Computational methods for large sparse power systems analysis : an object oriented approach I by S.A. Soman, S.A. Khaparde, Shubha Pandit.p. cm. --(The Kluwer international series in engineering and computer science ; SEes 651. Power electronics and power systems) Includes bibliographical references and index.

IEEE A sound design method is based upon a sound theoretical foundation, yet it offers degrees of freedom for artistic innovation. In the objectoriented paradigm, the world is viewed as a collection of objects interacting with each other to achieve a meaningful behavior. The design perspective provided in this article can be used for many applications, such as power system state estimation and optimal power flow (OPF), and the sparse matrix class can be developed further to include eigenvalue analysis. As such, the architecture presented in this article is scalable. Mathematical Modeling Tools Digital simulation of power system applications (PSA) has been a focus of research for the last 5 decades. Considerable literature has dwelt upon development of fast and numerically stable algorithms, applicable to large systems for a variety of applications. The domain of applications can be classified into steady-state analysis, dynamic analysis, and real-time decision making/automation. Steady-state analysis problems arise in system planning as well as operation of a power system. Such software is used either for offline analysis or online application in energy control centers. Some typical applications are load-flow analysis, shortcircuit analysis, relay coordination, network topology processing, observability analysis, power system state estimation, OPF, and contingency analysis. The other category of problems involving dynamics include transient stability and small signal stability. Mathematical modeling tools used in the two domains are distinct. Problems in steady-state analysis essentially require "good quality" large sparse linear system solvers (LSS), sparse matrix optimization, and graph theoretic computational tools. Problems involving dynamics require eigenvalue analysis, time domain simulations of differential equations, etc. This article focuses on applications belonging to the first category.

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This paper presents design of generic Linear System Solver (LSS) for a class of large sparse symmetric matrices over real and complex numbers. These matrices correspond to either of the following 1) Symmetric Positive Definite (SPD) matrices, 2) Complex Hermitian matrices, 3) Complex matrices with SPD real and imaginary matrices. Such matrices arise in various power system analysis applications like load flow analysis and short circuit analysis. Template facility of C++ is used to write a generic program on float, double and complex data types. Design of algorithm guarantees numerical stability and efficient sparsity implementation. A reusable class SET is defined to cater to graph theoretic computations. LSS problems with matrices upto 20 000 nodes have been tested. Another feature of the proposed LSS is implementation of associative array, which allows subscripting an array with character strings, such as bus names. This helps in making the power system analysis software user friendly. The proposed LSS reflects an important development toward a truly object oriented power system analysis software.Index Terms-Graph theoretic applications, linear system solver, LU decomposition, object oriented programming, sparse matrix computations.

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