Research On Key Problems Of The Higher-order Modal Interaction Analysis And Control In Power Systems

In recent years,due to the rapid growth of interconnected power grids and the electric power devices,the power system industry of China forms the distinctive situation of ‘high capacity units',‘bulk power grid',‘high parameters',‘(extra and ultra-)high voltage',‘remote transmission',‘AC-DC hybrid transmission',‘traditional energy and renewable energy hybrid generation' and ‘large-scale power networks interconnection',which give rise to ‘weak connection',‘heavy load demand',‘fast excitation' and ‘low damping' more and more serious.Nowadays,the modern power system becomes a strong nonlinear and large scale system with very complex structure,and its inherent vulnerability has been increased,in which the complex and singular phenomenon,such as the interaction of higher-order modes and its low-frequency oscillation,often happens.These complex higer-order modal interactions have become one of the very important nonlinear factors affecting the stability and safety of power system operation.The classical linear system theory is unable to explain these nonlinear singular phenomenons and reveal their mechanism and substance,because only the 1st order model is considered and it is very hard to and even can not know the internal nonlinear structures and information such as the higher-order modes.Currently,at home and abroad,the theory of Normal Form,the Modal Series method and the theory of Carleman linearization can provide higher-order modal analysis to study the dynamic characteristics of nonlinear power systems.The Normal Form theory,from 1990 s,is developed and widely applied to analyze the higher-order nonlinear behavior of power systems,while the Modal Series method,from 2003,is proposed and some researches are raised.But there are almost not any major breakthrough or significant development in researches and applications up to now,for their nonlinear transformation and multi-dimensional Laplace transformation.Especially,the expression of third-order solution based on modal series method is so considerably complicated that it is difficult and time-consuming to carry out in programs.The Carleman linearization theory is introduced to analyze power system nonlinearity only in the past few years and relevant papers are a little less.It's obvious that analyzing the much higher order modes and its nonlinearity characteristics still should be developed.It is also an important task for scholars and engineers in electric power to find some suitable simulation tools to research these nonlinear characteristics of interconnected systems quickly,reliably and efficiently.The improvement and application of Carleman linearization method,the perfection of solution based on Normal Form theory under modal resonance and the reduced-order mode reconstruction based on classification of modes are carried out in this dissertation.The main contributions are as follows:1.The traditional Carleman embedding technology and its linearizational model are studied.Combined with the normal form transformation,a novel Poincaré-like Carleman linearization solution was deduced,and their nonlinear contribution factors were also defined.Comparing with Prony analysis,the numerical simulation results of two power system cases show the validation of the combined approach.On the other hand,the higher-order vector field was reduced and the reduced Carleman linearizational model was deduced.The time domain solutions of not only single but higher-order variables were provided,and the corresponding nonlinear participation factors were defined.The simulation results show the higher-order variables' solutions and nonlinear participation factors can explain the interaction dynamics of each order variables.2.It is well known that the conventional normal form theory can not provide the closed form solution under modal resonance.However,by means of splitting the polynomial vector space,the normal form solutions under modal resonance were derived.The obtained solution is in a simple closed form,including both the non-resonant part and the resonant part.Numerical simulations are performed to verify the effectiveness of this approach.3.The nonlinear terms and the corresponding modes are categorized.Based on these,modal classification to identify the significant modes and a signal process algorithm such as least square method to estimate their coefficients,a reduced-order mode reconstruction is presented to carry out rapid and efficient nonlinear modal analysis.