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

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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

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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.

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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

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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.

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