复杂动态电力系统低频振荡的存在性仍是目前电力工程领域研究的热点之一，现有理论尚不能完全解释电网中存在的低频振荡现象。本项目拟采用基于能量的微分代数Hamilton系统周期解存在理论对非线性微分代数系统进行分析研究。在理论研究方面，给出基于能量函数理论的非线性微分代数Hamilton系统实现，采用具有辛结构的微分代数Hamilton函数方法分析电力系统存在周期性低频振荡的条件和判据。基于延迟系统的微分代数Hamilton系统实现结构进行定性分析并给出其周期解存在性的条件和判据。在应用研究方面，建立具有不确定扰动的复杂电力网络微分代数Hamilton系统实现的数学模型，研究广域量测信号延迟系统周期解的存在性，进行相应的动态性能分析和仿真验证。本课题的研究，将进一步完善微分代数Hamilton能量函数的定性分析理论体系，推广其在结构保持复杂动态电力系统低频振荡分析与抑制方面的应用。

The existence of low-frequency oscillation in complex dynamical power system is one of the hot spots in the research field of power engineering. The existing theory still can not fully explain the phenomenon of low-frequency oscillations in the power grid. This project intends to adopt the periodic solution existence theory of differential algebraic Hamilton system based on the energy to analyze and study the nonlinear differential algebraic systems. In theoretical research, nonlinear differential algebraic Hamiltonian system realization is given based energy function theory. The differential algebraic Hamiltonian function method with symplectic structure is used to analyze the conditions and criteria of the existence of periodic low-frequency oscillation in power system. Differential algebraic Hamilton system realization structure based on delay system is used for qualitative analysis, and the existence conditions and the criterion of periodic solution of the system are given. In applied research, the mathematical models of complex power network differential algebraic Hamiltonian systems realization with uncertain disturbances are established. The existence of periodic solutions of wide-area measurement signal delay system is studied and the dynamic performance analysis and simulation are performed. This subject will further improve the qualitative analysis theory based on differential algebraic Hamiltonian energy function, and promote its application in the analysis and control of low-frequency oscillation problems in structure preserving complex dynamic power system.