微分代数混杂系统稳定性及其在电力系统中的应用

结合混杂系统的一般定义,把各子系统不是由纯微分方程(ODE)描述,而是由微分代数方程(DAE)描述的混杂系统定义为微分代数混杂系统(DAHS),给出了DAHS模型的一般形式,继而,提出了DAHS的稳定性理论框架,利用多李雅普诺夫函数法得出了此类混杂系统稳定性及渐近稳定性的一般性结论.在抽象概括电力系统模型的基础上,指出电力系统为典型的混杂系统.最后的仿真结果表明,所提出的微分代数混杂系统的渐近稳定性结论可以成功地应用于电力系统电压稳定性问题的研究.

Stability of Differential Algebraic Hybrid System and Its Applications in Power Systems

Based on the general definition of hybrid systems, the hybrid system whose subsystems are described of not pure ordinary differential equation (ODE) but Differential Algebraic Equation (DAE) is defined as differential algebraic hybrid system (DAHS). After the general form of DAHS provided, the stability theory framework of DAHS is presented. The stable and asymptotical stable results are educed using multiple Lyapunov functions (MLF). Via the abstract of power system, it is pointed out that power system is a typical hybrid system. In the end, the simulation results show that the stability theory results of DAHS, put forward in the paper, can be successfully used in the analysis of voltage stability.