【正文】 an 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 外文翻譯（譯文） 13 潮流 不同排序方案的比較 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 。 c) Determine the new number of the node according to the positong of node in the end of the factorization。 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 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 外文翻譯（原 文） 8 , 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。 nodes 24 are load nodes. Following the original node number, the DC power flow equation is: To simulate puter numerical calculation operations, four significant figures will be used to solve the problem. Executing GEM without pivoting on (1) yields the solution[ θ2,θ3,θ4]T=[,]T, whose ponents differ from that of the exact solution [θ2, θ3,θ4]T=[,]T. A more exact solution could be obtained by plete pivoting: [θ2,θ3, θ4]T=[,]T, and the order of the node after row and column interchanges is 3,2,4. So this is a more reasonable ordering scheme for the purpose of getting more high accuracy. IV. THE INFLUENCE OF NODE REODERING ON THE PERFORMANCE OF NEWTONRAPHSON POWER FLOW METHOD 外文翻譯（原 文） 6 Sample 6node work On the basis of the abovementioned analysis, the scheme for node reordering will not only affect memory requirement but also the accuracy of the solution in solving linear simultaneous equations. So performance of NewtonRaphson power flow method will be different with various node ordering. In this section three schemes of ordering for different purpose will be applied to a sample 6node work shown in Fig 2 to pare the influence of them on the accuracy of the solution, the convergence rate, the calculated amount and the memory needed in power flow putation. The detail of the performance is shown in table IV. A. Puropse 1 Saving Memory as far as possible At present, there are various schemes widely used for node numbering in nearoptimal order to reduce fillins and save memory. The only information needed by the schemes is a table describing the nodebranch connection pattern of the works. An order that would be optimal for the reduction of the admittance matrix of the work is also optimal for the table of factors related Jacobian matrix. Different schemes reach different promise between programming plexity and optimality. In this paper, what we concern about is how the result of the numbering affects the putational performance. The programming efficiency is beyond the scope of the present work. To save memory, a dynamic node ordering scheme si milar 外文翻譯（原 文） 7 to the third scheme presented in [2] is adopted in this section. Execution steps of the algorithm are as follows. Scheme I a) Number the node degree of which is one. If more than one node meet this criterion, number the node with the smallest original number. If there are not su nodes any more, start with step b)。 NewtonRaphson method 。 sparsity。外文翻譯（原 文） 1 中文 4900字 A Comparison of Power Flow by Different Ordering Schemes 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 rationa