电力网的欠秩问题及其对称分析方法

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.

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。

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。. 本项目从理论物理学原理和电路理论出发，创新提出了基于物理规律对称性的电力网欠秩问题的对称分析方法，深入研究了电力网稳态模型中全节点雅可比矩阵关联的物理量互动机制，凝练了驱动求解全节点雅可比矩阵g-逆的对称性条件，创建了条件约束下全节点雅可比矩阵逆阵的对称g-逆解法。剖析了全节点雅可比矩阵对称g-逆的特点，并将其应用于电力网运行和控制。提出了网损灵敏度的对称获取方法，解决了已有方法获取的网损对参考节点注入功率的灵敏度恒为零、电路规律对参考节点电源失效的问题。提出了线路潮流灵敏度的对称获取方法，解决了已有方法获取的线路潮流对参考节点注入功率的灵敏度恒为零、电源激励不遵循一样的规律的问题。提出了节点电价计算与分解的对称方法，解决了已有方法获取的节点电价随参考节点变化而变化、量值不唯一和激励不精准的问题。提出了电压弱节点识别与调控的对称方法，解决了基于奇异值分解的已有方法结果不唯一和低效能问题。提出了输电拥塞缓解的对称方法，解决了已有输电拥塞缓解方法的方案不唯一和不高效的问题。. 研究结果表明，按理论物理学对称性原理，电力网欠秩问题都存在唯一解，且该种解都同等看待全网节点的源荷，因此是对称解。对称解满足同种对象遵守同一物理规律，因此本项研究给出的对称分析方法是精准高效的方法。