induction motor resembles, three-phase, squirrel-cage motor except that, at full speed, only a single winding in the stator is excited.

In a single-phase motor we have only a single field winding excited with alternating current; therefore, it does not have a revolving field like three-phase motors. Thus, it does not self-starting. Several methods have been devised to initiate rotation of the squirrel-cage rotor and the particular method employed to start the motor will designate the specific type.

Principle of operation

Synchronous Speed

As in the case of three-phase motors, the synchronous speed of all single-phase induction motors is given by the equation

(1)

Where n_s= synchronous speed [rpm]

            f = frequency of the source [Hz]

            p = number of poles

The rotor turn at slightly less than synchronous speed, and the full-load slip is typically 3 percent to 5 percent for fractional horsepower motors.

Torque-Speed Characteristic

Figure 1 is a schematic diagram of the rotor and main winding of a two-pole single-phase induction motor. Suppose the rotor is locked, if an ac voltage is applied to the stator, the resulting current I_s produces an ac flux F_s. The flux alternates back and forth but, unlike the flux in three-phase stator, no revolving field is produced. The flux induces an ac voltage in the stationary rotor which, in turn, creates large ac rotor currents. In effect, the rotor behaves like the short-circuited secondary of a transformer; consequently, the motor has no tendency to start rotating by itself. However, if we spin the rotor in one direction or the other, it will continue to rotate in the direction of spin and the rotor quickly accelerates until it reaches a speed slightly below synchronous speed. The acceleration indicates that the motor develops a positive torque as soon as it begins to turn. Although the starting torque is zero, the motor develops a powerful torque as it approaches synchronous speed.

 

Fig.1 (a) Currents in the rotor bars when the rotor is locked

     

         Fig.1 (b) Torque speed curve

Principle of Operation

Cross-field theory

 The principle of operation of a single-phase induction motor can be explained from the cross-field theory. As soon as the rotor begins to turn, a speed emf E is induced in the rotor conductors, as they cut the stator flux F_s. This voltage increases as the rotor speed increases. It causes current I_R to flow in the rotor bars facing the stator poles as shown in Fig. 2

 

Fig. 2 Current induced in the rotor bars due to rotation

These currents produce an ac flux F_R which act at right angle to the stator flux F_s. Equally important is the fact that F_R does not reach its maximum value at the same time as F_S does, in effect, F_R lags almost 90^o behind F_S, owing to the inductance of the rotor

The combined action of F_s and F_R produces a revolving magnetic field, similar to that in a three-phase motor. The value of F_R increases with increasing speed, becoming almost equal to F_s at synchronous speed. The flux rotates counterclockwise in the same direction as the rotor and it rotates at synchronous speed irrespective of the actual speed of the rotor. As the motor approaches synchronous speed, F_R becomes almost equal to F_s and a nearly perfect revolving field is produces.

Double-revolving field theory

The principle of operation of single-phase induction motor can also be explained by double revolving field theory.

The single-phase supply given to the single-phase winding will produce pulsating field in the air gap. However, any pulsating field can be resolved into two components, equal in magnitude but oppositely rotating, as shown in Fig. 3.

  Fig. 3 Pulsating field resolved into two oppositely rotating fields

The maximum value of each component is one-half of f . This method of analysis is commonly known as the double-revolving field theory. Each field component acts independently on the rotor and in a fashion similar to that of the rotating field in a three-phase motor. The clockwise component produces the torque characteristic T_cw while the counterclockwise component produces the torque T_ccw as shown in Fig. 4

 

Fig. 4 Torque-speed characteristic of a single phase motor

Observe that the resultant torque is zero at standstill. But, if the rotor were rotated slightly in any direction, a net torque will result and the motor will continue to rotate in that direction. For example, if the rotor is started in the clockwise direction, the torque T_cw will exceed T_ccw and the rotor will accelerate in that direction and reach the steady-state speed near synchronous speed at a slip dictated by the load.

Non-self starting is not a desirable feature in practice, and modifications are introduced to obtain the staring torque. To produce rotating magnetic field at starting an auxiliary winding is placed in the motor. Using this auxiliary winding a quadrature flux component in time and space with the stator main flux can be produced.

