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Mesh Analysis of RLC circuits: forming the meshes
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JayTee1947



Joined: 22 Dec 2008
Posts: 8
Location: Inverclyde

PostPosted: Fri Jul 03, 2020 1:08 pm    Post subject: Mesh Analysis of RLC circuits: forming the meshes Reply with quote

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.
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John-Silver



Joined: 30 Jul 2013
Posts: 1430
Location: Aerospace Valley

PostPosted: Fri Jul 03, 2020 3:52 pm    Post subject: Reply with quote

Your subject is somewhat specialised and you're probably barking up the wrong tree on what is after all a forum dedicated to a specific fortran compiler, and not an electrician's workshop Wink, however you could always try the usual method to start with
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JayTee1947



Joined: 22 Dec 2008
Posts: 8
Location: Inverclyde

PostPosted: Fri Jul 03, 2020 4:22 pm    Post subject: Reply with quote

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?
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PaulLaidler
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Joined: 21 Feb 2005
Posts: 6511
Location: Salford, UK

PostPosted: Fri Jul 03, 2020 6:56 pm    Post subject: Reply with quote

JayTee

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



Joined: 18 May 2012
Posts: 370
Location: Hamilton, Lanarkshire, Scotland.

PostPosted: Fri Jul 03, 2020 11:18 pm    Post subject: Reply with quote

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.
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LitusSaxonicum



Joined: 23 Aug 2005
Posts: 2172
Location: Yateley, Hants, UK

PostPosted: Sat Jul 04, 2020 10:18 am    Post subject: Reply with quote

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
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mecej4



Joined: 31 Oct 2006
Posts: 1411

PostPosted: Sat Jul 04, 2020 10:48 am    Post subject: Reply with quote

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".
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JayTee1947



Joined: 22 Dec 2008
Posts: 8
Location: Inverclyde

PostPosted: Sat Jul 04, 2020 2:30 pm    Post subject: Reply with quote

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
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Kenneth_Smith



Joined: 18 May 2012
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Location: Hamilton, Lanarkshire, Scotland.

PostPosted: Sat Jul 04, 2020 4:08 pm    Post subject: Reply with quote

Maybe this is what you are looking for?

https://www.researchgate.net/publication/283184514_Identifying_the_Loops_in_Mesh_Analysis
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John-Silver



Joined: 30 Jul 2013
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Location: Aerospace Valley

PostPosted: Mon Jul 06, 2020 2:29 am    Post subject: Reply with quote

... so many sparky's in one forum ! Wink, I know where to come the next time I'm unsure about doing some wiring LOL Smile
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Kenneth_Smith



Joined: 18 May 2012
Posts: 370
Location: Hamilton, Lanarkshire, Scotland.

PostPosted: Mon Jul 06, 2020 12:04 pm    Post subject: Reply with quote

Quote:
.. 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.
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John-Silver



Joined: 30 Jul 2013
Posts: 1430
Location: Aerospace Valley

PostPosted: Mon Jul 06, 2020 6:09 pm    Post subject: Reply with quote

... An Electrical Engineer walking through the utilities substation was told to follow electrical discharge safety measures and stay outside the ESD-safe area. He replies "Don't worry, I've been told I have no potential".

... A group of NASA engineers were brainstorming how they might overcome the thermal challenges involved in sending a manned probe to the sun. An electrical engineer overheard their discussion and suggested "why don't you just go at night?".

m'lord I rest my case Wink
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LitusSaxonicum



Joined: 23 Aug 2005
Posts: 2172
Location: Yateley, Hants, UK

PostPosted: Mon Jul 06, 2020 6:28 pm    Post subject: Reply with quote

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
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John-Silver



Joined: 30 Jul 2013
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PostPosted: Tue Jul 07, 2020 12:25 am    Post subject: Reply with quote

Quote:
Arendelle's toilets don't flush,


undoubtedly due to a case of bad wiring Wink #I-Ronnie
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Robert



Joined: 29 Nov 2006
Posts: 340
Location: Manchester

PostPosted: Tue Jul 07, 2020 2:41 pm    Post subject: Reply with quote

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