论文信息 - Load-Flow Solutions for Ill-Conditioned Power Systems by a Newton-Like Method

Load-Flow Solutions for Ill-Conditioned Power Systems by a Newton-Like Method

In this paper mathematician K.M. Brown's method is used to solve load-flow problems. The method is Particularly effective for solving of ill-conditioned non- linear algebraic equations. It is a variation of Newton's method incorporating Gaussian elimination in such a way that the most recent infonnation is always used at each step of the algorithm; similar to what is done in the Gauss-Seidel process. The iteration converges locally and the convergence is quadratic in nature. A general discussion of ill-conditioning of a system of algebraic equations is given, and it is also show by the fixed-point formulation that the proposed method falls in the general category of sucessive approximation methods. Digital computer solutions by the proposed method are given for cases for which the standard load-flow methods failed to converge, namely 11-, 13- and 43-bus ill-conditioned test systems. A comparison of this method with the standard load-flow methods is also presented for the well-conditioned AEP 30-, and 57-bus systems.

[1] Kenneth M. Brown,et al. COMPUTER ORIENTED ALGORITHMS FOR SOLVING SYSTEMS OF SIMULTANEOUS NONLINEAR ALGEBRAIC EQUATIONS**This work was supported in part by the National Science Foundation under Grant GJ-32552 and in part by the University Computer Center of the University of Minnesota. , 1973 .

[2] J. Meisel,et al. Application of Fixed-Point Techniques to Load-Flow Studies , 1970 .

[3] L. L. Freris,et al. Investigation of the load-flow problem , 1967 .

[4] J. W. Walker,et al. Direct solutions of sparse network equations by optimally ordered triangular factorization , 1967 .

[5] O. Alsac,et al. Fast Decoupled Load Flow , 1974 .

[6] Y. Tamura,et al. A Load Flow Calculation Method for Ill-Conditioned Power Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[7] Roger Fletcher,et al. A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[8] William F. Tinney,et al. Power Flow Solution by Newton's Method , 1967 .

[9] Albert M. Sasson,et al. Nonlinear Programming Solutions for Load-Flow, Minimum-Loss, and Economic Dispatching Problems , 1969 .

[10] A. Brameller,et al. Some improved methods for digital network analysis , 1962 .

[11] K. Brown. A Quadratically Convergent Newton-Like Method Based Upon Gaussian-Elimination , 1968 .

[12] G. W. Stagg,et al. Automatic Calculation of Load Flows , 1957, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.