[Jprogramming] ARE: xkcd 356
Don & Cathy Kelly
dhky at shaw.ca
Fri Jan 11 04:07:06 UTC 2013
A wee bit of a mix up between what I said and what Aai said (no
'quotes' appeared to distinguish between the two).
the 9:23 message was from Aai but the
f=: 13 : '+/-: %>: +:i.y'
and the result corresponds to a specific immediate "calculator' solution that I gave
]R100K=:+/0.5*%1+2*i.100000
I had not put it in the form that you present and I thank you for the re-programming as a function-Gee-I can interpret it- I must be learning something!!!.
As for an example of the Z-Bus method I gave a small example in a post at 6:12PM yesterday
I can give more examples but the practical ones I have on hand do involve complex impedances.
Wiki gives little information so it appears that I will have to put together some notes that I have - it appears that this approach is something known mainly in power system analysis.
This is the best I have found so far on line and it is inadequate:
http://en.wikipedia.org/wiki/Impedance_parameters#The_Z-parameter_matrix
Inadequate because it assumes the typical application is for a 2-port network.
In computer methods for electric circuits, the handling of a nodal form is much easier than the use of loop forms. This is due to the fact that the choice of equations comes down to selecting one node as reference or ground and from there it is an automatic procedure. For loop equations, one must make choices as to what are the loops to be considered before forming the equations. So load flow solutions, one of the earliest applications of computers to large networks (in or near 1964) were based on an admittance network. Fault studies depended upon reducing a large network to a Thevenin/Norton model. Inversion of this matrix gives the Z-bus matrix which presents both driving point and mutual impedences between nodes. The "maxima' approach may be a way to 'build" such a matrix without inversion of a large matrix (large in power systems can be in the order of 100's to 1000's of nodes).
However, I will put together a few simple examples and dig up some references or what I have in some notes on hand.
OK?
Don
On 09/01/2013 9:14 PM, Linda Alvord wrote:
> This is a look at your earlier message at 9:23:43 AM.
>
>
>
> f=: 13 : '+/-: %>: +:i.y'
>
> f 100000
>
> 3.36911
>
> 5!:4 <'f'
>
> -- [:
> +- / --- +
> │
> --+ -- [:
> │ +- -:
> L-----+ -- [:
> │ +- %
> L----+ -- [:
> │ +- >:
> L----+ -- [:
> L----+- +:
> L- i.
>
>
>
> A pretty tree. However you have left me with your 11:45 PM post unless you
> provide some small numerical examples of the matrices and the inverses you
> are looking for.
>
>
>
> Linda
>
>
>
>
>
> -----Original Message-----
> From: programming-bounces at forums.jsoftware.com
> [mailto:programming-bounces at forums.jsoftware.com] On Behalf Of Donald Kelly
> Sent: Wednesday, January 09, 2013 11:45 PM
> To: programming at jsoftware.com
> Subject: Re: [Jprogramming] xkcd 356
>
>
>
> In my opinion, in most cses computer solutions are much esier using nodal
> admittance methods once you select a node as a reference then it is very
> easy to set up an admittance matrix yii is the sum of admittances connected
> to node i from all nodes including the reference.
>
> yij=yji =-sum of admittances between i and j. There is no row or column
> related to the reference node.
>
> Invert this matrix to get a Z-Bus matrix which is a generalized Thevenin
> impedance The resultant zii terms are the driving point impedances (thevenin
> impedance between i and reference.
>
> for impedances between nodes i and j use zii+zjj -2zij which is the thevenin
> impedance between i and j Zbus can be built in steps avoiding inversion of a
> large matrix.
>
> This method is shown or should be shown in modern power system texts as it
> is very useful for fault analysis of large systems.
>
>
>
> Don
>
>
>
> ----- Original Message -----
>
> From: "Aai" < <mailto:agroeneveld400 at gmail.com> agroeneveld400 at gmail.com>
>
> To: <mailto:programming at jsoftware.com> programming at jsoftware.com
>
> Sent: Tuesday, January 8, 2013 9:23:43 AM
>
> Subject: Re: [Jprogramming] xkcd 356
>
>
>
> In fact this method is like measuring resistance with an okmmeter between
> points A and B of the network.
>
>
>
> FWIW here is my interpretation/translation of the Maxima code:
>
>
>
> nbrs=: 1 3 5 7&{@,
>
> swz=:0,.~0,.0,~0,]
>
>
>
> resistornw=: 4 :0
>
> 'h w'=.x
>
> 'al bl'=. (+w&*)~/"1 y
>
> d =.( <mailto:*=/~@i.@#> *=/~@i.@#) #&> ix=.,3 3 <@(<:#~0~:])@nbrs;. _3 swz
> 1+i.h,w r=. 1 al }zv=.0$~h*w A=. %. r (al)} d + _1:`[`]}&zv&>ix bl { A +/ .*
> 1 bl }zv
>
> )
>
>
>
> Your example is calculated like:
>
>
>
> 2 2 resistornw 0 0,:1 1
>
> 1
>
>
>
> Or as David pointed out:
>
>
>
> % +/ % +/"(1) 1 1 ,:1 1
>
> 1
>
>
>
>
>
>
>
> On 08-01-13 17:24, Raul Miller wrote:
>
>> I'm a bit confused by the maxima solution. For example, A is both a
>> specific node and it's also a 10 by 10 matrix. Similar for B. I can
>> assume that the matrix values are something like potential
>> contribution from the named node. But... k looks like the 10 10 #.
>> of an index pair (with a bit of off-by-one since the maxima solution
>> is using 1 based indices) except it's used as an index into A and B.
>> And... so maybe A and B are really representing logically different
>> kinds of data in different parts of their structure? But what is the
>> logical structure then.
>> ... anyways, the purpose of some of this code is not clear to me.
>
>
> --
>
> Met vriendelijke groet,
>
> @@i = Arie Groeneveld
>
>
>
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