Computations and circle diagrams:General , Circle Diagram for a Series Circuit and Circle Diagram for the Approxi- mate Equivalent Circuit

By -

General

In this chapter, it will be shown that the performance characteristics of an induction motor are derivable from a circular locus. The data necessary to draw the circle diagram may be found from no- load and blocked-rotor tests, corresponding to the open-circuit and short-circuit tests of a transformer. The stator and rotor Cu losses can be separated by drawing a torque line. The parameters of the motor, in the equivalent circuit, can be found from the above tests, as shown below.

Circle Diagram for a Series Circuit

It will be shown that the end of the current vector for a series circuit with constant reactance and voltage, but with a variable resistance is a circle. With reference to Fig. 35.1, it is clear that

image

It is the equation of a circle in polar coordinates, with diameter equal to V /X . Such a circle is drawn in Fig. 35.3, using the magnitude of the current and power factor angle f as polar co-ordinates of the point A . In other words, as resistance R is varied (which means, in fact, f is changed), the end of the current vector lies on a circle with diameter equal to V /X . For a lagging current, it is usual to orientate the circle of Fig. 35.3 (a) such that its diameter is horizontal and the voltage vector takes a vertical position, as shown in Fig. 35.3 (b). There is no difference between the two so far as X the magnitude and phase relationships are concerned.

image

Circle Diagram for the Approxi- mate Equivalent Circuit

The approximate equivalent diagram is redrawn in Fig. 35.4. It is clear that the circuit to the right of points ab is similar to a series circuit, having a constant voltage V 1 and reactance X 01 but variable resistance (corresponding to different values of slip s).

Hence, the end of current vector for I2¢ will lie on a circle with a diameter of V /X 01. In Fig. 35.5, I2¢ is the rotor current referred to stator, I0 is no-load current (or exciting current) and I1 is the total stator current and is the vector sum of the first two. When I2¢ is lagging and f2 = 90º, then the position of vector for I2¢ will be along OC i.e. at right Vr angles to the voltage vector OE. For any other value of f2, point A will move along the circle shown dotted. The exciting current I0 is drawn lagging V by an angle f0. If conductance G0 and susceptance

image

B0 of the exciting circuit are assumed constant, then I0 and f0 are also constant. The end of current vector for I1 is also seen to lie on another circle which is displaced from the dotted circle by an amount I0. Its diameter is still V /X 01 and is parallel to the horizontal axis OC. Hence, we find that if an induction motor is tested at various loads, the locus of the end of the vector for the current (drawn by it) is a circle.

Comments

Post a Comment

Popular posts from this blog

Total Loss in a D.C. Generator

By -
Image
Total Loss in a D.C. Generator The various losses occurring in a generator can be sub-divided as follows : where R a = resistance of armature and interpoles and series field winding etc. This loss is about 30 to 40% of full-load losses. Field copper loss. In the case of shunt generators, it is practically constant and I 2 R (or V I sh ). In the case of series generator, it is = I s e 2 R s e where R s e is resistance of the series field winding. This loss is about 20 to 30% of F.L. losses. (iii) The loss due to brush contact resistance. It is usually included in the armature copper loss. (b) Magnetic Losses (also known as iron or core losses), (i) hysteresis loss, W h µ B max f and ( ii ) eddy current loss, W e µ B max f These losses are practically constant for shunt and compound-wound generators, because in their case, field current is approximately constant. Both these losses total up to about 20 to 30% of F.L. losses. (c) Mechanica l Losses. These consist of :...
Read more

Transformer,three phase:Wye/Delta or Y/∆ Connection and Delta/Wye or ∆/Y Connection.

By -
Image
Wye/Delta or Y/∆  Connection The main use of this connection is at the substation end of the transmission line where the voltage is to be stepped down. The primary winding is Y -connected with grounded neutral as shown in Fig. 33.6. The ratio between the secondary and primary line voltage is 1/ 3 times the transformation ratio of each trans- former. There is a 30° shift between the primary and secondary line voltages which means that a Y - D transformer bank cannot be paralleled with either a Y - Y or a D - D bank. Also, third harmonic currents flows in the D to provide a sinusoidal flux. Delta/Wye or ∆/Y Connection This connection is generally employed where it is necessary to step up the voltage as for example, at the beginning of high tension transmission system. The connection is shown in Fig. 33.7. The neutral of the secondary is grounded for providing 3-phase 4-wire service. In recent years, this connection has gained considerable popularity because it can be used to s...
Read more

Testing of d.c.Machines:Brake Test

By -
Image
Brake Test It is a direct method and consists of applying a brake to a water-cooled pulley mounted on the motor shaft as shown in Fig. 31.1. The brake band is fixed with the help of wooden blocks gripping the pulley. One end of the band is fixed to earth via a spring balance S and the other is connected to a suspended weight W 1. The motor is running and the load on the motor is adjusted till it carries its full load current. The simple brake test described above can be used for small motors only, because in the case of large motors, it is difficult to dissipate the large amount of heat generated at the brake. Another simple method of measuring motor output is by the use of poney brake one form of which is shown in Fig. 31.2 ( a ). A rope is wound round the pulley and its two ends are attached to two spring balances S 1 and S 2. The tension of the rope can be adjusted with the help of swivels. Obviously, the force acting tangentially on the pulley is equal to the differ ence ...
Read more