Simultaneous Equation in Mathcad15

[ssato]

In Mathcad15 , the solution of the following simulataneous equation is  correct ?

Because the solution of MM,NN,LLKs is zero. If so, zero division is in equation.

One solution is also attached.

Please advise me.

<< one solution of above equation>>

[vlehner]

Please attach your Worksheet:

use "advanced Editor" and then you can attach the file.

Btw: you are using a solve block, but there are missing guess-Values for solving your equation system.

best regards, Volker

[vlehner]

I tryed to solve it with MathCad Prime4.0

There is no stable solution, you should rearrange your equation system to get a constant result, which means: wheather you choose any guess values you'll get the same results.

[ssato]

Volker Lehner-san

Thanks your reply in Mathcad Prime.

The solution is only one ?

Because I want only plus values for all solutions.

[vlehner]

we should check the equation-system to get a useful solution.

[ssato]

I attatched the file.

Best Regards.

[vlehner]

can you post the cirquit-diagramm please?

[ssato]

I attached drawing.

[vlehner]

We need an additional equation to get a clear solution.

[vlehner]

I tryed an analytical solution and that shows, there is no solution.

See attached File please.

The equations, derivated from the cirquit diagramm: It seems to be ok.

Volker

[ssato]

Thanks for your reply.

I have some question.

1. Lss　(equation 2)

    I calculate Lss by MATHCAD15. The result non-equal to your solution.

2.LLKp1,LLKp2

  LLKp1 is not equal LLKp2.

  If so ,we have two Lss.

3.If my simaltaneous equations has no solution, why Mathcad output no ERROR ?

4. I attached the result above 1 in MATHCAD15.

  And in this file, I calculate analytically LLKp,LLKs , Mathcad output the error "out of memory".

Sato

[vlehner · Accepted solution]

Hi Sato,

according to your questions:

1. Equation Lss: use definition markers (see point three) and you get the same result as mine:

revise your sheet and you can calculate all without memory problems.

2. LLKp1 and LLKp2: they are a result of a quadratic-equation, normally one solution (LLKp1 or LLKp2) is valid.

LLKp can be LLKp1 or LLKp2.

see:

I named this two solutions LLKp1 and LLKp2:

3. rearrange your worksheet. Use for definitions the ":=" symbol, not the boolean "=". and then you can simplify your expressions and get the same result as mine.

4. After you rearranged your worksheet, you should calculate it completely.

Use solve blocks for numerical solutions with initial guess-values. Symbolical makes no sense because of the very large and uncomfortable equations.

MathCad is a powerful tool to transform equations and find solutions with solve-blocks but sometimes the equations are very large and because of this, they can not be displayed.

A couple of days ago, i had the same problem with a mechanical system like you with the electric-transformers: I created  11 equations with 11 unknowns.

First of all, i got different results when changing the guess values. It is not that i got no solution but i got anytime different results.

An equation system must be unambiguous and must not have an infinite number of solutions.

BTW: what we have here, is a non linear equation-system.

So i had to check my equations again and again and when finding and taking a geometrical equation into account i got only one numerical solution-No matter what estimates I have assumed.

That was a "Heureca" for me and i solved the problem completely perfect.

I attached the MC15 sheet revised my way.

Best Regards and sucess, Volker

[ssato]

Hi Volker-san,

I thanks so mutch.   I had a mistake the caliculation.

I could trace your caliculation.

My equation is non linear equation-system.

In this case it is possibility that the equation has many solution ?

Best Rgards. S.Sato

[vlehner]

Hi Sato,

The equation system you've created has many solutions depending on the guess values are given.

To get one solution there should be replaced one equation of the system with one of the Kirchhoff laws for example-you should try it.

You can also add an equation to the equation system you have and maybe you get a stable solution with 5 unknowns (Think about a 'Kirchhoff law)

As said, there must be finally one stable solution.

I have an example attached, where you can change the guess values. Depending on the guess values, you'll get one possible and stable solution or no one.

Try and study it.

[ssato]

Hi Volker,

I tried the changing some initial value, but the solution is always LLKp=470uH,LLKs=MM=NN=0.

in MATHCAD 15. I also check your response 2017/06/06 23:46 . The solution is also same.

I will check in MATHCAD PRIME.

Also, I have deleted one equation and one unkonws.

I put temporaly value in this one unkown value.

     In this case I can get the solution.

    And I can check these values is correct.

Best Regards,

Sato