| Stability is a very important characteristic of the system.For most systems,stability is the premise to ensure the smooth operation of the system.Linear system is a very basic but very important dynamic system in modern control theory.Its theoretical basis plays an important role in practical engineering applications.Most industrial systems can be described by linear system model.In the power system,there are some factors that affect the stability of the system,such as the inaccuracy of modeling parameters,the inevitable time delay in the network signal transmission and the disturbance of the system itself.Because the power market is also a key part of the power system,it is related to the power supply and demand of the power system,so the study of its stability not only effectively adjust the distribution of power resources,but also effectively ensure the stability of the entire power transaction.In this paper,the stability analysis methods of several linear systems are combined and applied to the stability analysis of power systems.In the electric power model,the factors of system delay and disturbance are considered,and the knowledge of linear system theory,Lyapunov stability theory and networked power system analysis are used,combined with time-delay cutting,functional enhancement,different integral inequalities and other methods.The power market model based on sampling control system,the linear time-varying delay system and the linear time-varying delay system with uncertain parameters are analyzed respectively,and applied to the single-machine infinite system and the single-region LFC power system with time delay.It mainly includes the following work:(1)Based on the dynamic model of power market of Alvarado and Nutaro,a power market model based on sampling control system is established.This model takes into account the characteristics of market supply,market consumption,energy supply and demand imbalance and market price response,and a new bilateral closed-loop Lyapunov functional is constructed.Combined with the modified version of the free weight matrix integral inequality to deal with the integral term in the functional derivative,the stability criterion is derived,and four classical numerical examples are provided to analyze and verify the advantages of this method in reducing the conservatism.Finally,the proposed method is applied to the power market model based on sampling control system to obtain acceptable price signals to keep the power market stable.(2)A class of linear time-varying time-delay systems is introduced,and the stability criterion of the system is derived by adding relevant terms such as time-delay state information in the functional and using Bessel-Legendre inequality with few free variables to deal with the quadratic integral term after taking the derivative of LK functional.Then,the single-region LFC power system model considering time delay is transformed into a linear system model with time-varying delay,and the stability criterion is applied to this model.The maximum upper bound of LFC power system time delay under three different types of time delay and different PI control gain(K_P,K_I)is obtained through MATLAB platform.Finally,compared with the methods in previous literatures,the calculation results obtained by the method in this paper are less conservative.(3)considering the actual object with a variety of factors,it is impossible to achieve ideal status of time-delay systems,linear time-varying time-delay systems in the above,the uncertain parameters is introduced in through the front of LK functional proper deformation as well as the application of BL inequality in estimates,and connecting with the liberty of the matrix method,The stability criterion of the system with disturbance parameters is derived.The stability margin in the case of uncertainty in the system is obtained and compared with the previous literatures,the conservatism is reduced.Finally,the advantages and effectiveness of the proposed method are verified through the modeling and simulation of Simulink platform in MATLAB. |
