Error estimation and step size control with minimal subsystem interfaces

TL;DR

This paper reviews error estimation and step size control methods for co-simulation with minimal subsystem interfaces, focusing on black-box subsystems common in industry, and provides practical guidance for implementation.

Contribution

It introduces error estimation techniques and step size control algorithms tailored for black-box subsystems in co-simulation, with pseudocode and practical advice.

Findings

Error indicators effectively assess co-simulation quality

Step size control balances speed and accuracy

Guidelines help avoid common pitfalls

Abstract

We review error estimation methods for co-simulation, in particular methods that are applicable when the subsystems provide minimal interfaces. By this, we mean that subsystems do not support rollback of time steps, do not output derivatives, and do not provide any other information about their internals besides the output variables that are required for coupling with other subsystems. Such "black-box" subsystems are common in industrial applications, and the ability to couple them and run large-system simulations is one of the major attractions of the co-simulation paradigm. We also describe how the resulting error indicators may be used to automatically control macro time step sizes to strike a good balance between simulation speed and accuracy. The various elements of the step size control algorithm are presented in pseudocode so that readers may implement them and test them in their own applications. We provide practicable advice on how to use error indicators to judge the quality of a co-simulation, how to avoid common pitfalls, and how to configure the step size control algorithm.