Proper Selection of Obreshkov-Like Numerical Integrators Used as Numerical Differentiators for Power System Transient Simulation

TL;DR

This paper establishes criteria for selecting Obreshkov-like numerical integrators as differentiators in power system transient simulations, aiming to prevent oscillations and biases, and introduces a new optimized integrator for better accuracy.

Contribution

It proposes specific criteria for the proper use of Obreshkov-like integrators as numerical differentiators and introduces a frequency response optimized integrator for improved transient simulation accuracy.

Findings

Existing integrators can cause oscillations or bias if misused.

The proposed criteria help identify suitable integrators for differentiation.

A new optimized integrator improves transient simulation results.

Abstract

Obreshkov-like numerical integrators have been widely applied to power system transient simulation. Misuse of the numerical integrators as numerical differentiators may lead to numerical oscillation or bias. Criteria for Obreshkov-like numerical integrators to be used as numerical differentiators are proposed in this paper to avoid these misleading phenomena. The coefficients of a numerical integrator for the highest order derivative turn out to determine its suitability. Some existing Obreshkov-like numerical integrators are examined under the proposed criteria. It is revealed that the notorious numerical oscillations induced by the implicit trapezoidal method cannot always be eliminated by using the backward Euler method for a few time steps. Guided by the proposed criteria, a frequency response optimized integrator considering second order derivative is put forward which is suitable to be used as a numerical differentiator. Theoretical observations are demonstrated in time domain via case studies. The paper points out how to properly select the numerical integrators for power system transient simulation and helps to prevent their misuse.