Starting methods for single-phase induction motors

The various forms of a single-phase induction motor are grouped depending on the starting methods used.

Split-phase induction motor

One of the most widely used single-phase induction motor is the split-phase induction motor. It is used in refrigerators, washing machines, portable hoists, many small machine tools, blowers, fans, centrifugal pumps and many others. The essential parts of the split-phase motor are shown in Fig. 5.

 

Fig. 5 Single-phase split-phase motor

It shows the auxiliary winding also known as starting winding, in space quadrature with the main winding. The rotor is the squirrel-cage type. The starting winding is made of thin wire so that its impedance is different from that of the main winding. The two windings are connected in parallel to the ac supply. The phase difference between the two winding currents (about 30^o) will be sufficient to produce a rotating magnetic field resulting in a starting torque. When the motor has come to about 70 to 75% of the rated speed, a centrifugal switch disconnects the starting winding, and the motor will continue to run as a single-phase motor. A typical torque-speed characteristic is shown in Fig.6

Fig 6 Typical torque-speed characteristic of a split-phase motor.

Capacitor-start motors

If a capacitor is connected in series with the starting winding, the phase angle between the two winding currents will become more than 30^o (about 80^o) that is obtained in the split-phase motors. This increase in phase angle will increase the starting torque. Figure 7 shows the capacitor-start motor and the typical torque-speed characteristic. Because of their higher starting torques, capacitor-start motors are used in applications where not only higher starting torques are required, but also where reversible motors are needed. Typical applications are; washing machines, belted fans and blowers, dryers, pumps, and compressors.

 

Fig 7(a) Circuit diagram of a capacitor-star motor 

Fig. 7(b) Torque-speed characteristic of a capacitor-start motor

Permanent-split capacitor motor

In this motor, the capacitor in series with the auxiliary winding is not switched out after starting. It remains in the circuit, therefore the centrifugal switch is not needed. Since the capacitor and the auxiliary winding are in the circuit continuously, they should be properly designed.

Capacitor-start capacitor-run motors

Here two capacitors are used one for starting and one for running. Theoretically optimum starting and running performance can both be obtained.  The small value of capacitance required for optimum running is permanently connected in series with the auxiliary winding, and the much larger value required for starting is obtained by connecting another capacitor parallel to the running capacitor. The starting capacitor is disconnected after the motor starts.

Shaded-pole motors

The least expensive of the fractional-horsepower motors, generally rated up to 1 hp, are shaded-pole motors. They have salient stator poles, with one-coil-per-pole called main winding. The auxiliary winding consists of one (or rarely two) short-circuited copper straps wound on a portion of the pole and displaced from the center of each pole, as shown in Fig.8(a). The shaded-pole motor got its name from these shading bands. Induced currents in the shading coil cause the flux in the shaded portion of the pole to lag the flux in the other portion in time. The result is then like a rotating field moving in the direction from the unshaded to the shaded portion of the pole.  A low starting torque is produced; a typical torque-speed characteristic is shown in Fig. 8(b). Shaded-pole motors have a rather low efficiency.

 

 

Fig. 8 (a) Shaded pole motor   (b) Torque-speed Characteristics

Repulsion-induction motors

Before low-cost capacitors became available, repulsion-start and induction-run machines were the most widely used kind of single-phase motor in the range of 1/3 to 5 hp. This kind of motor has distributed rotor-windings connected to a commutator (like a dc machine) with short-circuited brushes and a distributed single-phase stator winding in the direct axis only. Repulsion-start motors have a centrifugal device that short-circuits all the commutator segments when the motor comes up to speed and lifts the brushes off the commutator. The permanently short-circuited rotor brushes are displaced from the direct axis by an angle of less than 90 electrical degrees so a rotor current is induced by transformer action. The flux produced by this current, which is fixed in position, acts with the main winding flux to create a torque.           

To avoid the centrifugal mechanism, some widely used repulsion-induction motors were designed with an additional deeply buried, low-resistance squirrel cage in the rotor to limit the no-load speed to a little above synchronism. Such machines fall under the general category of ac commutator machines; however, they have been replaced by capacitor motors.

