P-moment Stability Analysis Of Power Systems Considering Randomness

With the large-scale grid-connected generation of new energy,the stable operation of the power system has been significantly affected.In the context of the rapid development of new energy,using the research method of stochastic stability theory to study the random stability of multi-machine power systems under random excitation,it,is of great significance and value to discuss the random stability of power systems.This paper mainly studies the p-moment stability of two-machine and multi-machine power systems.Based on two-machine and multi-machine power system models,using mathematical,statistical,and power system knowledge,combined with research methods such as probability theory and stochastic differential equation theory,analyzed the p-moment stability of two-machine and multi-machine power systems.It mainly includes the following:(1)Using the Fokker-Planck equation of the Markov process and the Ito process,the properties of the Ito stochastic differential equation,and the properties of the probability density function,the functions of the multi-machine system are derived for the stochastic differential equations of the multi-machine power system.The steady-state density function of the angle provides a theoretical foundation for the subsequent chapters to discuss the stability of the system's power angle before and after the equivalent conversion.(2)For the two-machine power system,stochastic differential equation theory is uesd to study p-moment stability.The two-machine power system is equivalent to a single-machine system,and the two-machine system is taken as an actual example.The EM numerical method is used to simulate the trend of the system's power angle,speed,etc.over time.The sample mean is used to estimate the system power angle fluctuation.Draw the steady-state density function curve of the system power angle before and after the equivalent conversion of the two-machine system,and obtain the stability of the system before and after the equivalent conversion.At the same time,verify the third-moment and fourth-moment stability of the system's power angle.The p-moment stability of the mechanical system is supplementary.(3)For multi-machine power systems,the stochastic differential equation theory,EM numerical method,extended equal area method,and probability density function of system power angle are used to explore the p-moment stability of multi-machine power systems.The multi-machine power system is equivalent to a two-machine model.The coefficient matrix of the model after the equivalence is analyzed using the p-moment stability theorem.The four-machine system is used as a practical example to perform numerical simulation,and the probability of the system power angle is plotted The density function curve shows that the stability of the system remains the same before and after the equivalent conversion.The stability problem of the multi-machine system can be converted to two-machine analysis.The influence of two random excitation factors,the calculation step size and the excitation step size,on the power angle curve of the system is also studied.