【摘要】 为综合利用极坐标牛顿法潮流方程数少、雅可比矩阵J元素少以及直角坐标牛顿法中没有三角函数计算的特点,并克服极坐标牛顿法潮流J阵元素的不对称使其计算速度不理想的情况,提出一种对称极坐标牛顿法潮流的直角坐标解法。主要内容为,建立结构不完全对称的子阵形式的极坐标J阵,通过子阵建立子阵元素间的对应关系;拆分J阵元素的计算,建立子阵元素的部分对称关系;对J阵元素等计算公式进行三角变换,并按"二行+二列"的对称方式计算J阵元素;用四角规则而不是消元计算公式对J阵元素消元;将取倒的对角元素作为规格化因子以减少除法计算。新方法不但可实现J阵元素的部分对称计算,还可大量减少三角函数的运算以及消元过程中的除法运算,且无需计算公式直接完成消元计算。以IEEE-118节点系统为例,新方法生成J阵速度可提高约90%以上,潮流计算速度可提高约30%,并极利于编程。更多还原

【Abstract】 In order to make comprehensive use of the characteristics of fewer modified equations and fewer elements on Newton in polar coordinates power flow algorithm and no trigonometric function calculation in rectangular coordinate Newton method, and overcome the situation on unsymmetrical J-matrix elements in polar coordinates make its calculation speed is unsatisfactory, a rectangular coordinates algorithm for symmetrical Newton in polar coordinates power flow is presented in the paper. The main contents were to establish polar coordinate J-matrix in the form of submatrices with incomplete symmetrical structure and the corresponding elements relationship among submatrices; split the calculation on the J-matrix elements and establish the partial symmetry relation for the submatrices elements. Triangle transformation were carried out on the calculating formulas of the J-matrix elements et al; the J-matrix elements were calculated in the symmetric way of “two rows+two columns”; the four-angle rule was used instead of the eliminating formulas for the elimination of J-matrix elements; and the inverted diagonal elements were used to normalize to reduce division operation. The new method can not only realize the partial symmetrical calculation on J-matrix elements, but also greatly reduce the operation for triangle functions and the division operation in the eliminating process, and can be used to directly complete the eliminating calculation without the calculation formulas. Taking IEEE-118 bus system as an example, the new method can improve the generating speed on J-matrix by about 90% and the power flow calculating speed by about 30%,which is very good for programming.更多还原