The method of finding the resistance between the two nodes of an infinite grid of resistances (Don&Kathy Kelly) is erroneous. The method fails because a one ampere current flowing into the grid produces an infinite voltage. The superposition of the two cases amounts to adding minus infinity to plus infinity which does not produce a reliable result. By inverting the Y matrix for grids of up to 100 by 100 I have found that the resistance approaches 0.636 ohms
On Fri, Jan 11, 2013 at 6:20 PM, Don & Cathy Kelly <[email protected]> wrote: > It does assume that the reader knows what it is all about. For learning it > is veryy skimpy. > A more thorough reference is: > > http://nptel.iitm.ac.in/**courses/Webcourse-contents/** > IIT-KANPUR/machine/ui/chap3.**pdf<http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/machine/ui/chap3.pdf> > > The advantage of the Ybus is that it is easy to build -just choose a > reference node and go with the process at the other nodes. In power systems > the reference is generally the ground. > I have found a reference which discusses the Ybus and Zbus methods and the > way to build the latter without inversion of a large matrix. > Here is a simple example-- a square of 4 1 ohm resistors (conductance =1 > Siemen (mho) > > 1 o---/\/\--o 2 At each node there are 2 resistors each > of 1 so the Y00 =Y11 =Y22 > | | Between 2 and 1 there is a coupling of 1S > so Y01=_1 Y02=0 as there is no > / / direct connection. > \ \ > | | > 0 o---/\/\--o reference > > ] y=:>2 _1 0;_1 2 _1;0 _1 2 > 2 _1 0 > _1 2 _1 > 0 _1 2 > > this gives > ]z=:%.y > 0.75 0.5 0.25 > 0.5 1 0.5 > 0.25 0.5 0.75 > The resistance from node j to the reference is the Zjj term > The resistance from node j to node k is zjj+zkk-2zjk > nodes (buses) that are not of interest can be eliminated by simply > removing the row and column corresponding. > > Don. > > On 11/01/2013 6:47 AM, Raul Miller wrote: > >> On Thu, Jan 10, 2013 at 11:07 PM, Don & Cathy Kelly <[email protected]> wrote: >> >>> 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!!!. >>> >> Note that >> >> R=:13 :'+/0.5*%1+2*i.y' >> >> would be equally valid. >> >> 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<http://en.wikipedia.org/wiki/Impedance_parameters#The_Z-parameter_matrix> >>> >>> Inadequate because it assumes the typical application is for a 2-port >>> network. >>> >> What do you think of >> http://en.wikipedia.org/wiki/**Ybus_matrix<http://en.wikipedia.org/wiki/Ybus_matrix>? >> >> Thanks, >> >> > ------------------------------**------------------------------**---------- > For information about J forums see > http://www.jsoftware.com/**forums.htm<http://www.jsoftware.com/forums.htm> > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
