【正文】 以 稀疏矩陣技術(shù)為導(dǎo)向的節(jié)點(diǎn)重新排序算法已廣泛應(yīng)用于電力系統(tǒng)計(jì)算中 ，旨在最大限度地減少 內(nèi)存需求。雖然由于舍入誤差，部分 消元法在 有些極限點(diǎn)附近 不 能 提供準(zhǔn)確的解決 方法 。參考文獻(xiàn) [ 9 ]表明 部分 消元法和完全消元法外文翻譯（譯文） 15 是如何 影響 LU分解的靈敏度。然后在 第四部分 以 6 個節(jié)點(diǎn)的網(wǎng)絡(luò)作為一個例子， 對于 節(jié)點(diǎn) 排序?qū)Τ绷?性能 的 影響進(jìn)行了詳細(xì)分析 。因此，有必要討論節(jié)點(diǎn) 編號對計(jì)算 精度的影響。然而 ，如果 在潮流系統(tǒng)模型中存在 一系列非常高 或 低 的 阻抗，長的超高壓線路，串聯(lián)和并聯(lián)補(bǔ)償 等問題 ，對角占優(yōu)將 被 削弱和假設(shè)可能并不總是站不住腳的。這相當(dāng)于減少路徑的長度，但它可能會導(dǎo)致更多的 最小 填充，更大的復(fù)雜性和費(fèi)用。每種策略是在結(jié)果和執(zhí)行速度兩者之間的折中，并且它們都被大部分 工業(yè)所采納 。這一行動被稱為 最小填充 。線性方程組求解 的 效率和精度直接影響了牛頓 拉夫遜潮流算法的性能。 本文列舉出了三種不同目的的排序方案，旨在比較潮流計(jì)算的形式，并且以一個六節(jié)點(diǎn)網(wǎng)絡(luò)為例進(jìn)行具體討論。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 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) 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。 NewtonRaphson method 。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 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。 accuracy。 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)。 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 6