多机系统Hamilton实现的Hessian矩阵正定判定与应用  

Judgment and application of Hessian matrix positive definiteness for multi-machine system Hamiltonian realization

作　　者：殷婷[1] 王杰[1] 

机构地区：[1]上海交通大学电子信息与电气工程学院,上海200240

出　　处：《电力系统保护与控制》2013年第23期16-22,共7页Power System Protection and Control

基　　金：国家自然科学基金项目(61074042)~~

摘　　要：对于传统的电力系统广义Hamilton实现,判定Hamilton函数Hessian矩阵的正定性是保证系统Lyapunov意义下稳定的充分条件,而复杂电力系统中此Hessian矩阵通常为高维分块矩阵,其正定性判定较为困难。基于二次型和块对角占优的思想,推导出判断高阶分块矩阵正定性的一般方法,利用矩阵分块理论并结合矩阵块的行或列的性质来实现。计算过程简单,大大减小了计算量。运用电力系统暂态能量函数方法有助于控制的设计和研究,并使用上述方法判断系统在平衡点处Hessian矩阵的正定性。在四机系统中进行Simulink仿真,证明了所推导判据的准确性和控制策略的有效性,简化了广义Hamilton系统实现的Hessian矩阵正定性的判断过程。The positive definiteness judgment of Hessian matrix of Hamilton function is a sufficient condition to guarantee the system stability in the Lyapunov sense for the generalized Hamiltonian realization of the traditional power system.However,the Hessian matrices of complex power system are usually high-dimension blocked matrices and the judgments of positive definiteness are very difficult.The general method to judge the positive definiteness of high-order blocked matrix is derived based on the idea of quadratic form and block diagonal dominance,and it can be realized by using the characteristics of the blocked rows or columns of matrix and blocked matrix theory.The calculating process will be simpler,and it greatly reduces the amount of calculations.At the same time, it will be conducive to the research and design of the control by means of the transient energy function method of power system,and the positive definiteness of Hessian matrix at the equilibrium point is judged by the above methods.The simulation example is given for four-machine system to prove the accuracy of the criterion and the effectiveness of the control strategy,which simplifies the judgment process of the positive definiteness of Hessian matrix of generalized Hamiltonian realization.

关 键 词：HAMILTON系统 能量函数 HES sian矩阵 二次型 块对角占优矩阵 

分 类 号：O151.21[理学—数学]