Large Disturbance Stability Analysis Of Power System Based On Decomposition And Aggregation

Modern power systems are high-dimensional nonlinear systems characterized by diverse dynamics.Subjected to a large disturbance,each dynamic component will change its voltage,current and power,resulting in obvious deviations of the value at operating point.If power systems fail to maintain the balance between electricity production and consumption caused by large disturbances,large-scale outages and huge economic losses may occur.Apparently,the structure or parameters of power systems will change greatly under large disturbances.As a result,linear models are no longer suitable to describe the dynamic characteristics of power systems.Consequently,the effectiveness of the linear analysis methods will be severely challenged.We have to use nonlinear rules and nonlinear analysis methods to analyze the dynamic characteristics and stable domains.In view of the internal mechanism and variation trend of large disturbance stability of power system,lots of research works based on numerical methods,control system theories,nonlinear dynamic theories have been being carried out step by step.They aim to provide new insights into the stabilization mechanism and so as to develop practical tools.Although this process is difficult,it has never stopped.Therefore,this dissertation focuses on the transient response and the large disturbance stability of power systems based on decomposition and aggregation.Specifically,according to the structural features in mathematical models,analysis objects have been decomposed layer by layer.The stability of subsystems have been studied using novel nonlinear methods and then aggregated layer by layer to investigate the internal mechanism of large disturbance stability.Moreover,in the research on the dynamic relationship between input and output,multiple stability performance indicators have been aggregated to develop a systematic and visual analysis tool for the variation trend of large disturbance stability.The main innovations and contributions of this dissertation are as follows:1.The mixed monotonicity in the electromechanical transient process of AC power systems has been demonstrated.Specifically,for three types of synchronous machine models with different levels of detail,we have derived the analytical expressions or numerical calculation procedures of the corresponding Jacobian matrix elements.By proving that the Jacobian matrix has an invariant sign pattern subjected to a large disturbance,the AC power system can be regarded as a mixed monotone system with a order-preserving dynamic response.The sign-definite feature indicates that all the interactions among state variables remain unchanged during the electromechanical transient.Therefore,in a power system dominated by synchronous machines,its angle synchronization mechanism and voltage regulation mechanism have been further discussed.2.The dynamic characteristics and the stabilization mechanism of voltage response in a power system with excitation regulation have been studied.First,we have sorted out the monotone part and the negative feedback part of voltage dynamic model to clarify the structural features involved.Then,with the help of mixed monotone decomposition,an augmented monotone system can be conveniently constructed.Its order-preserving time-domain solution provides a bilateral estimation of the original system voltage response,which can be used for analyzing the influence of system uncertainty.Then,based on two sufficient conditions for the bounded asymptotic solution,the impacts of the gain coefficient,time constant and limiting link in the excitation regulator on voltage stability have been discussed.Finally,we have used the above estimation as a stable region to judge whether the voltage response is stable suffering from a large disturbance.The results help to understand the robust behavior of voltage dynamics.3.The rule of angle-voltage interaction has been studied,and the large disturbance stability of the closed-loop power system has been further analyzed.We propose a closed-loop model composed of an angle subsystem and a voltage subsystem to investigate the transient process.In terms of open-loop stability,the coupled oscillator theory has been applied to reveal the inherent synchronization of the angle subsystem.Then the open-loop characteristic has been quantitatively supplemented by using the concept of local input-state stability and the corresponding estimation method.Based on the small gain theorem of aggregate systems,the closed-loop stability under different initial states can be judged.Moreover,the maximum initial disturbance and the upper limit of the regulator's gain coefficient can also be roughly estimated.4.The dynamic relationship between inputs and outputs in the transient process of power systems has been studied,and the influence of parameter variation on large disturbance stability has been further analyzed.Suffering from a load shedding,the voltage amplitudes at grid nodes exhibit an order-preserving phenomenon.We have used a novel method called input-output monotonicity to illustrate the physical mechanism and investigate the impact of the load shedding on system state.In addition,for multi-input and multi-output cases,a new tool combining with numerical approximation and value set approach has been developed.It uses the non-intrusive numerical approximation to establish effective input-output expressions,and then applys the value set approach to integrate multiple expressions to form a value set function.The subsequent visualization results can map the impacts of multi-parameters on a complex plane.They intuitively display different system states under different parameter configurations,which are helpful for multi-parameter multi-objective optimization and large disturbance stability improvement.