中文摘要：

根据节点分裂法将大规模电力系统的离散无功优化模型转化成多区域分解形式，再采用引入离散惩罚的非线性原对偶内点法求解，获得具有分块结构的降阶线性修正方程组．对弱耦合系统，直接将非对角子矩阵置零即可实现修正方程的完全解耦，算法具有局部线性收敛特性．对于强耦合系统，可以采用与处理弱耦合系统类似的方法获得近似牛顿方向和解耦对角矩阵，以它们作为迭代初值和预处理器，采用GMRES法求解，保证算法具有良好的收敛性和较快的计算速度．文中以1062节点系统和一个实际538节点系统验证了算法的有效性，进一步提出了较实用的解耦判据．

英文摘要：

In this paper, the node tearing method is adopted to convert the discrete reactive-power optimization model of large-scale power systems into a multi-zone decomposition one, and the nonlinear primal-dual interior- point method with discrete penalty is employed to solve the decomposition model and to further obtain reduced-order linear correction equations with a block structure. In weak coupling systems, the complete coupling of the correc- tion equations is implemented by setting the off-diagonal submatrixes to zero, and the algorithm is of local linear convergence. However, in strong coupling systems, both the approximate Newton directions and the decoupled dia- gonal matrix, which are computed by the method similar to handling weak coupling systems, are respectively taken as the initial values and the preconditioner when solving the linear correction equations using the GMRES algo- rithm, thus resulting in good convergence and high calculation speed of the algorithm. The proposed algorithm is fi- nally applied to a 1062-bus and a real 538-bus systems, with its effectiveness being verified and some practical de- coupling criteria being presented.