电力网的欠秩问题及其对称分析方法

电力系统稳态方程的全节点雅可比矩阵，是规划运行控制的必备工具。但它在运行点处奇异或病态(对应天网或有线路对地电纳)、秩小于维数。这使模型或结果含该矩阵的一类问题(称为电力网欠秩问题)，在已有电力系统理论范畴内无解，或虽然有解但对小扰动很敏感、不可用。当前，国内外一律通过丢雅可比矩阵中参考节点的行和列建立近似问题模型求解，结果不仅让电路规律对参考节点电源失效、不满足电路电磁场唯一性定理，而且用于调度时无法保障方案可行最优、用于线路潮流安全调控时不能一次调控到位、实用效能低。 电力网欠秩问题是关系电力系统有无唯一运动规律的基础科学问题。本项目拟创新提出基于物理规律对称性的对称分析方法，证明电力网欠秩问题解的存在性和唯一性，探讨严格遵循电路电磁场规律的欠秩问题系统求解方法，创新电力系统知识并用于运行与控制，从根本上解决已有方法的低效能问题。这对全面促进智能电网安全经济高效运行有重大意义。

The full-bus Jacobian matrix associated with the power system steady-state equations is the necessary tool for the system planning and operation as well as control. It is, however, odd or ill-conditioned at power system operation points (when the grid is without or with grounded branches). Its rank is generally less than its dimension. As a result, the kind of problems (here called power grid rank-short problems) with this matrix involved in model or result either have no solution by the existing knowledge, or have solutions sensitive to small disturbance and useless. The worldwide existing solution methods of these problems all build approximate models to solve by employing the Jacobian matrix discarding rows and columns corresponding to reference bus. The results not only go against electric-circuit laws and are not unique, but also increase the times and lower the efficiency when used respectively in security regulation and economic dispatch. 　　The rank-short problems in a power grid belong to fundamental scientific ones concerning whether a power system has a unique motion rule. We are going to create a new physical-laws'-symmetry based method, called here the symmetrical analysis method. Using the symmetrical analysis method proves the existence and uniqueness of the solution of any rank-short problems, investigates systematic solution methods obeying electric-circuit laws and creates new knowledge of power sysems, so as to settle the problems of "the results of world-wide existing methods not only go against electric-circuit laws and are not unique, but also increase the times and lower the efficiency when used respectively in security regulation and economic dispatch". This is of important theoretical and practical meaning for thoroughly promoting secure and economic and high-efficient operation of smart grids.