基于Noether定理的多机系统能量函数构造方法

Construction Method of Multi-machine System Energy Function Based on Noether Theorem

将Noether定理应用于电力系统领域,根据作用量的每一种对称性均存在其对应的守恒定律,即对称性必然存在对应的守恒量这一特点,提出一种构造多机电力系统能量函数的新方法。该方法通过对多机系统模型进行微分方程力学化处理,进而由无限小变换得到系统的首次积分,即系统的能量函数。且在理论推导时考虑n维方程组,故可适用于各阶电力系统模型,具有良好的通用性。通过Matlab仿真,研究三阶电力系统模型下求得能量函数的变化曲线,验证了所提新方法的正确性。

This paper applies Noether theorem to power system for the first time,and proposes a new method for constructing the energy function of power system.This method is based on the idea that each symmetry of action has its corresponding conservation law,that is,the symmetry must have a corresponding conservation amount.This method uses infinitesimal transformation to obtain Noether equation of power system through differential equations of the power system.Then the first-time integral of the system,i.e.the energy function of the system,is obtained with the infinitesimal transformation.This method can obtain the energy function by directly solving the first-time integral of the system,applicable to all kinds of power system models with generalizability.Through Matlab simulation,correctness of the energy function obtained under the third-order power system model is verified.