Construction Method Of Energy Function Based On Noether Theorem And Its Application In Multi-machine Complex Power System

With the increasing dimension and non-linearity of modern power system,more and more people pay attention to the stability of power system.How to ensure the safe and stable operation of power system is an important research topic.According to statistics,most of the accidents caused by the instability of power system worldwide are due to the damage of its transient stability.Therefore,transient stability control is the first line of defense for the stable operation of power system.In many research directions of transient stability control,there is always a difficult problem,that is,the construction of correlation function.For example,when the transient energy function is constructed by direct method,some problems exist,such as the simple model which is usually a second-order classical model,and there is no unified method to obtain the first integral of the system in the higher-order multi-machine power system model.In the generalized Hamilton system control method,it is relatively difficult to construct an appropriate Hamilton function according to the complex nonlinear model of the power system,and then complete the Hamilton implementation.Currently,there is no unified method to solve the problem,and most of the construction is completed through mathematical experience.Aiming at the above problems,based on the analysis of various methods in mechanics,this paper conducts in-depth research on the differential equation models of various power systems.The main work is as follows:(1)The self-adjoint condition of the second order differential equation is given by the variational method,and the self-adjoint condition of the first order differential equation is derived from this condition.Based on the self-adjoint conditions obtained,the mechanicalization method of differential equations is given.For most systems that cannot be fully mechanised,generalized force Q is introduced to partially mechanise the system.(2)Noether theorem is applied in the field of power system for the first time,and a transient energy construction method that can be widely applied to the model of multi-machine power system is proposed.Since the theoretical derivation is carried out from the n-order differential equations,the first integral of the n-order multi-machine power system,namely the energy function of the system,is obtained through the infinite-small transformation.Therefore,this method has a high degree of unity and good universality.(3)Under the system model of WSCC 3 machine and 9 nodes,the energy function curve variation characteristics of the classical second-order model in the transient process were investigated.The change curves of the energy function constructed according to the third-order power system model in steady state and unstable state are studied.(4)Combining the mechanics method of differential equation with the control theory of generalized Hamilton system,a new idea of constructing Hamilton function required in control is proposed.By Hamilton transformation of part of the nonlinear system model,the required function is directly obtained,and then Hamilton implementation is completed.(5)According to the idea of constructing Hamilton function proposed in this paper,the excitation control strategy of multi-machine power system based on the generalized Hamilton system control theory is proposed,and the three-phase short-circuit grounding fault simulation is carried out under the IEEE 14 system model to verify the effectiveness of the control strategy.The control strategy of dual PWM permanent magnet direct drive fan is also proposed.The simulation in Simulink shows that the proposed control strategy has better control effect than the traditional PI control.The energy function construction method mainly studied in this paper not only solves the problem that there is no unified method to construct the energy function of power system with more than second order complex multi-machine.It also provides a new idea for the construction of Hamilton function and the realization of Hamilton system in the generalized Hamilton system control theory.In addition,the Noether structure method of energy function mentioned in this paper can also provide an important reference for the study of the stability domain.