【正文】 Walker. ―Direct solutions of sparse work equations by optimally ordered triangular factorization,‖ Proceedings of the IEEE, vol. 55, , pp. 18011809, November 1967. [3] K. M. Sambarapu and S. M. Halpin, ―Sparse matrix techniques in power 外文翻譯（原 文） 12 systems,‖ ThirtyNinth Southeastern Symposium on System Theory, March 2020. [4] W. F. Tinney and C. E. Hart, ―Power flow solution by Newton39。 b) Number the node so that no equivalent branches will be introduced when this node is eliminated. If more than one node meets this criterion, number the one with the smallest original number. If we can not start with step a) or step b), turn to step c)。 accuracy。外文翻譯（原 文） 1 中文 4897字 A Comparison of Power Flow by Different Ordering Schemes Wenbo Li, Xueshan Han, Bo Zhang The School of Electric Engineering Shandong University Jinan, China Email: Abstract—Node ordering algorithms, aiming at keeping sparsity as far as possible, are widely used today. In such algorithms, their influence on the accuracy of the solution is neglected because it won’t make significant difference in normal systems. While, along with the development of modern power systems, the problem will bee more illconditioned and it is necessary to take the accuracy into count during node ordering. In this paper we intend to lay groundwork for the more rationality ordering algorithm which could make reasonable promising between memory and accuracy. Three schemes of node ordering for different purpose are proposed to pare the performance of the power flow calculation and an example of simple sixnode work is discussed detailed. Keywords—power flow calculation。 NewtonRaphson method 。 c) Number the node so that the fewest branches will be introduced when this node is eliminated. If not only node could introduce fewest branches, number the one with the largest degree. Once certain node is numbered in the step above, update the degree of relevant nodes and topological information. Until all the nodes are numbered, the process of node numbering ends up. TABLE I. REORDERED NODES USING SCHEME ONE Following the steps of scheme I, the sequence of the node numbered for the 6node 外文翻譯（原 文） 8 work is given in table I. No fillin will be introduced during the procedure of solving the linear equation, so the table of factors and the Jacobian matrix will have pletely identical structure. So the memory requirement for the table of factors is , which is the same with that for the Jacobian matrix. Normally, an acceptable solution can be obtained in four or five iterations by NewtonRaphson method. While, the number of iterations required for this example is thirtythree because of the illconditioned caused by the small impedance branch. 123 multiply operations will be performed during forward substitution and backward substitution for each iteration, and 7456 multiply operations will be performed throughout the whole process of solving. B. Puropse 2: Improving Accuracy Using Complete Pivoting Considering that plete pivoting is numerically preferable to partial pivoting, in this section plete pivoting is adopted to improve accuracy of the solution of the linear equations, aiming at reducing the number of iterations. Here nodes relate to large determinant of the diagonal submatrices intend to be arrange in front. To some extern, the modulus of the entries on the main diagonal of the admittance matrix could indicate the magnitude of the determinant of the submatrices on the main diagonal of the Jacobian matrix. For convenience, we make use of admittance matrix to determine the order of numbers. Scheme II a) Form the nodal admittance matrix。s Method,‖ IEEE Transactions on Power Apparatus and Systems, Vol. PAS86, No. 11, pp. 14491460, November 1967. [5] W. F. Tinney, V. Brandwajn, and S. M. Chan, ―Sparse vector methods,‖ IEEE Transactions on Power Apparatus and Systems, Vol. PAS104, , pp. 295301, February 1985. [6] R. Betancourt, ―An efficient heuristic ordering algorithm for partial matrix refactorization,‖ IEEE Transactions on Power Systems, Vol. 3, No. 3, pp. 11811187, August 1988. [7] A. Gomez and . Franquelo. ―An efficient ordering algorithm to improve sparse vector methods,‖ IEEE Transactions on Power Systems, Vol. 3, No. 4, pp. 15381544, November 1988. [8] B. Stott, ―Review of loadflow calculation methods,‖ Proceedings of the IEEE, Vol. 62, No. 7, pp. 916929, July 1974. [9] X. W. Chang and C. C. Paige, ―On the sensitivity of the LU factorization,‖ BIT, Vol. 38, No. 3, pp. 486501, 1998. [10] . Businger, ―Monitoring the numerical stability of Gaussian elimination,‖ Numer. Math, Vol. 16, pp. 360361, 1971. [11] Paola Favati, Mauro Leoncini, and Angeles Martinez, ―On the robustness of gaussian elimination with partial pivoting,‖ BIT, Vol. 40, , , 2020 VII. BIOGRAPHIES Wenbo Li was born in Shandong Province in P. R. China, 1984. He received his B. S. from Electrical Engineering Institute of Shandong University, China, in 2020. He is currently pursuing the . degree at Shandong University. His main interest is in power system analysis and control. 外文翻譯（原 文） 13 Xueshan Han was born in Liaoning Province in P. R. China, 1959. He received B. S. and M .S. degree from Electrical Engineering Department of Northeast Institute of electrical Power, Jilin In 1990 and PhD from Harbin Institute of Technology, Harbin in 1994. Now he is a Professor of the School of Electrical Engineering, Shandong University, China. His interests focus on power system analysis and control. Bo Zhang was born in Shandong Province, China, 1963. Now he is a Professor of the School of Electrical Engineering, Shandong University, China. His interests focus on power system analysi