Study On The Multiple Time Scale Property Of The Synchronous Generator Model

With the versatile resources incorporated and the increasing application of power electronic technology in the grid,the power system dynamics over a larger range of time scale become more abundant,and the transient stability turns to be a more complicate problem for the power system.At the mean time,the importance of the generators in keeping the power balance is more eminent.The selection of the synchronous generator model is important for power system transient stability analysis.Compared with the detailed seventh-order generator model,the appropriate reduced-order model can describe the dynamics of machine with certain accuracy,while the computational burden is relieved and thus can contribute to improving the efficiency of stability analysis.To disclose the multiple time scale property of the synchronous generator model,the characteristic structure of the variables is studied in this paper by using the linear system theory and singular perturbation method.The main work carried out is the following.First,by eigenvalue analysis,the time scales are partitioned according to the velocity of variation of the modes.The abstract of the real part or the norm of the eigenvalue is taken as the base of the partition.The result is verified by the time domain response of the modes.The computational result reveals that,the detailed model includes the slow dynamics,the normal speed dynamics and the fast dynamics,while the fifth-order model neglects the fast dynamics,and the third-order model further neglects the normal speed mode,and only includes the slow dynamics.Second,via modal analysis,according to the participation factor of the variables in the modes,the dominant variable of each mode is determined.When the present method is used,the factor may appear extremely large pertaining to the slow dynamics in the multi-machine systems.To overcome this deficiency,it is proposed in this paper to normalize the left eigen vector,so that the factors can be obtained effectively.The method is verified on a three machine system.Third,via variable decomposition,the slow component is taken as the initial value of the reduced-order machine model,so that the accuracy of the reduced-order model can be improved.According to the the computational singular perturbation theory,the slow-and the fastcomponents are obtained by the g-scheme method.The impact of initial value on the model error is analyzed by comparison.The computational result shows that,after the decomposition,the error of the fifth-order model is reduced.The multiple time scale is the intrinsic characteristics of the synchronous generator.This paper classifies the time scales through eigenvalue analysis,and determines the dominant variable of each mode,which provides the base for the initial value correction,and thus improve the accuracy of the reduced-order model.