电力系统稳定性正规形分析法中Hessian矩阵的研究

Study on Hessian Matrix in Power System Stability by Using Normal Form

电力系统稳定性正规形分析法中出现的Hessian矩阵,是对系统非线性向量函数进行二阶偏导,它包含了系统的众多非线性信息,为了进一步简化求解过程,提出了一种新的Hessian矩阵数值微商优化算法。所提算法是在电力系统动态微分方程雅克比矩阵的基础上,直接进行Hessian矩阵计算,这种方法省去了解析法求解二阶偏导的复杂过程,提高了计算效率。通过对算例计算,结果表明所提方法的有效性。

Hessian matrix in power system stability analysis based on normal form theory is the second-order partial derivative of nonlinear vector function,which contains many nonlinear information.In order to simplify the solving process,a numerical differentiation optimization algorithm is presented in this paper.This algorithm is based on the Jacobi matrix of the power system dynamic differential equation,and calculates the Hessian matrix directly,which omits the need for evaluating the second-order derivative and improves the calculation efficiency.the presented algorithm is applied in an example power system.the simulation result shows its effectiveness.