Simplified time-domain simulation of detailed long-term dynamic models

Abstract

Abstract-Time-domain simulation of power system long-term dynamics involves the solution of large sparse systems of nonlinear stiff differential-algebraic equations. Simulation tools have traditionally focused on the accuracy of the solution and, in spite of many algorithmic improvements, time simulations still require a significant computational effort. In some applications, however, it is sufficient to have an approximate system response of the detailed model. The paper revisits the merits of the Backward Euler method and proposes a strategy to control its step size, with the objective of filtering out fast stable oscillations and focusing on the aperiodic behaviour of the system. The proposed method is compared to detailed simulation as well as to the quasi-steadystate approximation. Illustrative examples are given on a small but representative system, subject to long-term voltage instability.Index Terms-long-term dynamics, stiff decay property, backward Euler method, quasi-steady-state approximation, long-term voltage instability

Assessing the proximity of time evolutions through dynamic time warping

“…• fast solver: following the ideas in [11], the backward Euler method has been used to simulate the same detailed model as in the benchmark but with a large step size of 0.5 s and an appropriate handling of discrete events as explained in [12]. This approach is denoted by BE in the sequel;…”

“…The simplified solvers considered here are not aimed at reproducing the electromechanical oscillations [11].…”

Localization and latency concepts applied to time simulation of large power systems

“…For instance, the results presented in this paper have been obtained with Backward Differentiation Formulae (BDF), known to have the stiff decay property [13], allowing the step size to be increased [14,3]. The BDF of order o applied to the i-th injector is:…”

“…Since the LLE scheme basically exploits the block bordered structure of the Jacobian involved in Newton iterations, it applies equally well to the simplified simulation technique mentioned in the introduction and presented in [3]. In this paper, this simplified simulation is obtained by resorting to a BDF of order 2 with large steps to filter out Note that the model remains unchanged.…”

“…When modelling simplification is not easy (for instance because the above mentioned time-scale separation is not clear [2]) it may be attractive to simulate the detailed model but with a simplified solver, for instance a stiff-decay method with large time steps to filter out the fast dynamics [3]. This approach, however, cannot detect oscillatory instability of the fast dynamics.…”