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# Partial Updating Algorithm

IP.com Disclosure Number: IPCOM000089196D
Original Publication Date: 1977-Sep-01
Included in the Prior Art Database: 2005-Mar-04
Document File: 4 page(s) / 73K

IBM

## Related People

Hsieh, HY: AUTHOR [+3]

## Abstract

If portions of the solution vector in a macromodular block diagonal matrix do not converge, using the two-level iterative procedure, then some of the elements in the matrix may only require updating. The algorithm described in this article takes advantage of partial updating and also is efficient. It is especially designed for large networks exhibiting block diagonal forms. THEORETICAL BACKGROUND.

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Partial Updating Algorithm

If portions of the solution vector in a macromodular block diagonal matrix do not converge, using the two-level iterative procedure, then some of the elements in the matrix may only require updating. The algorithm described in this article takes advantage of partial updating and also is efficient. It is especially designed for large networks exhibiting block diagonal forms. THEORETICAL BACKGROUND.

While other formulations are available which are not restricted to either impedance or admittance matrix, a modified nodal matrix formulation will be considered initially for simplicity and for a smooth flow of ideas into the macromodular approach. It has been demonstrated that the tableau which represents the culmination of the formulation process can be reduced by symbolic Gaussian elimination to the modified nodal approach (MNA) of Ho, Ruehli and Brennan [*], and illustrates its relationship to Kron's tearing. The results of this procedure can be expressed as

(Image Omitted)

where i(zeta) represents the vector of branch currents and v(psi) the vector of node voltages; Y(psi psi) represents the nodal admittance matrix for the conventional nodal matrix, excluding the contributions due to ideal voltage sources, current-controlling elements, etc.; C(psi zeta) represents KCL with respect to the additional current variables, thus containing +/-1's for the elements whose branch relations are introduced; and Z(zeta zeta) can represent branch constitutive relations.

In tearing, however, the original network is divided into a number of subnetworks so that each subnetwork is isolated from the rest of the system. The matrix of coefficients for each subnetwork is inverted independently, as if the other component networks were nonexistent. The solution of the full network is then obtained from the full inverse matrices of the subnetworks. In clustering the subnetworks, a set of branches is removed from the original network and the equivalent current sources, i(psi), are substituted. The equivalent current sources, i(psi), substituting for the removed branches of the original network and the branch current, i(zeta), of the removed branches can be described through a connection matrix, C(psi zeta), following relation: i(psi) = C(zeta psi)i(zeta). The equivalent voltage sources, e(zeta), of the removed networks can be related to the nodal voltages, v(psi), of the original subnetworks by e(zeta) = B(psi zeta)v(psi) where B(psi zeta) = -C/ t/(psi zeta).

The corresponding matrix, Y(psi psi), of the original network can, therefore, be described in block diagonal form as follows:

(Image Omitted)

1

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Taking advantage of the block diagonal form of (7), the solution steps could be summarized as follows: (i) subdivide the original network into a number of component networks by removing selected branches; (ii) establish the appropriate connection matrix, C(psi zeta); (iii) obtain the solution of unknown nodal voltages from (...