The Stability Analysis And Application Research Of Power System Considering Stochastic Disturbances

Power system is a high-dimensional nonlinear network with many random disturbances such as random vibration of prime motor torque,random fluctuations of electrical loads and so on.Recently,with large-scale renewable power integration such as wind energy and solar energy,it has brought much more stochastic factors to the power system.The traditional deterministic linear analysis methods need to be improved.It has important value to use nonlinear differential equations to analyze the stochastic disturbance stability of the system and extend its application.Therefore,in order to ensure the safe and reliable operation of the whole system,it is necessary to utilize the theory of stochastic differential equations and stochastic analysis methods to study the system stability,to establish a much more realistic mathematical model of power system which takes the random perturbation into consideration and to apply reasonable numerical algorithm and simulation methods to do the relevant research based on a good grasp of the basic characteristics of random disturbances in the system.This research work is closely related to the development trend of the power industry in our country,which has a major part both in theory and application.As an essential mathematical tool,the stochastic differential equation can directly add the uncertain factors into the dynamic equations of the system.Currently,stochastic differential algebraic equations have been widely used in system control,statistical physics,finance and other fields.However,its application and research in the field of power system stability analysis is still in the initial stage.But in recent years,with the increase of the stochastic factors in the system,more and more scholars carry out the research work on the aspect of system randomness,which signifies that the theory of stochastic differential equations has a significant application value and a wide development prospect in the power system analysis.This paper firstly gives a brief introduction and classification of random disturbances.Meanwhile,the actuality of domestic and foreign research on power system stochastic analysis is summarized,and the basic theory of stochastic differential equations is discussed in detail.Secondly,aimed at the external stochastic excitation,the mathematical model of multi-machine system with random perturbations is established in the paper.Based on this model,the mean stability and mean square stability of the multi-machine system power angles and rotor speeds under the Gaussian random small disturbance are proved by using the It?stochastic differential equations,matrix and norm theory.The simulation of the4-machine 11-bus system and the 16-machine 68-bus system under the Gauss random perturbations have been carried out in Matlab,and the rationality of this proposed analysis method is verified through the comparison between theoretical proof and simulation results.Thirdly,from the perspective of nonlinear systems,Lyapunov second method is used to analyze the system stochastic stability.In this method,the Lyapunov function V of multi-machine system is formed,and the stochastic stability of this system can be determined according to the change of the function derivative V^?5?.Due to the existence of the random disturbance,the derivative V^?5?becomes a random variable,so it is need to combine the probability theory to describe the Lyapunov stability of the system which is subjected to random impacts qualitatively.Moreover,the feasibility of the Lyapunov stability theory application in the field of power system stochastic stability analysis is discussed,of which the deficiency and difficulty have been presented in the paper.Lastly,in view of high dimensional and nonlinear characteristics of the multi-generator system,the further study on the system stochastic stability is undertaken based on energy function method.The overflow of system state variables can be reflected indirectly through the fluctuation of the system energy.Then the stability problem can be simplified from the complex high-dimensional vector problem into the simple one-dimensional vector problem by using energy function.In this method,the energy varying is used to describe the influence of stochastic disturbances on the power grid,and combined with the Monte Carlo simulation method the stability probability of the multi-machine system under stochastic disturbance can be obtained.Lastly,the 4 machine 11 bus system is chosen as an example and the system stability probabilities under different stochastic disturbances are got by simulation.By analyzing the simulation results,the practicality and validity of this analysis method is verified.