Unable to solve these simultanesous equations. Any suggestions?

[SAJ]

Hello

Please see attached sheet, I am trying to solve these 6 equations to find my 6 unknowns. I am not sure what solver to use I tried the guess, find but unsuccessful, I worked the problem one way to show the expected results I am after. Please any suggestions. Thanks

[SAJ]

Version 11 in case

[MikeArmstrong]

To be perfectly honest with you, I was put off when I looked through your worksheet. Try tidying it up and making it clear exactly what your after. Remember people on this forum are contributing their own time to help, for nothing.

Mike

[SAJ]

Dear Mike

Unfortunately It is is complex problem and not sure how I can clear it up, I do appreciate everyone time and if somone have specific question or feedback I will try to explain as much as possible.

Basically I have complex matrix equations.

To know the answer I started with Z and Y known values and solve this equation above manually for V(x) and I(x). If there is an easier way to solve it please let me know.

Once solved and know the expected results I want to go backward and solve for Z and Y which are really the unknows I am after knowing V(x) and I(x) at 2 conditions. In my example V(0) I(0) V(200) I(200) which are 6 equations and I am looking for 6 unknowns. I have the 6 equations I just do not know or cant get Mathcad to numerically solve it since they are matrices plus complex involving square and Cosh sinh of matrices.....

Any questions or idea which method to try will be appreciated.

[RichardJ]

I can't really follow what you are trying to do. Equations 1 and 2 represent a series of differential equations. Are you trying to solve for the functions Va, Vb, Vc, Ia, Ib, Ic, or for the variables Z1, Z2, Z3, Y1, Y2, Y3?

The second part of the worksheet solves the differential equatoins using known Y and Z. I won't comment on whether or not your method is correct. I can't see how you arrived at Equation 3. Why didn't you use the built in ODE solvers to do this?

The last part of your worksheet attempts to solve for the variables. The variables you are trying to solve for don't appear in the solve block though. You need to make YYlong and ZZlong functions of Z1, Z2, Z3, and Y1, Y2, Y3. You also need to define ITlong, ZZOlong, ans YYOlong which are currently undefined. I have no idea what to do with the final set of equations, from "equation 3". As written, the have no dependence on any of the variables you are solving for, so they are irrelevant. Either they are valid equalities as written, or they are not. Changing the values of Z1, Z2, Z3, Y1, Y2, Y3 will not affect them though. Finally, the Find syntax should be Find(Z1,Z2,Z3,Y1,Y2,Y3).

[SAJ]

Dear Jackson:

Thanks for your reply. Here are my answers to your question.

I am trying to solve for variables Z1,Z2,Z3,Y1,Y2,Y3.

I solved for equations 1 and 2 first with known Z1,Z2,Z3,Y1,Y2,Y3 to know expected results and answer for them, I could not use odesolve these are complex numbers plus I needed the governing equations so I can plug in the solve block.

See attached sheet again all variables are defined I changed the definition from inside the solve block to outside but no results.

Find syntax is correct either way.

[RichardJ]

I won't comment on whether or not your method is correct. I can't see how you arrived at Equation 3.

I looked harder at it. Now I really don't see the connection with the differential equations at all. You have a couple of functions defined that apply functions to matrices (any function, or specifically a square root). Based on these you create new functions that apply exp, sinh, cosh to matrices. Where did exp sinh and cosh appear from? What connection do they have to equations 1 and 2?

[SAJ]

Ok regardless of connection to diff equations. Those set of equations work one way and calculate votlage. My question : can or why the solve block cant solve for Z1,Z2,Z3,Y1,Y2,Y3 using them. It should has no bearing on weather It is the solution for 1 and 2 not related.

I list 1 and 2 in case there is another way to find the solution we can compare answers but really for now the error in the solve block

[RichardJ]

The equations in the solve block have to depend on the variables you are solving for.

[SAJ]

Thanks Richard for the constructive feedback. I learned more about the guess find algorithm. Looks like you have to create functions in terms of the variable like you pointed. See attached sheet I made one change to a variable that I declared incorrectly before

The solution now is not as much sensitive to the guess value of Z but sensitive to the value of Y. Typically when solving I know Y will be small but not sure how I can guess close

The solution was based on laplace transform for equation 1 and 2 I can send you derivation for one equation if you interested.

Do you think there is much robust solver or easier way to find those unknowns starting from equation 1 or 2 if there is one that can handle complex number.

I started with the easy case 6 unknowns at the end I will end 12 unknowns and 12 equations.

Thanks again for your time and assistance much appreciated

[RichardJ]

The solution was based on laplace transform for equation 1 and 2 I can send you derivation for one equation if you interested.

No, that's OK. It's nice to know how you got there, but I don't really have the time to study it.

Do you think there is much robust solver or easier way to find those unknowns starting from equation 1 or 2 if there is one that can handle complex number.

Unfortunately, no.

Can you approximate the system somehow, to get a reasonable guess? I have successfully used that approach in the past when I needed good guess values. The approximation does not even have to be very good, just good enough to get a guess that allows convergence.

[SAJ]

Thanks for this great tip to use approximation as guess!