Xiaopeng Fu

Accurate dense output formula for exponential integrators using the scaling and squaring method

Abstract This paper proposes an accurate dense output formula for exponential integrators. The computation of matrix exponential function is a vital step in implementing exponential integrators. By scrutinizing the computational process of matrix exponentials using the scaling and squaring method, valuable intermediate results in this process are identified and then used to establish a dense output formula. Efficient computation of dense outputs by the proposed formula enables time integration methods to set their simulation step sizes more flexibly. The efficacy of the proposed formula is verified through numerical examples from the power engineering field.

Matrix exponential based electromagnetic transients simulation algorithm with Krylov subspace approximation and accurate dense output

The ever-increasing scale of system interconnection and diverse dynamic time constants of power equipment pose challenges to power system electromagnetic transients simulation algorithm. In this paper, an advanced numerical integration method based on matrix exponential operator is proposed. Krylov subspace approximation is utilized to effectively reduce the problem dimension, and an accurate dense output formula is established to enable the method adopting larger simulation step size and revealing higher frequency dynamic details simultaneously. Accuracy, numerical stability and computation efficiency is demonstrated through numerical case studies.

Multiscale Simulation of Power System Transients Based on the Matrix Exponential Function

Power system electro-magnetic transient programs (EMTP) have been popular among researchers and practitioners due to their detailed component modeling and high simulation accuracy for complex system operations. Despite broad applications in simulations with wide range of timescales, the small discretization step of these programs makes their use very time-consuming for system studies with long time span. Facing the increasingly complex power system transient characteristics and simulation demands, a multiscale algorithm that integrates the simulations of the electromagnetic and slower electromechanical transients is desirable. The multiscale simulation algorithm preserves the high fidelity of the EMTP and attains higher efficiency for the overall transient simulation. In this paper, we achieve this goal by exploiting the unique properties of the matrix exponential function. The proposed algorithm is capable of utilizing large step sizes to speed up the simulation of slow dynamics, whereas the fast transients are accurately reconstructed through efficient dense output mechanism, which is built upon the matrix exponential function computation. Numerical studies including a large-scale wind farm simulation are conducted to demonstrate the effectiveness of the proposed multiscale algorithm.

EMTP-type realization of model reduction algorithms for transient simulation of distribution networks

Model reduction is a popular trend in large-scale system simulations. It is also an effective way to improve the efficiency of distribution system simulations. In this paper, the realization of state-space-based model reduction methods in EMTP-type programs is presented. The state-space model of linear time-invariant distribution network is reduced and simulated with the detailed nodal model in EMTP-type programs. The combined state-space nodal analysis algorithm is adopted as the interface between the state-space models and the nodal models. Simulations are performed to show the feasibility and validity of the proposed method, and the improvement in efficiency with the application of model reduction.

Matrix exponential based algorithm for electromagnetic transient modeling and simulation of large-scale induction generator wind farms

Large-scale wind farm integration poses challenges to the modeling and simulation of power system electromagnetic transients. In this paper, state space modeling of typical induction generator wind farms is demonstrated using a subsystem assembly process, and a novel matrix exponential based simulation algorithm is applied, which is efficient, stable, and especially suitable for high dimensional nonlinear problems like wind farms. Numerical performance of the proposed algorithm is demonstrated through case studies.

Adaptive DAE solving algorithm for power system transient simulation via matrix exponential operator

The ever-increasing scale of system interconnection and diverse dynamic time constants of power equipment pose challenges to power system transient simulation algorithms. In this paper, an adaptive numerical integration method for DAE systems based on matrix exponential operator is presented. Krylov subspace technique is utilized to effectively reduce the problem dimension. A novel step adaption scheme is established to enable the method adjusting the computation step size according to error budget while maintaining the output step size unchanged. Acceleration is accomplished without perceived degradation in the simulation results. Numerical performance and computation efficiency is demonstrated through numerical case studies.