Research On Exponential Integrators For Multiscale Transient Simulation Of Power Systems With High Penetration Of Renewable Engery

The recently rapid development of renewable generation technologies has become an important means for meeting the enegy consumption and environmental constraints,which helps to ensure a sustainable energy future.Security and stablilty of the power system is the prerequisite for large scale renewable energy integration.A myriad of concerns,such as the inherent intermittency and stochastic nature of renewable energy sources,oscillatory phenomenon of power electronic interfaces under weak grid or microgrid conditions,unforeseeable harmful interactions between components in new operating conditions,is making transient simulation analysis prominent.This dissertation focuses on new transient simulation demands due to the advent of high renewable energy penetration.A multiscale transient simulation approach is proposed based on the cutting-edge research of exponential integrators from the field of numerical analytics.The work in this dissertation is summarized as follows:1)The application framework of exponential integrators in the power system transient simulation is studied.A local linearization strategy for exponential integrators is developed in the state-space analysis framework.The integrator approximation technique on the(extended)Krylov subspace is utilized to develop a class of subspace reduction-based exponential integration formulas,which is suited for large scale transient simulation.The subspace dimension and the Jacobian updating frequency of is adapted to optimize simulation efficiency.Case studies modified from a real wind farm have indicated good scalability of the algorithm for large problems.2)Dense output formulas based on the scaling & squaring computation of exponential function is constructed.Efficient step size adaption and variable step integration is achieved due to the scaling invariant property of the Krylov subspace.A multiscale transient simulation approach is proposed based on these two techniques.Fast and slow dynamics can be simulatied simultaneously with high efficiency.Numerical performance of the algorithm is demonstrated through comprehensive case studies.Significant acceleration is achieved in real system based test case.3)The simulation problem of coupled system with both lumped and distributed parameter elements are considered in the proposed multiscale simulation framework.With distributed parameter transmission line model as an example,the model discon-tinuities brought by the propagation delay is revealed and analyzed.Two types of exponential integrators are proposed for the delayed differential algebraic equation model of the coupled systems.An automatic integrator selection method is also developed.The proposed algorithm overcomes the step size constraint brought by the distributed parameter models.4)Multi-resolution modeling and simulation of large scale power converters is studied.A highly scalable natural decoupling and prediction-based decoupling method is proposed for the detailed switch model simulation.A multi-resolution simulation algorithm based on both switch function model and dynamic average model is developed.Case studies has confirmed that the proposed method has better accuracy and scalability compared to the traditional method.