Research On Projective Integration Methods For Dynamic Simulation Of Active Distribution Networks

The dynamic characteristics of active distribution networks(ADNs)have been becoming more and more complicated due to the integration of a high-penetration of distribution generators and the popularization of the advanced load control technologies.Dynamic simulation is the most direct and effective way to analyze the operating principles of ADNs.Therefore,this paper mainly focuses on the dynamic simulation of ADNs and some highly efficient simulation methods are proposed.The major work can be summarized as follows:(1)The framework of the dynamic simulation of ADNs considering the stochastic properties is built,which is suitable for the application of projective integration methods.This framework is based on differential-algebraic equations and stochastic differentialalgebraic equations,and it contains the models of the typical devices of ADNs considering their stochastic disturbances.It can precisely reflect the multi-time-scale and stochastic properties of ADNs.Moreover,the framework can be solved by the numerical algorithms of ordinary differential equations and stochastic differential equations,which lays a foundation for the study of projective integration methods.(2)The projective integration methods are proposed for the dynamic simulation of ADNs.This paper modifies the idea of the projective integration for the stiff differential equations,and an implicit projective integration method(IPIM)is proposed through combining explicit and implicit integration algorithms.The proposed IPIM has an accuracy of order 2,and the numerical stability is not influenced by its parameter.Based on this property,an error estimation and adaptive parameter control strategy is proposed for the IPIM to further improve its simulation speed.Furthermore,the dynamic simulation approach of ADNs based on the proposed projective methods are presented.Finally,the projective integration methods are demonstrated using different test systems under various scenarios,and the feasibility and efficiency of the proposed algorithms is verified against some classical numerical integration methods and commercial simulators.(3)A rolling projective integration method(RPIM)is proposed for the stochastic dynamic simulation of ADNs.This method combines the deterministic projective integration method and the mixed numerical algorithms of stochastic differential equations to reflect the stochastic characteristics of ADNs effectively.Moreover,the strong convergence and weak convergence of the RPIM is analyzed and compared with that of a classical numerical algorithm of stochastic differential equations.Case studies and numerical analyses show that the proposed RPIM is more accurate than the classical method and can achieve a higher efficiency at the same time.