Solving the electrical equivalent circuit equations containing complex numbers.

I have a huge set of complex number equations to solve. It is an equivalent circuit of an electrical circuit. The circuit is basically a DC circuit and the situation we are solving is a steady-state problem. The DC still has an AC ripple component on top of the DC component.

Mathematically the problem looks like this: [Z] * [I] = [U]. I have variables in every term of the equations. The unknown may be in different term (Z/I/U) on different rows. On row one I may know the current 'I' and the impedance 'Z'. On row two I may know some different things. For example I and U. etc. You get the idea.

• How to solve this kind of problem where variables/unknowns are located in different parts of the equations?
• What are the worksteps in this kind of situation?
• Should I definitely use Simulink or is it possible to solve this with pure Matlab-coding?

And the complex numbers also worry me:

• How about the complex numbers in general. Are they a problem?
• If the ripple effect is taken into account I assume that in every part of the circuit the complex numbers are present in all of the terms (Z/I/U). By this I mean that if the current would be perfect DC there wouldn't be any imaginary components in the currents or voltages.
• If the imaginary part is present in all of the terms, does this mean that I should have double amount of equations compared to completely steady state DC circuit?

Any help is appreciated.

[Lilian Kangethe]

Did you get an answer?

[darova]

Can you show your system of equations?