【正文】 ect the accuracy of the solution in section III. Then, taking a 6node work as an example, the effect of node ordering on the performance of power flow is analyzed detailed in section IV. Conclusion is given in section VI. II. CONTRADICTION BETWEEN MEMORY AND ACCURACY IN NODE ORDERING ALGORITHM According to numerical mathematics, plete pivoting is numerically preferable to partial pivoting for systems of liner algebraic equations by Gaussian Elimination Method (GEM). Many mathematical papers [911] focus their attention on the 外文翻譯（原 文） 4 discrimination between plete pivoting and partial pivoting in (GEM). Reference [9] shows how partial pivoting and plete pivoting affect the sensitivity of the LU factorization. Reference [10] proposes an effective and inexpensive test to recognize numerical difficulties during partial pivoting requires. Once the assessment criterion can not be met, plete pivoting will be adopted to get better numerical stability. In power flow calculations, partial pivoting is realized automatically without any rowinterchanges and columninterchanges because of the diagonally dominant features of the Jacobin matrix, which could guarantee numerical stability in floating point putation in most cases. While due to rounding errors, the partial pivoting does not provide the solution accurate enough in some illconditionings. If plete pivoting is performed, at each step of the process, the element of largest module is chosen as the pivotal element. It is equivalent to adjust the node ordering in power flow calculation. So the node relate to the element of largest module is tend to arrange in front for the purpose of improving accuracy. The node reordering algorithms guided by sparse matrix technology have wildly used in power system calculation, aiming at minimizing memory requirement. In these algorithms, the nodes with fewer adjacent nodes tend to be numbered first. The result is that diagonal entries in node admittance matrix tend to be arranged from least to largest according to their module. Analogously, every diagonal submatrices relate to a node tend to be arranged from least to largest according to their determinants. So the results obtained form such algorithms will just deviate form the principle follow which the accuracy of the solution will be enhance. That is what we say there is contradiction between node ordering guided by memory and accuracy. III. DIFFERENCE PRECISION OF THE SOLUTION USING PARTICAL PIVOTING AND COMPLETE PIVOTING It is said that plete pivoting is numerically preferable to partial pivoting for solving systems of linear algebraic equations. When the system coefficients are varying widely, the accuracy of the solution would be affect by rounding errors hardly 外文翻譯（原 文） 5 and it is necessary to take the influence of the ordering on the accuracy of the solution into consideration. DC model of Sample 4node work As an example, consider the DC model of sample 4node system shown in Figure 1. Node 1 is the swing node having known voltage angle。 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