Equivalent circuit

A single-phase motor receives its power from a single-phase source of defined voltage and frequency. This source causes a current to flow in the stator winding which will create an mmf. According to electromagnetic principles, this mmf can be resolved into two revolving mmfs, rotating in opposite directions. If the rotor is rotating at speed n_R, the component mmf rotating in the same direction as the rotor is called the forward-revolving field, and the oppositely rotating mmf is called the backward-rotating field. Each rotating mmf induces a voltage in the rotor winding. Therefore, two equivalent circuits are built: one for the forward component mmf and one for the backward-rotating component field. Then, the two component fields are combined and the two equivalent circuits are interconnected.

The forward rotating component field rotates at synchronous speed n_s in the same direction as the rotor. Therefore, the slip s⁺ of the rotor with respect to the forward-rotating field may be expressed as

              2



The amplitude of the forward component mmf is one half of the stator mmf. Hence, one half of the stator current may be associated with the forward mmf. The equivalent circuit for this situation is similar to that of three-phase induction motor, with the modification that the core loss represented by R_c is omitted from the equivalent circuit of the single-phase machine. The core loss is treated separately and is usually lumped with the rotational losses. Thus, the equivalent circuit is as shown in Fig. 9. In the diagram, V₁⁺ is the stator voltage corresponding to the forward component

  Fig 9. Equivalent circuit corresponding to the forward mmf

Next, the backward component field is considered. The stator current corresponding to this field is one half of the stator current, that is (½)I₁. because the rotor and the backward fields are rotating in opposite directions, the slip s^- of the rotor with respect to the backward-rotating field is expressed as:

  

    3

Therefore, from (3.2)

            s^- = 2 - s⁺......   4

The equivalent circuit corresponding to the backward-revolving field is shown in Fig. 10. 

Fig 10. Equivalent circuit corresponding to the backward mmf

The terminal voltage may be expressed in terms of its components:

Since one half of the current I flowing in an impedance Z has the same performance effect as the current I flowing in the impedance (½)Z, the equivalent circuits shown in Figs. 9 and 10 may be combined to form the overall equivalent circuit shown in Fig. 11. In this equivalent circuit, the resistances are combined into R₁, and the reactances are also combined into X₁. This equivalent circuit can be used to analyze the performance of a single-phase induction motor.

                                   Fig. 11, Single-phase induction motor equivalent circuit

To make the calculation simpler, let us define impedances Z_F and Z_B as

The current flowing in the induction motor’s stator winding is then given by

The air-gap power for the forward magnetic field can be expressed as

            P_AG,F = I₁²(0.5 R_F)                                                                               9

Similarly, the air-gap power for the reverse magnetic field can be expressed as

            P_AG,B = I₁²(0.5 R_B)                                                                               10

The total air-gap power in a single-phase induction motor is thus

            P_AG =   P_AG,F – P_AG,B                                                                           11

  The induced torque     T =Pag/w                                                                           12

Power converted         P_conv = (1 –s) P_AG                                                       13

Power output can be obtained by subtracting core losses, mechanical losses and stray losses from power converted.

Applications

Motors	General remark	Application
Split-phase motors	Have moderate starting torque with low starting current. Low cost.	Fans, blowers, centrifugal pumps and office equipment
Capacitor-start motors	High starting torque	Compressor, pumps, refrigeration and air-conditioning equipment, belt-driven loads and other loads requiring high starting torque
Permanent-split capacitor motors	Low starting torque. Quite running	Low starting torque load: Direct-connected fans and blowers
Capacitor-start capacitor-run motor	High starting torque and high power factor	Compressors, stokers, conveyors, and pumps
Shaded-pole motors	Low starting torque	Toys, small desk fans, hair dryers and other low-starting torque load

Operation of a three-phase induction motor on single-phase supply (Single-phasing)

If one line of a thee-phase line is accidentally opened while the three-phase motor is running the machine will continue to run as single-phase motor. The current drawn from the remaining two lines will almost double, and the motor will begin to overheat.  The torque-speed curve is seriously affected when a three-phase motor operates on single phase. The pull-out (maximum torque) decreases to about 40% of its original value, and the motor develops no starting torque at all. Figure 12 shows the typical torque-speed curves of a three-phase motor when it is running normally and when it is single-phasing. Note that the curves follow each other closely until the torque approaches the single-phase pull-out torque