## Theses

Thesis

1-31-1993

#### Degree Name

Master of Science in Electrical Engineering - (M.S.)

#### Department

Electrical and Computer Engineering

K. Denno

Kenneth Sohn

S. Pandey

#### Abstract

Recognizing that the prime purpose of the 3 phase induction motor is to deliver torque with minimum line current. This thesis studies the torque as well as the current response produced by the singularity changes in the induction machine slip. It is desirable that the torque to be maximized for a given value of line current at the corresponding load slip.

This thesis analyzes the torque and current response, when a slip at no-load is changed to a unit-step, Qu(t), a unit-impulse, Qδ(t), a pulse characterized by Q[u(t)-u(t-T)], a unit-ramp, Qt, and a sinusoidal, Qsint, slip. The responses are analyzed againts the time. All of the computations are based on the approximate equivalent circuit of the induction motor, with the stator resistance, Rs, and the stator reactive reactance, jXs, being neglected. It is clone to simplify the complexity of the computations and the computer programming, and it is a real and practical assumption.

The Laplace Transformation method is used in solving the differential equations for torque and for the current.. A computer program using FORTRAN language is simulated based on the final equation for both torque and current. The program calculates and graphs the computed results againts the time.

In addition, this thesis work analyzed the motor performance if it is running at high slip, as in the case of a low-drive induction motor, and when it is operating at negative slip, as an induction generator.

It is seen that the torque and current response of the motor and the induc¬tion generator are almost identical in nature. They follow the pattern of their slip changes, with the exception when the final slip is sinusoidal. The only difference is that the induction generator will absorb power, which is, in effect, supplying power, that is mostly of leading power-factor or almost unity power-factor.

The torque to current ratio, being one of the most important data in the per¬formance of induction motor, is also computed and plotted againts the time based on the previous calculations. Moreover, the torque response is also compared with respect to its maximum or breakdown torque.

It is seen that the most positively effective and practical among the slip functions is the unit-step. Because the response is constant at any period of time and the torque response will never exceed the breakdown torque as long as the slip does not exceed the slip at maximum torque. In the case of a sinusoidal and a unit ramp function, the maximum or breakdown torque is reached at a certain time, t, due to their time-dependent functions. While the unit-impulse and the rectangular pulse are also practical functions since they are time-independent functions. But the responses reached their maximum when operating as a low-drive motor, with high machine slip.

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