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[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 analysis and control. 外文翻譯（譯文） 14 潮流 不同排序方案 的比較 李文博，韓學(xué)山，張波 山東大學(xué)電氣工程學(xué)院 濟(jì)南，中國 郵箱： 摘 要： 今天 被廣泛應(yīng)用的節(jié)點(diǎn) 排序算法，旨在 盡可能地保證電力系統(tǒng)的稀疏性 。 NewtonRaphson method 。 accuracy。 TABLE II. REORDERED NODES USING SCHEME TWO 外文翻譯（原 文） 9 Executing scheme II, plete pivoting might automatic performed without row and column exchanges. The module of entries on main diagonal corresponding to such node may bee larger by summing more branch parameter, as a result, the nodes, degree of which is larger, tend to be numbered first. So the results of such scheme may depart form the principle of node numbering guided by sparse matrix methods and many fillins might be introduced. The sequence of the node numbered for 6node work is list in table II. Six fillins will be produced, so more memory () and more operations (321 multiply operations) are spent in the procedure of forward and backward substitution during once iteration. The total number of iterations required reduces to thirteen, which suggests that the calculation accuracy for linear equations could be raised by plete pivoting. Finally, the number of multiply operations reduces to 5573 thanks to smaller number of iterations. C. Puropse 3: Improving Accuracy while preserving the sparsity Only one small impedance branch exists in the system, so only four entries (submatrices) corresponding to node 4 and node 6 are very large in admittance matrix (Jacobin matrix). During the process of forward substitution, once node 4 or node 6 is elimination, the submatrix prised of rest elements could keep good numerical stability and numbering of rest nodes would not make a difference to the accuracy of the solution. To take both accuracy and sparsity into account, we numbered node 4 first, then numbered other nodes following the method used for purpose 1. That is what we called scheme III for the 6node work. The sequence of the node numbered for the 6node work is given in table III. 外文翻譯（原 文） 10 Since only one small impedance branch exists in the system and it connects to node 4, the degree of which is one. Scheme III will meet the request of purpose 1. So the number of fillins, memory requirements and operations needed for factorization are all the same with scheme I. Only nine iterations will be needed to insure the convergence, result in a large save of calculation (only 2107 multiply operations). The reduction on the number of iterations indicates that more exact solutions for the linear equations could be got using scheme III. After analysis and parison, the reasons are as follows: ? The diagonal element related to node 4 is just a little smaller than the one related to node 6, so eliminate node 4 first will not decrease accuracy. The scheme could meet plete pivoting approximately. ? Fewer operations in scheme III reduce the rounding error of calculator floatingpoint numbers. Especially, if eliminate node 6 first, very small value might be added to diagonal element of node 2 and node 5, which would cause serious rounding error. While, if eliminate node 4 first, a sizable value will be added to diagonal element of node 6, producing a value in the normal range. TABLE III. REORDERED NODES USING SCHEME THREE TABLE IV. PERFORMACNE OF NEWTON POWER FLOW USING DIFFERENT SCHMEMS OF NODE ORDERING 外文翻譯（原 文） 11 V. CONCLUSION Theoretical analysis and the result of numerical calculating suggest that it is necessary to consider the influence of node ordering on the accuracy of the power flow calculation. If the node ordering algorithm takes both memory and accuracy into account reasonably, the performance of power flow calculation could be further improved. Elementary conclusions of this paper are as