What is the practical use of Laplace Transform?

I am trying to understand the electrical model of 3-phase Induction Model. The rotor of the motor is modeled as a variable resistor in s-domain.

I fail to understand how that works practically. Can anyone explain me the practical relevance of LT and its use in the IM modelling?

Your help is highly appreciated.

edit: This is the link of the IM model: When load increases in rotor of induction motor how does stator draws more current?

• Post a link, or a picture of the relevant equation you're looking at along with the book reference, or something. – TimWescott Dec 27 '18 at 21:25
• As for the practical use of the Laplace transform -- if you don't like it, feel free to model the motor using ordinary linear differential equations and solving them by hand. It shouldn't take too many iterations before you're screaming for something that eases the tedium and helps with the bookkeeping, even if it still leaves you with all the hard math. When you get to that point -- look to the Laplace transform. – TimWescott Dec 27 '18 at 21:26
• I have edited the post to include the link. – scico111 Dec 28 '18 at 0:39
• @scico111 The "s" in that link is not the s-parameter of the Laplace transform; it is the "slip" of the induction motor. – panic attack Dec 28 '18 at 1:20

The "s" that you are referring to is not the "s" of the Laplace Domain. It is called "slip" and the definition is

$$\s = \frac{n_R}{n_S} = \frac{n_S-n}{n_S} = 1 - \frac{n}{n_S}\$$

where

$$\n\$$ is the rotational speed of the rotor

$$\n_S = \frac{f_S}{p}\$$ is synchronous rotational speed

$$\n_R = n_S - n\$$ is the relative rotational speed

$$\f_S\$$ is the electrical frequency - typically 50 or 60 Hz

and finally

$$\p\$$ are the # of poles of the stator

So, slip is a measure of how away the rotor speed is from the synchronous speed.

Any textbook provides the proof of how mechanical power can be represented by the power that is consumed by a resistor, the value of which is $$\R_R\frac{1-s}{s}\$$

Laplace Domain is basically a tool for solving the ODEs, by make them linear equations - it also gives information for the spectral content of the system, but that is a different story.

• I tried to find proof of how mechanical power is represented by the power that s consumed by a resistor but so far cannot find it anywhere. Pls point out any source for this info. – scico111 Dec 28 '18 at 8:56
• @scico111 eg. "Electric Machinery Fundamentals", Stephen J. Chapman, ed. 4. Chapter 7 presents the induction motor and at 7.3 the equivalent circuit is presented. eg2. "Electric Machinery", A. E. Fitzgerald, ed. 6. chapter 6.3. Basically every textbook that analyzes machines, has the equivalent circuit and the proof of why this circuit stands true – thece Dec 28 '18 at 10:35