Stability Analysis Of Disturbed Multi-machine Power System Based On Hamilton System Theory

In the modern era,power system is a high-dimensional complex non-linear dynamic network system with many random disturbances.Only when the system is stable,can it provide enough safe and reliable power energy for the national economy and social life.With the gradual growth of power demand,the stability of power system is facing more and more challenges,such as random load fluctuation,market adjustment,random vibration of prime mover torque and the incorporation of renewable new energy sources like photovoltaic and wind power into the power grid.All these factors bring about new stochastic problems to system operation.At the same time,with the gradual expansion of interconnected power grid scale,low frequency oscillation becomes a hidden danger of power grid stability.In view of the above problems,this paper is devoted to studying and analyzing the stability of multi-machine power system under disturbance through Hamilton system theory,then designs new control strategies pertinently.Hamilton system theory can effectively avoid the system error caused by linearization control method,so it has become an important tool for studying power system.By introducing the stochastic term to the state function of the system,a precise power system model with stochastic factors is established.The power angle and angular velocity(mean stability and mean square stability)of multi-machine systems under small Gauss random perturbations is proved to be stable when the intensity of the disturbance satisfies ????? using the mean stability,mean square stability theory and It(?) stochastic differential equation theory.Based on Hamilton energy function method,the stability problem can be simplified from the state variables problem of complex high-dimensional system into the simple one-dimensional energy problem.Define the stability region of the system corresponding to Hamilton energy function.At this time,the overflow of system state variables can be reflected indirectly through the fluctuation of the system energy,thus the dimensionality reduction and simplification of complex multi-dimensional vector problem to one-dimensional energy problem can be realized.The numerical method and Monte Carlo method are combined to simulate and analyze the probability distribution of Hamilton energy function of multi-machine system under random disturbances of different intensity,and the stability probability of the system in different stability regions is obtained.Taking the 4-machine-bus system as an example,the simulation analysis under different excitation conditions is carried out to verify the effectiveness of the proposed theoretical method.The mechanism and frequency analysis of low-frequency oscillation in power system are studied by Hamilton system theory.Firstly,based on least action principle,the criterion is provided for the Hamilton periodic orbit of a practical power system which is generally deemed as the source of power system low frequency oscillation by some researchers.The necessary conditions for the existence of periodic orbit of Hamilton system under sub-linear condition are proposed and the existence of periodic solution is proved by Minimax principle.The correctness of the above criteria is verified by simulation of a 3-machine 9-node system satisfying the above conditions.Secondly,for the disturbed multi-machine system,on the basis of the equivalent system,the corresponding Hamilton energy function of the equivalent simplified system is constructed by the Hamilton system theory,an exact expression of the low frequency oscillation frequency in this state is derived by the incomplete elliptic integral mathematical theory.This method can be used to predict and evaluate the anti-disturbance ability of multi-area power system,and also can be used as an auxiliary tool for the existing online analysis methods of low frequency oscillation.The simulation of the low-frequency oscillation of the 10-machine 39-bus system in New England verifies the practicability of the proposed method for predicting and analyzing various oscillation modes of the low-frequency oscillation of the multi-machine system.Based on the design idea of damping compensation and energy balance,a Hamilton energy function is constructed based on the generalized Hamilton system theory and Lyapunov stability theory,which can reflect the structural characteristics of the whole system model with TCSC.The generalized dissipative Hamiltonization of the system is accomplished.The control objective is set as the global transient energy decline of the system to design the feedback control strategy for the asymptotic stability of the system.The coordinated control of TCSC and generator excitation in the system is realized.The simulation test of 4-machine 11-node system under disturbance proves the practicability of the coordinated control strategy.At the same time,this paper presents two optimization algorithms for TCSC control measures,and discusses the robustness of applying suboptimal control measures to security period delay and control delay.The correctness and validity of the proposed optimization algorithm are verified by the simulation of the Italian actual power system.This paper mainly studies the application of Hamilton system theory in stability analysis of power system under disturbance.This theory not only provides a new analysis idea and criterion for the stochastic stability and low frequency oscillation of the system under small disturbances,but also proposes a method to construct the energy function of generalized Hamilton system in power system with TCSC devices and a solution to coordinated control of TCSC as well as excitation.