Equivalent Lorenz Models And Stability Analysis Of Synchronous Machine And Virtual Synchronous Machine

The virtual synchronous machine and the synchronous machine are the key equipments of the wind power generation systems in the grid-connected and islanded modes.The virtual synchronous machine controls the generator-side rectifier or the grid-connected inverter as a permanent-magnet synchronous machine so as to match the dynamics of the generator with ones of the grid,so the virtual synchronous machine and the synchronous machine have the same external characteristics.However,due to the nonlinearities the stability analysis of the virtual synchronous machine and the synchronous machine is a challenging problem,which devastately influences reliability of the grid-connected and the wind power generation systems.In a word,to study the stability analysis methods of the virtual synchronous machine and the synchronous machine has theoretical and practical meanings.Lorenz equations are the prestigious nonlinear model,which play a crucial role in the nonlinear analysis and stability analysis in varieties of engineering applications since 1960 s.So the Lorenz model can mimic lots of practical systems,the study of engineering applications transforms into the one of the Lorenz model.Therefore,the virtual synchronous machine and the synchronous machine are equivalent to the Lorenz equations and the derived equations.The stability analysis methods of the Lorenz equations can be utilized to study the stability of the virtual synchronous machine and the synchronous machine.The analytical stability criteria are derived,which provide the theoretical basis for the the grid-connected and the wind power generation systems.The main contributions of this thesis are summarized as follows:(1)Based on the time-scaling transformation and the affine transformation the Lorenz model of the direct-drive permanent-magnet synchronous wind power generator is built.According to the Kolmogorov theory the existence of the Lorenz chaotic attractor is utilized to analyze the chaos phenomenon of the permanent-magnet synchronous wind power generator under different cases,and the chaos generation mechanisms are further analyzed;the Casimir function is used to estimate the boundary of the chaotic attractor.The stability regions of the equilibrium points in the parameter space are discussed which provide insight into designing the stable operating parameters of the permanent-magnet synchronous generator.(2)The Lorenz model of the permanent-magnet synchronous wind power generatorrectifier system with the controlling parameters is built.The dissipation analysis of the permanent-magnet synchronous wind power generator with the permanent-magnet synchronous wind power generator is carried out to discuss the existence of the chaotic attactor.The chaos generation mechanisms under different cases are discussed.The Hamiltonian energy function is used to explain the physical meaning of the chaotic attractor.Then,the stability regions of the equilibrium points in the parameter space are acquired.(3)The Lorenz model of the synchronous reluctance dual motors drive system is built.The effects of the parameter mismatch of the cross-coupled drive system on the stability of the different equilibrium points are discussed.The basins of attraction of the stable equilibrium points are derived.The effects of the coupling coefficients on the dynamics of the cross-coupled drive system are analyzed.Finally,the stability mechanism and the toggle mechanism of the equilibrium points of the cross-coupled drive system are analyzed.(4)The generator-side three-phase voltage-source rectifier is controlled as a virtual synchronous motor,and its Lorenz model is built and further transformed into a Kolmogorov model.The stability regions of the equilibrium points in the parameter space is acquired.The chaos phenomenon is discussed.(5)The grid-side three-phase voltage-source inverter is controlled as a virtual synchronous generator,and its Lorenz model is further derived.Compared with the estimation method of the boundary ellipsoid of the chaotic attactor in the permanent-magnet synchronous generator,the stability analysis is carried out and the one in the virtual synchronous generator is estimated.Lastly,the stability regions of the equilibrium points in the parameter space are acquired.