Mesh Analysis of RLC circuits: forming the meshes

I'm designing a program to analyse large-scale electrical circuit transients involving linear/nonlinear R, L & C elements and (ideal) switches. First challenge is forming the meshes. I want to select the meshes so that nonlinear & switched branches are in the co-tree: so preserving/maximising sparsity and ensuring independent meshes.

Any ideas on suitable tree-forming algorithms? Most mesh analysis texts assume you can choose the meshes 'by eye' or 'just write them down'.

Seems to me there are two choices: (i) select the tree branches according their 'type' so that inductive/nonlinear/switched branches are in the co-tree; (ii) form the tree ignoring branch type(?) then sequentially swap tree and co-tree branches to the same end. But how to aim for sparsity? All suggestions welcomed, and maybe even acknowledged.

Thanks, I've tried Google, Youtube and several Maths forums: on the first two all I see are various lecturers demonstrating elementary mesh analysis involving DC and R only. And they all draw meshes 'by eye'. The maths forums dive straight into graph theory (further evidence that most math is 'made up') I'm sorry if you think this is somewhat specialised, but where else can I try?

JayTee

You don't need to apologise. There is a reasonable chance that someone here might be able to help.

The chapter “Network geometry and network variables” in INTRODUCTORY CIRCUIT THEORY by Ernst A . Guillemin. John Wiley & Sons, Inc., 1953, gives a much more comprehensive discussion than that given in more recent text books.

There is a 1958 paper 'Logic for Applying Topological Methods to Electric Networks', by Byerly, Long and King, published in the Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics. This includes an algorithm for selecting links and tree branches.

Ken is the on-Forum expert because he does (I think) related things.

If it comes down to an issue of how to design and code the interactive bit then I might be able to help. I've sent you a private message - the exposition is likely to be far longer than the individual post limits in the forum.

Eddie

Liquid flow in a piping network is quite analogous, once you admit nonlinearity.

In particular, the topological issues are quite similar, although the terminology is slightly different. For example, what you call 'mesh current' corresponds to 'loop flow'.

The problem of finding a minimal set of flow loops in a flow network has been studied extensively. Look up the 'Hardy Cross Method'.

That's a promising trio of responses: probably more than I deserve. @Mercej4. I looked up the Hardy-Cross method. It looks analogous to the power flow problem in electrical power networks, with Kirchhoff's 1st and 2nd laws (on loop voltage and node current) being replaced by loop potential and nodal flow laws (no surprise: same topological rules apply). Interesting, and serendipitous, but doesn't tell me how to select independent meshes with the requisite properties.

@ken: ordered Guillemin's book form IET library. No joy yet on Trans AIEE paper @Eddie (are your the count of the Saxon shore?). I'll reply by email to your kind message.

@John: just goes to show, some trees bear surprising fruit. I did try your suggestion (and I appreciate your candour), but the usual method got me back square one. Genuine tnx to all

Maybe this is what you are looking for?

https://www.researchgate.net/publication/283184514_Identifying_the_Loops_in_Mesh_Analysis

.. so many sparky's in one forum !

It’s Electrical Engineers developing algorithms in Fortran and using programs written in **Fortran **that’s been keeping the lights on and your computers running for the last 60 years.

Ken, JS has forgotten to add the [irony] tag!

I just watched Frozen II. After the dam has been destroyed, Arendelle's toilets don't flush, and there's no water. Civil Engineers who use Fortran in water resources engineering are appalled. Cases of cholera start to appear in the town, and diarrhoea is rife.

Even with the water supply, when the sea is frozen there is a nasty spreading stain under the ice, as Arendelle doesn't have a sewage works. I have seen such in ice-locked ships in the Gulf of Bothnia, but Disney doesn't show it.

Eddie

Blimey you are a tough crowd, give the guy a break.

23. 6. TINNEY, C. M. McINTYRE, A Digital Method for Obtaining a Loop Connection Matrix, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems, October 1960.

In structural analysis, calculation of the torsional properties for a closed cross-section requires the identification of internal loops. I have a 'subroutine loops' which achieves this for a 2-D set of connected points. It basically does this by testing if any connected points are inside the loop. There may be other documented approaches for calculation of torsional properties of closed cross-sections. This works well and has been tested for small 'circuits' (say 100 nodes) I have not considered how this would work for a 3-D data set.

I also have equation re-ordering algorithms for large sets of equations for FEA analysis (say up to million nodes). I have RCM, Sloan and Hoit algorithms coded, which are based on tree connectivity approaches. I also have another re-ordering algorithm that on average works better, which simply uses an ax+by+cz directed sort that typically works on meshes with local refinement. (Various a,b,c are tested)

Not sure if either of these approaches are relevant.